Global Fixed Income Portfolio

Asset Management

Global Fixed Income Portfolio

CfBS Center for Business Studies AG

Dr. Enzo Mondello, CFA, FRM, CAIA

August 2014

Content

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6

7

8

1

2

3

4

Risks Associated with Investing in Bonds

Fixed-Income Valuation

Term Structure of Interest Rates

Yield Measures

Interest Rate Risk: Duration and Convexity

Credit Risk: Fundamentals of Credit Analysis

Managing Bond Portfolio

Relative-Value Methodologies for Global

Corporate Bond Portfolio Management

9

10

11

12

Exchange Rate Risk: International Bond Investing

Managing Interest Rate Risk with Derivatives

Managing Credit Risk with Derivatives

Currency Risk Management

© Dr. Enzo Mondello, CFA, FRM, CAIA August 2014 2

1


Overview of Risk Factors

Interest rate risk is the risk that when interest rates increase, bond prices decline. Interest rate risk is the greatest risk faced by bond market investors.

Call risk is the risk that a bond will be paid off before its maturity date. The risks are:

– Higher uncertainty of the cash flows of the bond.

– Risk that principal proceeds will have to be reinvested at lower rates.

– Reduced capital gain potential in a falling rate environment.


1


Yield curve risk is the risk that the value of a bond portfolio might deteriorate because of a change in the shape of the yield curve

Reinvestment risk is defined as the risk that the received cash flows must be reinvested at a rate lower than the original investment. If coupon payments must be reinvested at lower rates, overall returns of the investment will be less than initially projected.

Credit (default) risk is the possibility that the issuer will be unable to repay the coupon payments and/or the principal amount to the bondholder as defined by the indenture

Liquidity risk is the risk that a security will not be able to be sold quickly without giving up a large price concession.

This bid-ask-spread is the best measure of liquidity risk; the wider the spread, the greater the liquidity risk is.

August 2014 4

© Dr. Enzo Mondello, CFA, FRM, CAIA

1


Exchange rate risk is the risk that the exchange rate between the currency in which a bond is denominated and the currency of the investor’s home country might change

Volatility risk describes the risk that changes in volatility of interest rates will affect the value of options embedded in a bond

Inflation risk is the risk that the purchasing power of the cash flows received from a bond (interest and principal) will decline over time because of inflation

Event risk is the risk that some unusual event could cause the price of bonds to decrease (e.g. natural disaster, corporate takeover, a regulatory change, or political factors)

Sovereign risk has two components:

1. A sovereign may be unable to service its bonds (no ability to pay)

2. A sovereign may be unwilling to service its bonds even though it has the resources to do so

August 2014 5


1


Bond Price and Risk Factors

Interest rate risk is the major risk faced by fixed-income investors

The bond price is the present value of the sum of future cash flows (coupon payments plus the principal amount)

Bond Price



(1

C



1 r) 1



(1

C



2 r) 2



(1

C



3 r) 3



.........



C

(1 n



 r)

P n

Therefore, if the discount rate r , which is the yield required by the market (which is related to interest rate levels) increases, the price of the bond decreases, and vice versa . This is true for almost all bonds.

August 2014 6


1


Coupon Rate > Required Market Yield:

Bond Price > Par Value ( Premium Bond )

Coupon Rate < Required Market Yield:

Bond Price < Par Value ( Discount Bond

Coupon Rate = Required Market Yield:

Bond Price = Par Value ( Par Bond )

)


1


The volatility of a bond (i.e. by what percentage the price of a bond will change for a given basis point change in interest rates) depends upon:

– Maturity: Long-term bonds are more volatile than short-term bonds, all other factors being equal

– Coupon: The lower a bond’s coupon is, the greater its volatility will be

– Yield: The higher the yield at which a bond trades, the lower its price sensitivity for a given basis point change in interest rates will be, all other factors being equal


1


Call Risk

Some bonds are callable. Therefore, they have a call option embedded in their price structure. This means that the owner of a callable bond can be viewed as owning a portfolio consisting of an option-free (straight) bond and a short position in a call option on the bond . The investor has a short position in the embedded call option because the issuer has the right to call the bond from the bondholder.

Therefore, the price structure of a callable bond can be modeled as follows:

Price Callable Bond = Price Noncallable Bond Price – Price of embedded Options


1


Call and prepayment risk is the risk that a bond will be paid off before its maturity date. The reasons why this is disadvantageous for an investor are:

– The cash flows are unknown.

– Reinvestment risk because bonds are usually called when interest rates are low so that the investor is forced to reinvest the proceeds at lower interest rates.

– The appreciation potential of a callable bond is limited (price compression).


1


Interest Rate Risk of a Floating-rate Security

The future cash flows of floating-rate notes are not fixed. They rise and fall directly with changes in interest rates.

Consequently, the price of a typical floating-rate security should change very little when interest rates change because the dollar value of its coupon (future cash flows) will change in the same direction as the rate at which the future cash flows will be discounted.

There are three reasons why floating-rate security prices can be affected by changes in interest rates:

– Reset dates : the longer the time between reset dates, the greater the interest risk will be.

– Reference rate : the quoted margin above the reference interest rate that the market requires can change.

– Cap risk : this is the risk that the reference interest rate will rise enough that a floating-rate security’s coupon rate will be capped out.

August 2014 11


1


Yield Curve Risk

The yield curve risk is the risk that the value of a bond portfolio will deteriorate because of the change in the shape of the yield curve

The yield curve is a graphical representation of interest rates across all maturities. When interest rates move, they do not change in an equal amount for all maturities .

Duration has a very restrictive interpretation: it is the percentage change in the value of a bond that will occur if the entire yield curve shifts in a parallel manner (all maturities move by the same increment)

Since a parallel shift is an unlikely scenario , duration is considered at best to be an approximation of a bond’s sensitivity, and is only accurate for small changes in interest rates


1


Reinvestment Risk

The factors that affect the reinvestment risk of a security are:

Changes in interest rates : The greater the change, the higher the risk

The size of the cash flows : The larger the cash flows to be reinvested, the greater the risk

The timing of the reinvestment cash flows : The faster the cash flows are received, the greater the reinvestment risk


1


Amortizing securities , such as mortgage-backed securities, have more reinvestment risk than non-amortizing securities , such as conventional bonds. There are two reasons for this:

– The periodic cash flows paid by amortizing securities consist of both coupon interest and the repayment of a portion of principal

– Amortizing securities typically pay their cash flows monthly, rather than semi-annually. The more frequently the cash flows are paid, the more frequently the reinvestments occur, and the higher the reinvestment risk.

Note that with zero-coupon bonds , there are no coupon payments to be reinvested over their term to maturity, and thus have no reinvestment risk


1


Types of Credit Risk

Default risk: is the risk that an issuer will fail to make interest or principal payments when they are due. If a bond defaults, the investors do not necessarily suffer a total loss. The recovery rate is the percentage of the investor’s investment that is not lost, but recovered.

Credit spread risk: is the risk that the market yield (due to the credit spread) will rise, causing the price of the bond to decline

Downgrade risk: is the risk that the price of a bond might fall because the credit rating agencies reduce its credit rating


1


AAA (or Aaa)

AA (or Aa)

Prime Grade

High Quality Grade

A Upper Medium Grade

BBB (or Baa) Medium Grade

BB (or Ba)

B

Low Grade

Speculative

CCC (or Caa) Poor Grade (substantial risk)

CC (or Ca) Very Speculative

C

CI

DDD, DD, D

Extremely Speculative

Noninterest Bearing Income Bonds

Default

Investment

Grade

Non

Investment

Grad

August 2014 16


1


Liquidity Risk

Liquidity risk is the risk that a security will not be able to be sold quickly without giving up a large price concession

The bid/asked spread is the best measure of liquidity risk: the wider the spread, the greater the liquidity risk

The market bid/asked spread can be determined by simply taking the difference between the lowest dealer asked and the highest dealer bid for an issue at a particular point in time

Liquidity risk is mostly a concern for investors who do not expect to hold a security to maturity or who must periodically mark it to market


1


Liquidity risk can change for a number of reasons:

– If the structure of a bond structure is popular, the bid-ask-spread will narrow. If the structure of a bond is unpopular, the bid-ask-spread will widen

– When interest rates become more volatile, the demand of bonds decline which will cause the bid-ask-spread to widen

– When important traders of a certain type of bond exit the market, the spreads will tend to widen because of a lack of liquidity


1


Exchange Rate Risk

Exchange rate risk is the risk that the exchange rate between the currency in which a bond is denominated and the currency of the investor’s home country might change

Inflation Risk

Inflation risk is the risk that the purchasing power of the cash flows received from a bond (interest and principal) will decline over time because of inflation

If an investor buys a bond with a 7% return but inflation is 6% the real return is only 1%


1


Volatility Risk

Volatility risk is the risk that changes in the expected volatility of interest rates can affect the value of any embedded options in a bond’s pricing structure, thereby affecting the value of the bond.

Price Callable Bond = Price Noncallable Bond – Price embedded Call Option

Price Putable Bond = Price Nonputable Bond + Price embedded Put Option

The value of both puts and calls increase if volatility increases. Because the embedded option values are affected by changes in volatility, the price of bonds with embedded options will also be affected.


1


Event Risk

Event risk is the risk that some unusual event could cause the price of bonds to decline:

– Natural disasters such as famine, war etc.

– Takeover, leveraged buy-out, or corporate debt restructuring that substantially increases an issuer’s debt-to-equity ratio and causes downgrading of its credit rating

– A regulatory change that requires an issuer to conduct its affairs in ways that result in a downgrading of its credit rating (i.e. lower regulatory capital for banks)

– Political factors or actions taken by government that impair an issuer’s ability or willingness to pay its debt service


Content

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Risks Associated with Investing in Bonds

Fixed-Income Valuation


Yield Measures






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2


Valuation Principles

Interest rate risk is the major risk faced by fixed-income investors

The bond price is the present value of the sum of future cash flows (coupon payments plus the principal amount)

Bond Price



(1

C



1 r) 1



(1

C



2 r) 2



(1

C



3 r) 3



.........



C

(1 n



 r)

P n

Therefore, if the discount rate r , which is the yield required by the market (which is related to interest rate levels) increases, the price of the bond decreases, and vice versa . This is true for almost all bonds


2


The appropriate discount rate is the sum of the risk-free rate and a risk premium (nominal spread).

The yield on a U.S. Treasury security with the same maturity as the bond being valued can be used as a proxy for the risk-free rate.

Discount Rate for the Bond = Yield-to-Maturity

= Yield-to-Maturity of Treasury Security + Nominal Spread

Pr ice



C

1

( 1

 r )

1



( 1

C

2

 r )

2



...



C n

( 1

 r ) n



Par

( 1

 r ) n where:

C

Par r t

1

... n

=

=

=

=

Coupon payments

Par value of the bond at maturity

Yield for maturity (discount rate)

Life time of the bond

August 2014 24


2


The appropriate discount rate (i) is the sum of the risk-free rate and a risk premium (i.e. the nominal spread).

Discount Rate = Yield to Maturity = Risk-free Rate + Nominal Spread

Example (valuing annual-pay bonds):

A 3-year corporate bond has an annual coupon rate of 5% and a face value of USD 1,000. The discount rate is 4%. The bond is paid back at par at maturity. Calculate the price of the bond!


2


Example (valuing semiannualy-pay bonds):

A 3-year corporate bond has a coupon rate of 5%, coupons are paid semiannualy and the bond has a face value of USD

1,000. The discount rate is 4%. The bond is paid back at par at maturity. Calculate the price of the bond!


2


Relationships among a Bond’s Price, Coupon Rate, Maturity, and Market Discount Rate (Yield-to-Maturity)

The farther into the future a cash flow is received, the lower its present value will be. The higher the discount rate

(yield to maturity) is, the lower the value of the bond will be, all other factors being equal.

A bond’s price and YTM are inversely related. An increase in YTM decreases the price and vice versa.

Prices are more sensitive to changes in YTM for bonds with lower coupon rates and longer maturities, and less sensitive to changes in YTM for bonds with higher coupon rates and shorter maturities.

If the yield-to-maturity of a bond is higher (lower) than its coupon rate, the bond will sell below (above) its par value. If the yield-to-maturity equals its coupon rate, the bond will sell at its par value.


2


Coupon Rate > Yield-to-Maturity:

Bond Price > Par Value ( Premium Bond )

Coupon Rate < Yield-to-Maturity:

Bond Price < Par Value ( Discount Bond

Coupon Rate = Yield-to-Maturity:

Bond Price = Par Value ( Par Bond )

)


2


There is a convex relationship between a bond’s price and its yield-to-maturity:

(Bond Price)


(Yield-to-Maturity)

August 2014 29

2


At a bond’s maturity date, the bond’s value is equal to its par value. As a bond moves closer to maturity (constant discount rate assumed), a bond’s value:

– A bond selling at a premium decreases over time

– A bond selling at a discount increases over time

Example:

A 7% coupon, 4-year semiannual paid bond is priced at 96.63 and has a yield-to-maturity of 8%. If the yield to maturity remains unchanged, what will the bond’s price be in one year?


2


Spot Rates and the Price of a Bond

Spot rates are market discount rates for single payments to be made in the future. The discount rates for zero-coupon bonds are spot rates because these rates do have no reinvestment risk.

Example:

The spot rates over the next 6 months, 12, months, 18 months, and 24 months are 4.0%, 4.2%, 4.4%, and 4.5%.

Therefore the no-arbitrage price of a 2-year, 6% coupon Treasury note is:

P



3



3



3



103



102 .

86

1 .

02 1 .

021 2 1 .

022 3 1 .

0225 4

The YTM of this issue is 4.489% (2,244% x 2);

N = 4, PMT = 3, PV = -102.86, FV = 100  I/Y = 2.244


2


Flat Price, Accrued Interest, and Full Price

Full Price = Flat Price + Accrued Interest

The full price (dirty price) of a bond includes interest accrued between coupon dates. The flat price (quoted or clean price) of a bond is the full price minus accrued interest.

Accrued interest for a bond transaction is calculated as the coupon payment times the portion of the coupon period from the previous payment date to the settlement date

Methods for determining the period accrued interest include actual (typically used for government bonds) or 30-day months and 360-day years (typically used for corporate bonds)


2


The full price of a fixed-income bond between two coupon payments given the market discount rate resp. the

YTM can be calculated as:

Full Pr ice



( 1



C

1

YTM )

1

 t / T



( 1



C

2

YTM )

2

 t / T



...



( 1



C n



Par

YTM ) n

 t / T

The next coupon payment (C) is discounted for the remainder of the coupon period, which is 1 – t / T. The second coupon payment is discounted for that fraction plus another full period, 2 – t / T. This equation is simplified by multiplying the numerator and denominator by the expression (1 + YTM) ^ t/T:

Full Pr ice



( 1



C

1

YTM )

1



( 1



C

2

YTM )

2



...



( 1

C

 n



Par

YTM ) n

 

1



YTM

 t / T

August 2014 33


2


Example

A 6% German corporate bond is priced for settlement on 18 June 2015. The bond makes semi-annual coupon payments on 19 March and 19 September of each year and matures on 19 September 2026. The corporate bond uses the 30/360 day-count convention for accrued interest. Calculate the full price, the accrued interest, and the flat price per EUR 100 par value for a yield-to-maturity of 6,2%?


