Real Versus Nominal Risk

The distinction between the real and the nominal rate of return is crucial in making investment choices when investors are interested in the future purchasing power of their wealth. Thus a U.S. Treasury bond that offers a "risk-free" nominal rate of return is not truly a risk-free investment—it does not guarantee the future purchasing power of its cash flow.

An example might be a bond that pays $1,000 on a date 20 years from now but nothing in the interim. Although some people see such a zero-coupon bond as a convenient way for individuals to lock in attractive, risk-free, long-term interest rates (particularly in IRA or Keogh4 accounts), the evidence in Table 5.3 is rather discouraging about the value of $1,000 in 20 years in terms of today's purchasing power.

Suppose the price of the bond is $103.67, giving a nominal rate of return of 12% per year (since 103.67 X 1.1220 = 1,000). We can compute the real annualized HPR for each inflation rate.

A revealing comparison is at a 12% rate of inflation. At that rate, Table 5.3 shows that the purchasing power of the $1,000 to be received in 20 years would be $103.67, the amount initially paid for the bond. The real HPR in these circumstances is zero. When the rate of inflation equals the nominal rate of interest, the price of goods increases just as fast as the money accumulated from the investment, and there is no growth in purchasing power.

At an inflation rate of only 4% per year, however, the purchasing power of $1,000 will be $456.39 in terms of today's prices; that is, the investment of $103.67 grows to a real value of $456.39, for a real 20-year annualized HPR of 7.69% per year.

4 A tax shelter for self-employed individuals.

INVESTING: WHAT TO BUY WHEN?

In making broad-scale investment decisions investors may want to know how various types of investments have performed during booms, recessions, high inflation and low inflation. The table shows how 10 asset categories performed during representative years since World War II. But history rarely repeats itself, so historical performance is only a rough guide to the figure.

Investment

Average Annual Return on Investment*

Recession

Boom

High Inflation

Low Inflation

Bonds (long-term government)

17%

4%

-1%

8%

Commodity index

1

-6

15

-5

Diamonds (1-carat investment grade)

-4

8

79

15

Goldt (bullion)

-8

-9

105

19

Private home

4

6

6

5

Real estate* (commercial)

9

13

18

6

Silver (bullion)

3

-6

94

4

Stocks (blue chip)

14

7

-3

21

Stocks (small growth-company)

17

14

7

12

Treasury bills (3-month)

6

5

7

3

*In most cases, figures are computed as follows: Recession—average of performance during calendar years 1946, 1975, and 1982; boom— average of 1951, 1965, and 1984; high inflation—average of 1947, 1974, and 1980; low inflation—average of 1955, 1961, and 1986.

tGold figures are based only on data since 1971 and may be less reliable than others.

Commercial real estate figures are based only on data since 1978 and may be less reliable than others.

Sources: Commerce Dept.; Commodity Research Bureau; DeBeers Inc.; Diamond Registry; Dow Jones & Co.; Dun & Bradstreet; Handy & Harman; Ibbotson Associates; Charles Kroll (Diversified Investor's Forecast); Merrill Lynch; National Council of Real Estate Investment Fiduciaries; Frank B. Russell Co.; Shearson Lehman Bros.; T. Rowe Price New Horizons Fund.

Source: Modified from The Wall Street Journal, November 13, 1987. Reprinted by permission of The Wall Street Journal, © 1987 Dow Jones & Company, Inc. All Rights Reserved Worldwide.

Table 5.3

Purchasing Power of $1,000 20 Years from Now and 20-Year Real Annualized HPR

Table 5.3

Purchasing Power of $1,000 20 Years from Now and 20-Year Real Annualized HPR

Assumed Annual Rate of Inflation

Number of Dollars Required 20 Years from Now to Buy What $1 Buys Today

Purchasing Power of $1,000 to Be Received in 20 Years

Annualized Real HPR

4%

$2.19

$456.39

7.69%

6

3.21

311.80

5.66

8

4.66

214.55

3.70

10

6.73

148.64

1.82

12

9.65

103.67

0.00

Purchasing price of bond is $103.67. Nominal 20-year annualized HPR is 12% per year. Purchasing power = $1,000/(1 + inflation rate)20. Real HPR, r, is computed from the following relationship:

Purchasing price of bond is $103.67. Nominal 20-year annualized HPR is 12% per year. Purchasing power = $1,000/(1 + inflation rate)20. Real HPR, r, is computed from the following relationship:

Again looking at Table 5.3, you can see that an investor expecting an inflation rate of 8% per year anticipates a real annualized HPR of 3.70%. If the actual rate of inflation turns out to be 10% per year, the resulting real HPR is only 1.82% per year. These differences show the important distinction between expected and actual inflation rates.

Even professional economic forecasters acknowledge that their inflation forecasts are hardly certain even for the next year, not to mention the next 20. When you look at an asset from the perspective of its future purchasing power, you can see that an asset that is riskless in nominal terms can be very risky in real terms.5

CONCEPT CHECK ^ QUESTION 3

Suppose the rate of inflation turns out to be 13% per year. What will be the real annualized 20-year HPR on the nominally risk-free bond?

