Power Point Slides for Financial Markets and Institutions

Power. Point Slides for: Financial Markets and Institutions 6 th Edition By Jeff Madura Prepared by David R. Durst The University of Akron

CHAPTER 8 Bond Valuation and Risk

Chapter Objectives Demonstrate how bond market prices are established and influenced by interest rate movements n Identify the factors that affect bond prices n Explain how the sensitivity of bond prices to interest rates is dependent on particular bond characteristics n Explain the benefits of diversifying the bond portfolio internationally n Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Valuation Process Bonds are debt obligations with long-term maturities issued by governments or corporations to obtain long-term funds n Commonly purchased by financial institutions that wish to invest funds for long-term periods n Bond price (value) = present value of cash flows to be generated by the bond n Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Valuation Process n 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 l Bond prices vary inversely with changes in market interest rates l u. Cash flows are contractual and remain the same each period u. Bond prices vary to provide the new owner the market rate of return Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Risks and Prices Higher risk n Higher discount rates n Lower bond prices n Lower risk n Lower discount rates n Higher bond prices n Note Inverse Relationship Between Risk, required returns and Bond Prices Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Valuation Process l Bond Price = present value of cash flows discounted at the market required rate of return u. C = Coupon period (PMT) u. Par = Face or maturity value (FV) u i = Discount rate (i) u n = Compounding periods to maturity C + PV = (1+ i)1 C + Par C +… (1+ i)2 (1+ i)n Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Valuation Process n 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… l A final $1000 payoff at maturity l Discounted at the market rate of return of 12% l Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Valuation Process PV = $100/(1+. 12)1 + $100/(1+. 12)2 + $1100/(1+. 12)3 = $951. 97 N I PV 3 12 ? PMT FV 1000 Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Valuation Process PV = $100/(1+. 12)1 + $100/(1+. 12)2 + $1100/(1+. 12)3 = $951. 97 N I 3 12 PV PMT FV – 951. 97 1000 Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Valuation Process n Valuation of Bonds with Semiannual Payments Most bonds pay interest semiannually l Double the number of compounding periods (N) and halve the annual coupon amount (PMT) and the discount rate (I) l Copyright© 2002 Thomson Publishing. All rights reserved.

n Re-work the above problem assuming semiannual compounding N I PV PMT FV 6 6 ? 50 1000 Copyright© 2002 Thomson Publishing. All rights reserved.

n Re-work the above problem assuming semiannual compounding N I PV PMT FV 6 6 950. 82 50 1000 Copyright© 2002 Thomson Publishing. All rights reserved.

Relationships Between Coupon Rate, Required Return, and Bond Price Zero-Coupon Bonds No periodic coupon l Pays face value at maturity l Trade at discount from face value l No reinvestment risk l Considerable price risk l Copyright© 2002 Thomson Publishing. All rights reserved.

Relationships Between Coupon Rate, Required Return, and Bond Price Discount bonds are bonds priced below face value; premium bonds above face value n Discounted bond n Coupon < Market rates l Rates have increased since issuance l Adverse risks factors that may have occurred l u. Price risk—depends on maturity u. Default risk may have increased u. Fisher effect of higher expected inflation Copyright© 2002 Thomson Publishing. All rights reserved.

Relationships Between Coupon Rate, Required Return, and Bond Price n Premium bond Coupon > Market l Rates decreased since issuance l Favorable risk experience l u. Price risk—depends on maturity u. Default risk might have decreased as economic activity has increased u. Low inflation expectations Copyright© 2002 Thomson Publishing. All rights reserved.

Relationships Between Coupon Rate, Required Return, and Bond Price Bond Maturity and Price Variability Long-term bond prices are more sensitive to given changes in market rates than short-term bonds l Changes in rates compounded many times for later coupon and maturity value, impacting price (PV) significantly l Short-term securities have smaller price movements l Copyright© 2002 Thomson Publishing. All rights reserved.

Exhibit 8. 4 1, 800 1, 600 1, 400 1, 200 1, 000 5 -Year Bond 10 -Year Bond 20 -Year Bond 800 600 400 200 0 0 5 8 10 12 15 20 Required Return (Percent) Copyright© 2002 Thomson Publishing. All rights reserved.

Relationships Between Coupon Rate, Required Return, and Bond Price Coupon Rates and Price Variability Low coupon bond prices more sensitive to change in interest rates l PV of face value at maturity a major proportion of the price l Copyright© 2002 Thomson Publishing. All rights reserved.

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 n The required return on a bond is primarily determined by n Prevailing risk-free rate l Risk premium l Copyright© 2002 Thomson Publishing. All rights reserved.

Explaining Bond Price Movements n Factors that affect the risk-free rate l Changes in returns on real investment u. Financial investment an alternative to real investment u. Opportunity cost of financial investment is the returns available from real investment u. Federal Government deficits/surplus position l Inflationary expectations u. Consumer price index u. Federal Reserve monetary policy position u. Oil prices and other commodity prices u. Exchange rate movements Copyright© 2002 Thomson Publishing. All rights reserved.