2


Matrix Pricing

Matrix pricing is a method used to estimate the YTM for bonds that are not traded or infrequently traded. The yield is estimated based on the yields of traded bonds with the same credit quality. If these bonds have different maturities than the bond being valued, linear interpolation is used to estimate the subject bond’s yield.

For example, suppose that an analyst needs to value a 3-year, 4% semi-annual coupon payment corporate bond, Bond

X. This bond is not actively traded. However, there are quoted prices for four corporate bonds that have similar credit quality:

– Bond A: 2-year, 3% semi-annual coupon paying bond with a price of 98.500,

– Bond B: 2-year, 5% semi-annual coupon paying bond with a price of 102.25,

– Bond C: 5-year, 2% semi-annual coupon paying bond with a price of 90.250

– Bond D: 5-year, 4% semi-annual coupon paying bond with a price of 99.125

August 2014 35


2


The semi-annual YTM of the four bonds are:

– Bond A: YTM = 3.786% (N = 4, PMT = 1.5, PV = - 98.5, FV = 100  I/Y = 1.8929)

– Bond B: YTM = 3.821% (N = 4, PMT 2.5, PV = -102.25, FV = 100  I/Y = 1.9104)

– Bond C: YTM = 4.181% (N = 10, PMT = 1, PV = -90.250, FV = 100  I/Y = 2.0906)

– Bond D: YTM = 4.196% (N = 10, PMT = 2, PV = -99.125, FV = 100  I/Y = 2.0979)

The average yields for the 2-year bonds of 3.8035% and for the 5-year bond of 4.1885% are calculated:

0 .

03786



0 .

03821



2

0 .

038035

0 .

04181



0 .

04196



0 .

041885

2

August 2014 36


2


The estimated 3-year YTM can be obtained with linear interpolation. The interpolated yield is 3,9318%:

0 .

038035



3

5





2

2



( 0 .

041885



0 .

038035 )



0 .

039318

Thus, the 3-year Bond X has an estimated price of 100.191 (N = 6, PMT = 2, I/Y = 1.9659, FV = 100)


2


Example

An analyst needs to assign a value to an illiquid 4-year, 4.5% annual coupon payment corporate bond. The analyst identifies two corporate bonds that have similar credit quality: One is a 3-year, 5.5% annual coupon payment bond priced at 107.5 per 100 of par value, and the other is a 5-year, 4.5% annual coupon payment bond priced at 104.75 per 100 of par value. Using matrix pricing, the estimated price of the illiquid bond per 100 of par value is closest to:

A. 103.895

B. 104.991

C. 106.125


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Term Structure of Interest Rates

Yield Measures






9

10

11

12






3


The three different shapes of the yield curve are:

– Normal: upward sloping (short rates < long rates)

– Flat: no slope (short rates = long rates)

– Inverted: (short rates > long rates)

Historically the yield curve has been upward sloping more often than the other shapes.

The slope of the yield curve captures what the market is willing to pay for bonds of different maturities .

The yield curve expresses the relationship between yield and maturity.

Typically the yields being measured are U.S. Treasury yields as these are default risk-free yields.

August 2014 40


3


Treasury Yield Curve

(Yields)


Normal Yield Curve

Flat Yield Curve

Inverted Yield Curve

(Maturity)

August 2014 41

3


The problems with using on-the-run Treasury issues are:

– On-the-run Treasury curve consists only of 6 points. Interpolation is needed

– Due to the strong dealer demand Treasury yields tend to be abnormally low, reducing their usefulness as a good benchmark

– They tend to have abnormally low reinvestment rate risk, and abnormally high interest rate risk

Despite the drawbacks of the on-the-run Treasury yield curve as the benchmark for valuing other fixed-income securities, it is the most widely used benchmark

An alternative to the on-the-run Treasury yield curve that is sometimes used is the yield curve for zero-coupon Treasury securities

The yield on zero-coupon bond securities is called the spot rate, with the yield on Treasury strips called the Treasury spot rate . When Treasury spot rates are plotted versus their maturities, the resulting curve is called the term structure of interest rates


3


A shift in the yield curve occurs when yields change.

In a parallel shift all yields change across the term structure by the same amount. A nonparallel shift occurs when the changes in yield are different for different maturities.

Yield

Yield

Initial

Curve

Initial

Curve

Maturity

Maturity

August 2014 43


3


A yield curve twist occurs when the curve (the slope of the curve ) flattens or steepens due to a nonparallel shift.

The yield curve can become flatter (less difference between long and short rates) or steeper (more difference between long and short rates).

A butterfly twist occurs when the curvature of the curve changes.

– Positive butterfly: the curve becomes more straight (less humped).

– Negative butterfly: the curve becomes less of a straight line (more humped).


3


Factors that Drive U.S. Treasury Security Returns

Researchers generally agree that three factors are responsible for changes in Treasury returns:

– Changes in the level of interest rates . This is by far the most important factor. It accounts for about 90% of historical returns and is measured by duration.

– Changes in the slope of the yield curve (distant second most influential factor). It accounts for about 8.5% of historical returns and is measured by key rate duration.

– Changes in the curvature of the yield curve (slight impact). It accounts for about 1.5% of historical bond returns.

Bond portfolio managers who want to hedge their interest rate risks, therefore, should be most concerned about protecting against the adverse effects of changes in the level of interest rates.


3


Various Universes of Treasury Securities used to Construct the Theoretical Spot Rate Curve

Constructing a theoretical spot rate yield curve is not simple. Ideally we would use the yield on default risk-free zero coupon bonds (to abstract from the coupon effect) for each maturity in the maturity spectrum.

There are several different combinations of Treasury securities that can be used to construct a default-free theoretical spot rate curve:

– On-the-run Treasury issues are the most recently auctioned issues of a given maturity. The Treasury is currently issuing bills with maturities of 1, 3, and 6 months, notes and bonds with maturities of 2, 5, 10, and 30 years. The bills are issued at a discount while the notes and bonds carry coupons. The resulting on-the-run yield curve is a par coupon curve because the notes and bonds are issued at par. Securities issued at par eliminate the tax effect that exist for securities issued at a discount or premium. The bootstrapping methodology is used to generate the theoretical spot rate curve. A potential criticism is that large maturity gaps exist, particularly after 5 years.

August 2014 46


3


Selected off-the-run Treasury issues can be added to the on-the-run issues to bridge the caps in on-the-run maturities. The par coupon yield curve is estimated and remaining gaps are filled by interpolation. Like with all on-therun issues, bootstrapping is used to generate the theoretical spot rate curve.

All Treasury issue so that all coupon securities and bills are used. As a practical matter issues that have special circumstances such as tax advantages, illiquid markets, futures contract delivery are usually omitted to avoid yield distortions. Adjustments are made for taxes and call features. The advantage is that all information available in prices can be used.

Treasury coupon strips are observable zero-coupon securities that can be used directly to create an actual spot rate curve. The relative illiquidity in the strips market implies that strip rates include a premium.


3


Swap Rate Curve (LIBOR Curve)

LIBOR is the rate at which high quality banks will borrow or lend U.S. dollars outside the U.S. amongst themselves, and 3 months LIBOR is the most common floating rate used in interest rate swap agreements. The LIBOR spot rate curve is calculated using the same bootstrapping procedure used to calculate Treasury spot rates.

The swap rate curve represents the swap rates available at various future time periods to convert fixed rates to floating rates and vice versa

The swap rate curve is used to hedge interest rates, to value bonds, and for performance evaluation


3


The swap rate curve tends to be better benchmark than the government bond curve for the following reasons:

– There is little or no government regulation of the swaps market.

– A large demand for government bonds in the repo market can unrealistically change the yield curve. The swaps market does not have these yield problems.

– The swap curve has the credit risk of the underlying banks. Credit risks are thus more similar in the swaps market

(LIBOR) than when comparing various government bond market.

– The swaps market has more bond maturities to construct a yield curve than the government bond market. Swap rates quoted in the swap market have maturities of 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, and 30 years.


3


Theories of the Term Structure of Interest Rates

Expectations

Theory

Pure Expectations

Theory

Segmentation

Theory

Biased Expectations

Theory

Broadest

Interpretation

Local

Expectations

Liquidity

Theory

Preferred

Habitat Theory

August 2014 50


3


Pure (unbiased) expectations theory says the investor’s expectations of future interest rates alone creates the shape of the yield curve. Forward rates are the expected future spot rates. This implies that if the yield curve is upward

(downward) sloping, short-term rates are expected to rise (fall), and if the yield curve is flat, the market expects shortterm rates to be constant. The drawback is that it fails to consider price risk and reinvestment risk, but interest risk increases as the term to maturity increases.

– The broadest interpretation is that given any investment horizon, investors expect the same return, regardless of the maturity of the investment vehicle selected. This ignores the price risk associated with selling a bond prior to its maturity.

– The local expectations form of the pure expectation theory is an interpretation that suggests that the return on bonds with different maturities will be identical over a short-term investment period, commencing immediately. This is the only interpretation of the pure expectation theory that can be sustained in equilibrium.

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3


The two form of biased expectations theory are the liquidity theory and the preferred habitat theory.

– Liquidity theory: duration measures the price risk of holding a bond. Duration increases as the bond’s maturity lengthens. Liquidity theory says that investors will demand a risk premium for holding bonds with long maturities because the risk of this bonds is higher. - The yield curve will typically be upward sloping as investors demand higher yields on longer bonds. The yield curve could slope downwards, however, if expectations for lower rates in the future overwhelm the risk premium.

– Preferred habitat theory also proposes that forward rates represent expected future spot rates plus a premium, but it does no support the view that this premium is directly related to maturity. The existence of an imbalance between supply and demand for funds in a given maturity range will induce lenders and borrowers to shift from their preferred habitat (maturity range) to one that has the opposite imbalance. To do so, they must be offered a risk premium to compensate for the price and/or reinvestment risk.


3


Market segmentation theory is similar to the preferred habitat theory in that it agrees that lenders and borrowers have preferred maturity ranges and there is no premium (or discount) large enough to induce investors out of their preferred maturity range.

Instead, the shape of the yield curve is proposed to be determined by the supply and demand for securities within a given maturity range. In the extreme, the segmentation theory implies that rates for a given maturity segment will be determined independently of all other maturities.

The shape of the yield curve depends exclusively on the supply and demand within maturity segments. Under this theory the yield curve can take any shape .


3


Spot Rate Curve, Yield Curve on Coupon Bonds, Par Curve, and Forward Rate Curve

A yield curve shows the term structure of interest rates by displaying yields across different maturities (i.e., yields of

U.S. Treasury coupon bonds). Yields are calculated for several maturities and yields for bonds with maturities between these are estimated by linear interpolation.

The spot rate curve is a yield curve for single payments in the future, such as 0%-bonds or stripped Treasury par bonds. Yields on zero-coupon government bonds are spot rates.

The par curve shows the coupon rates for bonds of various maturities that would result in bond prices equal to their par values. It is not calculated from yields on actual bonds but is constructed from the spot rate curve.


3


With spot rates of 1%, 2%, and 3%, a 3-year annual par bond will have payments that are:

PMT

 



( 1

PMT

.

02 )



PMT

( 1 .



03 )

100



100

2 3

Thus, the payment is 2,96 and the par bond coupon rate is 2.96%



PMT



2 .

96

A forward curve is a yield curve composed of forward rates, such as 1-year rates available at each year over a future period


3


Forward Rates

The general formula to calculate a semi-annual forward is: where:

1 f m



( 1

(



1

 z m z



1 m

)

) m m



1



1

1fm zm zm+1

Doubling the forward rate 1fm gives the bond equivalent yield for the forward rate that starts in m months for 6 months forward rate that starts in m semi-annual periods for 6 months spot rate for a period of m semi-annual periods spot rate for a period of m semi-annual periods plus 6 months

August 2014 56


3


Example

The spot rates for 6-month Treasury bills and 1-year Treasury bills are 2.50% and 2.80% respectively, expressed as bond equivalent yields. The 6-month forward rate expressed as bond equivalent yields is closest to:

A) 2.96%

B) 3.00%

C) 3.10%


3


Example

Given the following spot rate curve, the implied forward rate in 12 months for 6 months is closest to:

Maturity Spot Rate

6 months

12 months

18 months

24 months

A) 6.55%

B) 7.02%

C) 7.54%

3.00%

4.00%

5.00%

6.00%


3


The relationship between a T-period spot rate (zT), the current 6-month spot rate (z1), and the 6-month forward rates is stated as: where: z

T





( 1

 z

1

)( 1



1 f

1

)( 1



1 f

2

)......( 1



1 f

T



1



1 / T 

1

1f1

1f2 forward rate that starts in 6 months for 6 months forward rate that starts in 12 months for 6 months

Just know that a spot rate is a package of forward rates and that discounting at either the forward rates or the spot rate will give the same present value.


3


Example

The following forward rates are given:

Semi-annual Periods Notation Forward Rate

1

2

3

1f0

1f1

1f2

4 1f3

The 2-year spot rate is closest to:

A) 4.40%

B) 4.70%

C) 4.95%

4.00%

4.60%

5.00%

5.20%


3


Example

The following forward rates are given:

Semi-annual Periods Notation Forward Rate

1 1f0 4.00%

2

3

1f1

1f2

4.60%

5.00%

4 1f3 5.20%

A 6% coupon bond pays the coupons semi-annually and has a remaining maturity of 1.5 years. The price of the bond is closest to:

A) 101.56%

B) 102.00%

C) 102.12%

August 2014 61


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4




Yield Measures






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4

Yield Measures

Yield Measures for Fixed-Rate bonds, Floating Rate Notes, and Money Market Instruments

The effective yield of a bond depends on its periodicity, or annual frequency of coupon payments. For an annual-pay bond the effective yield is equal to the yield-to-maturity. For bonds with greater periodicity, the effective yield is greater than the YTM. For example, a semi-annual coupon paying bond with a YTM of 8% has a yield of 4% every 6 months and an effective yield of 1.04 ^2 – 1 = 8.16%.

A YTM quoted on a semi-annual basis is two times the semi-annual discount rate: 2 x 4% = 8%.


4

Yield Measures

An important tool used in fixed-income analysis is to convert an annual yield from one periodicity to another. These are called periodicity, or compounding, conversions . A general formula to convert an annual percentage rate for m periods per year, denoted as APRm, to an annual percentage rate for n periods per year, APRn, is the following equation:





1

APR m m 



 m

 



1

APR n n 



 n


4

Yield Measures

Example

A 5-year, 4.5% semi-annual coupon payment government bond is priced at 98 per 100 of par value. Calculate the annual yield-to-maturity stated on a semi-annual bond basis, rounded to the nearest basis point. Convert the annual yield to:

A. An annual rate that can be used for direct comparison with otherwise comparable bonds that make quarterly coupon payments and

B. An annual rate that can be used for direct comparison with otherwise comparable bonds that make annual coupon payments


4

Yield Measures

Investors of fixed-income securities obtain their total return from the following three sources:

– Coupon interest

– Capital gains / losses resulting from buying at a different price than the one received when the security is sold or matures

– Reinvestment income from investing interim cash flows (interest on interest)


4

Yield Measures

Current Yield

The current yield on a security is simply its coupon rate, divided by its market price:

Current Yield



Cash Coupon Payment

Bond Price per Year

This yield calculation ignores potential capital appreciation / depreciation and reinvestment income, and does not incorporate the influence of the time value of money.


