FNCE 4070: FINANCIAL MARKETS
AND INSTITUTIONS
Lecture 4: Understanding Interest
Rates and Risks in the Bond Markets
Various Measures of Interest Rates
Relationship of Market Interest
Rates to Bond Prices
Risks in the Bond Markets: Including
Price, Reinvestment , Inflation and
Default Risk
Concept of Duration
Where is this Financial Center?
Grand Cayman
Stingray City
Turtle Burgers
A Financial Center

A Financial Center is a location:


That has a heavy concentration of financial institutions
providing a wide range of financial services (including
banking, insurance, cash management, asset
management). London, New York, and Tokyo are regarded
as the world's three premier financial centers.
An Offshore Financial Center is a location:

That provides financial services to nonresidents on a scale
that is disproportionately larger in comparison to the size
and the financing of its domestic economy (IMF definition).

Examples include: The Cayman Islands, Gibraltar, Bahrain, and
Hong Kong


The Cayman Islands, with a domestic population of 52,000, has 250
banks, with approximately $415 billion in deposits (making it one of
the largest financial centers in the world).
Is London an offshore financial center?
Interest Rate Defined

“Dual” Definition:

Borrowing: the cost of borrowing or the price (%) paid
for the “rental” of funds.


Saving: the return from investing funds or the price
(%) paid to delay consumption.


A financial liability for “deficit” (borrowing) entities.
A financial asset for “surplus” (lending, investing) entities.
Both concepts are expressed as a percentage
per year (Percent per annum; “p.a.”).

True regardless of maturity of instrument of the
financial liability or financial asset.


Thus, all observed interest rate data is annualized.
See: http://www.federalreserve.gov/releases/h15/update/
Savings and Borrowing Rates:
They Move Together, 1977– 2011

Regression analysis: 1964 – 2010 (monthly data, 564 observations);
CD rate as dependent variable. R-squared = 88.55%
Basis Points and Interest Rates


Basis Point: A unit that is equal to 1/100th of 1%,
and is used to denote the changes in interest rates
or differences in interest rates between various debt
instruments.
The relationship between interest rate changes (or
differentials) and basis points can be summarized as
follows: 1% change (or difference) = 100 basis
points.



Example 1: If Bond A’s yield increases from 5% to 6.5%,
then Bond A’s yield increased150 basis points.
Example 2: If Bond B’s yield falls from 7.00% to 6.93%,
then Bond B’s yield decreased 7 basis points.
Example 2: If Bond C has a yield of 6% and Bond D a yield
of 2%, then Bond C is 400 basis points more than Bond D.
Commonly Used Interest Rate Measures

There are four important ways of measuring
(and reporting) interest rates on financial
instruments. These are:




Coupon yield: The “promised” annual percent return
on a coupon instrument.
Current Yield: Bond’s annual coupon payment divided
by its current market price.
Yield to Maturity: The interest rate that equates the
future payments to be received from a financial
instrument (coupons plus maturity value) with its
market price today (i.e., to its present value).
Discount Yield and Investment Yield: These are yields
on short term (one year or less) debt instruments that
have no coupon payments and are selling at a
discount of their par values.

These interest rates are the “implied” returns from buying a
debt instrument at a price below its par value.
Important Bond Terms

Par Value: The amount that the bond holder will
received when the bond matures.




Also called face value and maturity value.
In the U.S. all bonds have a par value of $1,000.
Coupon Payment: This is the (dollar) amount of
interest to be paid to the bond holder. Usually
expressed on an annual basis (even if the bond
pays interest semi-annually).
Market Price: This is the current market price for
an outstanding bond.


Premium bond: Market price above its par value
Discount bond: Market price below its par value
Coupon Yield



Coupon yield is the annual interest rate which was
promised by the issuer when a bond was first sold.
 Coupon information is found in the bond’s indenture
(legal contract).
 Indenture will state the coupon payment (as a percent
of the bond’s par value) and the schedule of payments
(semi-annual or annual).
Important: The coupon yield on a bond will not change
during the lifespan of the bond.
Go to Bloomberg to view coupon yields:
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
http://www.bloomberg.com/
Note: U.S. Treasuries, 12 months and less have no coupons.
Same is true for short term government bonds in other countries.
Par Values: Other Countries

Par values are different in other countries:

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Par value is also called the maturity value (or face
value).
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UK Government bonds (generally GBP100 par value; called gilts)
Japanese Government bonds (JPY10,000 par value; called
JGBs)
German Government bonds (minimum amount EUR100 par
value, called bunds)
French Government bonds (minimum amount EUR100; called
OATs (Obligations assimilables du Trésor).
Canadian Government bonds (CAD$1,000 par value)
Australian Government bonds (AUD$1,000 par value)
Recall, this is what the bond holder receives at maturity date.
Government bonds (including U.S. Treasuries) generally
pay interest semi-annually.
Example of a U.S. Treasury Bond

1.50% U.S. Treasury bond due April 30, 2019 (thus, a bond
with 7 year’s to maturity), paying interest semi-annually, with a
current market price of 100-12.




