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Complete the following textbook problems:

· Ch. 1, p. 25, #16

· Ch. 1, p. 25, #17

· Ch. 2, p. 22, #1

· Ch. 2, p. 22, #8

· Ch. 2, p. 23, #12

· Ch. 2, p. 23, #13

· Ch. 3, p. 30, #1

· Ch. 3, p. 30, #3

· Ch. 3, p. 30, #6

· Ch. 3, p. 30, #15

· Ch. 3, p. 30, #17

· Ch. 3, p. 31, #19

 

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3 Structure of Interest Rates

CHAPTER OBJECTIVES

The specific objectives of this chapter are to:

· ▪ describe how characteristics of debt securities cause their yields to vary,

· ▪ demonstrate how to estimate the appropriate yield for any particular debt security, and

· ▪ explain the theories behind the term structure of interest rates (relationship between the term to maturity and the yield of securities).

The annual interest rate offered by debt securities at any given time varies among debt securities. Individual and institutional investors must understand why quoted yields vary so that they can determine whether the extra yield on a given security outweighs any unfavorable characteristics. Financial managers of corporations or government agencies in need of funds must understand why quoted yields of debt securities vary so that they can estimate the yield they would have to offer in order to sell new debt securities.

3-1 WHY DEBT SECURITY YIELDS VARY

Debt securities offer different yields because they exhibit different characteristics that influence the yield to be offered. In general, securities with unfavorable characteristics will offer higher yields to entice investors. Some debt securities have favorable features; therefore, they can offer relatively low yields and still attract investors. The yields on debt securities are affected by the following characteristics:

· ▪ Credit (default) risk

· ▪ Liquidity

· ▪ Tax status

· ▪ Term to maturity

The yields on bonds may also be affected by special provisions, as described in  Chapter 7 .

3-1a Credit (Default) Risk

Because most securities are subject to the risk of default, investors must consider the creditworthiness of the security issuer. Although investors always have the option of purchasing risk-free Treasury securities, they may prefer other securities if the yield compensates them for the risk. Thus, if all other characteristics besides credit (default) risk are equal, securities with a higher degree of default risk must offer higher yields before investors will purchase them.

EXAMPLE

Investors can purchase a Treasury bond with a 10-year maturity that presently offers an annualized yield of 7 percent if they hold the bond until maturity. Alternatively, investors can purchase bonds that are being issued by Zanstell Co. Although Zanstell is in good financial condition, there is a small possibility that it could file for bankruptcy during the next 10 years, in which case it would discontinue making payments to investors who purchased the bonds. Thus there is a small possibility that investors could lose most of their investment in these bonds. The only way in which investors would even consider purchasing bonds issued by Zanstell Co. is if the annualized yield offered on these bonds is higher than the Treasury bond yield. Zanstell’s bonds presently offer a yield of 8 percent, which is 1 percent higher than the yield offered on Treasury bonds. At this yield, some investors are willing to purchase Zanstell’s bonds because they think Zanstell Co. should have sufficient cash flows to repay its debt over the next 1 0 years.

Credit risk is especially relevant for longer-term securities that expose creditors to the possibility of default for a longer time. Credit risk premiums of 1 percent, 2 percent, or more may not seem significant. But for a corporation borrowing $30 million through the issuance of bonds, an extra percentage point as a premium reflects $300,000 in additional interest expenses per year.

Investors can personally assess the creditworthiness of corporations that issue bonds, but they may prefer to rely on bond ratings provided by rating agencies. These ratings are based on a financial assessment of the issuing corporation, with a focus on whether the corporation will receive sufficient cash flows over time to cover its payments to bondholders. The higher the rating on the bond, the lower the perceived credit risk.

As time passes, economic conditions can change, which can influence the ability of a corporation to repay its debt. Thus bonds previously issued by a firm may be rated at one level, whereas a subsequent issue from the same firm is rated at a different level. The ratings can also differ if the collateral provisions differ among the bonds. Rating agencies can also change bond ratings over time in response to changes in the issuing firm’s financial condition or to changes in economic conditions.

3-1b Assessing Credit Risk

To assess the credit risk of a corporation that issues bonds, investors can evaluate the corporation’s financial statements. Specifically, investors use financial statements to predict the level of cash flows a corporation will generate over future periods, which helps determine if the company will have sufficient cash flows to cover its debt payments. However, financial statements might not indicate how a corporation will perform in the future. Many corporations that were in good financial condition just before they issued debt failed before they repaid their debt.

Rating Agencies  Many investors rely heavily on the ratings of debt securities assigned by rating agencies, so that they do not have to assess the financial statements of corporations. The rating agencies charge the issuers of debt securities a fee for assessing the credit risk of those securities. The ratings are then provided through various financial media outlets at no cost to investors. The most popular rating agencies are Moody’s Investors Service and Standard & Poor’s Corporation. A summary of their rating classification schedules is provided in  Exhibit 3.1 . The ratings issued by Moody’s range from Aaa for the highest quality to C for the lowest quality, and those issued by Standard & Poor’s range from AAA to D. Because these rating agencies use different methods to assess the creditworthiness of firms and state governments, a particular bond could be rated at a different quality level by each agency. However, the differences are usually small.

Commercial banks typically invest only in  investment-grade bonds , which are bonds rated as Baa or better by Moody’s and as BBB or better by Standard & Poor’s. Other financial institutions, such as pension funds and insurance companies, invest in bonds that are rated lower and offer the potential for higher returns.

WEB

www.moodys.com

Credit rating information.

Exhibit 3.1 Rating Classification by Rating Agencies

 

Accuracy of Credit Ratings  The ratings issued by the agencies are opinions, not guarantees. Bonds that are assigned a low credit rating experience default more frequently than bonds assigned a high credit rating, which suggests that the rating can be a useful indicator of credit risk. However, credit rating agencies do not always detect firms’ financial problems.

Credit rating agencies were criticized for being too liberal in their assignment of ratings on debt issued shortly before the credit crisis, as many highly rated debt issues defaulted over the next few years. The credit rating agencies might counter that they could not have anticipated the credit crisis and that they used all the information available to them when assigning ratings to new securities. Yet because credit rating agencies are paid by the issuers of debt securities and not the investors who purchase those securities, agencies may have a natural incentive to assign a high rating. Doing so facilitates a firm’s issuing of debt securities, which in turn should attract more business from other issuers of debt securities.

In response to the criticism, credit rating agencies made some changes to improve their rating process and their transparency. They now disclose more information about how they derived their credit ratings. In addition, employees of each credit rating agency that promote the services of the agency are not allowed to influence the ratings assigned by the rating agency. They are giving more attention to sensitivity analysis in which they assess how creditworthiness might change in response to abrupt changes in the economy.

Oversight of Credit Rating Agencies  The Financial Reform Act of 2010 established an Office of Credit Ratings within the Securities and Exchange Commission in order to regulate credit rating agencies. The act also mandated that credit rating agencies establish internal controls to ensure that their process of assigning ratings is more transparent. The agencies must disclose their rating performance over time, and they are to be held accountable if their ratings prove to be inaccurate. The Financial Reform Act also allows investors to sue an agency for issuing credit ratings that the agency should have known were inaccurate.

3-1c Liquidity

Investors prefer securities that are liquid, meaning that they could be easily converted to cash without a loss in value. Thus, if all other characteristics are equal, securities with less liquidity will have to offer a higher yield to attract investors. Debt securities with a short-term maturity or an active secondary market have greater liquidity. Investors that need a high degree of liquidity (because they may need to sell their securities for cash at any moment) prefer liquid securities, even if it means that they will have to accept a lower return on their investment. Investors who will not need their funds until the securities mature are more willing to invest in securities with less liquidity in order to earn a slightly higher return.

