Financial Transaction
8 Bond Valuation and Risk
CHAPTER OBJECTIVES
The specific objectives of this chapter are to:
· ▪ explain how bonds are priced,
· ▪ identify the factors that affect bond prices,
· ▪ explain how the sensitivity of bond prices to interest rates depends on particular bond characteristics,
· ▪ describe common strategies used to invest in bonds, and
· ▪ explain the valuation and risk of international bonds.
The values of bonds can change substantially over time. Hence, financial institutions that consider buying or selling bonds closely monitor their values.
8-1 BOND VALUATION PROCESS
Bonds are debt obligations with long-term maturities that are commonly issued by governments or corporations to obtain long-term funds. They are also purchased by financial institutions that wish to invest funds for long-term periods.
Bond valuation is conceptually similar to the valuation of capital budgeting projects, businesses, or even real estate. The appropriate price reflects the present value of the cash flows to be generated by the bond in the form of periodic interest (or coupon) payments and the principal payment to be provided at maturity. The coupon payment is based on the coupon rate multiplied by the par value of the bond. Thus a bond with a 9 percent coupon rate and $1,000 par value pays $90 in coupon payments per year. Because these expected cash flows are known, the valuation of bonds is generally perceived to be easier than the valuation of equity securities.
The current price of a bond should be the present value ( PV) of its remaining cash flows:
EXAMPLE
Consider a bond that has a par value of $1,000, pays $100 at the end of each year in coupon payments, and has three years remaining until maturity. Assume that the prevailing annualized yield on other bonds with similar characteristics is 12 percent. In this case, the appropriate price of the bond can be determined as follows. The future cash flows to investors who would purchase this bond are $100 in Year 1, $100 in Year 2, and $1,100 (computed as $100 in coupon payments plus $1,000 par value) in Year 3. The appropriate market price of the bond is its present value:
Exhibit 8.1 Valuation of a Three-Year Bond
This valuation procedure is illustrated in Exhibit 8.1 . Because this example assumes that investors require a 12 percent return, k is set equal to 0.12. At the price of $951.97, the bondholders purchasing this bond will receive a 12 percent annualized return.
WEB
More information on the process of valuing bonds.
When using a financial calculator, the present value of the bond in the previous example can be determined as follows:
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3 |
12 |
100 |
1000 |
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N |
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PMT |
FV |
CPT |
PV |
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Answer |
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951.97 |
8-1a Impact of the Discount Rate on Bond Valuation
The discount rate selected to compute the present value is critical to accurate valuation. Exhibit 8.2 shows the wide range of present value resulting at different discount rates for a $10,000 payment in 10 years. The appropriate discount rate for valuing any asset is the yield that could be earned on alternative investments with similar risk and maturity.
Exhibit 8.2 Relationship between Discount Rate and Present Value of $10,000 Payment to Be Received in 10 Years
Since investors require higher returns on riskier securities, they use higher discount rates to discount the future cash flows of these securities. Consequently, a high-risk security will have a lower value than a low-risk security even though both securities have the same expected cash flows.
8-1b Impact of the Timing of Payments on Bond Valuation
The market price of a bond is also affected by the timing of the payments made to bondholders. Funds received sooner can be reinvested to earn additional returns. Thus, a dollar to be received soon has a higher present value than one to be received later. The impact of maturity on the present value of a $10,000 payment is shown in Exhibit 8.3 (assuming that a return of 10 percent could be earned on available funds). The $10,000 payment has a present value of $8,264 if it is to be paid in two years. This implies that if $8,264 were invested today and earned 10 percent annually, it would be worth $10,000 in two years. Exhibit 8.3 also shows that a $10,000 payment made 20 years from now has a present value of only $1,486 and that a $10,000 payment made 50 years from now has a present value of only $85 (based on the 10 percent discount rate).
8-1c Valuation of Bonds with Semiannual Payments
In reality, most bonds have semiannual payments. The present value of such bonds can be computed as follows. First, the annualized coupon should be split in half because two payments are made per year. Second, the annual discount rate should be divided by 2 to reflect two six-month periods per year. Third, the number of periods should be doubled to reflect 2 times the number of annual periods. After these adjustments are incorporated, the present value is determined as follows:
Here C/2 is the semiannual coupon payment (half of what the annual coupon payment would have been), and k/2 is the periodic discount rate used to discount the bond. The last part of the equation has 2 n in the denominator's exponent to reflect the doubling of periods.
Exhibit 8.3 Relationship between Time of Payment and Present Value of Payment
EXAMPLE
As an example of the valuation of a bond with semiannual payments, consider a bond with $1,000 par value, a 10 percent coupon rate paid semiannually, and three years to maturity. Assuming a 12 percent required return, the present value is computed as follows:
When using a financial calculator, the present value of the bond in the previous example can be determined as follows: 1
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6 |
6 |
50 |
1000 |
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N |
I |
PMT |
FV |
CPT |
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950.82 |
The remaining examples assume annual coupon payments so that we can focus on the concepts presented without concern about adjusting annual payments.
8-1d Relationships between Coupon Rate, Required Return, and Bond Price
Bonds that sell at a price below their par value are called discount bonds. The larger the investor's required rate of return relative to the coupon rate, the larger the discount of a bond with a particular par value.
EXAMPLE
Consider a zero-coupon bond (which has no coupon payments) with three years remaining to maturity and $1,000 par value. Assume the investor's required rate of return on the bond is 13 percent. The appropriate price of this bond can be determined by the present value of its future cash flows:
The very low price of this bond is necessary to generate a 13 percent annualized return to investors. If the bond offered coupon payments, the price would have been higher because those coupon payments would provide part of the return required by investors.
Now consider another bond with a similar par value and maturity that offers a 13 percent coupon rate. The appropriate price of this bond would be
Observe that the price of this bond is exactly equal to its par value. This is because the entire compensation required by investors is provided by the coupon payments.
Exhibit 8.4 Relationship between Required Return and Present Value for a 10 Percent Coupon Bond with Various Maturities
Finally, consider a bond with a similar par value and term to maturity and coupon rate that offers a coupon rate of 15 percent, which is above the investor's required rate of return. The appropriate price of this bond, as determined by its present value, is
The price of this bond exceeds its par value because the coupon payments are large enough to offset the high price paid for the bond and still provide a 13 percent annualized return.
WEB
Calculates bond returns and yields.
From the examples provided, the following relationships should now be clear. First, if the coupon rate of a bond is below the investor's required rate of return, the present value of the bond (and therefore the price of the bond) should be below the par value. Second, if the coupon rate equals the investor's required rate of return, the price of the bond should be the same as the par value. Finally, if the coupon rate of a bond is above the investor's required rate of return, the price of the bond should be above the par value. These relationships are shown in Exhibit 8.4 for a bond with a 10 percent coupon and a par value of $1,000. If investors require a return of 5 percent and desire a 10-year maturity, they will be willing to pay $1,390 for this bond. If they require a return of 10 percent on this same bond, they will be willing to pay $1,000. If they require a 15 percent return, they will be willing to pay only $745. The relationships described here hold for any bond, regardless of its maturity.
8-2 EXPLAINING BOND PRICE MOVEMENTS
As explained earlier, the price of a bond should reflect the present value of future cash flows (coupon payments and the par value), based on a required rate of return ( k), so that
Δ Pb = f(Δk)
Since the required rate of return on a bond is primarily determined by the prevailing risk-free rate ( Rf), which is the yield on a Treasury bond with the same maturity, and the credit risk premium (RP) on the bond, it follows that the general price movements of bonds can be modeled as
Δ Pb = f(Δ Rf, ΔRP)
Notice how the bond price is affected by a change in either the risk-free rate or the risk premium. An increase in the risk-free rate on bonds results in a higher required rate of return on bonds and therefore causes bond prices to decrease. Thus bond prices are exposed to interest rate risk , or the risk that their market value will decline in response to a rise in interest rates. Bonds are also exposed to credit risk: an increase in the credit (default) risk premium also causes investors to require a higher rate of return on bonds and therefore causes bond prices to decrease.
The factors that affect the risk-free rate or default risk premiums, and therefore affect bond prices, are identified next.
WEB
http://research.stlouisfed.org/fred2
Assesses economic conditions that affect bond prices.
8-2a Factors That Affect the Risk-Free Rate
The long-term risk-free rate is driven by inflationary expectations (INF), economic growth (ECON), the money supply (MS), and the budget deficit (DEF):
The general relationships are summarized next.
Impact of Inflationary Expectations If the level of inflation is expected to increase, there will be upward pressure on interest rates (as explained in Chapter 2 ) and hence on the required rate of return on bonds. Conversely, a reduction in the expected level of inflation results in downward pressure on interest rates and thus on the required rate of return on bonds. Bond market participants closely monitor indicators of inflation, such as the consumer price index and the producer price index.
Inflationary expectations are partially dependent on oil prices, which affect the cost of energy and transportation. This is why bond portfolio managers must forecast oil prices and their potential impact on inflation in order to forecast interest rates. A forecast of lower oil prices results in expectations of lower interest rates, causing bond portfolio managers to purchase more bonds. A forecast of higher oil prices results in expectations of higher interest rates, causing bond portfolio managers to sell some of their holdings. The actions of bond portfolio managers change the supply of bonds for sale as well as the demand for bonds in the secondary market, which results in a new equilibrium price for the bonds.