The 1.50% is the stated coupon (as a percent of par)
This bond will pay $15.00 per year in interest (.0150 x $1,000); but
since it is a semi-annual bond, it will pay $7.50 every six months.
On April 30, 2019, the bond will pay $1,000 (par value) plus 6
months interest ($7.50) or a total of $1,007.50.
The current market price (100-12) is expressed as a percent
of par value.

The market price for U.S. Treasuries has two components:



The (1) “handle” (number to the left of the -) and (2) the 32nds
(number to the right of the -). We need to convert these two
components to a percentage.
Start with the 32nds; 12/32 = 0.375. Add this amount to the
handle = 100.375.
Thus the market price is 100.375% of par or $1003.75
Current Yield

Since bond prices are likely to change, we often
refer to a bond’s “current yield” which is measured
by dividing a bond’s annual coupon payment by its
current market price.


This provides us with a measure of the “current” interest
yield obtained at the bond’s current market price (i.e.,
cost associated with investing in a particular bond).
Current yield = annual coupon payment/market
price


Recall in our previous example, the 7 year, 1.50% bond
selling at $1,003.75 (thus it is a premium bond).
Thus the current yield = $15.00/1,003.75 = 1.4944%
Current Yield for Bonds Selling at a
Premium and at a Discount

Premium bonds: The current yield on these
bonds will always be below the coupon yield.




Current Yield = Annual coupon payment/>$1,000
Using the 1.5% coupon bond:
Current yield = $15.00/1,003.75 = 1.4944%
Discount bonds: The current yield on these
bonds will always be above the coupon yield
(assume a market price of $985).


Current Yield – Annual coupon payment/<$1,000
Current yield = $15.00/$985 = 1.5228%
Yield to Maturity


Yield to maturity is the interest rate which will discount
the incomes (i.e., cash-flows) of a bond to produce a
present value which is equal to the bond’s current
market price (or produce a net present value = 0).
Yield to maturity is calculated as:
C
C
C
C
PV
MP 



...


1  i  1  i 2 1  i 3
1  i n 1  i n

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
MP = Market price of a bond (i.e., present value)
C = Coupon payments (a future cash flow)
PV = Par, or face value, at maturity (a future cash flow)
n = Years to maturity (as stated in the indenture)
i = Yield to maturity (the discount rate)
Note: i is also the bond’s internal rate of return
Yield to Maturity Example

Assume the following given variables:
C =$40 (thus a 4.0% coupon issue; paid annually)
N =10
PV =$1,000
MP =$1,050 (note: premium bond, i.e., selling at a premium of
par)
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$1050 = $40/(1 + i)1 + $40/(1 + i)2 + . . . + $40/(1 + i)10
+ $1000/(1 + i)10
Solve for i, the yield to maturity
Note: The i calculated using this formula will be the
return that you will be getting when the bond is held
until it matures (and assuming that the periodic
coupon payments are reinvested at the same i yield).
In this example, the calculated i is 3.4%.
Yield to Maturity Second Example

Now assume the following:

C =$40
N =10
PV =$1,000
MP =$900.00 (note: bond is selling at a discount of
par)

$900 = $40/(1 + i)1 + $40/(1 + i)2 + . . . + $40/(1 + i)10
+ $1,000/(1 + i)10

Solve for i, the yield to maturity

Note: The i calculated in this example is 5.315%.
What one factor accounts for the yield to maturity
difference when compared to the previous slide, with
its i of 3.4%?

Useful Web Site for Calculating a
Bond’s Yield to Maturity


While yields to maturity can be determined
through a book of bond tables or through
business calculators, the following is a useful
web site for doing so:
http://www.moneyzine.com/Calculators/InvestmentCalculators/Bond-Yield-Calculator/
Bloomberg.com Web Site for
Yields to Maturity


Link to http://www.bloomberg.com/ to
examine U.S. Government bonds.
Make sure you:



Understand the coupon column
Understand the maturity column (how much will a
bond holder get on this date?)
Understand the price and yield column (looked at
2-year bonds down to 30-year bonds).