3-1d Tax Status

Investors are more concerned with after-tax income than before-tax income earned on securities. If all other characteristics are similar, taxable securities must offer a higher before-tax yield than tax-exempt securities. The extra compensation required on taxable securities depends on the tax rates of individual and institutional investors. Investors in high tax brackets benefit most from tax-exempt securities.

When assessing the expected yields of various securities with similar risk and maturity, it is common to convert them into an after-tax form, as follows:

Yat = Ybt (1 − T

where

Yat	= after-tax yield
Ybt	= before-tax yield
T	= investor’s marginal tax rate

Investors retain only a percentage (1 − T) of the before-tax yield once taxes are paid.

EXAMPLE

Consider a taxable security that offers a before-tax yield of 8 percent. When converted into aftertax terms, the yield will be reduced by the tax percentage. The precise after-tax yield is dependent on the tax rate T. If the tax rate of the investor is 20 percent, then the after-tax yield will be

Yat	= Ybt (1 − T)
	= 8% (1 − 0.2)
	= 16.4%

 Exhibit 3.2  presents after-tax yields based on a variety of tax rates and before-tax yields. For example, a taxable security with a before-tax yield of 6 percent will generate an after-tax yield of 5.4 percent to an investor in the 10 percent tax bracket, 5.10 percent to an investor in the 15 percent tax bracket, and so on. This exhibit shows why investors in high tax brackets are attracted to tax-exempt securities.

Exhibit 3.2 After-Tax Yields Based on Various Tax Rates and Before-Tax Yields

BEFORE-TAX YIELD
TAX RATE	6%	8%	10%	12%	14%
10%	5.40%	7.20%	9.00%	10.80%	12.60%
15	5.10	6.80	8.50	10.20	11.90
25	4.50	6.00	7.50	9.00	10.50
28	4.32	5.76	7.20	8.64	10.08
35	3.90	5.20	6.50	7.80	9.10

Computing the Equivalent Before-Tax Yield  In some cases, investors wish to determine the before-tax yield necessary to match the after-tax yield of a tax-exempt security that has a similar risk and maturity. This can be done by rearranging the terms of the previous equation:

Ybt  =

Yat

1 − T

For instance, suppose that a firm in the 20 percent tax bracket is aware of a tax-exempt security that is paying a yield of 8 percent. To match this after-tax yield, taxable securities must offer a before-tax yield of

Ybt =

Yat

1 − T

=

8%

1 − 02

= b

State taxes should be considered along with federal taxes in determining the after-tax yield. Treasury securities are exempt from state income tax, and municipal securities are sometimes exempt as well. Because states impose different income tax rates, a particular security’s after-tax yield may vary with the location of the investor.

3-1e Term to Maturity

Maturity differs among debt securities and is another reason that debt security yields differ. The  term structure of interest rates  defines the relationship between the term to maturity and the annualized yield of debt securities at a specific moment in time while holding other factors, such as risk, constant.

WEB

www.treasury.gov

Treasury yields among different maturities.

EXAMPLE

Assume that, as of today, the annualized yields for federal government securities (which are free from credit risk) of varied maturities are as shown in  Exhibit 3.3 . The curve created by connecting the points plotted in the exhibit is commonly referred to as a yield curve. Notice that the yield curve exhibits an upward slope.

Exhibit 3.3 Example of Relationship between Maturity and Yield of Treasury Securities (as of March 2013)

 

The term structure of interest rates in  Exhibit 3.3  shows that securities that are similar in all ways except their term to maturity may offer different yields. Because the demand and supply conditions for securities may vary among maturities, so may the price (and therefore the yield) of securities. A comprehensive explanation of the term structure of interest rates is provided later in this chapter.

WEB

www.bloomberg.com

The section on market interest rates and bonds presents the most recent yield curve.

Since the yield curve in Exhibit 3.3 is based on Treasury securities, the curve is not influenced by credit risk. The yield curve for AA-rated corporate bonds would typically have a slope similar to that of the Treasury yield curve, but the yield of the corporate issue at any particular term to maturity would be higher to reflect the risk premium.

3-2 EXPLAINING ACRUAL YIELD DIFFERENTIALS

Even small differentials in yield can be relevant to financial institutions that are borrowing or investing millions of dollars. Yield differentials are sometimes measured in basis points; a basis point equals 0.01 percent, so 100 basis points equals 1 percent. If a security offers a yield of 4.3 percent while the a risk-free security offers a yield of 4.0 percent, then the yield differential is 0.30 percent or 30 basis points. Yield differentials are described for money market securities next, followed by differentials for capital market securities.

3-2a Yield Differentials of Money Market Securities

The yields offered on commercial paper (short-term securities offered by creditworthy firms) are typically just slightly higher than Treasury-bill rates, since investors require a slightly higher return (10 to 40 basis points on an annualized basis) to compensate for credit risk and less liquidity. Negotiable certificates of deposit offer slightly higher rates than yields on Treasury bills (“T-bills”) with the same maturity because of their lower degree of liquidity and higher degree of credit risk.

Market forces cause the yields of all securities to move in the same direction. To illustrate, assume that the budget deficit increases substantially and that the Treasury issues a large number of T-bills to finance the increased deficit. This action creates a large supply of T-bills in the market, placing downward pressure on the price and upward pressure on the T-bill yield. As the yield begins to rise, it approaches the yield of other short-term securities. Businesses and individual investors are now encouraged to purchase T-bills rather than these risky securities because they can achieve about the same yield while avoiding credit risk. The switch to T-bills lowers the demand for risky securities, thereby placing downward pressure on their price and upward pressure on their yields. Thus the risk premium on risky securities would not disappear completely.

3-2b Yield Differentials of Capital Market Securities

Municipal bonds have the lowest before-tax yield, yet their after-tax yield is typically above that of Treasury bonds from the perspective of investors in high tax brackets. Treasury bonds are expected to offer the lowest yield because they are free from credit risk and can easily be liquidated in the secondary market. Investors prefer municipal or corporate bonds over Treasury bonds only if the after-tax yield is sufficiently higher to compensate for the higher credit risk and lower degree of liquidity.

To illustrate how capital market security yields can vary over time because of credit risk,  Exhibit 3.4  shows yields of corporate bonds in two different credit risk classes. The Aaa-rated bonds have very low credit risk, whereas the BAA bonds are perceived to have slightly more risk. Notice that the yield differential between BAA bonds and AAA bonds was relatively large during the recessions (shaded areas), such as in 1991 and in the 2000–2003 period when economic conditions were weak. During these periods, corporations had to pay a relatively high premium if their bonds were rated Baa. The yield differential narrowed during 2004–2007, when economic conditions improved. However, during the credit crisis of 2008–2009, the yield differential increased substantially. At one point during the credit crisis, the yield differential was about 3 percentage points.

Exhibit 3.4 Yield Differentials of Corporate Bonds

 

Many corporations whose bonds are rated Baa or below were unwilling to issue bonds because of the high credit risk premium they would have to pay to bondholders. This illustrates why the credit crisis restricted access of corporations to credit.

3-3 ESTIMATING THE APPROPRIATE YIELD

The discussion so far suggests that the appropriate yield to be offered on a debt security is based on the risk-free rate for the corresponding maturity, with adjustments to capture various characteristics. A model that captures this estimate may be specified as follows:

Yn = Rf,n + DP + LP + TA

where

Yn	= yield of an n-day debt security
Rf,n	= yield return of an n-day Treasury risk-free security
DP	= default premium to compensate for credit risk
LP	= liquidity premium to compensate for less liquidity
TA	= adjustment due to the difference in tax status

These are the characteristics identified earlier that explain yield differentials among securities (special provisions applicable to bonds also may be included, as described in  Chapter 7 ). Although maturity is another characteristic that can affect the yield, it is not included here because it is controlled for by matching the maturity of the security with that of a risk-free security.