Inflationary expectations are also partially dependent on exchange rate movements. Holding other things equal, inflationary expectations are likely to rise when a weaker dollar is expected because it will increase the prices of imported supplies. A weaker dollar also prices foreign competitors out of the market, allowing U.S. firms to increase their prices. Thus, U.S. interest rates are expected to rise and bond prices are expected to decrease when the dollar is expected to weaken. Foreign investors anticipating dollar depreciation are less willing to hold U.S. bonds because in that case the coupon payments will convert to less of their home currency. This could cause an immediate net sale of bonds, placing further downward pressure on bond prices.
Expectations of a strong dollar should have the opposite results. A stronger dollar reduces the prices paid for foreign supplies, thus lowering retail prices. In addition, because a stronger dollar makes the prices of foreign products more attractive, domestic firms must maintain low prices in order to compete. Consequently, expectations of a stronger dollar may encourage bond portfolio managers to purchase more bonds, which places upward pressure on bond prices.
Impact of Economic Growth Strong economic growth tends to generate upward pressure on interest rates (as explained in Chapter 2 ), while weak economic conditions put downward pressure on rates. Any signals about future economic conditions will affect expectations about future interest rate movements and cause bond markets to react immediately. For example, any economic announcements (such as measurements of economic growth or unemployment) that signal stronger than expected economic growth tend to reduce bond prices. Investors anticipate that interest rates will rise, causing a decline in bond prices. Therefore, they sell bonds, which places immediate downward pressure on bond prices.
Conversely, any economic announcements that signal a weaker than expected economy tend to increase bond prices because investors anticipate that interest rates will decrease and thereby cause bond prices to rise. Hence investors buy bonds, which places immediate upward pressure on bond prices. This explains why sudden news of a possible economic recession can cause the bond market to rally. When the credit crisis began in 2008, long-term interest rates declined, which resulted in higher Treasury bond prices.
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Calendar of upcoming announcements of economic conditions that may affect bond prices.
Bond market participants closely monitor economic indicators that may signal future changes in the strength of the economy, which signal changes in the risk-free interest rate and in the required return from investing in bonds. Some of the more closely monitored indicators of economic growth include employment, gross domestic product, retail sales, industrial production, and consumer confidence.
Impact of Money Supply Growth When the Federal Reserve increases money supply growth, two reactions are possible (as explained in Chapter 5 ). First, the increased money supply may result in an increased supply of loanable funds. If the demand schedule (demand curve) for loanable funds is not affected, the increased money supply should place downward pressure on interest rates, causing bond portfolio managers to expect an increase in bond prices and thus to purchase bonds based on such expectations.
In a high-inflation environment, however, bond portfolio managers may expect that the inflationary expectations will cause individuals and firms to borrow more now and spend more now before inflation occurs. In this case, the change in borrowing behavior can increase the demand for loanable funds (as a result of inflationary expectations), which would cause an increase in interest rates and lower bond prices. Such forecasts would encourage immediate sales of long-term bonds.
In response to the credit crisis, the Fed repeatedly increased money supply growth in order to reduce interest rates. At this time, economic growth was weak and inflation was low, and therefore did not counteract the Fed's actions. The Fed's goal was to reduce the cost of borrowing, and therefore encourage individuals and corporations to borrow and spend money. This resulted in a risk-free rate that was close to zero in 2012.
Impact of Budget Deficit As the annual budget deficit changes, so does the federal government's demand for loanable funds (as explained in Chapter 2). Increased borrowing by the Treasury can result in a higher required return on Treasury bonds. That is, the long-term risk-free rate rises, which results in lower prices on existing bonds with long terms remaining until maturity.
The higher budget deficit leads to the same expected outcome (when other factors are held constant) as higher inflationary expectations. In both cases, there is an increase in the amount of funds borrowed, which leads to higher interest rates. However, inflationary expectations result in more borrowing by individuals and firms, whereas an increased budget deficit results in more borrowing by the federal government.
8-2b Factors That Affect the Credit (Default) Risk Premium
The general level of credit risk on corporate or municipal bonds can change in response to a change in economic growth (ECON):
Δ RP = f (Δ ECON)
Strong economic growth tends to improve a firm's cash flows and reduce the probability that the firm will default on its debt payments. Conversely, weak economic conditions tend to reduce a firm's cash flows and increase the probability that it will default on its bonds. The credit risk premium is relatively low when economic growth is strong. When the economy is weak, however, the credit risk premium is higher: investors will provide credit in such periods only if they are compensated for the high degree of credit risk.
EXAMPLE
After the credit crisis began in 2008, the U.S. economy weakened and numerous U.S. companies defaulted on their bonds. In the most notable case, Lehman Brothers (a large securities firm) filed for bankruptcy and subsequently defaulted on bonds and other debt securities. As a result of the defaults of Lehman Brothers and other firms, investors became more concerned about the credit risk of bonds that corporations issued. Many investors shifted their investments from corporate bonds to Treasury bonds because they wanted to avoid credit risk. Consequently, corporations that needed to borrow long-term funds at this time could issue new bonds only if they were willing to offer a relatively high credit risk premium to compensate investors.
Changes in the Credit Risk Premium over Time As economic conditions change over time, the probability of default on bonds changes, along with credit (default) risk premiums. Exhibit 8.5 compares yields on Baa-rated corporate bonds and Treasury bonds over time. The yields among securities are highly correlated. Notice that the difference between the corporate and Treasury bond yields (which can be used to measure the credit risk premium) widened during periods when the economy was weak, such as during the 2008–2009 credit crisis when investors required a higher credit risk premium. When the credit crisis intensified, the Federal Reserve used a stimulative monetary policy to reduce the risk-free interest rate across maturities. Thus the Treasury bond yield declined. However, the Baa-rated corporate bond yield increased during the crisis, because the increase in the risk premium on the prices of Baa-rated corporate bonds more than offset the impact of the reduction in the risk-free rate.
Impact of Debt Maturity on the Credit Risk Premium The credit risk premium tends to be larger for bonds that have longer terms to maturity. Consider an extreme example in which an existing bond issued by a corporation has only one month until maturity. If this corporation is in decent financial condition, it should be capable of completely repaying this debt, because conditions should not change drastically over the next month. However, other bonds issued by this same corporation with 15 years until maturity have a higher risk of default, because the corporation's ability to repay this debt is dependent on its performance over the next 15 years. Because economic conditions over the next 15 years are very uncertain, so is the corporation's performance and its ability to repay long-term debt.
Exhibit 8.5 Bond Risk Premium over Time
Impact of Issuer Characteristics on the Credit Risk Premium A bond's price can also be affected by factors specific to the issuer of the bond, such as a change in its capital structure. If a firm that issues bonds subsequently obtains additional loans, it may be less capable of making its coupon payments, thus its credit risk increases. Consequently, investors would now require a higher rate of return if they were to purchase those bonds in the secondary market, which would cause the market value (price) of the bonds to decrease.
8-2c Summary of Factors Affecting Bond Prices
When considering the factors that affect the risk-free rate and the risk premium, the general price movements in bonds can be modeled as follows:
WEB
Treasury note and bond auction results.
The relationships suggested here assume that other factors are held constant. Yet other factors are actually changing, too, which makes it difficult to disentangle the precise impact of each factor on bond prices. The effect of economic growth is uncertain: a high level of economic growth can adversely affect bond prices by raising the risk-free rate, but it can favorably affect bond prices by lowering the default risk premium. To the extent that international conditions affect each of the factors, they also influence bond prices.
Exhibit 8.6 summarizes the underlying forces that can affect the long-term, risk-free interest rate and the default risk premium and thereby cause the general level of bond prices to change over time. When pricing Treasury bonds, investors focus on the factors that affect the long-term, risk-free interest rate because the credit risk premium is not applicable. Thus, for a given maturity, the primary difference in the required return of a risky bond (such as a corporate bond) and a Treasury bond is the credit risk premium, which is influenced by economic and industry conditions.
Exhibit 8.6 Framework for Explaining Changes in Bond Prices over Time
If the bond market is efficient, then bond prices should fully reflect all available public information. Thus any new information about a firm that changes its perceived ability to repay its bonds could have an immediate effect on the price of the bonds.
8-2d Implications for Financial Institutions
Many financial institutions such as insurance companies, pension funds, and bond mutual funds maintain large holdings of bonds. The values of their bond portfolios are susceptible to changes in the factors, described in this section, that affect bond prices. Any factors that lead to higher interest rates tend to reduce the market values of financial institution assets and therefore reduce their valuations. Conversely, any factors that lead to lower interest rates tend to increase the market values of financial institution assets and therefore increase their valuations. Many financial institutions attempt to adjust the size of their bond portfolio according to their expectations about future interest rates. When they expect interest rates to rise, they sell bonds and use the proceeds to purchase short-term securities that are less sensitive to interest rate movements. If they anticipate that the risk premiums of risky bonds will increase, they shift toward relatively safe bonds that exhibit less credit risk.
Systemic Risk Financial institutions that participate in bond markets could be exposed to systemic risk , which refers to the potential collapse of the entire market or financial system (systemic risk should not be confused with “systematic risk,” discussed in Chapter 11 ). When specific conditions cause a higher risk-free rate and a very high risk premium, they adversely affect the prices of most bonds. Thus all financial institutions that heavily invest in bonds will experience poor performance under these conditions. Many financial institutions rely heavily on debt to fund their operations, and they are interconnected by virtue of financing each other's debt positions. If a financial institution cannot repay its debt, then this may create cash flow problems for the financial institutions from which it borrowed funds.