Note: Yield is the calculated yield to maturity.
Note: 3-month, 6-month and 12 month issues do not
have a coupon (these are all Treasury Bills).
Treasury Obligations


The U.S. Treasury department sells a variety of
debt instruments with different maturities.
T-Bills refer to those instruments with original
maturities of 12 months or less.


Treasury notes and bonds are longer term debt
instruments.

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
T-Bills do not pay interest (i.e., there is no coupon
yield).
Notes out to about 7 years, and bonds out to 30.
These instruments pay interest (i.e., coupon issues).
Even though T-Bills do not pay interest, we still
need to calculate a return on these instruments.

The two “yields” we calculate are the discount yield
and the investment yield.
Discount and Investment Yield


Discount yields and investment yields are calculated
for U.S. T-bills and other short term money market
instruments (e.g., commercial paper and bankers’
acceptances) where there are no stated coupons
(and thus the assets are quoted at a discount of
their maturity value).
The discount yield relates the return to the
instrument’s par value (or face or maturity).


The discount yield is sometimes called the bank discount
rate or the discount rate.
The investment yield relates the return to the
instrument’s current market price.

The investment yield is sometimes called the coupon
equivalent yield, the bond equivalent rate, the effective
yield or the interest yield.
The Discount Yield

Discount yield = [(PV - MP)/PV] * [360/M]

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


PV = par (or face or maturity) value
MP = market price
M = maturity of bill.
Note: 360 = is the number of days used by banks
to determine short-term interest rates on
discounted instruments.
The discount yield relates the return to the
instrument’s par value (PV).
Discount Yield Example


What is the discount yield for a 182-day T-bill,
with a market price of $965.93 (per $1,000
par, or face, value)?
Discount yield = [(PV - MP)/PV] * [360/M]
Discount yield = [(1,000) - (965.93)] / (1,000)
* [360/182]
Discount yield = [34.07 / 1,000] * [1.978022]
Discount yield = .0673912 = 6.74%
Investment Yield


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
Investment yield = [(PV - MP)/MP] * [365 or
366/M]
The investment yield relates the return to the
instrument’s current market price (MP).
In addition, the investment yield is based on a
calendar year: 365 days, or 366 in leap years.
The investment yield is generally calculated so
that we can compare the return on T-bills to
“coupon” investment options.

Since the calculated investment yield is comparable to
the yields on coupon bearing securities (such as long
term bonds and notes) it is often referred to as the
bond or coupon equivalent yield.
Investment Yield Example


What is the investment yield of a 182-day Tbill, with a market price of $965.93 per $1,000
par, or face, value?
Investment yield = [(PV - MP)/MP] * [365/M]
Investment yield = [(1,000 – 965.93) /
(965.93)] * [365/182]
Investment yield = [34.07] / 965.93] *
[2.0054945]
Investment yield = .0707372 = 7.07%
Discount and Investment Yields

Looking at the last two examples we found:


Discount yield = [(PV - MP)/PV] * [360/M]
Discount yield = [(1,000 - 965.93)] / (1,000) * [360/182]
Discount yield = [34.07 / 1,000] * [1.978022]
Discount yield = .0673912 = 6.74%
Investment yield = [(PV - MP)/MP] * [365/M]
Investment yield = [(1,000 – 965.93)] / (965.93) * [365/182]
Investment yield = [34.07 / 965.93] * [2.0054945]
Investment yield = .0707372 = 7.07%

Note: The investment yield formula will tend to
“over-state” yields relative to those computed by the
discount method, because the market price (in the
investment yield formula) is (likely to be) lower than
the par value ($1,000).

However, if the market price is very close to the par value, the
yields will be very close to one another.
Bloomberg.com Web Site for
Discount and Investment Yields


Link to http://www.bloomberg.com/ to
examine U.S. Government bonds.
Look at the 3-month, 6-month and 12-month
issues.



Observe they do not carry a coupon.
Observe they sell at a discount (of par).
Under the column price/yield you will observe two
yields.

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The first yield (under price) is the discount yield.
The second yield (under yield) is the investment yield.
What Changes The Yield to Maturity?



