Relationship Between Risk and Return - Financial Management

The trade-off between risk and return is a key element of effective financial decision making. This includes both decisions by individuals (and financial institutions) to invest in financial assets, such as common stocks, bonds, and other securities, and decisions by a firm’s managers to invest in physical assets, such as new plants and equipment.

Risk and Return Relationship in Financial Management

The relationship between risk and required return was introduced. The relationship between risk and required rate of return can be expressed as follows:

Required rate of return = Risk-free rate of return + Risk premium

A risk premium is a potential “reward” that an investor expects to receive when making a risky investment. Investors are generally considered to be risk averse; that is, they expect, on average, to be compensated for the risk they assume when making an investment. Thus, over the long term, expected returns and required returns from securities will tend to be equal.

The rate of return required by investors in financial assets is determined in the financial marketplace and depends on the supply of funds available as well as the demand for these funds. Investors who buy bonds receive interest payments and a return of principal as compensation for postponing consumption and accepting risk. Similarly, common stock investors expect to receive dividends and price appreciation from their stock. The rate of return required by these investors represents a cost of capital to the firm.

This required rate of return is used by a firm’s managers when computing the net present value of the cash flows expected to be generated from the company’s investments. The required rate of return on a security is also an important determinant of the market value of financial securities, including common stock, preferred stock, and bonds. The following sections focus on the two components of the required rate of return —the risk-free return and the risk premium—and also look at the historical relationship between risk and rates of return on various types of securities.

Explain the Relationship Between Risk and Return

Risk-Free Rate of Return

The concept of a (nominal) risk-free rate of return, rf , refers to the return available on a security with no risk of default. In the case of debt securities, no default risk means that promised interest and principal payments are guaranteed to be made. Short-term U.S. government securities, such as Treasury bills, are generally considered to be risk-free investments.The risk-free rate of return, rf , is equal to the sum of a real rate of return and an expected inflation premium:

rf= Real rate of return + Expected inflation premium

The real rate of return is the return that investors would require from a security having no risk of default in a period of no expected inflation. It is the return necessary to convince investors to postpone current, real consumption opportunities. The real rate of return is determined by the interaction of the supply of funds made available by savers and the demand for funds for investment. Historically, the real rate of return has been estimated to average in the range of 2 to 4 percent.

The second component of the risk-free rate of return is an inflation premium or purchasing power loss premium. Investors require compensation for expected losses in purchasing power when they postpone current consumption and lend funds. Consequently, a premium for expected inflation is included in the required return on any security. The inflation premium is normally equal to investors’ expectations about future purchasing power changes. If, for example, inflation is expected to average 4 percent over some future period, the risk-free rate of return on U.S. Treasury bills (assuming a real rate of return of 3 percent) should be approximately equal to 3 percent + 4 percent = 7 percent by Equation . By extension, if inflation expectations suddenly increase from 4 to 6 percent, the risk-free rate should increase from 7 to 9 percent (3 percent real return plus 6 percent inflation premium).

At any point in time, the required risk-free rate of return on any security can be estimated from the yields on short-term U.S. government securities, such as 90-day Treasury bills. When considering return requirements on all types of securities, it is important to remember that increases in expected inflation rates normally lead to increases in the required rates of return on all securities.

Risk Premium

The risk premium assigned by an investor to a given security in determining the required rate of return (Equation 6.5) is a function of several different risk elements. These risk elements (and premiums) include

  • Maturity risk premium
  • Default risk premium
  • Seniority risk premium
  • Marketability risk premium

Each of these risk elements is examined here.

Maturity Risk Premium The return required on a security is influenced by the maturity of that security. The term structure of interest rates is the pattern of interest rate yields (required returns) for securities that differ only in the length of time to maturity. Plotting interest rate yields (percent) on the vertical axis and the length of time to maturity (years) on the horizontal axis results in a yield curve. Two yield curves for U.S. government securities are shown in Figure.

Two yield curves for U.S. government securities

Note the different shapes of the two yield curves. The yield curve for August 1981 is downward sloping, indicating that the longer the time to maturity, the lower the required return on the security. The yield curve for April 2004 is upward sloping, indicating that the longer the time to maturity, the higher the required return on the security.In general, the yield curve has been upward sloping more often than it has been downward sloping. For example, in April 2004, the yield on 3-month U.S. government Treasury bills was 0.97 percent. In contrast, the yield on 10-year U.S. government bonds was 4.54 percent, and the yield on 30-year U.S. government bonds was 5.31 percent.