Some financial institutions use their investments in debt securities as collateral when borrowing funds (such as when using repurchase agreements, discussed in Chapter 6). But this collateral may no longer be acceptable during a credit crisis, because potential lenders may question whether the collateral is subject to default. Thus financial institutions that need new financing to repay other financial institutions may no longer be able to obtain new debt financing because the perceived value of their collateral has deteriorated.
There are various derivative securities (such as credit default swaps, described in Chapter 15 ) that can insure a creditor against the default of debt securities that they are holding. However, the counterparty in each of those positions serves as the insurer and may itself incur large losses (and potential bankruptcy) if the debt securities that it insures default. Thus, although these securities could protect some participants during a credit crisis, they can result in major losses for the counterparties. This may prevent those counterparty financial institutions from making timely debt payments to other financial institutions from whom they borrowed funds in the past.
In general, most financial institutions are connected by the relationships just described, and the credit crisis illustrated how adverse effects can spread among them. The Financial Reform Act of 2010 was intended to recognize and protect against systemic risk. It resulted in the creation of the Financial Stability Oversight Council, which consists of heads of agencies that oversee key participants in the debt markets and in the debt derivatives (insuring against debt default), including the housing industry, securities trading, depository institutions, mutual funds, and insurance companies. This council is responsible for identifying risks in the U.S. financial system and for making regulatory recommendations that could reduce such risks.
8-3 SENSITIVITY OF BOND PRICES TO INTEREST RATE MOVEMENTS
The sensitivity of a bond's price to interest rate movements is a function of the bond's characteristics. Investors can measure the sensitivity of their bonds' prices to interest rate movements, which will indicate the potential damage to their bond holdings in response to an increase in interest rates (and therefore in the required rate of return on bonds). Two common methods for assessing the sensitivity of bonds to a change in the required rate of return on bonds are (1) bond price elasticity and (2) duration. Each method is described in turn.
8-3a Bond Price Elasticity
The sensitivity of bond prices ( Pb) to changes in the required rate of return ( k) is commonly measured by the bond price elasticity (), which is estimated as
Exhibit 8.7 Sensitivity of 10-Year Bonds with Different Coupon Rates to Interest Rate Changes
Exhibit 8.7 compares the price sensitivity of 10-year bonds with $1,000 par value and four different coupon rates: 0 percent, 5 percent, 10 percent, and 15 percent. Initially, the required rate of return ( k) on the bonds is assumed to be 10 percent. The price of each bond is therefore the present value of its future cash flows, discounted at 10 percent. The initial price of each bond is shown in Column 2. The top panel shows the effect of a decline in interest rates that reduces the investor's required return to 8 percent. The prices of the bonds based on an 8 percent required return are shown in Column 3. The percentage change in the price of each bond resulting from the interest rate movements is shown in Column 4. The bottom panel shows the effect of an increase in interest rates that increases the investor's required return to 12 percent.
The price elasticity for each bond is estimated in Exhibit 8.7 according to the assumed change in the required rate of return. Notice in the exhibit that the price sensitivity of any particular bond is greater for declining interest rates than for rising interest rates. The bond price elasticity is negative in all cases, reflecting the inverse relationship between interest rate movements and bond price movements.
Influence of Coupon Rate on Bond Price Sensitivity A zero-coupon bond, which pays all of its proceeds to the investor at maturity, is most sensitive to changes in the required rate of return because the adjusted discount rate is applied to one lump sum in the distant future. Conversely, the price of a bond that pays all its yield in the form of coupon payments is less sensitive to changes in the required rate of return because the adjusted discount rate is applied to some payments that occur in the near future. The adjustment in the present value of such payments in the near future due to a change in the required rate of return is not as pronounced as an adjustment in the present value of payments in the distant future.
Exhibit 8.7 confirms that the prices of zero- or low-coupon bonds are more sensitive to changes in the required rate of return than prices of bonds with relatively high coupon rates. The exhibit shows that, when the required rate of return declines from 10 percent to 8 percent, the price of the zero-coupon bonds rises from $386 to $463. Thus the bond price elasticity is
This implies that, for each 1 percent change in interest rates, zero-coupon bonds change by 0.995 percent in the opposite direction. Column 6 in Exhibit 8.7 shows that the price elasticities of the higher-coupon bonds are considerably lower than the price elasticity of the zero-coupon bond.
Financial institutions commonly restructure their bond portfolios to contain higher-coupon bonds when they are more concerned about a possible increase in interest rates (and therefore an increase in the required rate of return). Conversely, they restructure their portfolios to contain low- or zero-coupon bonds when they expect a decline in interest rates and wish to capitalize on their expectations by holding bonds that are price-sensitive.
Influence of Maturity on Bond Price Sensitivity As interest rates (and therefore required rates of return) decrease, long-term bond prices (as measured by their present value) increase by a greater degree than short-term bond prices because the long-term bonds will continue to offer the same coupon rate over a longer period of time than the short-term bonds. Of course, if interest rates increase, prices of the long-term bonds will decline by a greater degree.
8-3b Duration
An alternative measure of bond price sensitivity is the bond's duration, which is a measurement of the life of the bond on a present value basis. The longer a bond's duration, the greater its sensitivity to interest rate changes. A commonly used measure of a bond's duration (DUR) is
WEB
Contains links to many different concepts about bonds, including duration.
where
· Ct = coupon or principal payment generated by the bond
· t = time at which the payments are provided
· k = bond's yield to maturity reflects investors' required rate of return)
The numerator of the duration formula represents the present value of future payments weighted by the time interval until the payments occur. The longer the intervals until payments are made, the larger the numerator and the larger the duration. The denominator of the duration formula represents the discounted future cash flows resulting from the bond, which is the present value of the bond.
EXAMPLE
The duration of a bond with $1,000 par value and a 7 percent coupon rate, three years remaining to maturity, and a 9 percent yield to maturity is calculated as
By comparison, the duration of a zero-coupon bond with a similar par value and yield to maturity is
The duration of a zero-coupon bond is always equal to the bond's term to maturity. The duration of any coupon bond is always Less than the bond's term to maturity because some of the payments occur at intervals prior to maturity.
Duration of a Portfolio Bond portfolio managers commonly attempt to immunize their portfolio—that is, to insulate it from the effects of interest rate movements. A first step in this process is to determine the sensitivity of their portfolio to such movements. Once the duration of each individual bond is measured, the bond portfolio's duration (DURp) can be estimated as
where
· m = number of bonds in the portfolio
· wj = bond j's market value as a percentage of the portfolio market value
· DURj = bond j's duration
In other words, the duration of a bond portfolio is the weighted average of bond durations weighted according to relative market value. Financial institutions concerned with interest rate risk may compare their asset duration to their liability duration. A positive difference means that the market value of the institution's assets is more rate-sensitive than the market value of its liabilities. Thus, during a period of rising interest rates, the market value of the assets would be reduced by a greater degree than that of the liabilities. The institution's real net worth (market value of net worth) would therefore decrease.
Modified Duration The duration measurement of a bond or a bond portfolio can be modified to estimate the impact of a change in the prevailing bond yields on bond prices. The modified duration (denoted as DUR*) is estimated as
DUR* =
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DUR |
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(1 + k) |
where k denotes the prevailing yield on bonds.
The modified duration can be used to estimate the percentage change in the bond's price in response to a 1 percentage point change in bond yields. For example, assume that Bond X has a duration of 8 years and Bond Y has a duration of 12 years. Assuming that the prevailing bond yield is 10 percent, the modified duration is estimated for each bond as follows:
Given the inverse relationship between the change in bond yields and the response in bond prices, the estimate of modified duration should be applied such that the bond price moves in the opposite direction from the change in bond yields. According to the modified duration estimates, a 1 percentage point increase in bond yields (from 10 percent to 11 percent) would lead to a 7.27 percent decline in the price of Bond X and to a 10.9 percent decline in the price of Bond Y. A 0.5 percentage point increase in yields (from 10 percent to 10.5 percent) would lead to a 3.635 percent decline in the price of Bond X (computed as 7.27 × 0.5) and a 5.45 percent decline in the price of Bond Y (10.9 × 0.5). The percentage increase in bond prices in response to a decrease in bond yields is estimated in the same manner.
The percentage change in a bond's price in response to a change in yield can be expressed more directly with a simple equation:
%Δ Pb = −DUR × Δ y
where
This equation is simply a mathematical expression of the relationship discussed in the preceding paragraphs. For example, the percentage change in price for Bond X for an increase in yield of 0.2 percentage point would be
Thus, according to the modified duration estimate, if interest rates rise by 0.2 percentage point then the price of Bond X will drop 1.45 percent. Similarly, if interest rates decrease by 0.2 percentage point, the price of Bond X will increase by 1.45 percent.
Estimation Errors from Using Modified Duration If investors rely strictly on modified duration to estimate the percentage change in the price of a bond, they will tend to overestimate the price decline associated with an increase in rates and to underestimate the price increase associated with a decrease in rates.