4

Yield Measures

Yield to Maturity (YTM)

This yield is the single discount rate that when applied to all of the cash flows generated by a fixed-income security over its term to maturity, will make the present value of those cash flows equal to the current price of the bond:

Pr ice



( 1



C

1

YTM )

1



( 1



C

2

YTM )

2



...



( 1



C n

YTM ) n



( 1



Par

YTM ) n

The yield to maturity takes into account the time value of money and the potential for capital appreciation

This measure does not consider the reinvestment rate. In reality, the reinvestment rate rarely ever equates to the YTM.

The YTM also is based upon the assumption that the bond will be held to maturity.


4

Yield Measures

Example:

Suppose we have a 10-year, USD 1‘000 par value, 7% semi-annual coupon paying bond. The bond price today is USD

895.80. Compute the current yield and the yield to maturity!


4

Yield Measures

Yield to Call (YTC)

Callable bonds might not reach maturity because they can be called before their maturity date. Therefore, the yield-tocall was developed to measure the return on a bond if it were to be called on a particular date. The yield to first call is the same as yield to maturity, calculated through the first call date with the call price as the maturity value .

Pr ice



( 1



C

1

YTC )

1



( 1



C

2

YTC )

2



...



( 1



C n

YTC ) n



(

Call

1



Price

YTC ) n

where: n = number of periods to first call date

The YTC should be used whenever a callable bond is trading at a price greater than or equal to its par value. Any additional premium above this price could be lost if the bond were called away, and thus the YTC will be a more conservative return measure.

August 2014 70


4

Yield Measures

There are several problems with these yield-to-call measures:

– They assume the bond is held to the call date

– They assume the issuer calls the bond on the call date

– They assume the coupons are reinvested at the yield-to-call

Example

Compute the yield-to-first-call and the yield-to-first-par-call for a 8% coupon (paid semi-annually), 7-year bond priced at 93 that is callable in 4 years at 106 and in 6 years at 100!

Yield to first par call date

This measure is the same as YTC, using expected cash flows to the first date at which the issuer can call the bond at par

August 2014 71


4

Yield Measures

Yield to Worst (YTW)

Yield to worst involves the calculation of YTC for every possible call date as well as the YTM, and determining which of these results is the lowest expected return. This yield is supposed to be the worst possible yield that can be realized by the investor.

In reality, the YTW measure has little meaning because it does not identify a bond’s true return, except in the rare event that the worst possible conditions do happen to materialize

Furthermore, the YTW measure incorporates a conglomeration of different reinvestment risk exposures


4

Yield Measures

The yield to worst is a commonly cited yield measure for fixed-rate callable bonds used by bond dealers and investors.

However, a more precise approach is to use an option pricing model and an assumption about future interest rate volatility to value the embedded call option.

Option-adjusted price = flat price of bond + value of embedded call

The investor bears the call risk, so the embedded call option reduces the value of the bond from the investor’s perspective. The investor pays a lower price for the callable bond than if it were option-free. If the bond were noncallable, its price would be higher. The option-adjusted price is used to calculate the option-adjusted yield . – The option-adjusted yield is the required market discount rate whereby the price is adjusted for the value of the embedded call option.

Value of Call = Price of option-free Bond – Price of Callable Bond

August 2014 73


4

Yield Measures

Floating-rate Note Yields

Floating rate notes have a quoted margin relative to a reference rate, typically LIBOR

The quoted margin is positive for issuers with more credit risk than the banks that quote LIBOR and may be negative for issuers that have less credit risk than loans to these banks

The required margin on a floating rate note may be greater than the quoted margin if credit quality has decreased, or less than the quoted margin if credit quality has increased


4

Yield Measures

P



The valuation of a floating-rate note needs a pricing model:





( Index

1



Index

where:

Index

QM

FV

m

DM

N



QM m m



)



FV

DM



1



...



( Index





1





QM m

Index m

)





FV

DM





N

FV reference rate, quoted margin future value paid at maturity or par value of bond periodicity of the floating-rate note (number of payment periods per year) discount margin number of evenly spaced periods to maturity


4

Yield Measures

Example

A 4-year, French floating-rate note pays three-month Euribor plus 1.25%. The floater is priced at 98 per 100 of par value.

Calculate the discount margin for the floater assuming that three-month Euribor is constant at 2%. Assume the 30/360 day-count convention and evenly spaced periods.


4

Yield Measures

Yields for Money Market Instruments

For money market instruments yields may be quoted on a discount basis or an add-on basis, and may use 360-day or 365-day years. A bond-equivalent yield is an add-on yield based on a 365-day year.

Commercial papers, T-bills, and bankers’ acceptances often are quoted on a discount basis

Bank certificates of deposits, repos, and such indices as LIBOR and Euribor are quoted on an add-on basis


4

Yield Measures

where:

PV

FV

The pricing formula for money market instruments quoted on a discount rate basis is:

Days

Year

DR

PV



FV









1



Days

Year



DR





 

DR









Years

Days present value, or price of the money market instrument discount rate (stated as an annual percentage)





 instrument number of days between settlement and maturity number of days in the year







 FV



FV

PV future value paid at maturity, or face value of the money market








4

Yield Measures

Example

91-day U.S. Treasury bill with a face value of USD 1 million is quoted at a discount rate of 2.25% for an assumed 360-day year. What is the price of the T-bill?

Example

91-day U.S. Treasury bill with a face value of USD 1 million is quoted at a price of USD 976,450 for an assumed 360-day year. What is the quoted discount rate of the T-bill?


4

Yield Measures

where:

PV

FV

The pricing formula for money market instruments quoted on an add-on rate basis is:

PV

Days

Year

AOR









1



FV

Days

Year



AOR









AOR









Years

Days present value, or price of the money market instrument add-on rate (stated as an annual percentage)





 instrument number of days between settlement and maturity number of days in the year









FV



PV

PV future value paid at maturity, or face value of the money market








4

Yield Measures

Yield Spread Measures

Yield Spread = Bond Yield – Benchmark Yield

If the benchmark is a government bond yield, the spread is known as a government spread or G-spread .

If the benchmark is a swap rate, the spread is known as an interpolated spread or I-spread .

A disadvantage of G-spreads and I-spreads is that they are theoretically correct only if the spot yield curve is flat and approximately the same across maturities. However, the spot yield curve is normally upward-sloping.


4

Yield Measures

A zero-volatility spread or Z-spread is the percent spread that must be added to each spot rate on the benchmark yield curve to make the present value of a bond equal to its price. – Thus, the Z-spread accounts for the shape of the yield curve.

P



( 1

 z

C

1

1



Z )

1



( 1

 z

C

2

2



Z )

2



...



( 1

C

 n z n



Par



Z ) n

where:

z

Z

In practice, the Z-spread is usually calculated in a spreadsheet using a goal seek function or similar solver function. benchmark spot rates

Z-spread

August 2014 82


4

Yield Measures

Example

A 6% annual coupon corporate bond with two years remaining to maturity is trading at a price of 100.125. The 2-year, 4% annual payment government benchmark bond is trading at a price of 100.750. The 1-year and 2-year government spot rates are 2.1% and 3.635%, respectively, stated as effective annual rates.

1. What is the G-spread?

2. Demonstrate that the Z-spread is 234.22 bps


4

Yield Measures

Investors will require a larger spread for an issue with an embedded option that is favourable to the issuer

(call option).

If interest rates fall, the issuer will call the bond forcing the investor to reinvest at lower rates and reducing their return. The option-adjusted spread (OAS) is used to price bonds with embedded options. The OAS for a callable bond is calculated as follows:

OAS (bps.) = Z-Spread (bps.) – Option Value (bps.)

Since embedded options will clearly impact the spread one way or another, a Z-spread calculation does not give nearly as accurate a picture as an option-adjusted spread calculation.


4

Yield Measures

Option-adjusted spread (OAS) removes the effect of the embedded options and shows the average spread the investor will actually earn over a comparable Treasury security.

Credit

7-Year Maturity Bonds

First Call in Z-Spread OAS

Quality

AA

AA

Baa

1-year

3-years

3-years

55 bps.

89 bps.

77 bps.

30 bps.

28 bps.

40 bps.

The Z-spreads cannot be used to compare the bonds because they are based only on spot rates and do not take into account the impact of call features. The OAS is lower then the Z-spread for all the callable bonds because it considers the adverse affect of the embedded call.

August 2014 85


Content

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Yield Measures

Interest Rate Risk: Duration and Convexity





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5

Interest Rate Risk

Duration and Convexity

Macaulay Duration

Macaulay duration is named after Frederick Macaulay, a Canadian economist who first wrote about the statistic in

1938.

Macaulay duration is the weighted average of the time to receipt of the bond’s promised payments , where the weights are the shares of the full price that correspond to each of the bond’s promised future payments.


5



Example

1

A 4-year 5% annual coupon paying bond is trading at par. What is the Macaulay duration?

Period Cash Flow PV Weight

2

3

4



5

5

5

105

4.76

4.54

4.32

86.38

100.00

0.0476

0.0454

0.0432

0.8638

1.0000

The Macaulay duration is 3.7232 years

Period x Weight

0.0476

0.0908

0.1296

3.4552

3.7232

August 2014 88


5



There is also a general closed-form solution which can be used to calculate the Macaulay duration (MD):

MD where:







1

 r r



1 c





 r





1





N r





N

( c







1 r



)

 r







( t / T ) r c

N expected return (yield-to-maturity) coupon rate maturity of the bond

MD







1 .

05

0 .

05



1 .

05

0 .

05











4



( 0 .

05

1 .

05



4 



1





0 .

05 )



0 .

05







0



3 .

7232


5



Modified Duration

The calculation of the modified duration statistic of a bond requires a simple adjustment to Macaulay duration.

Modified where:

Duration



Macaulay

1



Duration r r expected return (yield-to-maturity)

For the example, the modified duration of the 4-year, 5% annual coupon paying bond is 3.546:

Modified Duration



3 .

7232



3 .

546

1 .

05

August 2014 90


5



Interpretation of duration:

1st interpretation of duration:

– Effective duration is the first derivative of the price-yield relationship of a security, divided by the initial price of the security:

D

E

 

dP/dy

P

– While correct, this interpretation is mathematically.


5



2nd interpretation of duration:

– Unadjusted duration (Macaulay duration) is a weighted average of time. – The Macaulay duration may be meaningful to an investment professional who understands that a bond with a duration of 6 years is more volatile than a bond with a duration of 2 years, but it does not have much meaning to most clients.

3rd interpretation of duration:

– Effective duration is a measure of how sensitive the return on a bond is to small changes in interest rates

D

E

 

dP/P dy

– This interpretation is easily understood by almost anybody. It indicates that if a bond has a duration of 4.0, its price will rise or fall by 4% every time interest rates fall or rise by 100 basis points.

August 2014 92


5



Approximate Modified Duration

An alternative approach is to approximate modified duration directly:

Approx where:

.

Modified Duration



2



P





P



(



Yield )



P

0

P– Price of the bond after a decrease in yield

P+ Price of the bond after an increase in yield.

Let’s assume a yield change of 50 bps. for your 4-year, 5% annual coupon paying bond. The approx. modified duration is:

Approx .

Modified Duration



101

2



.

(

794

0 .



005 )

98



.

247

100



3 .

547

August 2014 93


5



Example:

An option-free bond has a remaining maturity of 5 years and a coupon of 4.5% which is paid semi-annually. The yield to maturity of the bond is 4.8%. Calculate the approximate modified duration and (based on the duration) the new bond price if interest raise by 50 basis points.


5



Effective Duration

Another approach to assess the interest rate risk of a bond is to estimate the percentage change in price given a change in a benchmark yield curve. – The effective duration of a bond is the sensitivity of the bond’s price to a change in a benchmark yield curve:

Effective Duration



2



P 



P 

(



Curve )



P

0

The difference between approximate modified duration and effective duration is in the denominator. Modified duration is a yield duration statistic in that it measures interest rate risk in terms of a change in the bond’s own YTM. Effective duration is a curve duration statistic in that it measures interest rate risk in terms of a change in the benchmark yield curve (  Curve).

August 2014 95


5



Modified duration is the approximate price change in a bond‘s price for a 100 basis point change in yield, assuming that the bond‘s expected cash flows do not change when the yield changes (option-free bonds). When calculating P- and P+, the same cash flows used to calculate P

0

are used.

Effective (or option-adjusted) duration also estimates a bond‘s price sensitivity to a change in yield, but accounts for how changes in yield will affect cash flows .


5



Modified and Macaulay Duration assume that the cash flows of a bond will not change as yields change. – Thus effective duration is the appropriate measure of interest rate risk for bonds with embedded options because changes in interest rates may change their future cash flows.

Pricing models are used to determine the prices that would result from a given size change in the benchmark yield curve


5



How a Bond’s Maturity, Coupon, Embedded Option, and Yield Level Affect its Interest Rate Risk

Holder other factors constant:

– Duration increases (decreases) when maturity increases (decreases).

– Duration decreases (increases) when the coupon rate increases (decreases).

– Duration decreases (increases) when YTM increases (decreases).

With a call provision , the value of the call increases as yields fall, so a decrease in yield will have less effect on the price of the callable bond (price callable bond = price straight-bond – price of call)

With a put provision , the bondholder’s option to sell the bond back to the issuer at a set put price reduces the negative impact of the yield increases on the price of a putable bond (price putable bond = price straight-bond + price of put)

August 2014 98


5



Duration of a Portfolio

A portfolio‘s duration is the weighted average duration of the component securities

Example

Compute the duration of the following portfolio:

Bond:

A

B

C

Market Value:

USD 3,000,000

USD 4,000,000

USD 5,000,000

Duration:

3.75

4.25

2.55

% of portfolio:

....................

....................

....................


5



A second approach to calculate portfolio duration is to calculate the weighted average number of periods until cash flows will be received using the portfolio’s IRR (its cash flow yield). This method is better theoretically but cannot be used for bonds with embedded options. This approach is also inconsistent with duration capturing the relationship between price and YTM.

Duration will not provide meaningful percentage value change estimates for portfolios unless the yield curve shifts in a parallel manner

Bullet and barbell portfolios with the same durations have the same interest rate risk if the yield curve shifts in a parallel manner

Even if the bullet and barbell portfolios have the same durations, they do not have the same interest rate risk with respect to a non-parallel shift in the yield curve


5



Money Duration and Price Value of a Basis Point (PVBP)

The money duration of a bond (dollar duration) is expressed in currency units and calculated as follows:

Money Duration = Annual Modified Duration x Full Price of Bond

Money duration is sometimes expressed as money duration per 100 of bond par value:

Money Duration = Annual Modified Duration x Full Price of Bond per 100 of Par Value

The change in bond price can be calculated:

Change in Bond Price = Money Duration x Change in YTM


5



Example

A life insurance company holds a USD 10 million (par value) position in a 4.50% ArcelorMittal bond that matures on 25 February 2017. The bond is priced (flat) at 98.125 per 100 of par value to yield 5.2617% on a street-convention semi-annual bond basis for settlement on 27 June 2014. The total market value of the position, including accrued interest, is USD 9,965,000 or 99,65 per 100 par value. The bond’s (annual) Macaulay duration is 2.4988.