EXAMPLE

Suppose that the three-month T-bill’s annualized rate is 8 percent and that Elizabeth Company plans to issue 90-day commercial paper. Elizabeth Company must determine the default premium (DP) and liquidity premium (LP) to offer on its commercial paper in order to make it as attractive to investors as a three-month (13-week) T-bill. The federal tax status of commercial paper is the same as for T-bills. However, income earned from investing in commercial paper is subject to state taxes whereas income earned from investing in T-bills is not. Investors may require a premium for this reason alone if they reside in a location where state and (and perhaps local) income taxes apply.

Assume Elizabeth Company believes that a 0.7 percent default risk premium, a 0.2 percent liquidity premium, and a 0.3 percent tax adjustment are necessary to sell its commercial paper to investors. The appropriate yield to be offered on the commercial paper, Ycp, is then

Ycp,n	= Rf,n + DP + LP + TA
	= 8% + 0.7% + 0.2% + 0.3%
	= 9.2%

The appropriate commercial paper rate will change over time, perhaps because of changes in the risk-free rate and/or the default premium, liquidity premium, and tax adjustment factors.

Some corporations may postpone plans to issue commercial paper until the economy improves and the required premium for credit risk is reduced. Even then, however, the market rate of commercial paper may increase if interest rates increase.

EXAMPLE

If the default risk premium decreases from 0.7 percent to 0.5 percent but Rf,n increases from 8 percent to 8.7 percent, the appropriate yield to be offered on commercial paper (assuming no change in the previously assumed liquidity and tax adjustment premiums) would be

Ycp	= Rf,n + DP + LP + TA
	= 8.7% + 0.5% + 0.2% + 0.3%
	= 9.7%

The strategy of postponing the issuance of commercial paper would backfire in this example. Even though the default premium decreased by 0.2 percent, the general level of interest rates rose by 0.7 percent, so the net change in the commercial paper rate is +0.5 percent.

As this example shows, the increase in a security’s yield over time does not necessarily mean that the default premium has increased. The assessment of yields as described here could also be applied to long-term securities. If, for example, a firm desires to issue a 20-year corporate bond, it will use the yield of a new 20-year Treasury bond as the 20-year risk-free rate and add on the premiums for credit risk, liquidity risk, and so on when determining the yield at which it can sell corporate bonds.

A simpler and more general relationship is that the yield offered on a debt security is positively related to the prevailing risk-free rate and the security’s risk premium (RP). This risk premium captures any risk characteristics of the security, including credit risk and liquidity risk. A more detailed model for the yield of a debt security could be applied by including additional characteristics that can vary among bonds, such as whether the bond is convertible into stock and whether it contains a call premium. The conversion option is favorable for investors, so it could reduce the yield that needs to be offered on a bond. The call premium is unfavorable for investors, so it could increase the yield that needs to be offered on a bond.

3-4 A CLOSER LOOK AT THE TERM STRUCTURE

Of all the factors that affect the yields offered on debt securities, the one that is most difficult to understand is term to maturity. For this reason, a more comprehensive explanation of the relationship between term to maturity and annualized yield (referred to as the term structure of interest rates) is necessary.

Various theories have been used to explain the relationship between maturity and annualized yield of securities. These theories include pure expectations theory, liquidity premium theory, and segmented markets theory, and each is explained in this section.

3-4a Pure Expectations Theory

According to pure expectations theory, the term structure of interest rates (as reflected in the shape of the yield curve) is determined solely by expectations of interest rates.

Impact of an Expected Increase in Interest Rates  To understand how interest rate expectations may influence the yield curve, assume that the annualized yields of short-term and long-term risk-free securities are similar; that is, suppose the yield curve is flat. Then assume that investors begin to believe that interest rates will rise. Investors will respond by investing their funds mostly in the short term so that they can soon reinvest their funds at higher yields after interest rates increase. When investors flood the short-term market and avoid the long-term market, they may cause the yield curve to adjust as shown in Panel A of  Exhibit 3.5 . The large supply of funds in the short-term markets will force annualized yields down. Meanwhile, the reduced supply of long-term funds forces long-term yields up.

Even though the annualized short-term yields become lower than annualized long-term yields, investors in short-term funds are satisfied because they expect interest rates to rise. They will make up for the lower short-term yield when the short-term securities mature, and they reinvest at a higher rate (if interest rates rise) at maturity.

Assuming that the borrowers who plan to issue securities also expect interest rates to increase, they will prefer to lock in the present interest rate over a long period of time. Thus, borrowers will generally prefer to issue long-term securities rather than short-term securities. This results in a relatively small demand for short-term funds. Consequently, there is downward pressure on the yield of short-term funds. There is a corresponding increase in the demand for long-term funds by borrowers, which places upward pressure on long-term funds. Overall, the expectation of higher interest rates changes the demand for funds and the supply of funds in different maturity markets, which forces the original flat yield curve (labeled YC1 in the two rightmost graphs) to pivot upward (counterclockwise) and become upward sloping (YC2).

Impact of an Expected Decline in Interest Rates  If investors expect interest rates to decrease in the future, they will prefer to invest in long-term funds rather than short-term funds because they could lock in today’s interest rate before interest rates fall. Borrowers will prefer to borrow short-term funds so that they can refinance at a lower interest rate once interest rates decline.

Exhibit 3.5 How Interest Rate Expectations Affect the Yield Curve

 

Based on the expectation of lower interest rates in the future, the supply of funds provided by investors will be low for short-term funds and high for long-term funds. This will place upward pressure on short-term yields and downward pressure on long-term yields, as shown in Panel B of  Exhibit 3.5 . Overall, the expectation of lower interest rates causes the shape of the yield curve to pivot downward (clockwise).

Algebraic Presentation  Investors monitor the yield curve to determine the rates that exist for securities with various maturities. They can either purchase a security with a maturity that matches their investment horizon or purchase a security with a shorter term and then reinvest the proceeds at maturity. They may select the strategy that they believe will generate a higher return over the entire investment horizon. This could affect the prices and yields of securities with different maturities, so that the expected return over the investment horizon is similar regardless of the strategy used. If investors were indifferent to maturities, the return of any security should equal the compounded yield of consecutive investments in shorter-term securities. That is, a two-year security should offer a return that is similar to the anticipated return from investing in two consecutive one-year securities. A four-year security should offer a return that is competitive with the expected return from investing in two consecutive two-year securities or four consecutive one-year securities, and so on.

EXAMPLE

To illustrate these equalities, consider the relationship between interest rates on a two-year security and a one-year security as follows:

(1 + ti2)2 = (1 + ti1)(1 + t+1r1)

where

ti 2	= known annualized interest rate of a two-year security as of time t
ti 1	= known annualized interest rate of a one-year security as of time t
t+1 r 1	= one-year interest rate that is anticipated as of time t + 1 (one year ahead)

The term i represents a quoted rate, which is therefore known, whereas r represents a rate to be quoted at some point in the future, so its value is uncertain. The left side of the equation represents the compounded yield to investors who purchase a two-year security, and the right side represents the anticipated compounded yield from purchasing a one-year security and reinvesting the proceeds in a new one-year security at the end of one year. If time t is today, then t+1r1 can be estimated by rearranging terms:

 

The term t+1r1, referred to as the  forward rate , is commonly estimated in order to represent the market’s forecast of the future interest rate. Here is a numerical example. Assume that, as of today (time t), the annualized two-year interest rate is 10 percent and the one-year interest rate is 8 percent. The forward rate is then estimated as follows:

 

This result implies that, one year from now, a one-year interest rate must equal about 12.037 percent in order for consecutive investments in two one-year securities to generate a return similar to that of a two-year investment. If the actual one-year rate beginning one year from now (i.e., at time t + 1) is above 12.037 percent, the return from two consecutive one-year investments will exceed the return on a two-year investment.