Yield Curves Showing the Term Structure of Interest Rates for U.S.Treasury Securities
A number of theories have been advanced to explain the shape of the yield curve, including the expectations theory, liquidity (or maturity) premium theory, and market segmentation theory.

According to the expectations theory, long-term interest rates are a function of expected future (that is, forward) short-term interest rates. If future short-term interest rates are expected to rise, the yield curve will tend to be upward sloping. In contrast, a downwardsloping yield curve reflects an expectation of declining future short-term interest rates. According to the expectations theory, current and expected future interest rates are dependent on expectations about future rates of inflation. Many economic and political conditions can cause expected future inflation and interest rates to rise or fall. These conditions include expected future government deficits (or surpluses), changes in Federal Reserve monetary policy (that is, the rate of growth of the money supply), and cyclical business conditions.

The liquidity (or maturity) premium theory of the yield curve holds that required returns on long-term securities tend to be greater the longer the time to maturity. The maturity premium reflects a preference by many lenders for shorter maturities because the interest rate risk associated with these securities is less than with longer-term securities. As we shall see in Chapter, the value of a bond tends to vary more as interest rates change, the longer the term to maturity. Thus, if interest rates rise, the holder of a long-term bond will find that the value of the investment has declined substantially more than that of the holder of a short-term bond.

In addition, the short-term bondholder has the option of holding the bond for the short time remaining to maturity and then reinvesting the proceeds from that bond at the new higher interest rate. The long-term bondholder must wait much longer before this opportunity is available. Accordingly, it is argued that whatever the shape of the yield curve, a liquidity (or maturity) premium is reflected in it. The liquidity premium is larger for long-term bonds than for short-term bonds.

Finally, according to the market segmentation theory, the securities markets are segmented by maturity. Furthermore, interest rates within each maturity segment are determined to a certain extent by the supply and demand interactions of the segment’s borrowers and lenders. If strong borrower demand exists for long-term funds and these funds are in short supply, the yield curve will be upward sloping. Conversely, if strong borrower demand exists for short-term funds and these funds are in short supply, the yield curve will be downward sloping.

Several factors limit the choice of maturities by lenders. One such factor is the legal regulations that limit the types of investments commercial banks, savings and loan associations, insurance companies, and other financial institutions are permitted to make. Another limitation faced by lenders is the desire (or need) to match the maturity structure of their liabilities with assets of equivalent maturity.

For example, insurance companies and pension funds, because of the long-term nature of their contractual obligations to clients, are interested primarily in making long-term investments. Commercial banks and money market funds, in contrast, are primarily short-term lenders because a large proportion of their liabilities is in the form of deposits that can be withdrawn on demand. At any point in time, the term structure of interest rates is the result of the interaction of the factors just described. All three theories are useful in explaining the shape of the yield curve.

The Default Risk Premium U.S. government securities are generally considered to be free of default risk—that is, the risk that interest and principal will not be paid as promised in the bond indenture. In contrast, corporate bonds are subject to varying degrees of default risk. Investors require higher rates of return on securities subject to default risk. Bond rating agencies, such as Moody’s and Standard & Poor’s, provide evaluations of the default risk of many corporate bonds in the form of bond ratings.Moody’s, for example, rates bonds on a 9-point scale from Aaa through C,where Aaa-rated bonds have the lowest expected default risk.9 As seen in Table , the yields on bonds increase as the risk of default increases, reflecting the positive relationship between risk and required return.

Over time, the spread between the required returns on bonds having various levels of default risk varies, reflecting the economic prospects and the resulting probability of default. For example, during the relative prosperity of 1989, the yield on Baa-rated corporate bonds was approximately .97 percentage points greater than the yield on higher-quality (lower default risk) Aaa-rated bonds. By late 1990, as the U.S. economy weakened and headed toward a recession, this spread had increased to 1.38 percentage points. In mid-2000, the spread narrowed to 0.66 percentage points. The spread expanded to 0.71 percent in mid-2004.

Seniority Risk Premium Corporations issue many different types of securities. These securities differ with respect to their claim on the cash flows generated by the company and the claim on the company’s assets in the case of default. A partial listing of these securities, from the least senior (that is, from the security having the lowest priority claim on cash flows and assets) to the most senior, includes the following: common stock, preferred stock, income bonds, subordinated debentures, debentures, second mortgage bonds, and first mortgage bonds.

Generally, the less senior the claims of the security holder, the greater the required rate of return demanded by investors in that security. For example, the holders of bonds issued by ExxonMobil are assured that they will receive interest and principal payments on these bonds except in the highly unlikely event that the company faces bankruptcy.

