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CHAPTER SEVENTEEN MANAGING THE FIXED INCOME PORTFOLIO © 2001 South-Western College Publishing Outline Fixed Income Security Risk Default Risk Reinvestment Rate Risk Interest Rate Risk Duration Duration Measures Applying Duration 2 Outline Convexity Problems with Duration Simple Convexity An Example Using Convexity Management Strategies Active vs. Passive Management Classic Passive Management Strategies The Risk of Barbells and Ladders Indexing Active Management 3 Fixed Income Security Risk Default risk, or credit risk, is the possibility that a borrower will be unable to repay principal and interest as agreed upon in the loan document. Reinvestment rate risk refers to the possibility that the cash coupons received will be reinvested at a rate different from the bond’s stated rate. Interest rate risk refers to the chance of loss because of adverse movements in the general level of interest rates. 4 Interest Rate Risk : Malkiel’s Theorems A set of relationships among bond prices, time to maturity, and interest rates is widely referred to as Malkiel’s theorems. Theorem one: Bond prices move inversely with yields. Theorem two: Long-term bonds have more risk. Theorem three: Higher coupon bonds have less risk. 5 Interest Rate Risk : Malkiel’s Theorems Theorem four: The importance of theorem two diminishes with time. Theorem five: Capital gains from an interest rate decline exceed the capital loss from an equivalent interest rate increase. Bond A: matures in 8 years, 9.5% coupon Bond B: matures in 15 years, 11% coupon Which price will rise more if interest rates fall? Apparent contradictions can be reconciled by computing a statistic called duration. 6 Duration For a noncallable security, duration is the weighted average time until a bond’s cash flows are received. Duration is not limited to bond analysis. It can be determined for any cash flow stream. Duration is a direct measure of interest rate risk. The higher it is, the higher is the risk. Thinking of duration as a measure of time can be misleading if the life or the payments of the bond are uncertain. 7 Duration Measures Macaulay duration is the time-value-of-moneyweighted, average number of years necessary to recover the initial cost of the security. N D Ct t 11 R P t t where D = duration Ct = cast flow at time t R = yield to maturity (per period) P = current price of bond N = number of periods until maturity t = period in which cash flow is received 8 Duration Measures Chua’s closed-form duration is less cumbersome because it has no summation requirement. 1 R N 1 1 R RN FN Ct N N 2 1 R R 1 R D P where F = face value (par value) of the bond and all other variables are as previously defined. 9 Duration Measures Modified duration measures the percentage change in bond value associated with a onepoint change in interest rates. dP 1 1 C1 2C 2 NC N 1 1 2 N dR P 1 R 1 R 1 R 1 R P DMacaulay Dmodified 1+ R 2 10 Duration Measures Effective duration is a measure of price sensitivity calculated from actual bond prices associated with different interest rates. It is a close approximation of modified duration for small yield changes. P P Deffective P0 R R where P- = price of bond associated with a decline of x basis points P+ = price of bond associated with a rise of x basis point R- = initial yield minus x basis points R+ = initial yield plus x basis points P0 = initial price of the bond 11 Duration Measures Dollar duration determines the dollar amount associated with a percentage price change. modified bond price as a Ddollar = - duration x percentage of par Pnew = Pold + (Ddollar x change in yield) The price value of a basis point is the dollar price change in a bond associated with a single basis point change in the bond’s yield. 12 Applying Duration The yield curve experiences a parallel shift when interest rates at each maturity change by the same amount. Duration is especially useful in determining the relative riskiness of two or more bonds when visual inspection of their characteristics makes it unclear which is more vulnerable to changing interest rates. 13 price Problems with Duration The bond price - bond yield relationship is not linear. yield to maturity Graphically, duration is the tangent to the current point on the price-yield curve. Its absolute value declines as yield to maturity rises. Duration is a first derivative statistic. Hence, when the change is large, estimates made using the derivative alone will contain errors. 