The forward rate is sometimes used as an approximation of the market’s consensus interest rate forecast. The reason is that, if the market had a different perception, the demand and supply of today’s existing two-year and one-year securities would adjust to capitalize on this information. Of course, there is no guarantee that the forward rate will forecast the future interest rate with perfect accuracy.

The greater the difference between the implied one-year forward rate and today’s one-year interest rate, the greater the expected change in the one-year interest rate. If the term structure of interest rates is solely influenced by expectations of future interest rates, the following relationships hold:

SCENARIO	STRUCTURE OF YIELD CURVE	EXPECTATIONS ABOUT THE FUTURE INTEREST RATE
1. t+1 r 1 >  ti 1	Upward slope	Higher than today’s rate
2. t+1 r 1 =  ti 1	Flat	Same as today’s rate
3. t+1 r 1 <  ti 1	Downward slope	Lower than today’s rate

Forward rates can be determined for various maturities. The relationships described here can be applied when assessing the change in the interest rate of a security with any particular maturity.

The previous example can be expanded to solve for other forward rates. The equality specified by the pure expectations theory for a three-year horizon is

 

All other terms were defined previously. By rearranging terms, we can isolate the forward rate of a one-year security beginning two years from now:

 

If the one-year forward rate beginning one year from now (t+1r1) has already been estimated, then this estimate can be combined with actual one-year and three-year interest rates to estimate the one-year forward rate two years from now. Recall that our previous example assumed ti1 = 8 percent and estimated t+1r1 to be about 12.037 percent.

EXAMPLE

Assume that a three-year security has an annualized interest rate of 11 percent (i.e., ti3 = 11 percent). Given this information, the one-year forward rate two years from now can be calculated as follows:

 

Thus, the market anticipates that, two years from now, the one-year interest rate will be 13.02736 percent.

The yield curve can also be used to forecast annualized interest rates for periods other than one year. For example, the information provided in the last example could be used to determine the two-year forward rate beginning one year from now.

According to pure expectations theory, a one-year investment followed by a two-year investment should offer the same annualized yield over the three-year horizon as a three-year security that could be purchased today. This relation is expressed as follows:

(1 + t+1i3)3 = (1 + ti1)(1 + t + 1r2)2

where t+1r2 is the annual interest rate of a two-year security anticipated as of time t+1. By rearranging terms, t+1r2 can be isolated:

(1 + t+1r2)2 =

(1 + ti3)

1 + ti1

EXAMPLE

Recall that today’s annualized yields for one-year and three-year securities are 8 percent and 11 percent, respectively. With this information, t+1r2 is estimated as follows:

 

Thus, the market anticipates an annualized interest rate of about 12.53 percent for two-year securities beginning one year from now.

Pure expectations theory is based on the premise that forward rates are unbiased estimators of future interest rates. If forward rates are biased, investors can attempt to capitalize on the bias.

EXAMPLE

In the previous numerical example, the one-year forward rate beginning one year ahead was estimated to be about 12.037 percent. If the forward rate was thought to contain an upward bias, the expected one-year interest rate beginning one year ahead would actually be less than 12.037 percent. Therefore, investors with funds available for two years would earn a higher yield by purchasing two-year securities rather than purchasing one-year securities for two consecutive years. However, their actions would cause an increase in the price of two-year securities and a decrease in that of one-year securities, and the yields of these securities would move inversely with the price movements. Hence any attempt by investors to capitalize on the forward rate bias would essentially eliminate the bias.

If forward rates are unbiased estimators of future interest rates, financial market efficiency is supported and the information implied by market rates about the forward rate cannot be used to generate abnormal returns. In response to new information, investor preferences would change, yields would adjust, and the implied forward rate would adjust as well.

If a long-term rate is expected to equal a geometric average of consecutive short-term rates covering the same time horizon (as is suggested by pure expectations theory), longterm rates would likely be more stable than short-term rates. As expectations about consecutive short-term rates change over time, the average of these rates is less volatile than the individual short-term rates. Thus long-term rates are much more stable than short-term rates.

3-4b Liquidity Premium Theory

Some investors may prefer to own short-term rather than long-term securities because a shorter maturity represents greater liquidity. In this case, they may be willing to hold long-term securities only if compensated by a premium for the lower degree of liquidity. Although long-term securities can be liquidated prior to maturity, their prices are more sensitive to interest rate movements. Short-term securities are normally considered to be more liquid because they are more likely to be converted to cash without a loss in value.

The preference for the more liquid short-term securities places upward pressure on the slope of a yield curve. Liquidity may be a more critical factor to investors at some times than at others, and the liquidity premium will accordingly change over time. As it does, the yield curve will change also. This is the liquidity premium theory (sometimes referred to as the liquidity preference theory).

 Exhibit 3.6  contains three graphs that reflect the existence of both expectations theory and a liquidity premium. Each graph shows different interest rate expectations by the market. Regardless of the interest rate forecast, the yield curve is affected in a similar manner by the liquidity premium.

Exhibit 3.6 Impact of Liquidity Premium on the Yield Curve under Three Different Scenarios

 

Estimation of the Forward Rate Based on a Liquidity Premium  When expectations theory is combined with liquidity theory, the yield on a security will not necessarily be equal to the yield from consecutive investments in shorter-term securities over the same investment horizon. For example, the yield on a two-year security is now determined as

(1 + t+1i2)2 = (1 + ti1)(1 + t+1r1 + LP2

where LP2 denotes the liquidity premium on a two-year security. The yield generated from the two-year security should exceed the yield from consecutive investments in one-year securities by a premium that compensates the investor for less liquidity. The relationship between the liquidity premium and term to maturity can be expressed as follows:

0 < LP1 < LP2 < LP3 < ··· < LP20

where the subscripts represent years to maturity. This implies that the liquidity premium would be more influential on the difference between annualized interest rates on one-year and 20-year securities than on the difference between one-year and two-year securities.

If liquidity influences the yield curve, the forward rate overestimates the market’s expectation of the future interest rate. A more appropriate formula for the forward rate would account for the liquidity premium. By rearranging terms in the previous equation for forward rates, the one-year forward rate can be derived as follows:

t+1r1 =

(1 + ti2)2

1 + ti1

− 1 −

LP2

1 + ti1

EXAMPLE

Reconsider the example where i1 = 8 percent and i2 = 10 percent, and assume that the liquidity premium on a two-year security is 0.5 percent. The one-year forward rate can then be derived from this information as follows:

 

This estimate of the one-year forward rate is lower than the estimate derived in the previous related example in which the liquidity premium was not considered. The previous estimate (12.037 percent) of the forward rate probably overstates the market’s expected interest rate because it did not account for a liquidity premium. Thus forecasts of future interest rates implied by a yield curve are reduced slightly when accounting for the liquidity premium.

Even with the existence of a liquidity premium, yield curves could still be used to interpret interest rate expectations. A flat yield curve would be interpreted to mean that the market is expecting a slight decrease in interest rates (without the effect of the liquidity premium, the yield curve would have had a slight downward slope). A slight upward slope would be interpreted as no expected change in interest rates: if the liquidity premium were removed, this yield curve would be flat.

3-4c Segmented Markets Theory

According to the segmented markets theory, investors and borrowers choose securities with maturities that satisfy their forecasted cash needs. Pension funds and life insurance companies may generally prefer long-term investments that coincide with their long-term liabilities. Commercial banks may prefer more short-term investments to coincide with their short-term liabilities. If investors and borrowers participate only in the maturity market that satisfies their particular needs, then markets are segmented. That is, investors (or borrowers) will shift from the long-term market to the short-term market, or vice versa, only if the timing of their cash needs changes. According to segmented markets theory, the choice of long-term versus short-term maturities is determined more by investors’ needs than by their expectations of future interest rates.