Think of the yield to maturity as the “required return
on an investment.”
Since the required return changes over time, we can
expect these changes to produce inverse changes in
the prices on outstanding (seasoned) bonds.
Why will the required return change over time?

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Changes in inflation (inflationary expectations).
Changes in the economy’s credit conditions resulting from
change in business activity.
Changes in central bank policies.

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Generally, impacting on shorter term maturities (exception,
Operation Twist).
Changes in the assumptions about credit risk and announced
changes in credit risk ratings associated with the issuer of the
bond(i.e., risk of default).
Contagion effects
Safe haven effects (market uncertainty)
Illustrating the Relationship Between
Interest Rates and Bond Prices

Assume the following:


A 10 year corporate Aaa bond which was issued 8
years ago (thus it has 2 years to maturity) has a
coupon rate of 7%, with interest paid annually.
Thus, 7% was the required return when this bond was
issued.



This bond is referred to as an outstanding (or seasoned) bond.
Question: How much will a holder of this bond receive
in interest payments each year?
This bond has a par value of $1,000.

Question: How much will a holder of this bond receive in
principal payment at the end of 2 years?
What Happens when Interest Rates
Rise?

Assume, market interest rates rise (i.e., the required return rises)
and now 2 year Aaa corporate bonds are now offering coupon
returns of 10%.




This is the “current required return” (or “i” in the present value bond
formula)
Question: What will the market pay (i.e., market price) for the
outstanding 2 year, 7% coupon bond noted on the previous
slide?
 PV = $70/(1+.10) + $1,070/(1+.10)2
 PV = $947.94 (this is today’s market price)
Note: The 2 year bond’s price has fallen below par (selling at a
discount of its par value).
Conclusion: When market interest rates rise, the prices on
outstanding bonds will fall.
What Happens when Interest Rates
Fall?

Assume, market interest rates fall (i.e., the required return falls)
and now 2 year Aaa corporate bonds are now offering coupon
returns of 5%.




This is the “current required return” (or “i” in the present value bond
formula)
Question: What will the market pay (i.e., market price) for the
outstanding 2 year, 7% coupon bond?
2
 PV = $70/(1+.05) + $1,070/(1+.05)
 PV = $1,037.19 (this is today’s market price)
Note: The 2 year bond’s price has risen above par (selling at a
premium of its par value).
Conclusion: When market interest rates fall, the prices on
outstanding bonds will rise.
Bond Price Sensitivity to Changes
in Market Interest Rates (YTM)
Change in Market’s Required Return
Versus Change in Market Demand

The examples on the previous slides demonstrated
the impact of a change in the market’s required
return on bond prices.


Observation: Cause – effect relationship runs from
changes in required return to changes in market prices
(which produce the market’s new required return).
However, it is possible for a change in market
demand to produce changes in bond prices and
thus in market interest rates.


For example: Safe haven effects result in changes in
demand for particular assets.
Observation: Cause – effect relationship runs from
changes in demand to changes in prices (which have an
automatic impact on yields).
What if the Time to Maturity Varies?

Assume a one year bond (7% coupon) and the market
interest rate rises to 10%, or falls to 5%.



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
Now assume a two year bond (7% coupon) and the
market interest rate rises to 10%, or falls to 5%

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
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
PV@10% = $1,070/(1.10)
PV = $972.72
PV @5%= $1,070/(1.05)
PV = $1,019.05
PV@10% = $70/(1+.10) + $1,070/(1+.10)2
PV = $947.94
PV@5% = $70/(1.05) + $1,070/(1+.05) 2
PV = $1037.19
Conclusion: For a given interest rate change, the longer
the term to maturity, the greater the bond’s price change.
Summary: The Interest Rate Bond
Price Relationship




#1: When the market interest rate (i.e., the required
rate) rises above the coupon rate on a bond, the
price of the bond falls (i.e., it sells at a discount of
par).
#2: When the market interest rate (i.e., the required
rate) falls below the coupon rate on a bond, the
price of the bond rises (i.e., it sells at a premium of
par)
IMPORTANT: There is an inverse relationship
between market interest rates and bond prices (on
outstanding or seasoned bonds).
#3: The price of a bond will always equal par if the
market interest rate equals the coupon rate.
Summary: The Interest Rate Bond
Price Relationship Continued

#4: The greater the term to maturity, the greater the
change in price (on outstanding bonds) for a given
change in market interest rates.