EXAMPLE
Consider a bond with a 10 percent coupon that pays interest annually and has 20 years to maturity. If the required rate of return is 10 percent (the same as the coupon rate), the value of the bond is $1,000. Based on the formula provided earlier, this bond's modified duration is 8.514 years. If investors anticipate that bond yields will increase by 1 percentage point (to 11 percent), then they can estimate the percentage change in the bond's price to be
If bond yields rise by 1 percentage point as expected, the price (present value) of the bond would now be $920.37. (Verify this new price by using the time value function on your financial calculator.) The new price reflects a decline of 7.96 percent [calculated as ($920.37 − $1,000) ÷ $1,000]. The decline in price is Less pronounced than was estimated in the previous equation. The difference between the estimated percentage change in price (8.514 percent) and the actual percentage change in price (7.96 percent) is due to convexity.
Bond Convexity A more complete formula to estimate the percentage change in price in response to a change in yield will incorporate the property of convexity as well as modified duration.
The estimated modified duration suggests a linear relationship in the response of the bond price to a change in bond yields. This is shown by the straight line in Exhibit 8.8 . For a given 1 percentage point change in bond yields from our initially assumed bond yield of 10 percent, the modified duration predicts a specific change in bond price. However, the actual response of the bond's price to a change in bond yields is convex and is represented by the red curve in Exhibit 8.8 . Notice that if the bond yield (horizontal axis) changes slightly from the initial level of 10 percent, the difference between the expected bond price adjustment according to the modified duration estimate (the straight line in Exhibit 8.8 ) and the bond's actual price adjustment (the convex curve in Exhibit 8.8 ) is small. For relatively large changes in the bond yield, however, the bond price adjustment as estimated by modified duration is less accurate. The larger the change in the bond yield, the larger the error from estimating the change in bond price in response to the change in yield.
Exhibit 8.8 Relationship between Bond Yields and Prices
Since a bond's price change in response to a change in yields is positively related to the maturity of the bond, convexity is also more pronounced for bonds with a long maturity. The prices of low- or zero-coupon bonds are more sensitive to changes in yields. Similarly, bond convexity is more pronounced for bonds with low (or no) coupon rates.
8-4 BOND INVESTMENT STRATEGIES
Many investors value bonds and assess their risk when managing investments. Some investors such as bond portfolio managers of financial institutions commonly follow a specific strategy for investing in bonds. A few of the more common strategies are described here.
8-4a Matching Strategy
Some investors create a bond portfolio that will generate periodic income to match their expected periodic expenses. For example, an individual investor may invest in a bond portfolio that will provide sufficient income to cover periodic expenses after retirement. Alternatively, a pension fund may invest in a bond portfolio that will provide employees with a fixed periodic income after retirement. The matching strategy involves estimating future cash outflows and then developing a bond portfolio that can generate sufficient coupon or principal payments to cover those outflows.
8-4b Laddered Strategy
With a laddered strategy, funds are evenly allocated to bonds in each of several different maturity classes. For example, an institutional investor might create a bond portfolio with one-fourth of the funds invested in bonds with five years until maturity, one-fourth invested in 10-year bonds, one-fourth in 15-year bonds, and one-fourth in 20-year bonds. In five years, when the bonds that had five years until maturity are redeemed, the proceeds can be used to buy 20-year bonds. Since all the other bonds in the portfolio will have five years less until maturity than they had when the portfolio was created, a new investment in 20-year bonds achieves the same maturity structure that existed when the portfolio was created.
WEB
http://research.stlouisfed.org
Assess the yield of 30-year Treasury bonds over the last 24 months.
The laddered strategy has many variations, but in general this strategy achieves diversified maturities and therefore different sensitivities to interest rate risk. Nevertheless, because most bonds are adversely affected by rising interest rates, diversification of maturities in the bond portfolio does not eliminate interest rate risk.
8-4c Barbell Strategy
With the barbell strategy, funds are allocated to bonds with a short term to maturity as well as to bonds with a long term to maturity. The bonds with the short term to maturity provide liquidity if the investor needs to sell bonds in order to obtain cash. The bonds with the long term to maturity tend to have a higher yield to maturity than the bonds with shorter terms to maturity. Thus this strategy allocates some funds to achieving a relatively high return and other funds to covering liquidity needs.
8-4d Interest Rate Strategy
With the interest rate strategy, funds are allocated in a manner that capitalizes on interest rate forecasts. This strategy requires frequent adjustments in the bond portfolio to reflect the prevailing interest rate forecast.
EXAMPLE
Consider a bond portfolio with funds initially allocated equally across various bond maturities. If recent economic events result in an expectation of higher interest rates, the bond portfolio will be revised to concentrate on bonds with short terms to maturity. Because these bonds are the least sensitive to interest rate movements, they will limit the potential adverse effects on the bond portfolio's value. The sales of all the intermediate-term and long-term bonds will result in significant commissions paid to brokers.
Now assume that after a few weeks, new economic conditions result in an expectation that interest rates will decline in the future. Again the bond portfolio will be restructured, but now it will concentrate on long-term bonds. If interest rates decline as expected, this type of bond portfolio will be most sensitive to that interest rate movement and will experience the largest increase in value.
Although this type of strategy is rational for investors who believe that they can accurately forecast interest rate movements, it is difficult for even the most sophisticated investors to consistently forecast future interest rate movements. If investors guess wrong, their portfolio will likely perform worse than if they had used a passive strategy of investing in bonds with a wide variety of maturities.
8-5 VALUATION AND RISK OF INTERNATIONAL BONDS
The value of an international bond represents the present value of future cash flows to be received by the bond's local investors. Exhibit 8.9 shows the yields offered on newly issued bonds by various governments. Notice that yields vary among countries, since each yield represents the long-term, risk-free rate for the local country (assuming that the government is perceived to be free from default risk). Although the yields on newly issued government bonds vary among countries, the exhibit shows that they tend to move in the same direction. During the 2007–2012 period, interest rates declined in most countries and thus the yields offered on newly issued government bonds declined as well. The decline in yields was especially pronounced in response to the financial crisis in 2008, which prompted most central banks to lower their interest rates. As a result, the yields of newly issued bonds declined as well.
Exhibit 8.9 Government Bond Yields over Time
The value of government bonds changes over time in response to changes in the risk-free interest rate of the currency denominating the bond and in response to changes in the perceived credit risk of the bond. Since these two factors affect the market price of the bond, they also affect the return on the bond to investors over a particular holding period. An additional factor that affects the return to investors from another country is exchange rate risk. The influence of each of these factors is described next.
8-5a Influence of Foreign Interest Rate Movements
As the risk-free interest rate of a currency changes, the required rate of return by investors in that country changes as well. Thus the present value of a bond denominated in that currency changes. A reduction in the risk-free interest rate of the foreign currency will result in a lower required rate of return by investors who use that currency to invest, which results in a higher value for bonds denominated in that currency. Conversely, an increase in the risk-free rate of that currency results in a lower value for bonds denominated in that currency. In general, the return on a bond denominated in a specific currency over a particular holding period is enhanced if the corresponding interest rate declines over that period; the return is reduced if the corresponding interest rate increases over that period. U.S. bond prices may be rising (owing to a reduction in U.S. interest rates) while the prices of bonds denominated in other currencies are decreasing (owing to an increase in the interest rates of these currencies).
WEB
Yields of government securities from major countries.
8-5b Influence of Credit Risk
As the perceived credit (default) risk of an international bond changes, the risk premium within the required rate of return by investors is affected. Consequently, the present value of the bond changes. An increase in risk causes a higher required rate of return on the bond and therefore lowers its present value, whereas a reduction in risk causes a lower required rate of return on the bond and increases its present value. Thus investors who are concerned about a possible increase in the credit risk of an international bond will monitor economic and political conditions in the relevant country that could affect that risk.
8-5c Influence of Exchange Rate Fluctuations
Changes in the value of the foreign currency denominating a bond affect the U.S. dollar cash flows generated from the bond and thereby affect the return to U.S. investors who invested in it. Consider a U.S. financial institution's purchase of bonds with a par value of £2 million, a 10 percent coupon rate (payable at the end of each year), currently priced at par value, and with six years remaining until maturity. Exhibit 8.10 shows how the dollar cash flows to be generated from this investment will differ under three scenarios. The cash flows in the last year also account for the principal payment. The sensitivity of dollar cash flows to the pound's value is obvious.
From the perspective of the investing institution, the most attractive foreign bonds offer a high coupon rate and are denominated in a currency that strengthens over the investment horizon. Although the coupon rates of some bonds are fixed, the future value of any foreign currency is uncertain. Thus there is a risk that the currency will depreciate and more than offset any coupon rate advantage.
Exhibit 8.10 Dollar Cash Flows Generated from a Foreign Bond under Three Scenarios
|
SCENARIO I (STABLE POUND) |
YEAR 1 |
YEAR 2 |
YEAR 3 |
YEAR 4 |
YEAR 5 |
YEAR 6 |
|
Forecasted value of pound |
$1.50 |
$1.50 |
$1.50 |
$1.50 |
$1.50 |
$1.50 |
|
Forecasted dollar cash flows |
$300,000 |
$300,000 |
$300,000 |
$300,000 |
$300,000 |
$3,300,000 |
|
SCENARIO II (WEAK POUND) |
||||||
|
Forecasted value of pound |
$1.48 |
$1.46 |
$1.44 |
$1.40 |
$1.36 |
$1.30 |
|
Forecasted dollar cash flows |
$296,000 |
$292,000 |
$288,000 |
$280,000 |
$272,000 |
$2,860,000 |
|
SCENARIO III (STRONG POUND) |
||||||
|
Forecasted value of pound |
$1.53 |
$1.56 |
$1.60 |
$1.63 |
$1.66 |
$1.70 |
|
Forecasted dollar cash flows |
$306,000 |
$312,000 |
$320,000 |
$326,000 |
$332,000 |
$3,740,000 |
8-5d International Bond Diversification
When investors attempt to capitalize on investments in foreign bonds that have higher interest rates than they can obtain locally, they may diversify their foreign bond holdings among countries to reduce their exposure to different types of risk, as explained next.