14 Convexity Convexity measures the difference between the actual price and that predicted by duration, i.e. the inaccuracy of duration. The more convex the bond price-YTM curve, the greater is the convexity. 1 N t t 1C t N N 1F Convexity t 2 N 2 P t 1 1 R 1 R 15 Convexity : An Example Price forecasting accuracy is enhanced by incorporating the effects of convexity. Suppose a bond has a 15-year life, an 11% coupon, and a price of 93%. Macaulay duration = 7.42, yield-to-maturity = 12.00%, modified duration = 7.00, convexity = 97.71. If YTM rises to 12.50%, new price= 89.95% Actual price change = - 3.28% Price change predicted by duration = - 3.50% Price change predicted by duration and convexity = - 3.38% 16 bond price Using Convexity yield to maturity No matter what happens to interest rates, the bond with the greater convexity fares better. It dominates the competing investment. 17 Management Strategies An active strategy is one in which the investment manager seeks to improve the rate of return on the portfolio by anticipating events in the marketplace. A passive strategy is one in which the portfolio is largely left alone after its construction. Changes are made when securities mature or are called, but normally not for any other reason. 18 par value Classic Passive Management Strategies A laddered strategy distributes fixed income dollars throughout the yield curve. A barbell strategy differs from the laddered strategy in that less investment is made in the middle maturities. par value maturity maturity On the other hand, a credit barbell is a bond portfolio containing a mix of high-grade and low-grade securities. 19 The Risk of Barbells and Ladders If durationladdered portfolio > durationbarbell portfolio , rising interest rate falling interest rate interest rate barbell ladder risk favored favored reinvestment rate risk barbell favored ladder favored Yield curve inversion means short-term rates are rising faster than long-term rates. Duration as a pure measure of interest rate risk only works for parallel shifts in the yield curve. 20 Passive Management Strategies Indexing is predicated upon managers being unable to consistently predict market movements. Indexing involves attempting to replicate the investment characteristics of a popular measure of the bond market. The two best-known bond indexes are probably the Salomon Brothers Bond Index and the Lehman Kuhn Loeb Bond Index. 21 Active Management Strategies Active management techniques frequently involve a bond swap, which is usually intended to do one of four things: 1. increase current income 2. increase yield to maturity 3. improve the potential for price appreciation with a decline in interest rates 4. establish losses to offset capital gains or taxable income Active management strategies fall into four broad categories. 22 Strategy 1 : Duration Management Duration management techniques involve creating a structured portfolio - a collection of securities with characteristics that will accommodate a specific need or objective. A key concept is immunization - a technique that seeks to reduce or eliminate the interest rate risk in a portfolio. Bank immunization is achieved when the total dollar duration of a financial institution’s rate sensitive assets equals the total dollar duration of its rate sensitive liabilities. 23 Strategy 1 : Duration Management Bullet immunization seeks to ensure that a specific sum of money will be available at a point or series of points in the future. Cash matching is the special case when cash is generated exactly in line with cash demands. Another practice, known as duration matching, aims to get interest rate risk and reinvestment rate risk to cancel each other out. A dedicated portfolio is a separate portfolio that will generate cash equal to or greater than some required amount. 24 Active Management Strategies Strategy 2 : Yield Curve Reshaping If lower interest rates are expected, longterm premium bonds may be exchanged for long-term discount bonds, for example. Strategy 3 : Sector Selection Differences in market sectors sometimes cause otherwise similar bonds to behave differently in response to market changes. Strategy 4 : Issue Selection Analysts try to correctly anticipate bond rating changes or make profitable substitution swaps. 25 Review Fixed Income Security Risk Default Risk Reinvestment Rate Risk Interest Rate Risk Duration Duration Measures Applying Duration 26 Review Convexity Problems with Duration Simple Convexity An Example Using Convexity Management Strategies Active vs. Passive Management Classic Passive Management Strategies The Risk of Barbells and Ladders Indexing Active Management 27