EXAMPLE

Assume that most investors have funds available to invest for only a short period of time and therefore desire to invest primarily in short-term securities. Also assume that most borrowers need funds for a long period of time and therefore desire to issue mostly long-term securities. The result will be downward pressure on the yield of short-term securities and upward pressure on the yield of long-term securities. Overall, the scenario described would create an upward-sloping yield curve.

Now consider the opposite scenario in which most investors wish to invest their funds for a long period of time while most borrowers need funds for only a short period of time. According to segmented markets theory, this situation will cause upward pressure on the yield of short-term securities and downward pressure on the yield of long-term securities. If the supply of funds provided by investors and the demand for funds by borrowers were better balanced between the short-term and long-term markets, the yields of short-and long-term securities would be more similar.

The preceding example distinguished maturity markets as either short-term or longterm. In reality, several maturity markets may exist. Within the short-term market, some investors may prefer maturities of one month or less whereas others may prefer maturities of one to three months. Regardless of how many maturity markets exist, the yields of securities with various maturities should be influenced in part by the desires of investors and borrowers to participate in the maturity market that best satisfies their needs. A corporation that needs additional funds for 30 days would not consider issuing long-term bonds for such a purpose. Savers with short-term funds would avoid some long-term investments (e.g., 10-year certificates of deposit) that cannot be easily liquidated.

Limitation of the Theory  A limitation of segmented markets theory is that some borrowers and savers have the flexibility to choose among various maturity markets. Corporations that need long-term funds may initially obtain short-term financing if they expect interest rates to decline, and investors with long-term funds may make short-term investments if they expect interest rates to rise. Moreover, some investors with short-term funds may be willing to purchase long-term securities that have an active secondary market.

Some financial institutions focus on a particular maturity market, but others are more flexible. Commercial banks obtain most of their funds in short-term markets but spread their investments into short-, medium-, and long-term markets. Savings institutions have historically focused on attracting short-term funds and lending funds for long-term periods. Note that if maturity markets were completely segmented, then an interest rate adjustment in one market would have no impact on other markets. However, there is clear evidence that interest rates among maturity markets move nearly in concert over time. This evidence indicates that there is some interaction among markets, which implies that funds are being transferred across markets. Note also that the theory of segmented markets conflicts with the general presumption of pure expectations theory that maturity markets are perfect substitutes for one another.

Implications  Although markets are not completely segmented, the preference for particular maturities can affect the prices and yields of securities with different maturities and thereby affect the yield curve’s shape. For this reason, the theory of segmented markets seems to be a partial explanation for the yield curve’s shape but not the sole explanation.

A more flexible variant of segmented markets theory, known as preferred habitat theory, offers a compromise explanation for the term structure of interest rates. This theory proposes that, although investors and borrowers may normally concentrate on a particular maturity market, certain events may cause them to wander from their “natural” market. For example, commercial banks that obtain mostly short-term funds may select investments with short-term maturities as a natural habitat. However, if they wish to benefit from an anticipated decline in interest rates, they may select medium- and long-term maturities instead. Preferred habitat theory acknowledges that natural maturity markets may influence the yield curve, but it also recognizes that interest rate expectations could entice market participants to stray from their natural, preferred markets.

3-4d Research on Term Structure Theories

Much research has been conducted on the term structure of interest rates and has offered considerable insight into the various theories. Researchers have found that interest rate expectations have a strong influence on the term structure of interest rates. However, the forward rate derived from a yield curve does not accurately predict future interest rates, and this suggests that other factors may be relevant. The liquidity premium, for example, could cause consistent positive forecasting errors, meaning that forward rates tend to overestimate future interest rates. Studies have documented variation in the yield–maturity relationship that cannot be entirely explained by interest rate expectations or liquidity. The variation could therefore be attributed to different supply and demand conditions for particular maturity segments.

General Research Implications  Although the results of research differ, there is some evidence that expectations theory, liquidity premium theory, and segmented markets theory all have some validity. Thus, if term structure is used to assess the market’s expectations of future interest rates, then investors should first “net out” the liquidity premium and any unique market conditions for various maturity segments.

3-5 INTEGRATING THE THEORIES OF TERM STRUCTURE

In order to understand how all three theories can simultaneously affect the yield curve, first assume the following conditions.

· 1. Investors and borrowers who select security maturities based on anticipated interest rate movements currently expect interest rates to rise.

Exhibit 3.7Effect of Conditions in Example of Yield Curve

 

· 2. Most borrowers are in need of long-term funds, while most investors have only short-term funds to invest.

· 3. Investors prefer more liquidity to less.

The first condition, which is related to expectations theory, suggests the existence of an upward-sloping yield curve (other things being equal); see curve E in  Exhibit 3.7 . The segmented markets information (condition 2) also favors the upward-sloping yield curve. When conditions 1 and 2 are considered simultaneously, the appropriate yield curve may look like curve E + S in the graph. The third condition (regarding liquidity) would then place a higher premium on the longer-term securities because of their lower degree of liquidity. When this condition is included with the first two, the yield may be represented by curve E + S + L.

In this example, all conditions placed upward pressure on long-term yields relative to short-term yields. In reality, there will sometimes be offsetting conditions: one condition may put downward pressure on the slope of the yield curve while other conditions cause upward pressure. If condition 1 in the example here were revised so that future interest rates were expected to decline, then this condition (by itself) would result in a downward-sloping yield curve. So when combined with the other conditions, which imply an upward-sloping curve, the result would be a partial offsetting effect. The actual yield curve would exhibit a downward slope if the effect of the interest rate expectations dominated the combined effects of segmented markets and a liquidity premium. In contrast, there would be an upward slope if the liquidity premium and segmented markets effects dominated the effects of interest rate expectations.

3-5a Use of the Term Structure

The term structure of interest rates is used to forecast interest rates, to forecast recessions, and to make investment and financing decisions.

Forecasting Interest Rates  At any point in time, the shape of the yield curve can be used to assess the general expectations of investors and borrowers about future interest rates. Recall from expectations theory that an upward-sloping yield curve generally results from the expectation of higher interest rates whereas a downward-sloping yield curve generally results from the expectation of lower interest rates. Expectations about future interest rates must be interpreted cautiously, however, because liquidity and specific maturity preferences could influence the yield curve’s shape. Still, it is generally believed that interest rate expectations are a major contributing factor to the yield curve’s shape. Thus the curve’s shape should provide a reasonable indication (especially once the liquidity premium effect is accounted for) of the market’s expectations about future interest rates.

Although they can use the yield curve to interpret the market’s consensus expectation of future interest rates, investors may have their own interest rate projections. By comparing their projections with those implied by the yield curve, they can attempt to capitalize on the difference. For example, if an upward-sloping yield curve exists, investors expecting stable interest rates could benefit from investing in long-term securities. From their perspective, long-term securities are undervalued because they reflect the market’s (presumed incorrect) expectation of higher interest rates. Strategies such as this are effective only if the investor can consistently forecast better than the market.

Forecasting Recessions  Some analysts believe that flat or inverted yield curves indicate a recession in the near future. The rationale for this belief is that, given a positive liquidity premium, such yield curves reflect the expectation of lower interest rates. This in turn is commonly associated with expectations of a reduced demand for loanable funds, which could be attributed to expectations of a weak economy.

The yield curve became flat or slightly inverted in 2000. At that time, the shape of the curve indicated expectations of a slower economy, which would result in lower interest rates. In 2001, the economy weakened considerably. And in March 2007, the yield curve exhibited a slight negative slope that caused some market participants to forecast a recession. During the credit crisis in 2008 and in the following two years, yields on Treasury securities with various maturities declined. The short-term interest rates experienced the most pronounced decline, which resulted in an upward-sloping yield curve in 2010.