Reduction of Interest Rate Risk Institutional investors diversify their bond portfolios internationally to reduce exposure to interest rate risk. If all bonds in a portfolio are from a single country, their values will all be systematically affected by interest rate movements in that country. International diversification of bonds reduces the sensitivity of the overall bond portfolio to any single country's interest rate movements.
Reduction of Credit Risk Another key reason for international diversification is the reduction of credit (default) risk. Investment in bonds issued by corporations from a single country can expose investors to a relatively high degree of credit risk. The credit risk of corporations is strongly affected by economic conditions. Shifts in credit risk will likely be systematically related to the country's economic conditions. Because economic cycles differ across countries, there is less chance of a systematic increase in the credit risk of internationally diversified bonds. During the credit crisis of 2008–2009, however, there was a perception of higher credit risk (and therefore lower value) for most corporate bonds regardless of the issuer's country.
Reduction of Exchange Rate Risk Financial institutions may attempt to reduce their exchange rate risk by diversifying among foreign securities denominated in various foreign currencies. In this way, a smaller proportion of their foreign security holdings will be exposed to the depreciation of any particular foreign currency. Because the movements of many foreign currency values within one continent are highly correlated, a U.S. investor would reduce exchange rate risk only slightly when diversifying among securities. For this reason, U.S. financial institutions commonly attempt to purchase securities across continents rather than within a single continent. This fact is evident from a review of the foreign securities purchased by pension funds, life insurance companies, or most international mutual funds.
The conversion of many European countries to a single currency (the euro) in recent years has resulted in more bond offerings in Europe by European-based firms. Before the introduction of the euro, a European firm needed a different currency for every European country in which it conducted business and therefore borrowed currency from local banks in each country. Now, a firm can use the euro to finance its operations across several European countries and may be able to obtain all the financing it needs with a single, euro-denominated bond offering. The firm can then use a portion of the revenue (in euros) for making coupon payments to bondholders who have purchased the bonds. In addition, European investors based in countries where the euro serves as the local currency can now invest in euro-denominated bonds in other European countries without being exposed to exchange rate risk.
International Integration of Credit Risk The general credit risk levels of loans among countries is correlated, because country economies are correlated. When one country experiences weak economic conditions, its consumers tend to reduce their demand not only for local products but foreign products as well. The credit risk of the local firms increases, because the weak economy reduces their revenue and their earnings, and could make it difficult for them to repay their loans. Furthermore, as the country's consumers reduce their demand for foreign products, the producers of those products in foreign countries experience lower revenue and earnings, and may not be able to repay their loans to creditors within their own country. Thus, the higher credit risk in one country is transmitted to another country. This process is sometimes referred to as credit contagion, meaning that higher credit risk in one country becomes contagious to other countries whose economies are integrated with it.
8-5e European Debt Crisis
In the 2010–2012 period, the governments of Greece, Portugal, and Spain experienced debt crises because of large budget deficits and their inability to cover their debt payments. As their credit ratings declined, some investors were no longer willing to invest in their bonds, and the prices of outstanding bonds declined. Because these countries commonly obtained debt financing from financial institutions in other European countries, their financial problems have spread to these other countries, resulting in a European debt crisis. As the financial institutions that provided loans to the governments experience loan defaults, their own credit risk increases.
European countries that rely on the euro as their currency cannot use monetary policy to stimulate their economies, because they do not have control of their own money supply. They are part of the eurozone, and therefore subject to the monetary policy conducted by the European Central Bank that is applied to all countries that participate in the euro. Thus, they may want to use their fiscal policy to stimulate their economy. The typical fiscal policy that stimulates the economy is substantial government spending and lower taxes, but these actions would result in a larger budget deficit. This is not a desirable solution for countries that are presently unable to cover their existing debt. They cannot easily issue more bonds to cover a larger deficit when they are unable to repay their existing debt. Bondholders recognize the credit risk, and are only willing to provide credit if they are compensated for accepting the risk that the bonds might default.
The European Central Bank has been willing to provide credit to countries that are unable to cover their debt payments. However, when it provides credit, it commonly imposes austerity conditions that may enable the government to correct its budget deficit over time. These conditions are not necessarily desired by the government, because they might require the government to reduce its spending and increase taxes. The conditions can reduce budget deficits, but do not provide a quick cure to the weak economic conditions in Europe.
Some critics have argued that a country's government should abandon the euro rather than accept funding from the ECB, because the austerity conditions are too harsh. If a country abandons the eurozone, there are possible political implications. The country might be removed from the European Union, and its international trade with some European countries could be reduced. Also, if the country decides to default on its debt, other restrictions might be imposed by the governments of countries where the major creditors are based, such as restrictions on any new credit provided to the government that defaulted. At the very least, some creditors would cut off future funding to the government that defaulted on its debt.
The European debt crisis also raised concerns about credit risk in the United States and Asia. News of European debt repayment problems signaled potential economic weakness in Europe, which caused stock prices in Europe to decline. Moreover, the negative signal spread to other continents, due to the economic integration between continents through international trade. During the 2011–2012 period, the investor sentiment as the U.S. stock market opened each morning was often dependent on the latest news about government debt repayment issues in Europe.
SUMMARY
· ▪ The value of a debt security (such as bonds) is the present value of future cash flows generated by that security, using a discount rate that reflects the investor's required rate of return. As market interest rates rise, the investor's required rate of return increases. The discounted value of bond payments declines when the higher discount rate is applied. Thus the present value of a bond declines, which forces the bond price to decline.
· ▪ Bond prices are affected by the factors that influence interest rate movements, including economic growth, the money supply, oil prices, and the dollar. Bond prices are also affected by a change in credit risk.
· ▪ Investors commonly measure the sensitivity of their bond holdings to potential changes in the required rate of return. Two methods used for this purpose are bond price elasticity and duration. Other things being equal, the longer a bond's time to maturity, the more sensitive its price is to interest rate movements. Prices of bonds with relatively low coupon payments are also more sensitive to interest rate movements.
· ▪ Common investment strategies used to invest in bonds are the matching strategy, laddered strategy, barbell strategy, and interest rate strategy. The matching strategy focuses on generating income from the bond portfolio that can cover anticipated expenses. The laddered strategy and barbell strategy are designed to cover liquidity needs while also trying to achieve decent returns. The interest rate strategy is useful for investors who believe that they can predict interest rate movements and therefore shift into long-term bonds when they believe interest rates will decline.
· ▪ Foreign bonds may offer higher returns, but they are exposed to exchange rate risk and may also be subject to credit risk. International financial markets are highly integrated, so adverse conditions that cause high credit risk in one country may be contagious to other countries.
POINT COUNTER-POINT
Does Governance of Firms Affect the Prices of Their Bonds?
Point No. Bond prices are primarily determined by interest rate movements and therefore are not affected by the governance of firms that issued the bonds.
Counter-Point Yes. Bond prices reflect the risk of default. Firms with more effective governance may be able to reduce their default risk and thereby increase the price of their bonds.
Who Is Correct? Use the Internet to learn more about this issue and then formulate your own opinion.
QUESTIONS AND APPLICATIONS
· 1. Bond Investment Decision Based on your forecast of interest rates, would you recommend that investors purchase bonds today? Explain.
· 2. How Interest Rates Affect Bond Prices Explain the impact of a decline in interest rates on:
· a. An investor's required rate of return.
· b. The present value of existing bonds.
· c. The prices of existing bonds.
· 3. Relevance of Bond Price Movements Why is the relationship between interest rates and bond prices important to financial institutions?
· 4. Source of Bond Price Movements Determine the direction of bond prices over the last year and explain the reason for it.
· 5. Exposure to Bond Price Movements How would a financial institution with a large bond portfolio be affected by falling interest rates? Would it be affected more than a financial institution with a greater concentration of bonds (and fewer short-term securities)? Explain.
· 6. Comparison of Bonds to Mortgages Since fixed-rate mortgages and bonds have similar payment flows, how is a financial institution with a large portfolio of fixed-rate mortgages affected by rising interest rates? Explain.
· 7. Coupon Rates If a bond's coupon rate were above its required rate of return, would its price be above or below its par value? Explain.
· 8. Bond Price Sensitivity Is the price of a longterm bond more or less sensitive to a change in interest rates than to the price of a short-term security? Why?
· 9. Required Return on Bonds Why does the required rate of return for a particular bond change over time?
· 10. Inflation Effects Assume that inflation is expected to decline in the near future. How could this affect future bond prices? Would you recommend that financial institutions increase or decrease their concentration in long-term bonds based on this expectation? Explain.
· 11. Bond Price Elasticity Explain the concept of bond price elasticity. Would bond price elasticity suggest a higher price sensitivity for zero-coupon bonds or high-coupon bonds that are offering the same yield to maturity? Why? What does this suggest about the market value volatility of mutual funds containing zero-coupon Treasury bonds versus high-coupon Treasury bonds?
· 12. Economic Effects on Bond Prices An analyst recently suggested that there will be a major economic expansion that will favorably affect the prices of high-rated, fixed-rate bonds because the credit risk of bonds will decline as corporations improve their performance. Assuming that the economic expansion occurs, do you agree with the analyst's conclusion? Explain.