In contrast, ExxonMobil common stockholders have no such assurance regarding dividend payments. Also, in the case of bankruptcy, all senior claim holders must be paid before common stockholders receive any proceeds from the liquidation of the firm. Accordingly, common stockholders require a higher rate of return on their investment in ExxonMobil stock than do the company’s bondholders.

Marketability Risk Premium Marketability risk refers to the ability of an investor to buy and sell a company’s securities quickly and without a significant loss of value. For example, there is very little marketability risk for the shares of stock of most companies that are traded on the New York or American Stock Exchange or listed on the NASDAQ system for over the counter stocks. For these securities, there is an active market.

Trades can be executed almost instantaneously with low transaction costs at the current market price. In contrast, if you own shares in a rural Nebraska bank, you might find it difficult to locate a buyer for those shares (unless you owned a controlling interest in the bank).When a buyer is found,that buyer may not be willing to pay the price that you could get for similar shares of a largerbank listed on the New York Stock Exchange. The marketability risk premium can be significantfor securities that are not regularly traded, such as the shares of many small- and medium-size firm.

Business and Financial Risk11

Within individual security classes, one observes significant differences in required rates of return between firms. For example, the required rate of return on the common stock of US Airways is considerably higher than the required rate of return on the common stock of Southwest Airlines. The difference in the required rate of return on the securities of these two companies reflects differences in their business and financial risk.

The business risk of a firm refers to the variability in the firm’s operating earnings over time. Business risk is influencedby many factors, including the variability in sales and operating costs over a business cycle,the diversity of a firm’s product line, the market power of the firm, and the choice of production technology. Over the decade from 1991 to 2000, the operating profit margin ratio for Southwest Airlines was consistently higher and much less variable from year to year than for US Airways.As a stronger, and more efficient firm, Southwest Airlines can be expected to have a lower perceived level of business risk and a resulting lower required return on its common stock (all other things held constant).

Relationship-Between-Default-Risk-and-Required returns

Financial risk refers to the additional variability in a company’s earnings per share that results from the use of fixed-cost sources of funds, such as debt and preferred stock. In addition, as debt financing increases, the risk of bankruptcy increases. For example, US Airways had a debt-to-total-capitalization ratio of 91.6 percent in 2001. By August 2002, US Airways was forced to enter Chapter 11 bankruptcy as a way of reorganizing and hopefully saving the company. Although it emerged from bankruptcy in 2003, it faced renewed bankruptcy riskin 2004.

In comparison, the debt-to-total-capitalization ratio was 33.3 percent for Southwest Airlines in 2001. This difference in financial risk will lead to lower required returns on thecommon stock of Southwest Airlines compared to the common stock of US Airways, all other things being equal. Indeed, because of the 2002 bankruptcy filing, common stock investors in US Airways lost virtually all of their investment value in the firm.

Business and financial risk are reflected in the default risk premium applied by investors to a firm’s securities. The higher these risks are, the higher the risk premium and required rate of return on the firm’s securities.

Risk and Required Returns for Various Types of Securities

illustrates the relationship between required rates of return and risk, as represented by the various risk premiums just discussed. As shown in Figure 6.5, the lowest risk security is represented by short-term U.S. Treasury bills. All other securities have one or more elements of additional risk, resulting in increasing required returns by investors. The order illustrated in this figure is indicative of the general relationship between risk and required returns of various security types. There will be situations that result in differences in the ordering of risk and required returns.


For example, it is possible that the risk of some junk (high-risk) bonds may be so great that investors require a higher rate of return on these bonds than they require on high-grade common stocks. The relationship between risk and return can be observed by examining the returns actually earned by investors in various types of securities over long periods of time. Finance professionals believe that investor expectations of the relative returns anticipated from various types of securities are heavily influenced by the returns that have been earned on these securities over long periods in the past. Over the period from 1926 to 2003, investors in small-company common stocks earned average returns of 17.5 percent compared with 12.4 percent for investors in large-company stocks.12 However, these higher returns on smallcompany stocks have come with substantially more variability in annual returns. This variation, as measured by the standard deviation, has been approximately 33 percent for smallcompany stocks versus about 20 percent for large-company stocks.

Returns on long-term corporate bonds have averaged about 6 percent, or less than one-half the returns on largecompany stocks, but the risk (standard deviation) of the returns on these bonds have also been much lower. Short-term U.S. Treasury bills have offered the lowest average annual returns (less than 4 percent), but have also had the lowest risk of all the securiites examined.

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