Making Investment Decisions  If the yield curve is upward sloping, some investors may attempt to benefit from the higher yields on longer-term securities even though they have funds to invest for only a short period of time. The secondary market allows investors to implement this strategy, which is known as riding the yield curve. Consider an upward-sloping yield curve such that some one-year securities offer an annualized yield of 7 percent while 10-year bonds offer an annualized yield of 10 percent. An investor with funds available for one year may decide to purchase the bonds and sell them in the secondary market after one year. The investor earns 3 percent more than was possible on the one-year securities, but only if the bonds can be sold (after one year) at the price for which they were purchased. The risk of this strategy is the uncertainty in the price for which the security can be sold in the near future. If the upward-sloping yield is interpreted as the market’s consensus of higher interest rates in the future, then the price of a security would be expected to decrease in the future.

The yield curve is commonly monitored by financial institutions whose liability maturities are distinctly different from their asset maturities. Consider a bank that obtains much of its funds through short-term deposits and uses the funds to provide long-term loans or purchase long-term securities. An upward-sloping yield curve is favorable to the bank because annualized short-term deposit rates are significantly lower than annualized long-term investment rates. The bank’s spread is higher than it would be if the yield curve were flat. However, if it believes that the upward slope of the yield curve indicates higher interest rates in the future (as predicted by expectations theory), then the bank will expect its cost of liabilities to increase over time because future deposits would be obtained at higher interest rates.

Making Decisions about Financing  The yield curve is also useful for firms that plan to issue bonds. By assessing the prevailing rates on securities for various maturities, firms can estimate the rates to be paid on bonds with different maturities. This may enable them to determine the maturity of the bonds they issue. If they need funds for a two-year period, but notice from the yield curve that the annualized yield on one-year debt is much lower than that of two-year debt, they may consider borrowing for a one-year period. After one year when they pay off this debt, they will need to borrow funds for another one-year period.

3-5b Why the Slope of the Yield Curve Changes

If interest rates at all maturities were affected in the same manner by existing conditions, then the slope of the yield curve would remain unchanged. However, conditions may cause short-term yields to change in a manner that differs from the change in long-term yields.

EXAMPLE

Suppose that last July the yield curve had a large upward slope, as shown by yield curve YC1 in  Exhibit 3.8 . Since then, the Treasury decided to restructure its debt by retiring $300 billion of long-term Treasury securities and increasing its offering of short-term Treasury securities. This caused a large increase in the demand for short-term funds and a large decrease in the demand for long-term funds. The increase in the demand for short-term funds caused an increase in short-term interest rates and thereby increased the yields offered on newly issued short-term securities. Conversely, the decline in demand for long-term funds caused a decrease in long-term interest rates and thereby reduced the yields offered on newly issued long-term securities. Today, the yield curve is YC2 and is much flatter than it was last July.

Exhibit 3.8 Potential Impact of Treasury Shift from Long-term to Short-term Financing

 

3-5c How the Yield Curve Has Changed over Time

Yield curves at various dates are illustrated in  Exhibit 3.9 . The yield curve is usually upward sloping, but a slight downward slope has sometimes been evident (see the exhibit’s curve for March 21, 2007). Observe that the yield curve for March 18, 2013, is below the other yield curves shown in the exhibit, which means that the yield to maturity was relatively low regardless of the maturity considered. This curve existed during the credit crisis, when economic conditions were extremely weak.

3-5d International Structure of Interest Rates

 

Because the factors that affect the shape of the yield curve can vary among countries, the yield curve’s shape at any given time also varies among countries. Exhibit 3.10 plots the yield curve for six different countries in July 2013. Each country has a different currency with its own interest rate levels for various maturities, and each country’s interest rates are based on conditions of supply and demand.

Interest rate movements across countries tend to be positively correlated as a result of internationally integrated financial markets. Nevertheless, the actual interest rates may vary significantly across countries at a given point in time. This implies that the difference in interest rates is attributable primarily to general supply and demand conditions across countries and less so to differences in default risk premiums, liquidity premiums, or other characteristics of the individual securities.

Exhibit 3.9 Yield Curves at Various Points in Time

 

Exhibit 3.10 Yield Curves among Foreign Countries (as of July 2013)

 

Because forward rates (as defined in this chapter) reflect the market’s expectations of future interest rates, the term structure of interest rates for various countries should be monitored for the following reasons. First, with the integration of financial markets, movements in one country’s interest rate can affect interest rates in other countries. Thus some investors may estimate the forward rate in a foreign country to predict the foreign interest rate, which in turn may affect domestic interest rates. Second, foreign securities and some domestic securities are influenced by foreign economies, which are dependent on foreign interest rates. If the foreign forward rates can be used to forecast foreign interest rates, they can enhance forecasts of foreign economies. Because exchange rates are also influenced by foreign interest rates, exchange rate projections may be more accurate when foreign forward rates are used to forecast foreign interest rates.

If the real interest rate were fixed, inflation rates for future periods could be predicted for any country in which the forward rate could be estimated. Recall from  Chapter 2  that the nominal interest rate consists of an expected inflation rate plus a real interest rate. Because the forward rate represents an expected nominal interest rate for a future period, it also represents an expected inflation rate plus a real interest rate in that period. The expected inflation in that period is estimated as the difference between the forward rate and the real interest rate.

SUMMARY

· ▪ Quoted yields of debt securities at any given time may vary for the following reasons. First, securities with higher credit (default) risk must offer a higher yield. Second, securities that are less liquid must offer a higher yield. Third, taxable securities must offer a higher before-tax yield than tax-exempt securities. Fourth, securities with longer maturities offer a different yield (not consistently higher or lower) than securities with shorter maturities.

· ▪ The appropriate yield for any particular debt security can be estimated by first determining the risk-free yield that is currently offered by a Treasury security with a similar maturity. Then adjustments are made that account for credit risk, liquidity, tax status, and other provisions.

· ▪ The term structure of interest rates can be explained by three theories. The pure expectations theory suggests that the shape of the yield curve is dictated by interest rate expectations. The liquidity premium theory suggests that securities with shorter maturities have greater liquidity and therefore should not have to offer as high a yield as securities with longer terms to maturity. The segmented markets theory suggests that investors and borrowers have different needs that cause the demand and supply conditions to vary across different maturities; in other words, there is a segmented market for each term to maturity, which causes yields to vary among these maturity markets. Consolidating the theories suggests that the term structure of interest rates depends on interest rate expectations, investor preferences for liquidity, and the unique needs of investors and borrowers in each maturity market.

POINT COUNTER-POINT

Should a Yield Curve Influence a Borrower’s Preferred Maturity of a Loan?

Point  Yes. If there is an upward-sloping yield curve, then a borrower should pursue a short-term loan to capitalize on the lower annualized rate charged for a short-term period. The borrower can obtain a series of short-term loans rather than one loan to match the desired maturity.

Counter-Point  No. The borrower will face uncertainty regarding the interest rate charged on subsequent QUESTIONS AND APPLICATIONS 1. Characteristics That Affect Security Yields Identify the relevant characteristics of any security that can affect its yield. 2. Impact of Credit Risk on Yield What effect does a high credit risk have on securities? 3. Impact of Liquidity on Yield Discuss the relationship between the yield and liquidity of securities. 4. Tax Effects on Yields Do investors in high tax brackets or those in low tax brackets benefit more from tax-exempt securities? Why? At a given point in time, loans that are needed. An upward-sloping yield curve suggests that interest rates may rise in the future, which will cause the cost of borrowing to increase. Overall, the cost of borrowing may be higher when using a series of loans than when matching the debt maturity to the time period in which funds are needed.

