Financial Markets and Institutions PowerPoint Slides for: Financial Markets and Institutions By Jeff Madura

Bond Valuation and Risk 8

Chapter Objectives Demonstrate how bond market prices are established and influenced by interest rate movements Identify the factors that affect bond prices Explain how the sensitivity of bond prices to interest rates is dependent on particular bond characteristics Explain the benefits of diversifying the bond portfolio internationally

Bond Valuation Process Bonds are debt obligations with long-term maturities issued by governments or corporations to obtain long-term funds Commonly purchased by financial institutions that wish to invest funds for long-term periods Bond price (value) = present value of cash flows to be generated by the bond

Bond Valuation Process Impact of the Discount Rate on Bond Valuation Discount rate = market-determined yield that could be earned on alternative investments of similar risk and maturity Bond prices vary inversely with changes in market interest rates Cash flows are contractual and remain the same each period Bond prices vary to provide the new owner the market rate of return

Bond Risks and Prices Higher risk Higher discount rates Lower bond prices Lower risk Lower discount rates Higher bond prices Note Inverse Relationship Between Risk, required returns and Bond Prices

Bond Valuation Process Bond Price = present value of cash flows discounted at the market required rate of return C = Coupon per period (PMT) Par = Face or maturity value (FV) i = Discount rate (i) n = Compounding periods to maturity C C C + Par + + … PV = (1+ i)1 (1+ i)2 (1+ i)n

Bond Valuation Process Consider a $1000, 10% coupon (paid annually) bond that has three years remaining to maturity. Assume the prevailing annualized yield on other bonds with similar risk is 12 percent. Calculate the bond’s value. The expected cash flows of a coupon bond includes periodic interest payments, and… A final $1000 payoff at maturity Discounted at the market rate of return of 12%

Bond Valuation Process PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3 = $951.97 N I PV PMT FV 3 12 ? 100 1000

Bond Valuation Process PV = $100/(1+.12)1 + $100/(1+.12)2 + $1100/(1+.12)3 = $951.97 N I PV PMT FV 3 12 –951.97 100 1000

Bond Valuation Process Valuation of Bonds with Semiannual Payments Most bonds pay interest semiannually Double the number of compounding periods (N) and halve the annual coupon amount (PMT) and the discount rate (I)

Re-work the above problem assuming semiannual compounding PV PMT FV 6 ? 50 1000

Re-work the above problem assuming semiannual compounding PV PMT FV 6 950.82 50 1000

Relationships Between Coupon Rate, Required Return, and Bond Price No periodic coupon Pays face value at maturity Trade at discount from face value No reinvestment risk Considerable price risk Zero-Coupon Bonds

Relationships Between Coupon Rate, Required Return, and Bond Price Discount bonds are bonds priced below face value; premium bonds above face value Discounted bond Coupon < Market rates Rates have increased since issuance Adverse risks factors that may have occurred Price risk—depends on maturity Default risk may have increased Fisher effect of higher expected inflation

Relationships Between Coupon Rate, Required Return, and Bond Price Premium bond Coupon > Market Rates decreased since issuance Favorable risk experience Price risk—depends on maturity Default risk might have decreased as economic activity has increased Low inflation expectations

Relationships Between Coupon Rate, Required Return, and Bond Price Long-term bond prices are more sensitive to given changes in market rates than short-term bonds Changes in rates compounded many times for later coupon and maturity value, impacting price (PV) significantly Short-term securities have smaller price movements Bond Maturity and Price Variability

a a Exhibit 8.4 20-Y ear Bond 10-Y ear Bond 5-Y ear Bond 1,800 1,600 20-Y ear Bond 1,400 10-Y ear Bond 1,200 5-Y ear Bond 1,000 800 600 400 200 5 8 10 12 15 20 Required Return (Percent)

Relationships Between Coupon Rate, Required Return, and Bond Price Low coupon bond prices more sensitive to change in interest rates PV of face value at maturity a major proportion of the price Coupon Rates and Price Variability

Explaining Bond Price Movements The price of a bond should reflect the present value of future cash flows discounted at a required rate of return The required return on a bond is primarily determined by Prevailing risk-free rate Risk premium