1. Calculate the money duration per 100 in par value for the ArcelorMittal Bond?

2. Using the money duration, estimate the loss on the position for each 1 bp increase in the yield-to-maturity for that settlement date?


5



The price value of a basis point is the change in the value of a bond, expressed in currency units, for a change in

YTM of one basis point (0.01%):

PVBP

Example



P 



2

P 

A newly issued, 10-year, 5% annual coupon paying bond is priced at 92.64. The price value of a basis point for this bond assuming a par value of USD 1 million is closest to:

A. USD 10

B.

C.

USD 700

USD 1,400

August 2014 103


5



Approximate Convexity and Effective Convexity

The divergence from the bond price curve to the straight line (duration) is called convexity

Positive convexity is a larger increase in price than decrease in price, for the same change in interest rates – The upside is greater than the downside

All option-free bonds have positive convexity, but the actual degree of duration and convexity of bonds will vary, depending on the level of interest rates, coupon, and maturity. A longer maturity, a lower coupon rate, or a lower YTM will all increase convexity, and vice versa. For two bonds with equal duration, the one with cash flows that are more dispersed over time will have the greater convexity.


5



Convexity, is used to approximate the change in price that is not explained by duration .

The approximate convexity of a bond can be computed as follows: approx .

Convexity



P





P





2 P

0

P

0

(

change in Yield

)

2

Example:

Compute the convexity of a 6-year, 7% seminannual corporate bond which actually has yield to maturity of 5% when we assume a change in interest rates by 100 basis points

August 2014 105


5



Effective convexity , like effective duration, must be used for bonds with embedded options. The approximate effective convexity of a bond can be computed as follows: approx .

effective

Convexity



P





P





2 P

0

P

0

(

change in Curve

)

2


5



For callable bonds : The decline in yield will reach the point where the rate of increase in the price of the bond will start slowing down and eventually level off → negative convexity . – This is due to the fact that the issuer has the right to retire the bond prior to maturity at some specified call price.

As long as yields remain below a certain level, callable bonds will exhibit price compression, or negative convexity .

As long as yields are above a certain level, those same callable bonds will exhibit all the properties of positive convexity .

With putable bonds as interest rates move from high to low the duration will increase. Convexity will be positive at all rate levels and convexity will be highest when interest rates are in the area where the put begins to acquire value.


5



Taylor Approximation

Given values for approximate annual modified duration and approximate annual convexity, the percentage change in the full price of a bond can be calculated as follows:

Estimated price change in % = –Duration (  y) + 0.5 Convexity (  y) 2

Example:

Compute the estimated price change in % when the duration is 5.5 and the convexity is 30.5 and assuming an interest shift by 120 basis points!


5



Duration predicts a straight linear-relationship between changes in yield and changes in price. In reality, the price/yield relationship for a bond is convex. Duration therefore underestimates the price increase and overestimates the price decline .


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Yield Measures


Credit Risk: Fundamentals of Credit Analysis




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Credit Risk

Fundamentals of Credit Analysis

Overview

Default risk: This is the risk that the interest or principal on a bond will not be paid.

Credit risk has two components:

– Default risk (probability of default)

– Loss severity or loss given default

Expected credit loss = Default risk x Loss severity

Recovery rate is the percentage of a bond’s value an investor will receive if the issuer defaults


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Credit Risk


Credit spread risk: This is the risk that the yield spread on a fixed-income security over some benchmark yield (such as a comparable Treasury security) will widen due to a change in the return the market demands for taking credit risk.

Downgrade risk: This is the risk that the price of a fixed-income security may fall because its credit rating is downgraded by one or more of the credit-rating agencies

Market liquidity risk: Selling a bond less than its market value and is reflected in the size of the bid-ask spread.

This risk is greater for bonds with less creditworthy issuers and for bonds of smaller issuers with relatively little publicly traded debt.


6

Credit Risk


Each category of debt from the same issuer is ranked in accordance to a priority of claims in the event of default

Secured debt is backed by a collateral

Unsecured debt or debentures reflect a general claim to the issuer’s assets and cash flows

General seniority rankings for debt repayment priority are:

– First lien or first mortgage (specific asset is pledged)

– Senior secured debt

– Junior secured debt

– Senior unsecured debt

– Senior subordinated debt

– Subordinated debt

– Junior subordinated debt

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Credit Risk


All debt with the same category is ranked as pari passu (same priority of claim)

A bankruptcy reorganization plan is confirmed by a vote among all classes of investors with less than 100% recovery rate. Typically a reorganization plan does not strictly conform to the original priority of claims.


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Credit Risk


Issuer credit ratings , or corporate family ratings, represent a debt issuer’s overall creditworthiness and typically apply to a company’s senior unsecured debt

Issue-specific ratings , or corporate credit ratings, represent the credit risk of a specific debt issue

Cross default provision : default in one of the outstanding bonds may trigger default on the remaining issues

Notching refers to the practice of adjusting an issue credit rating upward or downward from the issuer credit rating to reflect the seniority and other provisions of a debt issue. Notching is less common for highly rated issues than for lower-rated issues. For lower-rated issues, higher default risk results in significant differences between recovery rates of debt with different seniority rankings, leading to more notching.


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Credit Risk


Lenders and bond investors should not rely exclusively on credit ratings from rating agencies for the following reasons:

– Credit ratings are dynamic and can change during the life of a debt issue

– Rating agencies are not perfect and cannot always judge credit risk accurately

– Event risk is difficult to asses: unforeseen events are not reflected in credit ratings

– Market prices of bonds often adjust more rapidly than credit ratings


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Credit Risk


Moody’s S&P Fitch

High-Quality

Grade

Upper-Medium

Grade

Aaa

Aa1

Aa2

Aa3

A1

A2

A3

AAA

AA+

AA

AA 

A+

A

A 

AAA

AA+

AA

AA 

A+

A

A 

Low Medium

Grade

Baa1

Baa2

Baa3

BBB+

BBB

BBB 

BBB+

BBB

BBB 

____________________________________________________________________________________

Low Grade or

Ba1

Ba2

BB+

BB

BB+

BB

Speculative Grade ....

C

....

C

.....

C

____________________________________________________________________________________

Default C D D

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Credit Risk


Components of Traditional Credit Analysis

In traditional credit analysis, the following four C’s of credit are considered: capacity, collateral, covenants, and character

Character: Management’s ability to manage potential crises is a key factor in assessing a borrower’s character.

Management should have demonstrated their ability to define and execute a strategic plan. The track record can be used to measure the character of the management.

Assessing the quality of the management by the rating agencies include:

– Understanding of business strategies and policies

– Financial philosophy and strategic direction

– Conservative approach to business

– Track record

– Succession planning (continuity of management)

– Well-developed business plans

– Well-developed control systems

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Credit Risk


Capacity to repay: A firm will receive the funds to service its debt (interest and principal payments) from its cash flow.

Sales less operating expenses must be enough to cover interest charges. An analyst can calculate the capacity to repay the debt burden by the use of ratios and cash flows derived from the financial statements.

Analysis of collateral (underlying capital): A corporate debt obligation can be secured or unsecured. In a liquidation, the proceeds from bankruptcy are distributed to creditors based on the absolute priority rule (risk of loss is reduced for secured debt). However, in the case of a reorganization the absolute priority rule does typically not hold.

A secured creditor may receive only a portion of its claim, while unsecured creditors may receive distributions for their entire claim. This is the case because a reorganization requires approval of all parties. – As a consequence, analysts place less emphasis on the collateral.

Issue covenants: Covenants include limitations and restrictions on the borrower’s activities


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Credit Risk


The bond indenture should contain terms and conditions that are appropriate to ensure payment of the debt. Covenants are usually imposed by the bondholders to restrict companies from taking action that might not be in the bondholders’ best interest .

There are two general types of covenants:

– Affirmative covenants (the debtor promises to take action)

– Negative covenants (the debtor promises not to do certain things)

Examples of affirmative covenants are to make interest and principal payments and to keep the equipment in good working order

Examples of negative covenants are not to incur additional debt and not to exceed limits on solvency, capitalization, or coverage ratios

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Credit Risk


Sources of liquidity are:

Liquid assets are needed to pay debt obligations as they come due

The primary source is cash flow which is derived from net sales less operating costs

Additional sources of liquidity come from the firm’s ability to obtain additional financing to meet immediate needs.

These additional sources include:

– A line of bank credit

– Securitization of loans or receivables

– Third party guarantees


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Credit Risk


Factors that Influence the Level and Volatility of Yield Spreads

Yield of option-free bond = Real risk-free rate + Expected inflation rate + Maturity premium + Liquidity premium +

Credit Spread

Yield spread = Liquidity premium + Credit Spread

The level and volatility of yield spreads are affected by:

– Credit and business cycles

– Performance of financial markets as a whole

– Availability of capital from broker-dealers, and

– Supply and demand for debt issues

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Credit Risk


Yield spreads tend to narrow when:

– Credit cycle is improving

– Economy is expanding

– Financial markets are strong, and/or

– Investor demand for new debt issues is strong

On the other hand, yield spreads tend to widen when:

– Credit cycle is weakening,

– Economy is weakening,

– Financial markets are weakening,

– Broker-dealer capital is insufficient for market making, and/or

– Supply of new debt issues is heavy


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Credit Risk


Example:

Which bonds are likely to exhibit the greatest spread volatility?

A. Bonds from issuers rated AA

B. Bonds from issuers rated B

C. Bonds from issuers rated A

Example:

If investors become increasingly worried about the economy – say, as shown by declining stock prices- what is the most likely impact on credit spreads?

A. No change to credit spreads because they are not affected by equity markets

B. Narrower spreads will occur because investors will move out of equities into debt securities

C. Wider spreads will occur because investors are concerned about weaker creditworthiness

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Credit Risk


Return Impact of Spread Changes

Small spread changes:

Return impact  (  Modified Duration) x (  Spread)

Larger spread changes:

Return impact  (  Modified Duration) x (  Spread) + 0.5 x (Convexity) x (  Spread)^2


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Credit Risk


Longer maturity bonds have higher duration and as a consequence higher spread sensitivity. Longer maturity bonds have higher credit spreads. Longer maturity bonds also tend to have larger bid-ask spreads (i.e., higher transaction costs), implying investors in longer maturity bonds would require higher spreads.

Credit curves are typically upward sloping

Active bond managers have to forecast spread changes and expected credit losses for individual bonds and for the overall bond portfolio in order to improve portfolio performance


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Credit Risk


Yield = Benchmark Yield + Risk Premium (Spread) where:

Benchmark yield = risk-free rate = expected inflation rate + expected real rate

Risk premium = credit risk + liquidity risk + taxation

Estimated price change in % = –Duration (  spread) + 0.5 Convexity (  spread) 2


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Credit Risk


Example

The flat price on a fixed-rate corporate bond falls one day from 92.25 to 91.25 per 100 of par value because of poor earnings and an unexpected ratings downgrade of the issuer. The (annual) modified duration for the bond is 7.24. Which of the following is closest to the estimated change in the credit spread on the corporate bond, assuming benchmark yields are unchanged?

A.

B.

C.

15 bps.

100 bps.

129 bps.


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Credit Risk


High Yield Bonds

High yield bonds are more likely to default than investment grade bonds, which increases the importance of estimating loss severity. Analysis of high yield debt should focus on:

– Liquidity

– Projected financial performance

– The issuer’s corporate and debt structures

– Debt covenants

A credit analyst will need to calculate leverage for each level of the debt structure when an issuer has multiple layers of debt with a variety of expected recovery rates

High yield issuers for whom secured bank debt is a high proportion of the capital structure are so called top heavy and have less capacity for additional bank borrowings in financially stressful period

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Credit Risk


Issuers of high-yield bonds typically have a holding company structure . The assets and cash flows that are available to pay the debt service will reside in operating subsidiaries .

A financial analysis of every subsidiary may be necessary in order to determine if the individual subsidiaries will be able to generate sufficient excess cash flow to pay to the parent so that the parent can meet its debt service requirements

High-yield issuers are risky in the first place. It is, therefore, very important to analyze the covenants in their indentures to determine whether or not they are sufficiently limiting so as to “force” the company to preserve cash and assets as collateral.


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Credit Risk


Important covenants for high yield debt include:

– Change of control put: debt holders have the right to require the issuer to buy back debt (at or above par) in the event of an acquisition

– Restricted payments: amount of cash that may be paid to equity holders is limited

– Limitations on liens: amount of secured debt that a borrower can carry is limited

– Restricted versus unrestricted subsidiaries: restricted subsidiaries’ cash flows and assets can be used to service the debt of the parent holding company


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Credit Risk


High-yield debt is not as risky as equity investments, but it is more risky than investment quality bonds. –

The empirical evidence is that the returns on high-yield debt are more closely correlated with the returns on equities than the returns on bonds .

The best way to analyze high-yield bonds is to perform the same type of long-term cash flow projection that is used to analyze the value of equity because these bonds tend to have below average solvency and interest coverage ratios and above average debt-to-capital ratios

For example, analysts can compare companies based on the difference between their EV/EBITDA and Debt/EBITDA ratios. Companies with a wider difference between these two ratios have greater equity relative to their debt and therefore have less credit risk.


6

Credit Risk


Sovereign Bonds

Sovereign debt is the debt of foreign governments. This kind of debt is unique insofar as it is necessary to analyze both

– A sovereign government’s ability to pay its debt

– And its willingness to pay its debts .

Rating agencies consider the following factors:

– Political risk

– Income and economic structure

– Economic growth prospects

– Fiscal flexibility

– Public debt burden

– Price stability (inflation)

– Balance of payment flexibility

– External debt and liquidity

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Credit Risk


S&P assigns two ratings:

– Local currency denominated debt rating

– Foreign currency denominated debt rating

Historically the risk of defaults has been greater on debts not denominated in the issuer’s local currency. While a country can levy taxes (or print money) to repay its local currency debts, it must generate real economic activity to repay debts in another currency.

Sovereign defaults can be caused by events such as war, political instability, severe devaluation of the currency, or large declines in the prices of the country’s export commodities. Access to debt markets can be difficult in bad economic times.

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Yield Measures



Managing Bond Portfolio



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Introduction

Set investment objectives

– It depends upon the institution and is typically expressed in terms of return and risk

Establish investment policy

– It begins with asset allocation. Client and regulatory constraints in addition to tax and financial reporting implications must be considered


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Select portfolio strategy

– The portfolio strategy must be consistent with objectives and guidelines. May be active, passive, or a combination of the two

Select assets

– This is an attempt to construct a portfolio with the greatest return for the given level of risk

Measure and evaluate performance (monitoring)

– The performance should be assessed relative to a predetermined benchmark

Adjusting the portfolio


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There are two broad investment objectives that are associated with two different types of benchmark.

If the investment objective is to satisfy liabilities, then the benchmark should be structured to provide an index of those liabilities  Benchmark in terms of its liability structure

If the objective is to provide performance in excess of some benchmark, then the benchmark should be a suitable bond index  Benchmark as a bond index

The benchmark specified must reflect the client’s investment objectives from a risk/return perspective. The objective returns must be appropriate.