Who Is Correct?  Use the Internet to learn more about this issue and then formulate your own opinion.

QUESTIONS AND APPLICATIONS

· 1. Characteristics That Affect Security Yields Identify the relevant characteristics of any security that can affect its yield.

· 2. Impact of Credit Risk on Yield What effect does a high credit risk have on securities?

· 3. Impact of Liquidity on Yield Discuss the relationship between the yield and liquidity of securities.

· 4. Tax Effects on Yields Do investors in high tax brackets or those in low tax brackets benefit more from tax-exempt securities? Why? At a given point in time, which offers a higher before-tax yield: municipal bonds or corporate bonds? Why? Which has the higher aftertax yield? If taxes did not exist, would Treasury bonds offer a higher or lower yield than municipal bonds with the same maturity? Why?

· 5. Pure Expectations Theory Explain how a yield curve would shift in response to a sudden expectation of rising interest rates, according to the pure expectations theory.

· 6. Forward Rate What is the meaning of the forward rate in the context of the term structure of interest rates? Why might forward rates consistently overestimate future interest rates? How could such a bias be avoided?

· 7. Pure Expectation Theory Assume there is a sudden expectation of lower interest rates in the future. What would be the effect on the shape of the yield curve? Explain.

· 8. Liquidity Premium Theory Explain the liquidity premium theory.

· 9. Impact of Liquidity Premium on Forward Rate Explain how consideration of a liquidity premium affects the estimate of a forward interest rate.

· 10. Segmented Markets Theory If a downward-sloping yield curve is mainly attributed to segmented markets theory, what does that suggest about the demand for and supply of funds in the short-term and long-term maturity markets?

· 11. Segmented Markets Theory If the segmented markets theory causes an upward-sloping yield curve, what does this imply? If markets are not completely segmented, should we dismiss the segmented markets theory as even a partial explanation for the term structure of interest rates? Explain.

· 12. Preferred Habitat Theory Explain the preferred habitat theory.

· 13. Yield Curve What factors influence the shape of the yield curve? Describe how financial market participants use the yield curve.

Advanced Questions

· 14. Segmented Markets Theory Suppose that the Treasury decides to finance its deficit with mostly longterm funds. How could this decision affect the term structure of interest rates? If short-term and long-term markets were segmented, would the Treasury’s decision have a more or less pronounced impact on the term structure? Explain.

· 15. Yield Curve Assuming that liquidity and interest rate expectations are both important for explaining the shape of a yield curve, what does a flat yield curve indicate about the market’s perception of future interest rates?

· 16. Global Interaction among Yield Curves Assume that the yield curves in the United States, France, and Japan are flat. If the U.S. yield curve suddenly becomes positively sloped, do you think the yield curves in France and Japan would be affected? If so, how?

· 17. Multiple Effects on the Yield Curve Assume that (1) investors and borrowers expect that the economy will weaken and that inflation will decline, (2) investors require a small liquidity premium, and (3) markets are partially segmented and the Treasury currently has a preference for borrowing in short-term markets. Explain how each of these forces would affect the term structure, holding other factors constant. Then explain the effect on the term structure overall.

· 18. Effect of Crises on the Yield Curve During some crises, investors shift their funds out of the stock market and into money market securities for safety, even if they do not fear rising interest rates. Explain how and why these actions by investors affect the yield curve. Is the shift best explained by expectations theory, liquidity premium theory, or segmented markets theory?

· 19. How the Yield Curve May Respond to Prevailing Conditions Consider how economic conditions affect the default risk premium. Do you think the default risk premium will likely increase or decrease during this semester? How do you think the yield curve will change during this semester? Offer some logic to support your answers.

· 20. Assessing Interest Rate Differentials among Countries In countries experiencing high inflation, the annual interest rate may exceed 50 percent; in other countries, such as the United States and many European countries, annual interest rates are typically less than 10 percent. Do you think such a large difference in interest rates is due primarily to the difference between countries in the risk-free rates or in the credit risk premiums? Explain.

· 21. Applying the Yield Curve to Risky Debt Securities Assume that the yield curve for Treasury bonds has a slight upward slope, starting at 6 percent for a 10-year maturity and slowly rising to 8 percent for a 30-year maturity. Create a yield curve that you believe would exist for A-rated bonds and a corresponding one for B-rated bonds.

· 22. Changes to Credit Rating Process Explain how credit raters have changed their process following criticism of their ratings during the credit crisis.

Interpreting Financial News

Interpret the following comments made by Wall Street analysts and portfolio managers.

· a. “An upward-sloping yield curve persists because many investors stand ready to jump into the stock market.”

· b. “Low-rated bond yields rose as recession fears caused a flight to quality.”

· c. “The shift from an upward-sloping yield curve to a downward-sloping yield curve is sending a warning about a possible recession.”?

Managing in Financial Markets

Monitoring Yield Curve Adjustments As an analyst of a bond rating agency, you have been asked to interpret the implications of the recent shift in the yield curve. Six months ago, the yield curve exhibited a slight downward slope. Over the last six months, long-term yields declined while short-term yields remained the same. Analysts said that the shift was due to revised expectations of interest rates.

· a. Given the shift in the yield curve, does it appear that firms increased or decreased their demand for long-term funds over the last six months?

· b. Interpret what the shift in the yield curve suggests about the market’s changing expectations of future interest rates.

· c. Recently, an analyst argued that the underlying reason for the yield curve shift is that many large U.S. firms anticipate a recession. Explain why an anticipated recession could force the yield curve to shift as it has.

· d. What could the specific shift in the yield curve signal about the ratings of existing corporate bonds? What types of corporations would be most likely to experience a change in their bond ratings as a result of this shift in the yield curve?

PROBLEMS

· 1. Forward Rate

· a. Assume that, as of today, the annualized two-year interest rate is 13 percent and the one-year interest rate is 12 percent. Use this information to estimate the one-year forward rate.

· b. Assume that the liquidity premium on a two-year security is 0.3 percent. Use this information to estimate the one-year forward rate.

· 2. Forward Rate Assume that, as of today, the annualized interest rate on a three-year security is 10 percent and the annualized interest rate on a two-year security is 7 percent. Use this information to estimate the one-year forward rate two years from now.

· 3. Forward Rate If ti1 > ti2, what is the market consensus forecast about the one-year forward rate one year from now? Is this rate above or below today’s one-year interest rate? Explain.

· 4. After-Tax Yield You need to choose between investing in a one-year municipal bond with a 7 percent yield and a one-year corporate bond with an 11 percent yield. If your marginal federal income tax rate is 30 percent and no other differences exist between these two securities, which would you invest in?

· 5. Deriving Current Interest Rates Assume that interest rates for one-year securities are expected to be 2 percent today, 4 percent one year from now, and 6 percent two years from now. Using only pure expectations theory, what are the current interest rates on two-year and three-year securities?

· 6. Commercial Paper Yield

· a. A corporation is planning to sell its 90-day commercial paper to investors by offering an 8.4 percent yield. If the three-month T-bill’s annualized rate is 7 percent, the default risk premium is estimated to be 0.6 percent, and there is a 0.4 percent tax adjustment, then what is the appropriate liquidity premium?

· b. Suppose that, because of unexpected changes in the economy, the default risk premium increases to 0.8 percent. Assuming that no other changes occur, what is the appropriate yield to be offered on the commercial paper?

· 7. Forward Rate

· a. Determine the forward rate for various one-year interest rate scenarios if the two-year interest rate is 8 percent, assuming no liquidity premium. Explain the relationship between the one-year interest rate and the one-year forward rate while holding the two-year interest rate constant.

· b. Determine the one-year forward rate for the same one-year interest rate scenarios described in question (a) while assuming a liquidity premium of 0.4 percent. Does the relationship between the one-year interest rate and the forward rate change when the liquidity premium is considered?