Explaining Bond Price Movements n Factors that affect the credit or default risk premium l Strong economic growth u. High level of cash flows u. Investors bid up bond prices; lower default premium l Weak economic growth u. Lower profits and cash flows u. Impact on specific industries varied u. Investors flee from risky bonds to Treasury bonds u. Bond prices fall; default premiums increase Copyright© 2002 Thomson Publishing. All rights reserved.

Exhibit 8. 8 U. S. Fiscal Policy U. S. Monetary Policy U. S. Economic Conditions Long-Term Risk-Free Interest Rate (Treasury Bond Rate) Issuer’s Industry Conditions Issuer’s Unique Conditions Risk Premium of Issuer Required Return on the Bond Price Copyright© 2002 Thomson Publishing. All rights reserved.

Sensitivity of Bond Prices to Interest Rate Movements Bond Price Elasticity = Bond price sensitivity for any % change in market interest rates n Bond Price Elasticity = n (% Change In Price)/(% Change In Interest Rates) n Increased elasticity means greater price risk Copyright© 2002 Thomson Publishing. All rights reserved.

Sensitivity of Bond Prices to Interest Rate Movements n Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. l First, calculate the price of the bond for both rates u. When k = 10%, PV = ? u. When k = 8%, PV = ? u. Hint: Remember zero-coupon or no PMT in this calculation u. The price of a zero-coupon bond is the present value of a single future value cash flow. Copyright© 2002 Thomson Publishing. All rights reserved.

Sensitivity of Bond Prices to Interest Rate Movements n Calculate the price sensitivity of a zero-coupon bond with 10 years until maturity if interest rates go from 10% to 8%. l First, calculate the price of the bond for both rates u. When k = 10%, PV = $386 u. When k = 8%, PV = $463 Copyright© 2002 Thomson Publishing. All rights reserved.

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 Copyright© 2002 Thomson Publishing. All rights reserved.

Sensitivity of Bond Prices to Interest Rate Movements n Price-Sensitive Bonds Longer maturity—more price variation for a change in interest rates l Lower coupon rate bonds are more price sensitive (the PV is a greater % of current value) l Zero-coupon bonds most sensitive, approaching – 1 price elasticity l Greater for declining rates than for increasing rates l Copyright© 2002 Thomson Publishing. All rights reserved.

Sensitivity of Bond Prices to Interest Rate Movements Duration Measure of bond price sensitivity l Measures the life of bond on a PV basis l Duration = Sum of discounted, time-weighted cash flows divided by price l Copyright© 2002 Thomson Publishing. All rights reserved.

Sensitivity of Bond Prices to Interest Rate Movements Duration The longer a bond’s duration, the greater its sensitivity to interest rate changes l The duration of a zero-coupon bond = bond’s term to maturity l The duration of any coupon bond is always less than the bond’s term to maturity l Copyright© 2002 Thomson Publishing. All rights reserved.

Sensitivity of Bond Prices to Interest Rate Movements n 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 Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Investment Strategies Used by Investors Matching Strategy Create bond portfolio that will generate income that will match their expected periodic expenses l Used to provide retirement income from savings accumulation l Estimate cash flow needs then select bond portfolio that will generate needed income l Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Investment Strategies Used by Investors Laddered Strategy Funds are allocated evenly to bonds in several different maturity classes l Example: ¼ funds invested in bonds with 5 years until maturity, ¼ in 10 -year bonds, ¼ in 15 -year bonds, and ¼ in 20 -year bonds l Investor receives average return of yield curve over time as maturing bonds are reinvested l Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Investment Strategies Used by Investors Barbell Strategy Allocated funds to short-term bonds and long-term bonds l Short-term bonds provide liquidity from maturity l Long-term bonds provide higher yield (assuming up-sloping yield curve) l Copyright© 2002 Thomson Publishing. All rights reserved.

Bond Investment Strategies Used by Investors Interest Rate Strategy Funds are allocated in a manner that capitalizes on interest rate forecasts l Example: if rates are expected to decline, move into longer-term bonds l Problems: l u. High transaction costs because of higher trading u. Difficulty in forecasting interest rates Copyright© 2002 Thomson Publishing. All rights reserved.

Foreign Exchange Rates and Interest Rates Country interest rate differences reflect expected future spot foreign exchange rates n Expected future spot foreign exchange rates (forward forex rates) reflect expected inflation differences between countries n Expected return on foreign bond portfolio related to return on bonds adjusted for expected changes in forex rates n Copyright© 2002 Thomson Publishing. All rights reserved.

Diversifying Bonds Internationally n Investor may diversify by: Credit risk l Country risk l Foreign exchange risk l Interest rate risk l n Seek lower total variability of returns per level of risk assumed Copyright© 2002 Thomson Publishing. All rights reserved.