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Using liabilities as a benchmark is most appropriate for investors whose primary concern is the satisfaction of those liabilities when they come due

Investors who follow an investment policy of strategic asset allocation on the other hand, will want to compare investment performance to a bond index

Occasionally, investors with liabilities, like pension plan sponsors, will pursue a bond index strategy on the assumption that over a long time period bond performance that mimics an index will be sufficient to satisfy the liabilities


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Managing a Fixed-Income Portfolio against a Bond Market Index

Investors must choose an index with characteristics that match the objectives of their portfolios. In order to choose the appropriate index the most important characteristics to examine are:

– Market value risk:

It is the change in the market value of a portfolio as interest rates shift

Investors who are most adverse to market value risk should invest in portfolios with short or intermediate durations and use short or intermediate-term indexes as performance benchmarks. Only less risk averse investors should compare their higher risk portfolios to long-term indexes.


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Income risk:

– It refers to the instability and unpredictability of the income generated by the portfolio.

– Investors who are seeking a stable income stream that will persist for years into the future should choose longerterm portfolios and judge them against long-term indexes. – Short-term assets create an unpredictable income stream that can vary from the income needs of the investor.

Credit risk:

– The average credit risk and diversification of the benchmark index should be compatible with the amount of credit risk the investor is willing to take and the amount of diversification that is desired

Liability framework risk:

– Investors who must fund long-term liabilities such as a pension fund should invest in long-term fixed-income assets to fund their long-term liabilities


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Taxable investors face a tax liability . They should attempt to maximize their after-tax portfolio returns. Therefore, managers with clients whose returns are fully taxable should choose a benchmark index made up of either taxable or non-taxable bonds, depending upon which is expected to produce the higher after-tax return for their clients.


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Example

A portfolio manager has three fixed-income clients, a risk-averse individual who does not want to risk much of a loss in the value of his portfolio, a college endowment fund that wants stable long-term income to fund future expansion programs, and a property and casualty insurance company that relies on the fund to meet short-term automobile accident claims. The manager’s firm has three benchmark portfolios available for investment:

Portfolio A, which is made up of A-rated, 1–3 year corporate bonds

Portfolio B, which is made up of high yield (junk) bonds

Portfolio C, which is made up of A-rated, 5–7 year corporate bonds

Portfolio D, which is made up of Baa or better, 10–25 year corporate bonds


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(1) Passive management

– The manager’s primary job is to select the bond index that best matches the risk and constraint profile of his client, and attempt to construct a portfolio that matches the chosen index and tracks its return closely

– A passive (indexing) strategy has three advantages :

Indexing is a low-cost strategy

It is difficult to outperform an index, so indexing may not sacrifice returns

Indexing produces excellent diversification, which reduces risk


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A passive (indexing) strategy has the following disadvantage :

– Management and transaction costs that produce a net return to the client that is less than the return of the benchmark index a) Pure bond indexing

– It attempts to replicate the index by owning all the bonds in the index and in the same percentage by market weight

– Disadvantages: With this technique is difficult to beat the benchmark because the portfolio pays expenses and transaction costs where the index does not. The approach is difficult to implement because not all the bonds in the index will be available to purchase (highly illiquid). – This approach will lag the benchmark index by the amount of manager’s expenses and transaction costs.

– Advantage: It will perfectly match the benchmark

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Managing Bond Portfolio b) Enhanced indexing by matching primary risk factors

– This approach invests in a large sample of bonds such that the portfolio risk factors such as duration, cash flow distribution, sector, quality and call exposure match the index

– Advantage: It does not require owning all the index’s bonds, therefore implementation costs are lower

– Disadvantage: The portfolio will have a higher tracking error than pure bond indexing. Tracking error can be kept relatively low, by making sure that the portfolio is constructed to match the risk profile of the benchmark as closely as possible.

– Through the use of under-priced securities and efficient construction, it is possible to slightly outperform the index’s return


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The risk profile of a bond index is a detailed analysis of its risk exposure. The most important risk exposures relate to the yield curve. These include:

– Interest rate risk : the index’s sensitivity to parallel shifts in the yield curve, measured by the index’s duration and convexity

– Yield curve risk : the index’s sensitivity to yield curve reshapings (non-parallel changes of the yield curve), measured by key rate durations . Key rate durations are used to measure the price change of a bond or bond portfolio to changes in yields at specific points on the yield curve.

– Spread risk : the index’s sensitivity to the spread between non-Treasury and Treasury yields, due to changes in the creditworthiness of specific issue, or to changes in the credit conditions either generally or within specific sectors of the market


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– Call risk : the likelihood that the index will not respond very favorably if interest rates fall to very low levels because of the likelihood that certain callable bonds within the index will be called

– Event risk : the index’s exposure to credit rating changes because of restructurings and other idiosyncratic factors unique to individual issues or sectors

Therefore, an enhanced indexer must make sure that he constructs a portfolio that is exposed to these risks in exactly the same way as is the benchmark bond index whose risk exposures are to be replicated


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The following strategies can be used to align the interest rate risk and yield curve risks of a portfolio to those of a benchmark index :

– Cell-matching (stratified planning): The bonds within the benchmark index are categorized into “cells” that represent the various risk exposures within index. The manager then selects a (random) sample of the bonds from each cell for inclusion in the portfolio, making sure that the weight given to each cell in the portfolio matches that cell’s weighting in the benchmark index.

– Multifactor modeling : The manager must construct a portfolio that has the same effective duration, effective convexity and important key rate duration as the benchmark index. Simulations should be run to ensure the desired interest rate behavior of the portfolio vs. the benchmark index.

– Cash flow matching : The manager constructs a portfolio so that the percentage of the present values of all the cash flows generated by the bonds in it that fall into a series of non-overlapping time periods match period-toperiod with the same percentages for the benchmark index


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To align the spread risk exposure of the portfolio with that of the benchmark bond index, the enhanced indexer should make sure:

– Sector and quality weightings of the portfolio match those of the benchmark index

– The sector contributions to the overall portfolio’s duration are the same , sector-by-sector, for the constructed portfolios as for the benchmark index

– The amount of duration that comes from various quality sectors in the portfolio matches that of the benchmark index

– Managers should make sure that their portfolio’s spread risk is the same as that of the benchmark index


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Spread Duration

Spread is the difference between the yield on a bond and a reference rate, typically U.S. Treasury securities of similar maturity

Spread duration measures the percentage change in the value of a bond or portfolio of non-Treasury bonds for a change in the yield spread between those assets and their benchmark Treasury bond .

Spread duration is important because as spreads change the value of the portfolio may change far in excess of its modified duration

In addition, it can be used to measure the sensitivity of the value of a portfolio as a result of spread changes independent of changes in Treasury


7


Example:

A 8-year, A-rated, corporate bond yields 8%, and an 8-year Treasury bond yields 7%. What will happen to the price of the corporate bond if the nominal spread between the two widens to 125 basis points? – The spread duration of the corporate bond is 6.2.


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There are three spreads used in determining spread durations:

– Nominal spread (or G-Spread) is the difference between the yield of a non-Treasury security and the yield of a Treasury security of comparable maturity. The nominal spread duration measures the percentage price change in price of the non-Treasury for a change in the nominal spread.

– Zero volatility spread is the spread over the Treasury spot rate. Zero volatility spread duration measures the change in price of the non-Treasury for a change in the zero-volatility spread.


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– Option-adjusted spread is determined using a binomial interest rate tree. It can be interpreted as measuring the average incremental return of the non-Treasury compared to the return of the benchmark Treasury over a range of possible future interest rate paths and the bond cash flows that would occur along each such path. – The option adjusted spread duration measures the percentage change in price of the non-Treasury for a change in the

OAS.

The manager should always use the spread duration that matches the method in which the spread was measured.


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Call risk exposure can be matched by

– making sure that the callable bond weighting of the portfolio matches that of the benchmark index. The sector, coupon, and maturity weightings of callable bonds in the portfolio should match those of the callable bonds in the benchmark index as well.

Event risk exposures can be matched by making sure that

– the number of issues in the portfolio is large . Bond indexes contain thousands of issues. This high degree of diversification reduces event risk in the benchmark to a very low level.


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Managing Bond Portfolio c) Enhanced indexing with small risk factor mismatches

– This approach is similar to the one above except that it allows minor mismatches in the risk factors (except duration).

Duration is matched to control interest rate risk because changes in interest rates account for 90% of the benchmark index’s return. Then the manager attempts to enhance the portfolio’s return by a small amount by using the following techniques:

Tight cost controls (low trading costs and management fees)

Issue selection : undervalued bonds are included in the portfolio and overvalued issues are avoided.

The manager performs independent credit analyses to select bonds whose credit rating will likely be upgraded and avoid issues that are likely to be downgraded.

Yield curve positioning : Overweight maturities along the yield curve that are undervalued and underweight those that are overvalued


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– Sector and quality positioning : Tilt toward short duration corporate issues, which is where the best yield spread per unit of duration is usually found.

Anticipate yield changes: When credit conditions will be expected to deteriorate, tilt the portfolio from corporate bonds slightly toward an overweighting in Treasuries, and vice versa.

Call exposure positioning: Underweight callable issues that are likely to be called due to an expected decline in interest rates

– Tracking error should still be low


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(2) Active management

– Active management requires the manager to successfully challenge the market’s expectations with his own superior forecasting ability

– If the manager can forecast the interest rate outlook, credit market conditions, or some other relevant factors with better accuracy than the market, he should be able to “tilt” the portfolio away from the benchmark indexes weightings in ways that will generate higher returns than those produced by the benchmark index


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Managing Bond Portfolio d) Active management with risk factor mismatches

– This strategy involves larger mismatches in the risk factors to add greater value. – Duration may also be mismatched to some degree, allowing the portfolio to take some interest rate risk.

– The portfolio is tilt in the direction of attractive sectors and to adopt an aggressive posture with risk factors where the manager believes there is mispricing

– Advantage: It can enhance returns relative to the benchmark index without incurring undue risk

– Disadvantage: It is more costly and somewhat more risky than the purely passive strategies

– The tracking error risk will be more substantial


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Managing Bond Portfolio e) Full-blown active management (unrestricted active management)

– This is the riskiest approach, with large duration and sector bets being made

– The manager deviates from the benchmark to a much greater degree as long as his forecasts about the level of interest rates, the shape of the yield curve, or credit conditions differ from those implied by the market’s behavior

– Advantage: The manager can outperform the index by a wide margin if his forecasts are consistently better than those of the market

– Disadvantage: The manager can underperform the benchmark by a wide margin if his forecasts are (even occasionally) significantly wrong

– The tracking error is the highest with this approach


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In attempting to outperform the benchmark index by a significant amount, active managers must undertake a number of activities that are not required of passive managers such as:

– Identifying which index mismatches to exploit . This depends on the manager’s areas of expertise (interest rate risk and credit risk expertise)

– Determining the market’s expectations regarding the mismatches that might be exploited.

Market data can provide insight as to what market expectations are. – For example, calculating forward rates along the yield curve can provide some insight as to what the market expects interest rates will be doing in the future.

– Making independent forecasts in the areas where the manager has the most expertise in order to find overvalued or undervalued issues. An exploitable opportunity exists whenever the market’s expectations differ from that of the manager.

– Identifying areas of under- or overvaluation using relative value analysis of securities in the market , which the active manager can exploit


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Tracking risk describes the risk that the return of the portfolio will be different from the return of the benchmark portfolio. It is measured by computing the tracking error of a portfolio’s returns. It is the standard deviation of the portfolio’s active return (actual return – benchmark returns) over a period of time.

Tracking

Risk









Active

Return

 n

Average

Active



1

Return





Tracking errors arises in both active and passive strategies

In an actively managed bond portfolio , the portfolio characteristics are deliberately designed to deviate from the characteristics of the benchmark. They are willing to accept a large amount of tracking risk in order to try to produce larger returns than those of the benchmark index.

In a passively managed bond portfolio , the risk is likely to be very small and be positive or negative

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Tracking error risk will be higher when the managed portfolio differs from the benchmark. The bond weightings in the portfolio do not match the weightings of the bonds in the index .

– The managed portfolio may have a different risk profile because it includes securities or sectors that are not included in the benchmark. For example, if the managed portfolio includes mortgage backed securities but the benchmark does not, the managed portfolio will have higher exposure to prepayment risk which could give rise to tracking error.

– The more the managed portfolio deviates from the benchmark in terms of the types of bonds included, the higher the tracking error will be


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Further reasons for tracking error are:

– Tracking error risk will be higher when administrative problems occur, which include commissions paid on security purchases and sales, getting new funds fully invested without delay, selecting a mix of securities that will match the performance of the index

– Management fee reduce the return of a managed portfolio relative to the return of a benchmark index

Passively managed portfolios tend to have little tracking error (consisting of management fees and other administrative reasons). Actively managed portfolios can generate large, positive or negative tracking error .


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Yield Measures




Relative-Value Methodologies for Global

Corporate Bond Portfolio Management

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Relative-Value Methodologies for Global/Corporate Bond Portfolio

Management

Relative value analysis is defined as ranking fixed income sectors, structures, issuers, and issues by expected return

A top-down approach begins with asset allocation and large-scale economic developments to identify attractive sectors within the bond market

A bottom-up approach focuses on individual issues and their relative attractiveness. They will outperform their peer group based on individual security misevaluation


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Management

Classic relative value analysis attempts to combine the best of top-down and bottom-up approaches. – The goal is to pick the best sectors, find the best issues in those sectors, and select the issuers’ securities that best match the investor’s opinions of the markets.

There are seven methodologies:

– Total return analysis

– Primary market analysis

– Liquidity and trading analysis,

– Secondary trading rationales and trading constraints

– Spread analysis

– Structure analysis

– Corporate curve analysis

– Credit analysis

– Asset allocation/sector analysis

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Management

Primary market analysis focuses on supply and demand for new issues . The expectation is that more supply will hurt spreads as demand is stretched over a larger number of issues. In contrast empirical evidence is that new supply in the corporate market has not hurt spreads.

Globalization is listed as the most important development in the primary corporate bond market

On the supply side, medium term notes as well as structured securities have become more popular. The primary motive is to satisfy a broad range of investor needs thereby lowering funding costs. Bonds with embedded options are scarce, the supply of long-dated maturities has declined, and credit derivatives have become more popular.


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Management

Both short and long-term liquidity influence portfolio management decisions

Some managers are hesitant to purchase issues that are not liquid, such as smaller-sized issues, private placements, and non-local corporate issuers. Other managers see the lack of liquidity as an opportunity to earn higher yields.

Liquidity varies with the economic cycle, credit cycle, yield curve shape, supply, and the season. In addition, shocks to the system can dry-up liquidity quite quickly


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Management

Rationales for Secondary Market Trading

The secondary market trades seasoned issues while the primary market trades new issues

The rationales for secondary trading are:

– Yield/spread pickup trades

– Credit upside trades

– Credit defense trades

– New issue swaps

– Sector rotation trades

– Curve adjustment trades

– Structure trades

– Cash flow reinvestment

Constructing a secondary market trade simply means comparing the relative values and selecting the most attractive

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Management

Yield/spread pickup trades : they account for most of the secondary trades that occur. The goal is to trade one security for another in order to improve the yield or spread.