· c. Determine how the one-year forward rate would be affected if the quoted two-year interest rate rises; hold constant the quoted one-year interest rate as well as the liquidity premium. Explain the logic of this relationship.

· d. Determine how the one-year forward rate would be affected if the liquidity premium rises and if the quoted one-year interest rate is held constant. What if the quoted two-year interest rate is held constant? Explain the logic of this relationship.

· 8. After-Tax Yield Determine how the after-tax yield from investing in a corporate bond is affected by higher tax rates, holding the before-tax yield constant. Explain the logic of this relationship.

· 9. Debt Security Yield

· a. Determine how the appropriate yield to be offered on a security is affected by a higher risk-free rate. Explain the logic of this relationship.

· b. Determine how the appropriate yield to be offered on a security is affected by a higher default risk premium. Explain the logic of this relationship.

FLOW OF FUNDS EXERCISE

Influence of the Structure of Interest Rates

Recall that Carson Company has obtained substantial loans from finance companies and commercial banks. The interest rate on the loans is tied to the six-month Treasury bill rate (and includes a risk premium) and is adjusted every six months. Therefore, Carson’s cost of obtaining funds is sensitive to interest rate movements. The company expects that the U.S. economy will strengthen, so it plans to grow in the future by expanding its business and by making acquisitions. Carson anticipates needing substantial long-term financing to pay for its growth and plans to borrow additional funds, either through loans or by issuing bonds; it is also considering issuing stock to raise funds in the next year.

· a. Assume that the market’s expectations for the economy are similar to Carson’s expectations. Also assume that the yield curve is primarily influenced by interest rate expectations. Would the yield curve be upward sloping or downward sloping? Why?

· b. If Carson could obtain more debt financing for 10- year projects, would it prefer to obtain credit at a longterm fixed interest rate or at a floating rate? Why?

· c. If Carson attempts to obtain funds by issuing 10-year bonds, explain what information would help in estimating the yield it would have to pay on 10-year bonds. That is, what are the key factors that would influence the rate Carson would pay on its 10-year bonds?

· d. If Carson attempts to obtain funds by issuing loans with floating interest rates every six months, explain what information would help in estimating the yield it would have to pay over the next 10 years. That is, what are the key factors that would influence the rate Carson would pay over the 10-year period?

· e. An upward-sloping yield curve suggests that the initial rate financial institutions could charge on a longterm loan to Carson would be higher than the initial rate they could charge on a loan that floats in accordance with short-term interest rates. Does this imply that creditors should prefer offering Carson a fixed-rate loan to offering them a floating-rate loan? Explain why Carson’s expectations of future interest rates are not necessarily the same as those of some financial institutions.

INTERNET/EXCEL EXERCISES

· 1. Assess the shape of the yield curve by using the website  www.bloomberg.com . Click on “Market data” and then on “Rates & bonds.” Is the Treasury yield curve upward or downward sloping? What is the yield of a 90-day Treasury bill? What is the yield of a 30-year Treasury bond?

· 2. Based on the various theories attempting to explain the yield curve’s shape, what could explain the difference between the yields of the 90-day Treasury bill and the 30-year Treasury bond? Which theory, in your opinion, is the most reasonable? Why?

WSJ EXERCISE

Interpreting the Structure of Interest Rates

· a. Explaining Yield Differentials Using the most recent issue of the Wall Street Journal, review the yields for the following securities:

TYPE	MATURITY	YIELD
Treasury	10-year	___
Corporate: high-quality	10-year	___
Corporate: medium-quality	10-year	___
Municipal (tax-exempt)	10-year	___

· If credit (default) risk is the only reason for the yield differentials, then what is the default risk premium on the corporate high-quality bonds? On the medium-quality bonds?

·    During a recent recession, high-quality corporate bonds offered a yield of 0.8 percent above Treasury bonds while medium-quality bonds offered a yield of about 3.1 percent above Treasury bonds. How do these yield differentials compare to the differentials today? Explain the reason for any change.

·    Using the information in the previous table, complete the following table. In Column 2, indicate the before-tax yield necessary to achieve the existing after-tax yield of tax-exempt bonds. In Column 3, answer this question: If the tax-exempt bonds have the same risk and other features as high-quality corporate bonds, which type of bond is preferable for investors in each tax bracket?

MARGINAL TAX BRACKET OF INVESTORS	EQUIVALENT BEFORE-TAX YIELD	PREFERRED BOND
10%	___	___
15%	___	___
20%	___	___
28%	___	___
34%	___	___

· b. Examining Recent Adjustments in Credit Risk Using the most recent issue of the Wall Street Journal, review the corporate debt section showing the high-yield issue with the biggest price decrease.

· ▪ Why do you think there was such a large decrease in price?

· ▪ How does this decrease in price affect the expected yield for any investors who buy bonds now?

· c. Determining and Interpreting Today’s Term Structure Using the most recent issue of the Wall Street Journal, review the yield curve to determine the approximate yields for the following maturities:

TERM TO MATURITY	ANNUALIZED YIELD
1 year	___
2 years	___
3 years	___

·    Assuming that the differences in these yields are due solely to interest rate expectations, determine the one-year forward rate as of one year from now and the one-year forward rate as of two years from now.

· d. The Wall Street Journal  provides a “Treasury Yield Curve.” Use this curve to describe the market’s expectations about future interest rates. If a liquidity premium exists, how would this affect your perception of the market’s expectations?

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. credit risk

· 2. credit ratings AND risk

· 3. risk premium

· 4. yield curve

· 5. yield curve AND interest rate

· 6. interest rate AND liquidity premium

· 7. interest rate AND credit risk

· 8. rating agency AND risk

· 9. term structure AND maturity

· 10. yield curve AND financing

PART 1 INTEGRATIVE PROBLEM: Interest Rate Forecasts and Investment Decisions

This problem requires an understanding of how economic conditions affect interest rates and bond yields ( Chapters 1 ,  2 , and  3 ).

Your task is to use information about existing economic conditions to forecast U.S. and Canadian interest rates. The following information is available to you.

· 1. Over the past six months, U.S. interest rates have declined and Canadian interest rates have increased.

· 2. The U.S. economy has weakened over the past year while the Canadian economy has improved.

· 3. The U.S. saving rate (proportion of income saved) is expected to decrease slightly over the next year; the Canadian saving rate will remain stable.

· 4. The U.S. and Canadian central banks are not expected to implement any policy changes that would have a significant impact on interest rates.

· 5. You expect the U.S. economy to strengthen considerably over the next year but still be weaker than it was two years ago. You expect the Canadian economy to remain stable.

· 6. You expect the U.S. annual budget deficit to increase slightly from last year but be significantly less than the average annual budget deficit over the past five years. You expect the Canadian budget deficit to be about the same as last year.

· 7. You expect the U.S. inflation rate to rise slightly but still remain below the relatively high levels of two years ago; you expect the Canadian inflation rate to decline.

· 8. Based on some events last week, most economists and investors around the world (including yourself) expect the U.S. dollar to weaken against the Canadian dollar and against other foreign currencies over the next year. This expectation was already accounted for in your forecasts of inflation and economic growth.

· 9. The yield curve in the United States currently exhibits a consistent downward slope. The yield curve in Canada currently exhibits an upward slope. You believe that the liquidity premium on securities is quite small.

Questions

· 1. Using the information available to you, forecast the direction of U.S. interest rates.

· 2. Using the information available to you, forecast the direction of Canadian interest rates.

· 3. Assume that the perceived risk of corporations in the United States is expected to increase. Explain how the yield of newly issued U.S. corporate bonds will change to a different degree than will the yield of newly issued U.S. Treasury bonds.

 

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