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## Chapter 12 Bond Selection

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**Malkiel’s Interest Rate Theorems**• Definition • Theorem 1 • Theorem 2 • Theorem 3 • Theorem 4 • Theorem 5**Definition**• Malkiel’s interest rate theorems provide information about how bond prices change as interest rates change • Any good portfolio manager knows Malkiel’s theorems**Theorem 1**• Bond prices move inversely with yields: • If interest rates rise, the price of an existing bond declines • If interest rates decline, the price of an existing bond increases**Theorem 2**• Bonds with longer maturities will fluctuate more if interest rates change • Long-term bonds have more interest rate risk**Theorem 3**• Higher coupon bonds have less interest rate risk • Money in hand is a sure thing while the present value of an anticipated future receipt is risky**Theorem 4**• When comparing two bonds, the relative importance of Theorem 2 diminishes as the maturities of the two bonds increase • A given time difference in maturities is more important with shorter-term bonds**Theorem 5**• Capital gains from an interest rate decline exceed the capital loss from an equivalent interest rate increase**Duration as A Measure of Interest Rate Risk**• The concept of duration • Calculating duration**The Concept of Duration**• For a noncallable security: • Duration is the weighted average number of years necessary to recover the initial cost of the bond • Where the weights reflect the time value of money**The Concept of Duration (cont’d)**• Duration is a direct measure of interest rate risk: • The higher the duration, the higher the interest rate risk**Calculating Duration**• The traditional duration calculation:**Calculating Duration (cont’d)**• The closed-end formula for duration:**Calculating Duration (cont’d)**Example Consider a bond that pays $100 annual interest and has a remaining life of 15 years. The bond currently sells for $985 and has a yield to maturity of 10.20%. What is this bond’s duration?**Calculating Duration (cont’d)**Example (cont’d) Solution: Using the closed-form formula for duration:**Bond Selection - Introduction**• In most respects selecting the fixed-income components of a portfolio is easier than selecting equity securities • There are ways to make mistakes with bond selection**The Meaning of Bond Diversification**• Introduction • Default risk • Dealing with the yield curve • Bond betas**Introduction**• It is important to diversify a bond portfolio • Diversification of a bond portfolio is different from diversification of an equity portfolio • Two types of risk are important: • Default risk • Interest rate risk**Default Risk**• Default risk refers to the likelihood that a firm will be unable to repay the principal and interest of a loan as agreed in the bond indenture • Equivalent to credit risk for consumers • Rating agencies such as S&P and Moody’s function as credit bureaus for credit issuers**Default Risk (cont’d)**• To diversify default risk: • Purchase bonds from a number of different issuers • Do not purchase various bond issues from a single issuer • E.g., Enron had 20 bond issues when it went bankrupt**Dealing With the Yield Curve**• The yield curve is typically upward sloping • The longer a fixed-income security has until maturity, the higher the return it will have to compensate investors • The longer the average duration of a fund, the higher its expected return and the higher its interest rate risk**Dealing With the Yield Curve (cont’d)**• The client and portfolio manager need to determine the appropriate level of interest rate risk of a portfolio**Bond Betas**• The concept of bond betas: • States that the market prices a bond according to its level of risk relative to the market average • Has never become fully accepted • Measures systematic risk, while default risk and interest rate risk are more important**Choosing Bonds**• Client psychology and bonds selling at a premium • Call risk • Constraints**Client Psychology and Bonds Selling at A Premium**• Premium bonds held to maturity are expected to pay higher coupon rates than the market rate of interest • Premium bond held to maturity will decline in value toward par value as the bond moves towards its maturity date**Client Psychology & Bonds Selling at A Premium (cont’d)**• Clients may not want to buy something they know will decline in value • There is nothing wrong with buying bonds selling at a premium**Call Risk**• If a bond is called: • The funds must be reinvested • The fund manager runs the risk of having to make adjustments to many portfolios all at one time • There is no reason to exclude callable bonds categorically from a portfolio • Avoid making extensive use of a single callable bond issue**Constraints**• Specifying return • Specifying grade • Specifying average maturity • Periodic income • Maturity timing • Socially responsible investing**Specifying Return**• To increase the expected return on a bond portfolio: • Choose bonds with lower ratings • Choose bonds with longer maturities • Or both**Specifying Grade**• A legal list specifies securities that are eligible investments • E.g., investment grade only • Portfolio managers take the added risk of noninvestment grade bonds only if the yield pickup is substantial**Specifying Grade (cont’d)**• Conservative organizations will accept only U.S. government or AAA-rated corporate bonds • A fund may be limited to no more than a certain percentage of non-AAA bonds**Specifying Average Maturity**• Average maturity is a common bond portfolio constraint • The motivation is concern about rising interest rates • Specifying average duration would be an alternative approach**Periodic Income**• Some funds have periodic income needs that allow little or not flexibility • Clients will want to receive interest checks frequently • The portfolio manager should carefully select the bonds in the portfolio**Maturity Timing**• Maturity timing generates income as needed • Sometimes a manager needs to construct a bond portfolio that matches a particular investment horizon • E.g., assemble securities to fund a specific set of payment obligations over the next ten years • Assemble a portfolio that generates income and principal repayments to satisfy the income needs**Socially Responsible Investing**• Some clients will ask that certain types of companies not be included in the portfolio • Examples are nuclear power, military hardware, “vice” products**Example: Monthly Retirement Income**• The problem • Unspecified constraints • Using S&P’s Bond Guide • Solving the problem**The Problem**• A client has: • Primary objective: growth of income • Secondary objective: income • $1,100,000 to invest • Inviolable income needs of $4,000 per month**The Problem (cont’d)**• You decide: • To invest the funds 50-50 between common stocks and debt securities • To invest in ten common stock in the equity portion (see next slide) • You incur $1,500 in brokerage commissions**The Problem (cont’d)**• Characteristics of the fund: • Quarterly dividends total $3,001 ($12,004 annually) • The dividend yield on the equity portfolio is 2.44% • Total annual income required is $48,000 or 4.36% of fund • Bonds need to have a current yield of at least 6.28%**Unspecified Constraints**• The task is meeting the minimum required expected return with the least possible risk • You don’t want to choose CC-rated bonds • You don’t want the longest maturity bonds you can find**Using S&P’s Bond Guide**• Figure 11-4 is an excerpt from the Bond Guide: • Indicates interest payment dates, coupon rates, and issuer • Provides S&P ratings • Provides current price, current yield**Solving the Problem**• Setup • Dealing with accrued interest and commissions • Choosing the bonds • Overspending • What about convertible bonds?**Setup**• You have two constraints: • Include only bonds rated BBB or higher • Keep the average maturities below fifteen years • Set up a worksheet that enables you to pick bonds to generate exactly $4,000 per month (see next slide)