Credit-upside trades : they occur when the manager buys a bond in anticipation of an upgrade in the issuer’s credit rating that is not already reflected in the bond price. Good credit analysis is required and are profitable in the crossover sector (from speculative grade to investment grade).

Credit-defense trades : they are important when the firm deteriorates. Investors increase credit quality in reaction to uncertainties arising from secular changes in a sector (or also due to a rating downgrade, mandated by the portfolio guidelines).

New issue swaps : they occur when managers rotate their portfolios into more current (and often larger) issues to improve liquidity


8


Management

Sector rotation trading : It is a strategy where the manager shifts out of a sector expected to underperform and into a sector expected to outperform (macro and micro sector rotation)

Yield curve adjustment trades are made to reposition a portfolio’s duration

– For example if investor believes that corporate spreads will narrow, with other rates remaining relatively stable, the investor may shift the portfolio’s exposure to longer duration issues in that specific sector

– In contrast, portfolio duration should be reduced when interest rates are anticipated to increase so as to minimize potential price declines


8


Management

Example:

Given the following bond portfolio and anticipated changes in interest rates, recommend whether to sell the CDS or Treasury bonds and replace them with the XXX bonds if the only objective is to maximize short-term price appreciation

2-year

Yield curve today

4.7%

Anticipated yield curve

4.1%

4.7%

5.0%

5-year

30-year

Weight % Issuer

30%

40%

30%

5.2%

5.5%

Maturity Mod. Duration

U.S. Treasury 2-year

YYY

CDS

5-year

30-year

Bond being considered for purchase

XXX 5-year

Eff. Duration

2.8

4.2

12.3

4.2

Current portfolio

2.8

4.2

2.8

4.2

August 2014 173


8


Management

Structure trades : they involve swapping into structures (e.g., callable, bullet, or put structures) that are expected to outperform based on projected movements in volatility and the shape of the yield curve

Cash flow reinvestment : this forces managers into the secondary market on a regular basis to reinvest any cash flows received as a result of coupon payments or maturities


8


Management

Often, a trading constraint for one portfolio manager can become a trading opportunity for another portfolio manager

Constraints of trading are:

– (1) Portfolio restriction prevent a portfolio from trading even when it is otherwise beneficial. For example, some funds prevent a portfolio manager from holding non-domestic bonds, or force managers to sell a security immediately if it is downgraded. Thus, such securities can become very attractively priced to another manager who is not constrained.

– (2) “Story disagreement”: times, when there is little agreement about a security’s value often indicate an opportunity to take a position that may be very profitable if the manager turns out to be right


8


Management

– (3) Buy-and-hold strategies: can be dictated by accounting constraints or by the desire to curb portfolio turnover. A buy-and-hold manager is often prevented from buying and selling even when it would be advantageous to do so.

– (4) Seasonality: There are slow periods during the year when dealers and portfolio managers are more focused on closing their books, preparing reports, etc. Trading is very light at these times of year and some securities can become very attractively priced.


8


Management

Spread Analysis

Spread analysis is a common tool for identifying profitable bond trades:

– When yield spreads are expected to narrow, the bond with the higher spread duration will outperform the bond with the lower spread duration

– If spreads are expected to widen, the bond with the lower spread duration should outperform

– If spreads are expected to remain stable, the bond with the higher yield will outperform the bond with the lower yield

Spread analysis can be done using:

– Nominal spreads

– Static spreads

– Option-adjusted spreads

– Swap spreads

August 2014 177


8


Management

Swap spread analysis is a relatively recent tool for comparing fixed to floating-rate bonds

Example:

On January 1, 2001, an investor owns USD 10 million of GMAC 8.0% bonds due 2011. These bonds are trading at the bid side price of 145 basis points over the 10-year U.S. Treasury yield of 6.2%. Thus, the yield-to-maturity is 7.65%

(6.2% + 1.45%). On the same date, a 10-year interest-rate swap has the following terms: fixed rate 10-year Treasury + 95 basis points floating rate LIBOR flat

The investor is considering selling the GMAC bond to buy a 10-year floating rate GMAC bond that pays LIBOR + 30 basis points. Calculate the fixed rate GMAC bond’s spread over LIBOR and advise the investor on the trade.


8


Management

The major advantage to a swaps framework is that it allows managers to more easily compare securities across fixedrate and floating rate markets. – This comparison cannot be done with traditional spread analysis tools.


8


Management

Mean-reversion analysis: The mean is the average spread over a defined period, usually one economic cycle.

This analysis assumes the yield spread will return to its average historical value. Mean reversion implies a bond should be purchased when spreads are at historic highs as it assumes spreads will narrow and the price of the target bond will increase. The main drawback to mean-reversion analysis is to successfully predict when spreads will return to their historic values.

Quality spread analysis focuses on credit spread. It looks at spread between high and low-quality credits. Managers may decide to swap into lower quality debt in anticipation of an economic expansion, or swap into higher quality debt in anticipation of weak economic conditions. The spreads between the two levels of quality may help determine whether these swaps are attractive.


8


Management

Percent spread analysis examines the ratio of corporate yields to government yields for securities of similar duration.

A contraction of corporate percent yield spreads is considered a risk for future underperformance of the corporate asset class.

– This methodology ignores other factors that determine attractiveness, including demand and supply, profitability, defaults, and so forth. It is more a derivative than an explanatory, or predictive variable.


8


Management

Structure Analysis

Structural analysis investigates the performance of the different structures – bullet, callable, putable, and sinking fund structures

The importance of structural analysis has declined as intermediate bullets have become the predominant bond type.

Credit differentiation is often more important than the structural differences.

Callable structures usually provide 5 to 10 years of call protection before the issuer can exercise the option to refinance debt in a lower-interest rate environment. Typically, issuers pay an annual spread premium of 30-40 basis points to entice investors to buy callable bonds. As would be expected, callables underperform bullets in periods of declining interest rates due to the higher risk of call (negative convexity). In bear markets, callables often outperform as they have little risk of being called and they pay a spread premium.


8


Management

Bullet structures

– Front-end bullets (1 to 5 year maturities) are used by investors pursuing a barbell strategy. They want to gain an enhanced yield.

– Intermediate corporate bullets (5 to 12 year maturities) are extremely popular. Their durations are reasonably high and many investors find them attractive relative to longer-term credits.

– Longer-term credits include the most popular long-term security, the 30-year maturity. These longer-term securities provide high convexity, while only modestly increasing duration compared to intermediate-term bonds.

Sinking fund structures allow issuers to execute a series of partial calls prior to maturity. Investors use bonds with sinking fund structures to help protect against rising interest rates as a portion of the calls are mandatory. Thus, these bonds may outperform bullets and callables during periods of rising rates.


8


Management

Putables are bonds where investors have a put option to demand full repayment at par. Put structures provide investors with a defense against sharp increases in interest rates. In addition, investors can choose to put a bond where the credit quality is deteriorating (assuming the issuer can meet the obligation).


8


Management

Credit Curve Analysis

Corporate curve analysis

Many portfolio managers opt to take credit risk in short and intermediate term maturities and to use government securities in long-duration buckets. Credit barbell strategy .

As the time to maturity lengthens, the credit curve for poorly rated securities is steeper than for investment-grade securities. That means the spreads widen with the time to maturity.

Credit curves change shape in response to economic cycles and the economic outlook

– When the market is worried about interest rates and general credit risk, spreads widen and the spread curve becomes steeper


8


Management

Example:

Which of the following portfolios reflect a credit barbell strategy? All portfolios have the same durations.

Portfolio Tr.

1 to 5 years

Corp. Tr.

5 to 12 years

Corp. Tr.

Long

A

B

C

0%

15%

30%

30%

15%

0%

25%

30%

30%

25%

20%

20%

20%

0%

10%

Corp .

0%

20%

10%

Identify the economic environment in which portfolio A would be most likely to underperform portfolio B, and explain why


8


Management

Credit Analysis

Good credit analysis identifies credit upgrades and downgrades before market prices and credit ratings reflect the credit changes

However, such analysis requires detailed bottom up analysis of financial statements, corporate management and industry trends. – This takes time and is challenging as global privatization of assets creates a growing list of credits to analyze.


Content

5

6

7

8

1

2

3

4




Yield Measures






9

10

11

12

Exchange Rate Risk: International Bond Investing





9


International Bond Investing

Potential Sources of Excess Return

Foreign bonds offer several potential sources of excess return for the fixed-income portfolio manager:

– Country market selection: This strategy identifies those countries that are going to produce above-average returns and overweights the portfolio in the assets of those countries. – The economic cycles of countries are not synchronized. A portfolio manager can still earn a return advantage over treasuries by moving his credit allocation from one country to another country.

– Currency selection: This strategy identifies and overweights those currencies that will appreciate relative to the domestic currency and underweights the portfolio in those currencies that will depreciate.

– Duration/yield curve management: This can be executed within each country, based on expectations for interest rates in each country.


9



– Sector selection: Opportunities are generally limited outside the U.S. because non-government bonds make up only a small fraction of those markets. For example, the securitized mortgage market in Europe is less developed compared to the U.S. market. A European portfolio manager wishing to take a view on convexity would be more constrained if the were not allowed to invest in U.S. mortgages.

– Security selection : International bond investing gives the portfolio manager access to a much broader set of names to consider for the portfolio. In addition, a manager can take advantage of any mispricing of a given issuer across markets

– “Core-Plus” strategies: Some managers have domestic currency benchmarks but are sometimes given permission to invest in “non-benchmark” securities. – This strategy identifies a market or bonds that are not included in the benchmark index that will outperform the index and add it to the portfolio to enhance relative performance.


9



Change in Bond Value

Portfolios that contain foreign bonds make duration difficult to compute and interpret

Yield changes are not consistent across countries , so the duration of a portfolio including foreign bonds would be subject to differing yield changes for each respective country represented in the portfolio

It is important to focus on the correlation between domestic interest rates and rates in each foreign country

Change in value of foreign bond = Duration x Country beta x  i

The change in foreign yield given a change in domestic yield is estimated via regression analysis . The result is country beta, which measures the change in foreign yield per unit change in domestic yield.


9



To measure the contribution of a foreign bond to a domestic portfolio’s duration, simply multiply the country beta by the bond’s duration

Example:

The duration of a Swedish bond is 8 and the country beta for Sweden is 0.85 (compared to the U.S). Compute the duration contribution to a USD denominated portfolio!


9



The duration of each country’s bond is adjusted by the country beta that takes into account the less then perfect correlation of interest rates across countries

Example:

A portfolio consists of a domestic and a foreign bond. The domestic bond has a weight of 60% and a duration of 6 years, while the foreign bond with a duration of 7 years has a country beta of 1.1. Compute the duration of the portfolio!

It is difficult to assess the duration impact of a foreign bond to a domestic portfolio. It requires knowing the bond’s duration measured against foreign interest rates and the correlation between domestic and foreign rates.


9



Hedge or not Hedge Currency Risk in a Bond Portfolio

Example:

A U.S. investor purchases a U.K. stock selling at 10 pounds sterling when the British pound is USD 1.70. One year later, the stock is sold for 12 pounds sterling in the U.K. market, but the British pound exchange rate has changed to USD 1.50.

– What is the return to a U.K. investor measured in British pounds? What is the return in U.S. dollars to a U.S. investor?


9



The unhedged return to domestic investor from a foreign security can be calculated in the following way:

R

H

= (1 + r i

) x (1 + e

H,i

) – 1  r i

+ e

H,I where:

R

H r e i

H,i

Example: return to the domestic investor, in the home currency local market return of country i in its own currency

% return of currency i relative to the domestic home currency where currency units are expressed as H/i

Same data as previous example. Calculate the return to the U.S. investor with the above stated equation.

August 2014 195


9



Managers of international portfolios can avoid the currency risk by hedging the currency. Hedging is normally done by using currency futures or forward contracts.

To hedge the currency risk , the manager will sell the currency forward using a contract with an expiration date comparable to the time period over which the manager desires to hedge the currency risk

Example:

Same data as previous example. The U.S. investor has sold the British pound forward at USD 1.55/GBP. What would be the currency return and total return on the investment to the U.S. investor?


9



The forward premium is defined as the differential between the forward and spot currency exchange rates. It can be expressed as a price difference or a percentage difference though the percentage price difference is more useful in the following analysis.

Forward premium = F

Y/X

Forward premium (%) =

– S

F

S

Y/X

Y / X

Y / X



1

Thus the forward premium could be either positive or negative. Frequently, if the premium is a negative value it is referred as a forward discount.


9



Alternatively, by combining the forward premium calculation with the interest rate parity relationship it can be shown that the forward premium can be calculated directly from the interest rate differentials between the two countries.

Forward Premium (%) =

F

S

Y

Y

/

/

X

X



1



1

1



 r r

Y

X



1

 r

Y

 r

X


9



Example:

Calculate the forward premium or discount (in %) of the U.S. dollar to the Euro for the 6-month currency contract if the following information is given:

U.S. interest rate

Euro interest rate

Spot exchange rate

Forward exchange rate

3%

5%

USD 1.00/EUR

USD 0.99024/EUR


9



Calculating returns for an international portfolio where:

For an international portfolio with allocations in a number of countries, the return to the investor in the investor’s home currency will be:

R

H

 w

1



( r

1

 e

H , 1

)

 w

2



( r

2

 e

H , 2

)



....

 w n



( r n

 e

H , n

) w i r i e

H,i

H/i percentage portfolio weighting by each country local market return of country i in its own currency percent return of currency i relative to the domestic home currency where currency units are expressed as

More properly, (r

1

+ e

H,1

) would be ((1 + r

1

) x (1 + e

H,1

) – 1), but simple addition of returns provides a close approximation, and is used in the primary readings to simplify the equations and demonstrate the core concepts.

August 2014 200


9



1.

Invest in the domestic market:

The return of the portfolio is the local market return r

H

of the home market

R

H

= r

H

2. Invest in the foreign market (i) without hedging currency (i):

The return of the portfolio is the return of the local foreign market (r i

) and the return of the foreign currency (e

H,i

)

R

H i,

 or approx.

( 1



R

H,i

 r i

+ e

H,i r i

)( 1

 e

H i,

)



1

August 2014 201


9



3. Invest in the foreign market and hedge the currency back to the home currency by selling the foreign currency forward

The return of the portfolio is the return of the local foreign market r i

and the forward premium, or discount. The forward premium or discount can be assumed to be the periodic interest rate differential in the two countries.

Hedged return (HR or approx.

HR

H,i

 r i

+ c

H

– c i

H,i

) =

( 1

 r i

)





1

1



 c c

H i







1

August 2014 202


9



HR

H,i

 c

H

+ (r i

– c

Hedged Return = Domestic Interest Rate + Bond’s Local Risk Premium i

)

A bond’s hedged return equals the investor’s domestic interest rate plus the bond’s risk premium (local bond currency return – foreign interest rate):

The investor can simply compare expected risk premia across markets. The investor should invest (on a hedged basis) in those markets that offer the highest risk premia.


9



Example:

Short-term interest rates are 4% in the U.S. and 1% in Japan. The U.S. manager expects the Japanese yen to appreciate by 2.5% versus the U.S. dollar over the next year. Assuming that interest rate parity holds, should the investor hedge or not hedge his Japanese government bond holdings?

