Fundamentals of the bond Valuation Process The Value of a Bond.

Computing Bond Yields Yield Measure Purpose Nominal Yield Measures the coupon rate Current yieldMeasures current income rate Promised yield to maturity Measures expected rate of return for bond held to maturity Promised yield to call Measures expected rate of return for bond held to first call date Realized (horizon) yield Measures expected rate of return for a bond likely to be sold prior to maturity. It considers specified reinvestment assumptions and an estimated sales price. It can also measure the actual rate of return on a bond during some past period of time.

Rates of Return Approximate Promised Yield APY = C + (Par – Market Price)/ NMaruity.60 ( Market Price) +.4 (Par).60 ( Market Price) +.4 (Par) Yield to Call: Yield to Call: AYC = C + (Call Price – Market Price)/ NCall.60 ( Market Price) +.4 (Call Price).60 ( Market Price) +.4 (Call Price) Approximate Realized Yield ARY = C + (Realized Price – Market Price)/ NRealize.60 ( Market Price) +.4 (Realize Price)

Corporate Bond Quotes Cur Net Cur Net Bonds Yld Vol Close Chg Bonds Yld Vol Close Chg ATT 8 1 / / / 4 ATT 8 1 / / / 4 Issued by AT&T 8.125% coupon rate; matures in 2022 Current yield = coupon/market price = 7.7% 52 of these bonds traded that day The closing price was / 8 % of par which was up 1/4 from the prior day

Term Structure of Interest Rates The relationship between maturity and interest rates. It is also known as the Yield Curve. Expectations Hypothesis suggests that the long-term rate is an average of the expectations of the future short-term rates over the applicable time horizon. Reinforced by borrower/lender strategies.

Maturity Yield c Maturity Yield a Maturity b Yield d Normal Figure 12-1 Term Structure of Interest Rates

The Movement of Interest Rates (cont.) Liquidity Preference Theory states that the shape of the yield curve is upward sloping. Investors will pay a higher price for short-term securities because they are more easily turned into cash without the risk of large price changes. Investors demand higher returns from longer- term securities.

The Movement of Interest Rates (cont.) Market Segmentation Theory focuses on the demand side of the market. –Banks tend to prefer Short Term liquid securities to match the nature of their deposits. –Life insurance companies invest in Long-Term bonds to match their Long-Term obligations.

Investment Strategy: Interest- Rate Considerations Bond Pricing Rules –1.Bond prices and interest rates are inversely related. –2.Prices of long-term bonds are more sensitive to a change in yields to maturity than short-term bonds. –3.Bond price sensitivity increases at a decreasing rate as maturity increases.

Investment Strategy: Interest-Rate Considerations (cont.) –4. Bond prices are more sensitive to a decline in market YTM than to a rise in YTM. –5. Prices of low-coupon bonds are more sensitive to a change in YTM than high coupon bonds. –6. Bond prices are more sensitive when YTM is low than when YTM is high. –7. Margin trading magnifies profits and losses of bond investments by a factor of 1/(margin requirement).

What Determines the Price Volatility for Bonds Five observed behaviors 1. Bond prices move inversely to bond yields (interest rates) 2. For a given change in yields, longer maturity bonds post larger price changes, thus bond price volatility is directly related to maturity 3. Price volatility increases at a diminishing rate as term to maturity increases 4. Price movements resulting from equal absolute increases or decreases in yield are not symmetrical 5. Higher coupon issues show smaller percentage price fluctuation for a given change in yield, thus bond price volatility is inversely related to coupon

What Determines the Price Volatility for Bonds The maturity effect The coupon effect The yield level effect Some trading strategies

The Duration Measure Since price volatility of a bond varies inversely with its coupon and directly with its term to maturity, it is necessary to determine the best combination of these two variables to achieve your objective A composite measure considering both coupon and maturity would be beneficial

The Duration Measure Developed by Frederick R. Macaulay, 1938 Where: t = time period in which the coupon or principal payment occurs t = time period in which the coupon or principal payment occurs C t = interest or principal payment that occurs in period t i = yield to maturity on the bond i = yield to maturity on the bond

Characteristics of Duration Duration of a bond with coupons is always less than its term to maturity because duration gives weight to these interim payments –A zero-coupon bond’s duration equals its maturity There is an inverse relation between duration and coupon There is a positive relation between term to maturity and duration, but duration increases at a decreasing rate with maturity There is an inverse relation between YTM and duration Sinking funds and call provisions can have a dramatic effect on a bond’s duration

Modified Duration and Bond Price Volatility An adjusted measure of duration can be used to approximate the price volatility of a bond Where: m = number of payments a year YTM = nominal YTM

Duration and Bond Price Volatility Bond price movements will vary proportionally with modified duration for small changes in yields An estimate of the percentage change in bond prices equals the change in yield time modified duration Where:  P = change in price for the bond P = beginning price for the bond D mod = the modified duration of the bond  i = yield change in basis points divided by 100

Trading Strategies Using Duration Longest-duration security provides the maximum price variation If you expect a decline in interest rates, increase the average duration of your bond portfolio to experience maximum price volatility If you expect an increase in interest rates, reduce the average duration to minimize your price decline Note that the duration of your portfolio is the market-value-weighted average of the duration of the individual bonds in the portfolio

Matched-Funding Techniques Immunization Strategies –A portfolio manager (after client consultation) may decide that the optimal strategy is to immunize the portfolio from interest rate changes –The immunization techniques attempt to derive a specified rate of return during a given investment horizon regardless of what happens to market interest rates

Immunization Strategies Components of Interest Rate Risk – Price Risk – Coupon Reinvestment Risk

Classical Immunization Immunization is neither a simple nor a passive strategy An immunized portfolio requires frequent rebalancing because the modified duration of the portfolio always should be equal to the remaining time horizon (except in the case of the zero-coupon bond)

Classical Immunization Duration characteristics –Duration declines more slowly than term to maturity, assuming no change in market interest rates –Duration changes with a change in market interest rates –There is not always a parallel shift of the yield curve –Bonds with a specific duration may not be available at an acceptable price