· 13. Impact of War When tensions rise or a war erupts in the Middle East, bond prices in many countries tend to decline. What is the link between problems in the Middle East and bond prices? Would you expect bond prices to decline more in Japan or in the United Kingdom as a result of the crisis? (The answer is tied to how interest rates may change in those countries.) Explain.
· 14. Bond Price Sensitivity Explain how bond prices may be affected by money supply growth, oil prices, and economic growth.
· 15. Impact of Oil Prices Assume that oil-producing countries have agreed to reduce their oil production by 30 percent. How would bond prices be affected by this announcement? Explain.
· 16. Impact of Economic Conditions Assume that breaking news causes bond portfolio managers to suddenly expect much higher economic growth. How might bond prices be affected by this expectation? Explain. Now assume that breaking news causes bond portfolio managers to suddenly anticipate a recession. How might bond prices be affected? Explain.
Advanced Questions
· 17. Impact of the Fed Assume that bond market participants suddenly expect the Fed to substantially increase the money supply.
· a. Assuming no threat of inflation, how would bond prices be affected by this expectation?
· b. Assuming that inflation may result, how would bond prices be affected?
· c. Given your answers to (a) and (b), explain why expectations of the Fed's increase in the money supply may sometimes cause bond market participants to disagree about how bond prices will be affected.
· 18. Impact of the Trade Deficit Bond portfolio managers closely monitor the trade deficit figures, because the trade deficit can affect exchange rates, which can affect inflationary expectations and therefore interest rates.
· a. When the trade deficit figure is higher than anticipated, bond prices typically decline. Explain why this reaction may occur.
· b. On some occasions, the trade deficit figure has been very large but the bond markets did not respond to the announcement. Assuming that no other information offsets the impact, explain why the bond markets may not have responded to the announcement.
· 19. International Bonds A U.S. insurance company purchased British 20-year Treasury bonds instead of U.S. 20-year Treasury bonds because the coupon rate was 2 percent higher on the British bonds. Assume that the insurance company sold the bonds after five years. Its yield over the five-year period was substantially less than the yield it would have received on the U.S. bonds over the same five-year period. Assume that the U.S. insurance company had hedged its exchange rate exposure. Given that the lower yield was not because of default risk or exchange rate risk, explain how the British bonds could have generated a lower yield than the U.S. bonds. (Assume that either type of bond could have been purchased at the par value.)
· 20. International Bonds The pension fund manager of Utterback (a U.S. firm) purchased German 20-year Treasury bonds instead of U.S. 20-year Treasury bonds. The coupon rate was 2 percent lower on the German bonds. Assume that the manager sold the bonds after five years. The yield over the five-year period was substantially more than the yield the manager would have received on the U.S. bonds over the same five-year period. Explain how the German bonds could have generated a higher yield than the U.S. bonds for the manager, even if the exchange rate was stable over this five-year period. (Assume that the price of either bond was initially equal to its respective par value.) Be specific.
· 21. Implications of a Shift in the Yield Curve Assume that there is a sudden shift in the yield curve such that the new yield curve is higher and more steeply sloped today than it was yesterday. If a firm issues new bonds today, would its bonds sell for higher or lower prices than if it had issued the bonds yesterday? Explain.
· 22. How Bond Prices May Respond to Prevailing Conditions Consider the prevailing conditions for inflation (including oil prices), the economy, the budget deficit, and the Fed's monetary policy that could affect interest rates. Based on prevailing conditions, do you think bond prices will increase or decrease during this semester? Offer some logic to support your answer. Which factor do you think will have the biggest impact on bond prices?
· 23. Interaction between Bond and Money Markets Assume that you maintain bonds and money market securities in your portfolio, and you suddenly believe that long-term interest rates will rise substantially tomorrow (even though the market does not share your view) while short-term interest rates will remain the same.
· a. How would you rebalance your portfolio between bonds and money market securities?
· b. If other market participants suddenly recognize that long-term interest rates will rise tomorrow and they respond in the same manner as you do, explain how the demand for these securities (bonds and money market securities), supply of these securities for sale, and prices and yields of these securities will be affected.
· c. Assume that the yield curve is flat today. Explain how the slope of the yield curve will change tomorrow in response to the market activity.
· 24. Impact of the Credit Crisis on Risk Premiums Explain how the prices of bonds were affected by a change in the risk-free rate during the credit crisis. Explain how bond prices were affected by a change in the credit risk premium during this period.
· 25. Systemic Risk Explain why there are concerns about systemic risk in the bond and other debt markets. Also explain how the Financial Reform Act of 2010 was intended to reduce systemic risk.
· 26. Link Between Market Uncertainty and Bond Yields When stock market volatility is high, corporate bond yields tend to increase. What market forces cause the increase in corporate bond yields under these conditions?
· 27. Fed's Impact on Credit Risk This chapter explains how the Fed can change money supply, which can affect the risk-free rate offered on bonds. Why might the Fed's policy also affect the risk premium on corporate bonds?
· 28. Spread of European Debt Crisis Explain why debt crises in some European countries can cause financial problems in other European countries.
· 29. European Debt Repayment and Monetary Policy Explain why monetary policy is not normally effective in stimulating the economy of a European country that is experiencing debt repayment problems.
· 30. European Debt Repayment and Fiscal Policy Explain why fiscal policy is not normally effective in stimulating the economy of a European country that is experiencing debt repayment problems.
· 31. Conditions Imposed on ECB Loans to Governments with Debt Problems Describe the conditions imposed by the European Central Bank (ECB) when it provides credit to European country governments with debt repayment problems.
Interpreting Financial News
Interpret the following statements made by Wall Street analysts and portfolio managers.
· a. “Given the recent uncertainty about future interest rates, investors are fleeing from zero-coupon bonds.”
· b. “Catrell Insurance Company invests heavily in bonds, and its stock price increased substantially today in response to the Fed's signal that it plans to reduce interest rates.”
· c. “Bond markets declined when the Treasury flooded the market with its new bond offering.”
Managing in Financial Markets
Bond Investment Dilemma As an investor, you plan to invest your funds in long-term bonds. You have $100,000 to invest. You may purchase highly rated municipal bonds at par with a coupon rate of 6 percent; you have a choice of a maturity of 10 years or 20 years. Alternatively, you could purchase highly rated corporate bonds at par with a coupon rate of 8 percent; these bonds also are offered with maturities of 10 years or 20 years. You do not expect to need the funds for five years. At the end of the fifth year, you will definitely sell the bonds because you will need to make a large purchase at that time.
· a. What is the annual interest you would earn (before taxes) on the municipal bond? On the corporate bond?
· b. Assume that you are in the 20 percent tax bracket. If the level of credit risk and the liquidity for the municipal and corporate bonds are the same, would you invest in the municipal bonds or the corporate bonds? Why?
· c. Assume that you expect all yields paid on newly issued notes and bonds (regardless of maturity) to decrease by a total of 4 percentage points over the next two years and to increase by a total of 2 percentage points over the following three years. Would you select the 10-year maturity or the 20-year maturity for the type of bond you plan to purchase? Why?
PROBLEMS
· 1. Bond Valuation Assume the following information for an existing bond that provides annual coupon payments:
Par value = $1,000
Coupon rate = 11%
Maturity = 4 years
Required rate of return by investors = 11%
· a. What is the present value of the bond?
· b. If the required rate of return by investors were 14 percent instead of 11 percent, what would be the present value of the bond?
· c. If the required rate of return by investors were 9 percent, what would be the present value of the bond?
· 2. Valuing a Zero-Coupon Bond Assume the following information for existing zero-coupon bonds:
Par value = $100,000
Maturity = 3 years
Required rate of return by investors = 12%
How much should investors be willing to pay for these bonds?
· 3. Valuing a Zero-Coupon Bond Assume that you require a 14 percent return on a zero-coupon bond with a par value of $1,000 and six years to maturity. What is the price you should be willing to pay for this bond?
· 4. Bond Value Sensitivity to Exchange Rates and Interest Rates Cardinal Company, a U.S.-based insurance company, considers purchasing bonds denominated in Canadian dollars, with a maturity of six years, a par value of C$50 million, and a coupon rate of 12 percent. Cardinal can purchase the bonds at par. The current exchange rate of the Canadian dollar is $0.80. Cardinal expects that the required return by Canadian investors on these bonds four years from now will be 9 percent. If Cardinal purchases the bonds, it will sell them in the Canadian secondary market four years from now. It forecasts the exchange rates as follows:
|
YEAR |
EXCHANGE RATE OF C$ |
YEAR |
EXCHANGE RATE OF C$ |
|
1 |
$0.80 |
4 |
$0.72 |
|
2 |
0.77 |
5 |
0.68 |
|
3 |
0.74 |
6 |
0.66 |
· a. Refer to earlier examples in this chapter to determine the expected U.S. dollar cash flows to Cardinal over the next four years. Determine the present value of a bond.
· b. Does Cardinal expect to be favorably or adversely affected by the interest rate risk? Explain.
· c. Does Cardinal expect to be favorably or adversely affected by exchange rate risk? Explain.
· 5. Predicting Bond Values (Use the chapter appendix to answer this problem.) Bulldog Bank has just purchased bonds for $106 million that have a par value of $100 million, three years remaining to maturity, and an annual coupon rate of 14 percent. It expects the required rate of return on these bonds to be 12 percent one year from now.