The decision to hedge or not hedge depends on the investor’s ability to forecast the unexpected component of the currency return : forex return – forward forex discount or premium

August 2014 204


9



Breakeven Spread Analysis

Although foreign yields can sometimes look very enticing, the investor needs to be aware of the risk that any spread advantage can evaporate through spread widening (ignoring any currency impacts). Breakeven analysis addresses the conditions under which two investments will produce the same return over some time horizon.

Example:

YTM

Effective Duration

Risk-free rate

10-year British bond 9.6%

5%

8-year U.S. bond 7.2%

4%

How much can the spread widen over one quarter before the British bond underperforms?

6.7

5.4

August 2014 205


9



Example:

Same data as previous example. Let’s assume that the pound will decline by 25 bps over the next 3 months. What is the break even spread change?


9



Risks of Investing in Emerging Market Debt

Emerging market debt refers to public and private bonds issued by governments and corporations located in developing countries. This is a very large market of approx. more than USD 3 trillion.

Many of these countries have relatively high credit ratings . – In fact, some emerging market debt is rated investment grade. However, investors are attracted to the wider spread offered by many bonds.


9



The issues are:

Although there are many issuers, a large portion of debt is concentrated in just a handful of countries such as Mexico and Brazil. This can pose a concentration risk .

Emerging market bonds may not be as liquid as other international bonds, especially in periods of higher than usual market volatility

Emerging market debt shares some characteristics with high-yield debt: higher negative skewness , implying higher tail risk due to the possibility of large negative returns

Sovereign emerging market debt also contains sovereign risk . This is the risk that the issuing government can repudiate its debt. – Measuring and monitoring sovereign risk requires different skills than the usual credit risk analysis that is familiar to most portfolio managers.


Content

5

6

7

8

1

2

3

4




Yield Measures






9

10

11

12


Managing Interest Rate Risk with Derivatives




10


Interest Rate Futures

Managers generally find the interest rate futures market to be an efficient and lower cost way to manage their interest rate risk. Interest rate futures used are Treasury bond futures .

Dollar Duration per

Futures Contract



$100,000



CTD Duration



CTD Price

Conversion Factor

Number of

Futures Contract





Duration

Target



Duration

Portfolio





Market Value of Bond Portfolio

Dollar Duration of Futures Contract

August 2014 210


10


Example:

A bond manager owns a USD 100 million market value bond portfolio with an effective duration of 4. The manager would like to increase the duration to 5.0. The price of the cheapest-to-deliver bond (CTD) is 107 with a duration of 8.4 and a conversion factor of 1.1787. What is the number of futures contracts to buy or sell to raise the portfolio’s duration from 4 to 5?


10


Using futures to adjust a portfolio’s duration is fast, easy, and cheap. However, one potential drawback is basis risk. –

Basis risk is defined as the risk that changes in the futures price may not track changes in the cash price of the portfolio.

Basis risk arises from several sources, including:

– Futures-CTD basis risk : Changes in the price of the futures contract may not track changes in the price of the underlying CTD bond

– Cash-Futures basis risk : Changes in the value of the manager’s portfolio may not track changes in the value of the futures position


10


The manager is holding corporate bonds and he decides to immunize the portfolio to a schedule of liabilities provided by the client. In order to change the duration of the bond portfolio the manager will use Treasury bond futures. – Despite this duration hedge the manager will be exposed to basis risk because the yield of the corporate bond portfolio will change more or less than the yield of the cheapest-to-deliver bond.

One way to deal with this potential basis risk is to use regression to estimate a yield beta . A yield beta measures how much the portfolio’s yield changes per basis point change in the CTD bond’s yield.

Yield on Bond (Portfolio) to be Hedged = α + ß x Yield on CTD Bond + Error Term


10


Example:

A bond manager owns a USD 35 million market value corporate bond portfolio with an effective duration of 10. The manager decides to immunize the portfolio to a schedule of liabilities provided by his client. The duration of the liabilities is

9. In order to immunize the portfolio the manager will use Treasury bond futures. The price of the cheapest-to-deliver bond

(CTD) is 107 with a duration of 8.4 and a conversion factor of 1.1787. The yield beta is 1.08. What is the number of futures contracts to buy or sell to immunize the portfolio?


10


Interest rate swaps

Another quick and inexpensive way to adjust portfolio duration is to execute an interest rate swap

Unlike futures, an interest rate swap is an OTC derivative contract. Swaps are very liquid and are common interest rate risk management tool.

Dollar Duration of a Receiver Swap = Dollar Duration of Fixed-Rate Bond – Dollar Duration of Floating-Rate Bond > 0

Dollar Duration of a Payer Swap = Dollar Duration of Floating-Rate Bond – Dollar Duration of Fixed-Rate Bond < 0

The advantage of interest rate swaps is that they can be customized to the manager’s specific requirements whereas the manager is limited to just a handful of available futures contracts


10


Interest rate options

There are options on physical Treasury bonds and on Treasury bond futures contracts

To use options in interest rate risk management, the portfolio manager must measure the duration of the option contract

– First the manager must identify the underlying instrument

– The manager must measure how much the option price will change as the underlying price changes – delta

Duration of Option = Duration of Underlying Instrument x Delta

Not only can options be used to adjust a portfolio’s duration, but they can be used to create asymmetric returns, using a protective put or a covered call strategy

August 2014 216


Content

5

6

7

8

1

2

3

4




Yield Measures






9

10

11

12



Managing Credit Risk with Derivatives



11


In recent years, bond dealers have begun to offer a variety of derivative instruments designed specifically to manage the credit risk of fixed-income portfolios. – In many cases, these derivatives are designed to protect the portfolio against the effects in changes in the interest-rate spread between the portfolio and assets that do not have credit risk such as Treasury securities.

All of the credit derivatives discussed in the primary readings are OTC contracts. – Thus, they have counterparty risk.


11


Credit risk type Derivative instrument for hedging

Default: the borrower cannot meet interest and principal

– Binary credit options

– Credit swaps payments when due

Credit spread: yield differences – Credit spread options between risky and riskless debt – Credit forwards widen (after purchase)

Downgrade: the rating agency – Binary credit options based on a credit rating reduces the credit rating on an – Credit swaps issuer – it would likely cause the the spread to widen and liquidity to deteriorate (many investors are not permitted to hold bonds below a certain rating category)


11


If a portfolio’s credit exposure is not at the manager’s desired level, the manager will need to make an adjustment. The manager can reduce credit exposure in a number of ways:

Selling cash bonds with greater credit risk sensitivity and buying bonds with lower credit sensitivity

Credit swaps

Credit options

Credit forwards


11


(1) Cash Market

For example, if the portfolio’s credit exposure is too low, the manager can sell a bond with a spread duration of 2 and use the proceeds to buy a bond with a spread duration of 5

Adjusting a portfolio’s duration using cash bond transactions can be difficult and costly. Especially for credit bonds, it can take considerable time to find willing sellers and buyers.

In addition, cash market transactions can be expensive in terms of the bid-ask spread


11


(2) Total Return Swap

Capital Markets

LIBOR

LIBOR +

1%

Investor

(Credit Protection

Seller)

Dealer

(Credit Protection

Buyer)

Asset Total

Return

Cash

Cash to buy

Asset

Asset Total

Return

Referenced

Asset

August 2014 222


11


Total return swap transfer all of the economic exposure of a referenced asset to the credit swap purchaser. In return for receiving this exposure to an underlying asset, the credit swap purchaser pays a floating rate plus a spread

(i.e., 1%) to the credit swap seller.

If the reference obligation is a sector of a bond index, the swap is called a total return index swap. – The total return in the swap includes both periodic cash flows received from the reference asset as well as any capital appreciation or depreciation.

The party who is selling the credit protection gains exposure to the reference obligations without financing the exposure. – In addition, the party can gain exposure to a diversified basket of assets without incurring the cost of several cash market transaction (just using the total return swap). Finally, a total return swap allows a manager to short one or more corporate bonds efficiently.


11


(3) Credit default swaps are similar to credit options and allow to hedge credit exposure

The investor returns from investing in a risky asset. At the same time, the investor pays a swap premium to a counterparty and receives a cash payment if the risky asset defaults or some other trigger event occurs.

Risky

Asset

Total

Return

Investment

Investor

(Credit Protection

Buyer)

Swap

Premium

Cash Payment

if default occurs

Counterparty

(Credit Protection

Seller)

August 2014 224


11


If there is only one reference obligation, the swap is called a single-name credit default swap , while a swap involving a portfolio of reference obligations is called a basket default swap

The protection buyer can pay the swap premium over several settlement dates and can receive payments at intermediate settlement dates as compared to only one payment under a credit option contract

Credit default swaps may be settled in cash or by physical delivery of the reference obligation by the buyer to the protection seller in exchange for the seller’s cash payment (most common settlement method for single-name credit default swaps)


11


(4) Credit Options (Binary Credit Options)

A standard bond option’s payoff would be based on change in the bond’s price which is basically due to a general change in the level of interest rates. – In contrast, a credit option is designed to respond specifically to credit risk and changes in interest rate spreads .

Credit option structures include:

– Binary credit options:

They pay a single predetermined amount if some trigger event occurs, or nothing if it does not

– Credit spread options:

They have a payout determined by a formula based on a change in credit spread

August 2014 226


11


Binary credit option: (put option)

Such an option allows investors to put the bonds back to the issuer at face value if a certain condition exists like the credit rating falls below investment grade

The put option protects the bondholder from any decrease in value due to a widening credit spread (caused by a downgrading)

The value of a credit put can be computed as:

Value of Put = (S t

– V t

) x (Notional Principal) where:

S t

V t strike price of the option at time t (normally at par) value of the bond at time t

August 2014 227


11


Example:

An investor buys a binary credit put option on USD 40,000,000 par value of XYZ bond with a two-year-term. The investor paid an option premium of USD 400,000. The trigger event is defined as a bond rating below BBB-.

Calculate the net payoff if the credit rating falls to BB+ and if the price of the bond is 89.12


11


Credit spread option (call option written on credit spread)

Credit spread options are designed to compensate the buyer for any price deterioration in the bond due to the spread widening to a level greater than some strike spread

RS

SS t

RF t

The value of a credit spread call can be computed as:

Value of Call = Max ((RS t

– SS t where:

) x (Notional Principal) x (RF)), 0) actual spread over the benchmark rate at time t specified strike spread over the benchmark risk factor, or an adjustment for interest rate sensitivity

August 2014 229


11


Example:

The 10-year 8.25% annual coupon bonds were issued with a credit spread option with a strike price of 250 basis points over LIBOR. Let assume that LIBOR is 5.0% today. The actual spread amounts to 325 basis points. The face value of the bond is USD 5 million and we assume a risk factor of 2.5. Calculate the option payoff of the credit spread call!


11


Example:

A manager owns USD 50,000,000 of XYZ bonds and buys the following credit spread call option to protect the portfolio from an anticipated deterioration in XYZ’s credit quality and spread:

Notional

Strike spread

Term

Premium

USD 50,000,000

175 basis points six months

75 basis points

Risk factor 4.2

The spread is calculated as the yield of XYZ bond, less the yield on the Treasury 8% with the same maturity of the bond. a) Calculate the cost of the option b) Calculate the option net payoff if the spread narrows to 125 bp. c) Calculate the option net payoff if the spread widens to 225 bp.

August 2014 231


11


Credit spread option can be used to:

– Protect against macroeconomic events such as an economic slowdown leading to a flight to quality (widening spreads)

– Protect against or speculate that the credit quality of an issuer will decline (a microeconomic event)

– Enhance income through writing the option

Credit put options written on an underlying bond pay off when the bond rating falls or default occurs. The owner of the put option can put (sell) the bond at an agreed upon price (the strike price).

Credit call options written on a credit spread gain value if the spread widens. These options have value independent of the level of interest rates. Selling these options can be used to gain income when the writer believes spreads will not widen enough to make the call valuable.

August 2014 232


11


(5) Credit forwards are written on a spread over benchmark Treasury bonds

If the credit spread widens, the long side of the contract will receive payments. If the credit spread declines, the long must make payments to the short. – There is no option premium to enter the contract.

Credit options on the other hand, have one-sided payoffs where cash flows change hands only if the option is in the money. They protect the buyer if spreads widen, while allowing the buyer to benefit from the relative appreciation in the bond if spread narrows.

The forward payoff can be calculated as follows:

FV = (RS t

– SS t

) x (Notional Principal) x (Risk Factor)


11


Example:

A bond portfolio manager holds USD 40 million of XYZ bonds and buys the following credit forward contract to protect the portfolio against spread widening on the bonds:

Notional

Contracted spread

Risk factor

USD 40,000,000

175 bp

4.2

Calculate the payout of the credit forward contract if the spread narrows to 125 bp. and widens to 225 bp.


Content

5

6

7

8

1

2

3

4




Yield Measures






9

10

11

12




Currency Risk Management


12


An investment priced in a foreign currency has two sources of risk and return:

– Return on asset in the foreign currency (RFC)

– Return on the foreign currency (RFX)

R

DC



( 1



R

FC

)( 1



R

FX

)



1



R

FC



R

FX



( R

FC

)( R

FX

)


12


Example

A US-based investor holds a portfolio of securities that trade in CHF. Over a one-year holding period, the value of the portfolio increases by 10% (in CHF) and the CHF-USD exchange rate increases from 1.10 USD/CHF to 1.15 USD/CHF.

The investor’s return in domestic currency is closest to:

A. 5%

B.

C.

12%

15%

 The FX return calculation is based on the foreign currency as the base currency (denominator):

Return FX = EV / BV – 1

August 2014 237


12


Domestic currency return on a portfolio of multiple foreign assets will be equal to: where:

R

DC

 i n 



1 w i

( 1



R

FC , i

)( 1



R

FX , i

)



1

RFC

RFX wi foreign currency return on the i-th foreign asset appreciation/depreciation of the i-th foreign currency against the domestic currency portfolio weights of the foreign-currency assets (defined as the percentage of the aggregate domestic currency value of the portfolio); ∑wi = 1 (short positions have a negative weight)

RFX is defined with the domestic currency as the price currency and the foreign currency as the base currency.

August 2014 238


12


Example:

A portfolio consisting of two foreign assets denominated in GBP and EUR is held by an investor in India. Performance is measured in terms of the Indian rupee (INR) and the weights of the two assets in the portfolio are 75% for the GBPdenominated asset and 25% for the EUR-denominated asset, respectively.