This becomes very important when developing a bond
portfolio-maturity strategy which incorporates
expected changes in interest rates.
This is the strategy used by bond traders:


What if you think interest rates will fall? Where should
you concentrate the maturity of your bonds?
What if you think interest rates will rise? Where should
you concentrate the maturity of your bonds?
Interest Rate (or Price) Risk on a
Bond




Defined: The risk associated with a reduction
in the market price of a bond, resulting from a
rise in market interest rates.
This risk is present because of the “inverse”
relationship between market interest rates
and bond prices.
The longer the maturity of the fixed income
security, the greater the risk and hence the
greater the impact on the overall return.
For a historical examples, see the next slide.
Relationship of Maturity to Returns

Note: Return = coupon + change in market price
Price Risk: 1950 - 1970
Reinvestment Risk on a Bond


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


Reinvestment risk occurs because of the need to “roll
over” securities at maturity, i.e., reinvesting the par value
into a new security.
Problem for bond holder: The interest rate you can
obtain at roll over is unknown while you are holding
these outstanding securities.
Issue: What if market interest rates fall?
You will then re-invest at a lower interest rate then the
rate you had on the maturing bond.
Potential reinvestment risk is greater when holding
shorter term fixed income securities.
With longer term bonds, you have locked in a known
return over the long term.

For a historical example, see the next slide
Reinvestment Risk: 1985 - 2011
Other Risk Associated with Bonds

Inflation Risk:



Risk the future “unanticipated” inflation will erode the
real value of future payments.
Can reduce this risk through inflation protected
instruments (TIPs in the U.S.)
Default Risk:


Risk that the issuer of the bond will encounter financial
difficulties which will render coupon and principal
payments difficult (or impossible).
Can “insure” against default with credit default swaps.
Inflation Risk: U.S. 5-Year
Government Bonds and the CPI
Standard & Poor’s Annual Default
Data

In 2011, 53 global corporate issuers defaulted, down
from 81 defaults in 2010 and the record high of 265
in 2009.


U.S. companies accounted for the majority of defaults, with
39, while other developed nations had seven (Europe
accounted for four).
The debt amount affected by these 53 defaults fell to $84.2
billion, from $95.7 billion in 2010 (All-time high of $627
billion in 2009).


•Texas Competitive Electric Holdings Co. was the single largest
defaulter in 2011 based on debt volume. The company
accounted for $32.46 billion in debt, which is nearly 40% of the
total amount affected by defaults in 2011.
Data based on the 15,299 companies that Standard
& Poor's rated up to Dec. 31, 2011.
Global Corporate Defaults
Sovereign Defaults

The term sovereign default refers to the failure of a
government to comply with interest payment or debt
repayment obligations on its bonds or bank loans.




Before the 19th century, sovereign defaults arose mainly from
domestic politics or wartime refusal to make payments to enemy
creditors.
In the early 20th century, defaults were mainly associated with the
First World War or with the great depression.
There were relatively few post-war defaults until the 1980s.
However, from 1980 to 2004 there were over 110 default and
debt restructuring episodes involving African and South American
governments. Most of these were related to a combination of
external shocks (e.g., a currency crisis) or a banking or currency
crises.
In most cases, a sovereign default is followed by a
restructuring agreement (e.g., the Paris Club) between the
defaulting government and its creditors, and the resumption
of payments.

Greece (February 21, 2012): Private bond holders agreed to a
53.5% “haircut” on the nominal value of their Greek bonds.
Cycles of Sovereign Defaults

Percent of Countries in Default or Restructuring
Hedging with Credit Default Swaps





CDS are financial instruments used for swapping the risk of debt
default. A credit event occurs when there is a substantial, identifiable
loss.
The buyer of a credit default swap pays a premium for effectively
insuring against a debt default. The buyer receives a lump sum
payment if the debt instrument is defaulted. Swaps pay the buyer
face value should a borrower fail to adhere to its debt agreements.
The buyer of a credit swap receives credit protection, whereas the
seller of the swap guarantees the credit worthiness of the product.
By doing this, the risk of default is transferred from the holder of the
fixed income security to the seller of the swap.
CDS are quoted in basis points. A basis point equals $1,000
annually on a swap protecting $10 million of debt.
Credit events applicable to governments are failure to pay on the
debt or restructuring of the debt. Generally speaking, a restructuring
involves reduced payments or payments that are spread over time
without compensation.
CDS spreads can be interpreted as a measure of the perceived risk
that a government will restructure or default on its debt.
Appendix 2
PIIGS Interest Rates Pre and During
Debt Crisis
Run Up to the February 21, 2012
Greek Sovereign Debt Re-Structuring