· a. At what price could Bulldog Bank sell these bonds one year from now?
· b. What is the expected annualized yield on the bonds over the next year, assuming they are to be sold in one year?
· 6. Predicting Bond Values (Use the chapter appendix to answer this problem.) Sun Devil Savings has just purchased bonds for $38 million that have a par value of $40 million, five years remaining to maturity, and a coupon rate of 12 percent. It expects the required rate of return on these bonds to be 10 percent two years from now.
· a. At what price could Sun Devil Savings sell these bonds two years from now?
· b. What is the expected annualized yield on the bonds over the next two years, assuming they are to be sold in two years?
· c. If the anticipated required rate of return of 10 percent in two years is overestimated, how would the actual selling price differ from the forecasted price? How would the actual annualized yield over the next two years differ from the forecasted yield?
· 7. Predicting Bond Values (Use the chapter appendix to answer this problem.) Spartan Insurance Company plans to purchase bonds today that have four years remaining to maturity, a par value of $60 million, and a coupon rate of 10 percent. Spartan expects that in three years, the required rate of return on these bonds by investors in the market will be 9 percent. It plans to sell the bonds at that time. What is the expected price it will sell the bonds for in three years?
· 8. Bond Yields (Use the chapter appendix to answer this problem.) Hankla Company plans to purchase either (1) zero-coupon bonds that have 10 years to maturity, a par value of $100 million, and a purchase price of $40 million; or (2) bonds with similar default risk that have five years to maturity, a 9 percent coupon rate, a par value of $40 million, and a purchase price of $40 million.
Hankla can invest $40 million for five years. Assume that the market's required return in five years is forecasted to be 11 percent. Which alternative would offer Hankla a higher expected return (or yield) over the five-year investment horizon?
· 9. Predicting Bond Values (Use the chapter appendix to answer this problem.) The portfolio manager of Ludwig Company has excess cash that is to be invested for four years. He can purchase four-year Treasury notes that offer a 9 percent yield. Alternatively, he can purchase new 20-year Treasury bonds for $2.9 million that offer a par value of $3 million and an 11 percent coupon rate with annual payments. The manager expects that the required return on these same 20-year bonds will be 12 percent four years from now.
· a. What is the forecasted market value of the 20-year bonds in four years?
· b. Which investment is expected to provide a higher yield over the four-year period?
· 10. Predicting Bond Portfolio Value (Use the chapter appendix to answer this problem.) Ash Investment Company manages a broad portfolio with this composition:
|
|
PAR VALUE |
PRESENT MARKET VALUE |
YEARS REMAINING TO MATURITY |
|
Zero-coupon bonds |
$200,000,000 |
$ 63,720,000 |
12 |
|
8% Treasury bonds |
300,000,000 |
290,000,000 |
8 |
|
11% corporate bonds |
400,000,000 |
380,000,000 |
10 |
|
|
|
$733,720,000 |
|
· Ash expects that in four years, investors in the market will require an 8 percent return on the zero-coupon bonds, a 7 percent return on the Treasury bonds, and a 9 percent return on corporate bonds. Estimate the market value of the bond portfolio four years from now.
· 11. Valuing a Zero-Coupon Bond
· a. A zero-coupon bond with a par value of $1,000 matures in 10 years. At what price would this bond provide a yield to maturity that matches the current market rate of 8 percent?
· b. What happens to the price of this bond if interest rates fall to 6 percent?
· c. Given the above changes in the price of the bond and the interest rate, calculate the bond price elasticity.
· 12. Bond Valuation You are interested in buying a $1,000 par value bond with 10 years to maturity and an 8 percent coupon rate that is paid semiannually. How much should you be willing to pay for the bond if the investor's required rate of return is 10 percent?
· 13. Predicting Bond Values A bond you are interested in pays an annual coupon of 4 percent, has a yield to maturity of 6 percent, and has 13 years to maturity. If interest rates remain unchanged, at what price would you expect this bond to be selling eight years from now? Ten years from now?
· 14. Sensitivity of Bond Values
· a. How would the present value (and therefore the market value) of a bond be affected if the coupon payments are smaller and other factors remain constant?
· b. How would the present value (and therefore the market value) of a bond be affected if the required rate of return is smaller and other factors remain constant?
· 15. Bond Elasticity Determine how the bond elasticity would be affected if the bond price changed by a larger amount, holding the change in the required rate of return constant.
· 16. Bond Duration Determine how the duration of a bond would be affected if the coupons were extended over additional time periods.
· 17. Bond Duration A bond has a duration of five years and a yield to maturity of 9 percent. If the yield to maturity changes to 10 percent, what should be the percentage price change of the bond?
· 18. Bond Convexity Describe how bond convexity affects the theoretical linear price-yield relationship of bonds. What are the implications of bond convexity for estimating changes in bond prices?
FLOW OF FUNDS EXERCISE
Interest Rate Expectations, Economic Growth, and Bond Financing
Recall that if the economy continues to be strong, Carson Company may need to increase its production capacity by about 50 percent over the next few years to satisfy demand. It would need financing to expand and accommodate the increase in production. Recall that the yield curve is currently upward sloping. Also recall that Carson is concerned about a possible slowing of the economy because of potential Fed actions to reduce inflation. It needs funding to cover payments for supplies. It is also considering issuing stock or bonds to raise funds in the next year.
· a. At a recent meeting, the chief executive officer (CEO) stated his view that the economy will remain strong, as the Fed's monetary policy is not likely to have a major impact on interest rates. So he wants to expand the business to benefit from the expected increase in demand for Carson's products. The next step would be to determine how to finance the expansion. The chief financial officer (CFO) stated that if Carson Company needs to obtain long-term funds, the issuance of fixed-rate bonds would be ideal at this point in time because she expects that the Fed's monetary policy to reduce inflation will cause long-term interest rates to rise. If the CFO is correct about future interest rates, what does this suggest about future economic growth, the future demand for Carson's products, and the need to issue bonds?
· b. If you were involved in the meeting described here, what do you think needs to be resolved before deciding to expand the business?
· c. At the meeting described here, the CEO stated: “The decision to expand should not be dictated by whether interest rates are going to increase or not. Bonds should be issued only if the potential increase in interest rates is attributed to a strong demand for loanable funds rather than the Fed's reduction in the supply of loanable funds.” What does this statement mean?
INTERNET/EXCEL EXERCISES
Go to www.giddy.org/db/corpspreads.htm . The spreads are listed in the form of basis points (100 basis points= 1 percent) above the Treasury security with the same maturity.
· 1. First determine the difference between the AAA and CCC spreads. This indicates how much more of a yield is required on CCC-rated bonds versus AAA-rated bonds. Next, determine the difference between AAA and BBB spreads. Then determine the difference between BBB and CCC spreads. Is the difference larger between the AAA and BBB or the BBB and CCC spreads? What does this tell you about the perceived risk of the bonds in these rating categories?
· 2. Compare the AAA spread for a short-term maturity (such as two years) versus a long-term maturity (such as 10 years). Is the spread larger for the short-term or the long-term maturity? Offer an explanation for this.
· 3. Next, compare the CCC spread for a short-term maturity (such as two years) versus a long-term maturity (such as 10 years). Is the spread larger for the short-term or the long-term maturity? Offer an explanation for this. Notice that the difference in spreads for a given rating level among maturities varies with the rating level that you assess. Offer an explanation for this.
ONLINE ARTICLES WITH REAL-WORLD EXAMPLES
Find a recent practical article available online that describes a real-world example regarding a specific financial institution or financial market that reinforces one or more concepts covered in this chapter.
If your class has an online component, your professor may ask you to post your summary of the article there and provide a link to the article so that other students can access it. If your class is live, your professor may ask you to summarize your application of the article in class. Your professor may assign specific students to complete this assignment or may allow any students to do the assignment on a volunteer basis.
For recent online articles and real-world examples related to this chapter, consider using the following search terms (be sure to include the prevailing year as a search term to ensure that the online articles are recent):
· 1. bond AND valuation
· 2. bond prices AND economic growth
· 3. bond prices AND inflation
· 4. bond prices AND money supply
· 5. bond prices AND budget deficit
· 6. bond AND duration
· 7. bond AND performance
· 8. bond AND strategy
· 9. international bonds AND exchange rate
· 10. international bonds AND credit risk
APPENDIX 8 Forecasting Bond Prices and Yields
FORECASTING BOND PRICES
To illustrate how a financial institution can assess the potential impact of interest rate movements on its bond holdings, assume that Longhorn Savings and Loan recently purchased Treasury bonds in the secondary market with a total par value of $40 million. The bonds will mature in five years and have an annual coupon rate of 10 percent. Longhorn is attempting to forecast the market value of these bonds two years from now because it may sell the bonds at that time. Therefore, it must forecast the investor's required rate of return and use that as the discount rate to determine the present value of the bonds' cash flows over the final three years of their life. The computed present value will represent the forecasted price two years from now.
To continue with our example, assume the investor's required rate of return two years from now is expected to be 12 percent. This rate will be used to discount the periodic cash flows over the remaining three years. Given coupon payments of $4 million per year (10% × $40 million) and a par value of $40 million, the predicted present value is determined as follows:
An illustration of this exercise is provided in Exhibit 8A.1, using a time line. The market value of the bonds two years ahead is forecasted to be slightly more than $38 million. This is the amount Longhorn expects to receive if it sells the bonds then.