One year ago Today

INR/GBP spot rate

INR/EUR spot rate

GBP-denominated asset value 1

EUR-denominated asset value 1

84.12

65.36

42.25

14.08

85.78

67.81

50.70

12.17

1 Millions of units of foreign currency; today’s asset values are prior to rebalancing.


12


An investor investing in a foreign currency denominated asset has two sources of risk:

– Fluctuation of the foreign currency

– Fluctuation in foreign currency price of the foreign asset

The variance of RDC can be calculated as follows:

 2

( R

DC

)

 w

2

( R

FC

)

 2

( R

FC

)

 w

2

( R

FX

)

 2

( R

FX

)



2 w ( R

FC

) w ( R

FX

)



( R

FC

)



( R

FX

)



( R

FC

,

This basic two asset variance equation can be simplified when a domestic investor holds a single foreign currency

R

FX denominated asset. The exposures (weights) to RFC and RFX are each 100%:

)

 2

( R

DC

)

  2

( R

FC

)

  2

( R

FX

)



2



( R

FC

)



( R

FX

)



( R

FC

, R

FX

)

August 2014 240


12


If RFC is a risk-free return: the standard deviation of the risk-free asset is 0 and the correlation coefficient with the

RFX is 0 as well. Thus, RFX is the only source of risk for the domestic investor in the foreign asset and the risk can be calculated as follows:



( R

DC

)

 

( R

FX

)

August 2014 241


12


Arguments made for not hedging currency risk are:

– It is best to avoid the time and cost of hedging or trading currencies.

– In the long-run, unhedged currency effects are a “zero-sum game”; if one currency appreciates, another must depreciate.

– In the long-run, currencies revert to a theoretical fair value.

The argument for active management of currency risk are:

– In the short-run, currency movements can be extreme.

– Inefficient pricing of currencies can be exploited to add to portfolio return. Many foreign exchange trades are dictated by international trade transactions or central bank policies. These are not motivated by consideration of fair value and may drive currency prices away from their fair value.


12


Currency management strategies include:

– Passive hedging: typically matches the portfolio’s currency exposure to that of the benchmark used to evaluate the portfolio’s performance. It will require periodic rebalancing to maintain the match. The objective is to eliminate currency risk relative to the benchmark.

– Discretionary hedging: deviates modestly (e.g. 5%) from passive hedging (benchmark) by a specified percentage. The objective is to reduce currency risk while allowing the manager to pursue modest incremental currency returns relative to the benchmark.

– Active currency management: greater deviations from benchmark currency exposures. The objective is to generate incremental return (alpha), not to lower risk.


12


Currency overlay: outsourcing currency management. At the extreme, currency will be treated as an asset class and may take positions independent of other portfolio assets. For example, a manager who is bullish Yen for a portfolio with no exposure to Yen would go long the Yen. The manager is purely seeking alpha (incremental return), not risk reduction.


12


Active Currency Trading Strategies

1) Economic fundamentals

– This approach assumes that, in the long term, currency value will converge to fair value (i.e., purchasing power parity will determine long-run exchange rates).

– Several factors will impact the eventual path of convergence over the short and intermediate terms. Increases in the value of a currency occur because of:

Currencies are more undervalued relative to their fundamentals.

Currencies have the greatest rate of increase in their fundamental value.

Currencies with higher real or nominal interest rates.

Currencies with lower inflation relative to other countries.

Currencies of countries with decreasing risk premiums.

August 2014 245


12


2) Technical Analysis

– The underlying assumptions are:

Past price data can predict future price movement and because those prices reflect fundamental and other relevant information, there is no need to analyze such information.

Fallible human beings react to similar events in similar ways and therefore past price patterns tend to repeat.

It is unnecessary to know what the currency should be worth (based on fundamental value); it is only important to know where it will trade.

– Typical patterns to be exploited are:

Overbought or oversold market has gone up or down too far and the price is likely to revert.

Support level (a price that falls to that level is likely to reverse).

Resistance level (a price that rises to that level is likely to reverse).

August 2014 246


12


3) Carry Trade

– A carry trade refers to borrowing in a lower interest rate currency and investing the proceeds in a higher interest rate currency.

Covered interest rate arbitrage: difference between spot (S0) and forward (F0) exchange rates equals the difference in the interest rates of the two currencies. Thus, forward exchange rate is an unbiased estimate of the spot exchange rate that will occur in the future.

– Currency with the higher interest rate trades at a forward discount (F0 < S0).

– Currency with a lower interest rate trades at a forward premium (F0 > S0).


12


The carry trade is based on a violation of uncovered interest rate parity.

– The currency with the higher interest rate will decrease in value by the amount of the initial interest rate differential and vice versa. If these expectation do hold, a carry trade would earn a return of 0%.

With a carry trade the forward rate bias is traded . Historical evidence indicates:

– On average, higher interest rate currency has depreciated less than predicted by IRP or even appreciated (profit with a carry trade).

– A few times, the higher interest currency has depreciated substantially more than predicted by IRP (loss with a carry trade).


12


Covered interest rate parity is stated as:

F

P / B



S

P / B









1

1





i i

p

B









Actual

360

Actual

360

















Assuming a one-year time horizon (360 days), the forward premium or discount (expressed as a percentage of the spot rate): is:

F

P / B

S



S

P / B 





 i

P

1



 i

B







P / B i

B

Being low-yield currency and trading at a forward premium or being high-yield currency and trading at a forward discount. Borrowing in the low-yield currency and investing in the high-yield currency (carry trade) is hence equivalent to selling currencies that have a forward premium and buying currencies that have a forward discount – trading the forward rate bias .

August 2014 249


12


The carry trade can also be implemented by borrowing in the lower interest rate currency of developed economies

(funding currencies) and investing in the higher interest rate currencies of emerging economies (investing currencies).  significant losses in periods of financial distress.

Buy/Invest Sell/Borrow

Implement the carry trade

Trading the forward bias high-yield currency forward discount currency low-yield currency forward premium currency


12


Example

The spot exchange rate is CHF/USD 0.90. The interest rates in the two countries are 1% and 5%, respectively.

1. What is the 1-year forward exchange rate for the CHF?

2. State the steps to initiate the carry trade?

3. What is the profit on the trade if the spot exchange rate is unchanged and the trade is initiated by borrowing 100 currency units (over 1 year)?

4. What is the primary risk of this trade?


12


4) Volatility Trading

– Volatility trading permits managers to profit from predicting changes in currency volatility.

– Delta hedging: small changes in the price of the underlying asset are eliminated, but will be exposed to changes in implied volatility.

– Long straddle (at-the-money long call and long put): expectation is that volatility goes up – positive vega and delta-neutral.

– Short straddle (at-the-money short call and short put): expectation is that volatility goes down – negative vega, delta-neutral, negative gamma.

– Long strangle (out-of-the-money long call and long put with same absolute delta); initial costs are lower compared to a straddle; expectation is that volatility goes up.

August 2014 252


12


Relative currency:

Volatility

Market conditions

Expectations

Appreciation

Depreciation

Increase

Decrease

Stable

Crisis

Action

Reduce the hedge on or increase the long position in the currency

Increase the hedge on or decrease the long position in the currency

Long straddle (or strangle)

Short straddle (or strangle)

Carry trade

Discontinue carry trade


12


A hedge can be static (held until expiration) or dynamic (periodically rebalanced). The choice of hedging approach should consider:

– Shorter term contracts or dynamic hedges with more frequent rebalancing tend to increase transaction costs but improve the hedge result.

– Higher risk aversion suggests more frequent rebalancing.

– Lower risk aversion and strong manager views suggest allowing the manager greater discretion around the strategic hedging policy.


12


Hedging also exposes the portfolio to roll yield or roll return . Roll yield is a return from the movement of the forward price over time toward the spot price of an asset. The roll yield is determined as follows:

Roll Yield



Forward Price

Spot



Spot

Price

Price

Roll yield is a cost of hedging. Positive roll yield will shift the analysis toward hedging and negative roll yield will shift the analysis away from hedging.


12


If the hedge requires:

A long forward position in

Currency B, the hedge earns:

A short forward position in

Currency B, the hedge earns:

FP/B > SP/B; iP > iB FP/B < SP/B; iP < iB forward price curve forward price curve is upward-sloping is downward-sloping

Negative roll yield, which increases hedging costs and discourages hedging.

Positive roll yield, which decreases hedging costs and encourages hedging.

Positive roll yield, which decreases hedging costs and encourages hedging.

Negative roll yield, which increases hedging costs and discourages hedging.


12


Trading Strategies to Reduce Hedging Costs

To lower hedging costs, the manager can increase the size of trades that earn positive roll yield and reduce the size of trades that earn negative roll yield.

Forward hedging also incurs opportunity costs . With a forward contract the downside risk as well as the upside opportunity is eliminated. – Opportunity costs can be reduced with discretionary or option-based hedging strategies.


12


Selection of Currency Management Strategies

Forward contracts

Option contracts OTM options

Over-/under-hedging

Risk reversals

Put/call spreads

Seagull spreads

Exotic options Knock-in/out features

Digital options

Profit from market view

Cheaper than ATM

Sell options to earn premiums



Reduced downside/upside exposure

Extreme payoff strategies


12


1) Over- or under-hedge with forward contracts based on the manager’s view.

If the manager expects the

EUR to appreciate, he can reduce the hedge ratio, hedging less than the full exposure to EUR. If the EUR is expected to depreciate, he can increase the hedge ratio, hedging more than the full exposure to EUR risk. If successful, this strategy creates “positive convexity”; gains will be increased and losses will be reduced. This is a relatively low cost strategy.

2) Buy at-the-money put options (protective put strategy). All downside risk is eliminated and all upside potential is retained (reduced by the option premium paid). The strategy is relatively expensive and the put option has only time value (no intrinsic value). This strategy has the highest initial cost but no opportunity cost.


12


3) Buy out-of-the-money put options. Puts are less expensive the further they are out-of-the-money, but also offer less downside protection. The manger will have downside exposure down to the exercise price of the puts. The initial costs are lower compared to the strategy with the at-the-money puts but does not eliminate all downside risk.

4) Risk reversal or collar: buying calls and selling puts with the same delta. The out-of-the money puts provide some downside protection while costing less than at-the-money puts. The sale of out-of-the-money calls remove some upside potential (increasing opportunity costs) but generates premium income to further reduce initial cost. This strategy further reduces initial cost but also limits upside potential compared to a put only strategy.


12


5) Put spread: Buy out-of-the-money puts and sell puts that are further out-of-the-money. There is downside protection, which begins at the exercise price of the bought put, but if the currency falls below the lower exercise price of the sold put, that downside protection is lost. This strategies reduces initial cost and also reduces downside protection compared to a long put only strategy.

6) Seagull spread: Put spread combined with a short call. Compared to put spread, this hedge has less initial costs and the same downside protection, but limits upside potential.

7) Exotic options: A knock-in option comes only into existence if the underlying first reaches some pre-specified level. A knock-out option ceases to exist if the underlying reaches some pre-specified level. A binary or digital option pay a fixed amount that does not vary with the difference in price between the exercise price and underlying price.

August 2014 261


12


Cross hedges, Macro hedges, and Minimum-Variance-Hedge Ratios

A cross hedge (or proxy hedge) refers to hedging with an instrument that is note perfectly correlated wit the currency exposure being hedged. Such a hedge can also introduce additional risk – when the correlation of returns between the hedging instrument and the position being hedged is imperfect, the residual risk increases.

A macro hedge is a type of cross hedge that addresses portfolio-wide risk factors rather than the risk of individual portfolio assets. One type of currency macro hedges uses a derivative contract based on a fixed basket of currencies to modify currency exposure at a macro (portfolio) level.


12


A mathematical approach to determining the optimal cross-hedging ratio is known as the minimum-variance hedge ratio . It is a regression of the past changes in value of the portfolio (RDC) to the past changes in value of the hedging instrument (RF) to minimize the value of the tracking error between these two variables. The hedge ratio is the beta

(slope coefficient) of that regression.

Cov



RDC , RF

2

RDC , RF

 

RDC , RF







RDC



RF





Because the hedge ratio is based on historical returns, if the correlation between the returns on the portfolio and the returns on the hedging instrument change, the hedge will not perform as well as expected.

The minimum-variance hedge ratio can be used to jointly optimize over changes in value of RFX and RDC to minimize the volatility of RDC.

August 2014 263


12


For example, a foreign country where the economy is heavily dependent on imported oil. Appreciation of the currency

(+RFX) would make imports less expensive, which is likely to decrease production costs, increasing profits and asset values (+RFC). Strong positive correlation between RFX and RFC increases the volatility of RDC. A hedge ratio greater than 1 would lower the volatility of RDC.

For example, a foreign country where the economy is heavily dependent on exports. Appreciation of the currency

(+RFC) would make its exports more expensive, likely reducing sales, profits, and asset values (–RFC). Strong negative correlation between RFX and RFC naturally decreases the volatility of RDC. A hedge ratio less than 1 would lower the volatility of RDC.


12


A portfolio manager who is long the base currency in the P/B quote and wants to hedge that price risk needs to understand the following:

– Because the portfolio has a long exposure to base currency, to neutralize this risk the hedge will attempt to build a short exposure out of that currency’s derivatives using some combination of forward and/or option contracts.

– A currency hedge is not a free good. The hedge cost, real or implied, will consist of some combination of lost upside potential, potentially negative roll yield (forward points at a discount or time decay on long option positions), and upfront payments of option premiums.

– The cost of any given hedge structure will vary depending on market conditions (i.e., forward points and implied volatility).


12


For a manager with a long exposure to a currency, the cost of this “core” hedge will be the implicit costs of a short position in a forward contract (no upside potential, possible negative roll yield) or the upfront premium on a long position in a put option. Either of these two forms of insurance can be expensive. However, there are various cost mitigation methods that can be used alone or in combination to reduce these core hedging costs:

– Write options to gain upfront premiums.

– Varying exercise prices of the options written or bought.

– Varying notional amounts of the derivative contracts.

– Using various “exotic” features, such as knock-ins or knock-outs.

These cost mitigations approaches involve some combination of reduced upside and/or reduced downside protection.


12


There are often “natural” hedges within the portfolio, in which some residual risk exposures are uncorrelated with each other and offer portfolio diversification effects. Cross hedges and macro hedges bring basis risk into the portfolio, which will have to be monitored and managed.

There is no single or best way to hedge currency risk. The portfolio manager will have to perform a due diligence examination of potential hedge structures and make a rational decision on a cost/benefit basis.


12


The majority of investable asset value and FX transactions are in the six largest developed market currencies.

Transactions in other currencies pose additional challenges because of:

– higher transaction costs, “high markups” and

– increased probability of extreme events.

Non-deliverable forwards: Emerging markets governments (i.e., Brazil, China, Russia) frequently restrict movement of their currency into or out of the country to settle normal derivative transactions. They are an alternative to deliverable forwards and require a cash settlement of gains or losses in a developed market currency at settlement rather than a currency exchange.


Global Fixed Income Portfolio

Global Fixed Income Portfolio

CfBS Center for Business Studies AG

Dr. Enzo Mondello, CFA, FRM, CAIA

August 2014

Risks Associated with Investing in Bonds

Fixed-Income Valuation

Term Structure of Interest Rates

Yield Measures

Current Yield

Cash Coupon Payment

Bond Price per Year

Interest Rate Risk: Duration and Convexity

D

dP/dy

P

D

dP/P dy

change in Yield

effective

change in Curve

Credit Risk: Fundamentals of Credit Analysis

Managing Bond Portfolio

Relative-Value Methodologies for Global

Corporate Bond Portfolio Management

Exchange Rate Risk: International Bond Investing

Managing Interest Rate Risk with Derivatives

Number of

Futures Contract

Duration

Duration

Market Value of Bond Portfolio

Dollar Duration of Futures Contract

Managing Credit Risk with Derivatives

Currency Risk Management

F

S

1

1

i i

Actual

360

Actual

360

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