Yields to Maturity on 2-Year Greek
Government Bonds
PIIGS: 1993 – 2011; Yields to
Maturity on 10 year Governments
PIIGS: Spreads Over 10-Year Bunds
Appendix 2
Bond Duration
Concept of Bond Duration
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Issue: The fact that two bonds have the same term to
maturity does not necessarily mean that they carry the
same interest rate risk (i.e., potential for a given change
in price).
Assume the following two bonds:
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(1) A 20 year, 10% coupon bond and
(2) A 20 year, 6% coupon bond.
Which one do you think has the greatest interest rate
(i.e., price change) risk for a given change in interest
rates?
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Hint: Think of the present value formula (market price of a bond)
and which bond will pay off more quickly to the holder (in terms of
coupon cash flows). The one that pays off more quickly, has less
price risk.
Solution to Previous Question
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Assume interest rates change (increase) by 100
basis points, then for each bond we can
determine the following market price.
20-year, 10% coupon bond’s market price (at a
market interest rate of 11%) = $919.77
20-year, 6% coupon bond’s market price (at a
market interest rate of 7%) = $893.22
Observation: The bond with the higher coupon,
(10%) will pay back quicker (i.e., produces more
income early on), thus the impact of the new
discount rate on its cash flow is less.
Duration and Interest Rate Risk
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Duration is an estimate of the average lifetime of
a security’s stream of payments.
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Duration rules:
(1) The lower the coupon rate (maturity equal), the
longer the duration.
(2) The longer the term to maturity (coupon equal), the
longer duration.
(3) Zero-coupon bonds, which have only one cash
flow, have durations equal to their maturity.
Duration is a measure of risk because it has a
direct relationship with price volatility.
The longer the duration of a bond, the greater
the interest rate (price) risk and the shorter the
duration of a bond, the less the interest rate risk.
Calculated Durations
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Duration for a 10 year bond assuming
different coupons yields:
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Coupon 10%
Coupon 5%
Zero Coupon
Duration 6.54 yrs
Duration 7.99 yrs
Duration 10 years
Duration for a 10% coupon bond assuming
different maturities:
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5 years
10 years
20 years
Duration 4.05yrs
Duration 6.54 yrs
Duration 9.00 yrs
Using Duration in Portfolio
Management
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Given that the greater the duration of a bond, the
greater its price volatility (i.e., interest rate risk), we
can apply the following:
(1) For those who wish to minimize interest rate risk,
they should consider bonds with high coupon
payments and shorter maturities (also stay away
from zero coupon bonds).
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Objective: Reduce the duration of their bond portfolio.
(2) For those who wish to maximize the potential for
price changes, they should consider bonds with low
coupon payments and longer maturities (including
zero coupon bonds).
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Objective: Increase the duration of their bond portfolio
Another Web Site for Calculating Yields
and Testing Your Understanding
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Visit the web site below. It allows you to calculate the
current yield and yield to maturity for specific data you
input on:
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It also allows you to calculate present values.
Use this web site to test your understanding of the
relationship between bond prices and interest rates.
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Current Market Price
Coupon Rate
Years to Maturity
See what happens to the calculated interest rates when
you change the bond price above and below the par value.
Note the inverse relationship.
http://www.moneychimp.com/calculator/bond_yield_calc
ulator.htm
Internet Source of Interest Rate Date
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Historical and Current Data for U.S.
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http://www.federalreserve.gov/releases/h15/update/
Real Time Data (U.S. and other major countries)
 http://www.bloomberg.com
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Go to Market Data and then to Rates and Bonds
Other Countries:
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Economist.com (both web source or hard copy)
Appendix 3
Using Excel to Calculate the Duration of
a Bond
Using Excel to Calculate Duration
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Go to Formulas in Microsoft Excel
Go to Financial
Go to Duration
Insert Your Data:
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Example for 10 year, 10% coupon bond with market
rate of 10%:
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Settlement: DATE(2009,2,1) Assume, Feb 1, 2009
Maturity: DATE(2019,2,1) Note: 10 years to maturity
Rate: 10% (this is the coupon yield)
Yld: 10% (this is the yield to maturity)
Frequency: 2 (assume interest is paid semi-annually)
Basis: 3 (this basis uses a 365 day calendar year)
Formula result = 6.54266