As a second example, assume that Aggie Insurance Company recently purchased corporate bonds in the secondary market with a par value of $20 million, a coupon rate of 14 percent (with annual coupon payments), and three years until maturity. The firm desires to forecast the market value of these bonds in one year because it may sell the bonds at that time. It expects the investor's required rate of return on similar investments to be 11 percent in one year. Using this information, it discounts the bonds' cash flows ($2.8 million in annual coupon payments and a par value of $20 million) over the final two years at 11 percent to determine their present value (and therefore market value) one year from now:
Exhibit 8A.1 Forecasting the Market Value of Bonds
Thus the market value of the bonds is expected to be slightly more than $21 million one year from now.
FORECASTING BOND YIELDS
The yield to maturity can be determined by solving for the discount rate at which the present value of future payments (coupon payments and par value) to the bondholder would equal the bond's current price. The trial-and-error method can be used by applying a discount rate and computing the present value of the payments stream. If the computed present value is higher than the current bond price, the computation should be repeated using a higher discount rate. Conversely, if the computed present value is lower than the current bond price, try a lower discount rate. Calculators and bond tables are also available to determine the yield to maturity.
If bonds are held to maturity, the yield is known. However, if they are sold prior to maturity, the yield is not known until the time of sale. Investors can, however, attempt to forecast the yield with the methods just demonstrated, in which the forecasted required rate of return is used to forecast the market value (and therefore selling price) of the bonds. This selling price can then be incorporated into the cash flow estimates to determine the discount rate at which the present value of cash flows equals the investor's initial purchase price. Suppose that Wildcat Bank purchases bonds with the following characteristics:
· ▪ Par value = $30 million
· ▪ Coupon rate = 15 percent (annual payments)
· ▪ Remaining time to maturity = 5 years
· ▪ Purchase price of bonds = $29 million
The bank plans to sell the bonds in four years. The investor's required rate of return on similar securities is expected to be 13 percent at that time. Given this information, Wildcat forecasts its annualized bond yield over the four-year period in the following manner.
The first step is to forecast the present value (or market price) of the bonds four years from now. To do this, the remaining cash flows (one final coupon payment of $4.5 million plus the par value of $30 million) over the fifth and final year should be discounted (at the forecasted required rate of return of 13 percent) back to the fourth year when the bonds are to be sold:
This predicted present value as of four years from now serves as the predicted selling price in four years.
The next step is to incorporate the forecasted selling price at the end of the bond portfolio's cash flow stream. Then the discount rate that equates the present value of the cash flow stream to the price at which the bonds were purchased will represent the annualized yield. In our example, Wildcat Bank's cash flows are coupon payments of $4.5 million over each of the four years it holds the bonds; the fourth year's cash flows should also include the forecasted selling price of $30,530,973 and therefore sum to $35,030,973. Recall that Wildcat Bank purchased the bonds for $29 million. Given this information, the equation to solve for the discount rate ( k) is
The trial-and-error method can be used to determine the discount rate if a calculator is not available. With a discount rate of 17 percent, the present value would be
This present value is slightly less than the initial purchase price. Thus the discount rate at which the present value of expected cash flows equals the purchase price is just slightly less than 17 percent. Consequently, Wildcat Bank's expected return on the bonds is just short of 17 percent.
It should be recognized that the process for determining the yield to maturity assumes that any payments received prior to the end of the holding period can be reinvested at the yield to maturity. If, for example, the payments could be reinvested only at a lower rate, the yield to maturity would overstate the actual return to the investor over the entire holding period.
With a computer program, the financial institution could easily create a distribution of forecasted yields based on various forecasts for the required rate of return four years from now. Without a computer, the process illustrated here must be completed for each forecast of the required rate of return. The computer actually follows the same steps but is much faster.
Financial institutions that forecast bond yields must first forecast interest rates for the point in time when they plan to sell their bonds. These forecasted rates can be used along with information about the securities to predict the required rate of return that will exist for the securities of concern. The predicted required rate of return is applied to cash flows beyond the time of sale to forecast the present value (or selling price) of the bonds at the time of sale. The forecasted selling price is then incorporated when estimating cash flows over the investment horizon. Finally, the yield to maturity on the bonds is determined by solving for the discount rate that equates these cash flows to the initial purchase price. The accuracy of the forecasted yield depends on the accuracy of the forecasted selling price of the bonds, which in turn depends on the accuracy of the forecasted required rate of return for the time of the sale.
FORECASTING BOND PORTFOLIO VALUES
Financial institutions can quantitatively measure the impact of possible interest rate movements on the market value of their bond portfolio by separately assessing the impact on each type of bond and then consolidating the individual impacts. Assume that Seminole Financial, Inc., has a portfolio of bonds with the required return ( k) on each type of bond as shown in the upper portion of Exhibit 8A.2 . Interest rates are expected to increase, causing an anticipated increase of 1 percent in the required return of each type of bond. Assuming no adjustment in the portfolio, Seminole's anticipated bond portfolio position is displayed in the lower portion of Exhibit 8A.2 .
The anticipated market value of each type of bond in the exhibit was determined by discounting the remaining year's cash flows beyond one year by the anticipated required return. The market value of the portfolio is expected to decline by more than $12 million as a result of the anticipated increase in interest rates.
This simplified example assumed a portfolio of only three types of bonds. In reality, a financial institution may have several types of bonds, with several maturities for each type. Computer programs are widely available for assessing the market value of portfolios. The financial institution inputs the cash flow trends of all bond holdings and the anticipated required rates of return for each bond at the future time of concern. The computer uses the anticipated rates to estimate the present value of cash flows at that future time. These present values are then consolidated to determine the forecasted value of the bond portfolio.
Exhibit 8A.2 Forecasts of Bond Portfolio Market Value
|
PRESENT BOND PORTFOLIO POSITION OF SEMINOLE FINANCIAL, INC. |
||||
|
TYPE OF BONDS |
PRESENT k |
PAR VALUE |
YEARS TO MATURITY |
PRESENT MARKET VALUE OF BONDS |
|
9% coupon Treasury bonds |
9% |
$ 40,000,000 |
4 |
$ 40,000,000 |
|
14% coupon corporate bonds |
12% |
100,000,000 |
5 |
107,209,552 |
|
10% coupon gov't agency bonds |
10% |
150,000,000 |
8 |
150,000,000 |
|
|
|
$290,000,000 |
|
$297,207,200 |
|
FORECASTED BOND PORTFOLIO POSITION OF SEMINOLE FINANCIAL, INC. |
||||
|
TYPE OF BONDS |
FORECASTED k |
PAR VALUE |
YEARS TO MATURITY AS OF ONE YEAR FROM NOW |
FORECASTED MARKET VALUE OF BONDS IN ONE YEAR |
|
9% coupon Treasury bonds |
10% |
$ 40,000,000 |
3 |
$ 39,005,259 |
|
14% coupon corporate bonds |
13% |
100,000,000 |
4 |
102,974,471 |
|
10% coupon gov't agency bonds |
11% |
150,000,000 |
7 |
142,931,706 |
|
|
|
$290,000,000 |
|
$284,915,840 |
The key variable in forecasting the bond portfolio's market value is the anticipated required return for each type of bond. The prevailing interest rates on short-term securities are commonly more volatile than rates on longer-term securities, so the required returns on bonds with three or four years to maturity may change to a greater degree than on the longer-term bonds. In addition, as economic conditions change, the required returns of some risky securities could change even if the general level of interest rates remains stable.
FORECASTING BOND PORTFOLIO RETURNS
Financial institutions measure their overall bond portfolio returns in various ways. One way is to account not only for coupon payments but also for the change in market value over the holding period of concern. The market value at the beginning of the holding period is perceived as the initial investment. The market value at the end of that period is perceived as the price at which the bonds would have been sold. Even if the bonds are retained, the measurement of return requires an estimated market value at the end of the period. Finally, the coupon payments must be accounted for as well. A bond portfolio's return is measured the same way as an individual bond's return. Mathematically, the bond portfolio return can be determined by solving for k in the following equation:
where
· MVP = today's market value of the bond portfolio
· Ct = coupon payments received at the end of period t
· MVP n = market value of the bond portfolio at the end of the investment period of concern
· k = discount rate that equates the present value of coupon payments and the future portfolio market value to today's portfolio market value
To illustrate, recall that Seminole Financial, Inc., forecasted its bond portfolio value for one year ahead. Its annual coupon payments ( C) sum to $32,600,000 (computed by multiplying the coupon rate of each type of bond by the respective par value). Using this information along with today's MVP and the forecasted MVP (called MVP n), its annual return is determined by solving for k as follows:
The discount rate k is estimated to be about 7 percent. (Work this yourself for verification.) Therefore, the bond portfolio is expected to generate an annual return of about 7 percent over the one-year investment horizon. The computations to determine the bond portfolio return can be tedious, but financial institutions use computer programs. If this type of program is linked with another program to forecast future bond prices, a financial institution can input forecasted required returns for each type of bond and let the computer determine projections of the bond portfolio's future market value and its return over a specified investment horizon.
1 Technically, the semiannual rate of 6 percent is overstated. For a required rate of 12 percent per year, the precise six-month rate would be 5.83 percent. With the compounding effect, which would generate interest on interest, this semiannual rate over two periods would achieve a 12 percent return. Because the approximate semiannual rate of 6 percent is higher than the precise rate, the present value of the bonds is slightly understated.