Explaining Bond Price Movements Factors that affect the risk-free rate Changes in returns on real investment Financial investment an alternative to real investment Opportunity cost of financial investment is the returns available from real investment Federal Government deficits/surplus position Inflationary expectations Consumer price index Federal Reserve monetary policy position Oil prices and other commodity prices Exchange rate movements

Explaining Bond Price Movements Factors that affect the credit or default risk premium Strong economic growth High level of cash flows Investors bid up bond prices; lower default premium Weak economic growth Lower profits and cash flows Impact on specific industries varied Investors flee from risky bonds to Treasury bonds Bond prices fall; default premiums increase

Exhibit 8.8 a U.S. Fiscal Policy U.S. Monetary Policy U.S. Economic Conditions Issuer’s Industry Conditions Issuer’s Unique Conditions Long-T erm Risk-Free Interest Rate (T reasury Bond Rate) Risk Premium of Issuer Required Return on the Bond Bond Price

Sensitivity of Bond Prices to Interest Rate Movements Bond Price Elasticity = Bond price sensitivity for any % change in market interest rates Bond Price Elasticity = (% Change In Price)/(% Change In Interest Rates) Increased elasticity means greater price risk

Sensitivity of Bond Prices to Interest Rate Movements Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. First, calculate the price of the bond for both rates When k = 10%, PV = ? When k = 8%, PV = ? Hint: Remember zero-coupon or no PMT in this calculation The price of a zero-coupon bond is the present value of a single future value cash flow.

Sensitivity of Bond Prices to Interest Rate Movements Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. First, calculate the price of the bond for both rates When k = 10%, PV = $386 When k = 8%, PV = $463

Sensitivity of Bond Prices to Interest Rate Movements Calculate the bond elasticity: Bond elasticity or price sensitivity to changes in interest rates approaches the limit at –1 for zero-coupon bonds. Price sensitivity is lower for coupon bonds. The inverse relationship between k and p causes the negative numbers

Sensitivity of Bond Prices to Interest Rate Movements Price-Sensitive Bonds Longer maturity—more price variation for a change in interest rates Lower coupon rate bonds are more price sensitive (the PV is a greater % of current value) Zero-coupon bonds most sensitive, approaching –1 price elasticity Greater for declining rates than for increasing rates

Sensitivity of Bond Prices to Interest Rate Movements Measure of bond price sensitivity Measures the life of bond on a PV basis Duration = Sum of discounted, time-weighted cash flows divided by price Duration

Sensitivity of Bond Prices to Interest Rate Movements The longer a bond’s duration, the greater its sensitivity to interest rate changes The duration of a zero-coupon bond = bond’s term to maturity The duration of any coupon bond is always less than the bond’s term to maturity Duration

Sensitivity of Bond Prices to Interest Rate Movements Modified duration is an easily calculated approximate of the duration measure DUR* is a linear approximation of DUR which measures the convex relationship between bond yields and prices

Bond Investment Strategies Used by Investors Create bond portfolio that will generate income that will match their expected periodic expenses Used to provide retirement income from savings accumulation Estimate cash flow needs then select bond portfolio that will generate needed income Matching Strategy

Bond Investment Strategies Used by Investors Funds are allocated evenly to bonds in several different maturity classes Example: ¼ funds invested in bonds with 5 years until maturity, ¼ in10-year bonds, ¼ in 15-year bonds, and ¼ in 20-year bonds Investor receives average return of yield curve over time as maturing bonds are reinvested Laddered Strategy

Bond Investment Strategies Used by Investors Allocated funds to short-term bonds and long-term bonds Short-term bonds provide liquidity from maturity Long-term bonds provide higher yield (assuming up-sloping yield curve) Barbell Strategy

Bond Investment Strategies Used by Investors Funds are allocated in a manner that capitalizes on interest rate forecasts Example: if rates are expected to decline, move into longer-term bonds Problems: High transaction costs because of higher trading Difficulty in forecasting interest rates Interest Rate Strategy

Foreign Exchange Rates and Interest Rates Country interest rate differences reflect expected future spot foreign exchange rates Expected future spot foreign exchange rates (forward forex rates) reflect expected inflation differences between countries Expected return on foreign bond portfolio related to return on bonds adjusted for expected changes in forex rates

Diversifying Bonds Internationally Investor may diversify by: Credit risk Country risk Foreign exchange risk Interest rate risk Seek lower total variability of returns per level of risk assumed