SUMMARY

1. The economy's equilibrium level of real interest rates depends on the willingness of households to save, as reflected in the supply curve of funds, and on the expected profitability of business investment in plant, equipment, and inventories, as reflected in the demand curve for funds. It depends also on government fiscal and monetary policy.

2. The nominal rate of interest is the equilibrium real rate plus the expected rate of inflation. In general, we can directly observe only nominal interest rates; from them, we must infer expected real rates, using inflation forecasts.

3. The equilibrium expected rate of return on any security is the sum of the equilibrium real rate of interest, the expected rate of inflation, and a security-specific risk premium.

4. Investors face a trade-off between risk and expected return. Historical data confirm our intuition that assets with low degrees of risk provide lower returns on average than do those of higher risk.

5. Assets with guaranteed nominal interest rates are risky in real terms because the future inflation rate is uncertain.

KEY TERMS

nominal interest rate real interest rate risk-free rate risk premium excess return risk aversion

Returns on various equity indexes can be located on the following sites.

http://www.bloomberg.com/markets/wei.html

http://app.marketwatch.com/intl/default.asp

http://www.quote.com/quotecom/markets/snapshot.asp

Current rates on U.S. and international government bonds can be located on this site:

http://www.bloomberg.com/markets/rates.html

The sites listed below are pages from the bond market association. General information on a variety of bonds and strategies can be accessed on line at no charge. Current information on rates is also available on the investinginbonds.com site.

http://www.bondmarkets.com http://www.investinginbonds.com

5 In 1997 the Treasury began issuing inflation-indexed bonds called TIPS (for Treasury Inflation Protected Securities) which offer protection against inflation uncertainty. We discuss these bonds in more detail in Chapter 14. However, the vast majority of bonds make payments that are fixed in dollar terms; the real returns on these bonds are subject to inflation risk.

PART I Introduction

WEBSITES

The sites listed below contain current and historical information on a variety of interest

rates. Historical data can be downloaded in spreadsheet format and is available through

the Federal Reserve Economic Database (FRED)

http://www.stls.frb.ors/

http://www.stls.frb.org/docs/publications/mt/mt.pdf

PROBLEMS

1. You have $5,000 to invest for the next year and are considering three alternatives:

a. A money market fund with an average maturity of 30 days offering a current yield of 6% per year.

b. A one-year savings deposit at a bank offering an interest rate of 7.5%.

c. A 20-year U.S. Treasury bond offering a yield to maturity of 9% per year. What role does your forecast of future interest rates play in your decisions?

2. Use Figure 5.1 in the text to analyze the effect of the following on the level of real interest rates:

a. Businesses become more pessimistic about future demand for their products and decide to reduce their capital spending.

b. Households are induced to save more because of increased uncertainty about their future social security benefits.

c. The Federal Reserve Board undertakes open-market purchases of U.S. Treasury securities in order to increase the supply of money.

3. You are considering the choice between investing $50,000 in a conventional one-year bank CD offering an interest rate of 7% and a one-year "Inflation-Plus" CD offering 3.5% per year plus the rate of inflation.

a. Which is the safer investment?

b. Which offers the higher expected return?

c. If you expect the rate of inflation to be 3% over the next year, which is the better investment? Why?

d. If we observe a risk-free nominal interest rate of 7% per year and a risk-free real rate of 3.5%, can we infer that the market's expected rate of inflation is 3.5% per year?

4. Look at Table 5.1 in the text. Suppose you now revise your expectations regarding the stock market as follows:

State of the Economy

Probability

Ending Price

HPR

Boom

.35

$140

44%

Normal growth

.30

110

14

Recession

.35

80

-16

Use equations 5.1 and 5.2 to compute the mean and standard deviation of the HPR on stocks. Compare your revised parameters with the ones in the text.

5. Derive the probability distribution of the one-year HPR on a 30-year U.S. Treasury bond with an 8% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows:

Bodie-Kane-Marcus: I I. Introduction I 5. History of Interest Rates I I © The McGraw-Hill

Investments, Fifth Edition and Risk Premiums Companies, 2001

CHAPTER 5 History of Interest Rates and Risk Premiums

State of the Economy

Probability

YTM

Boom

.20

11.0%

Normal growth

.50

8.0

Recession

.30

7.0

For simplicity, assume the entire 8% coupon is paid at the end of the year rather than every six months.

Using the historical risk premiums as your guide, what would be your estimate of the expected annual HPR on the S&P 500 stock portfolio if the current risk-free interest rate is 6%?

Compute the means and standard deviations of the annual HPR of large stocks and long-term Treasury bonds using only the last 30 years of data in Table 5.2, 1970-1999. How do these statistics compare with those computed from the data for the period 1926-1941? Which do you think are the most relevant statistics to use for projecting into the future? During a period of severe inflation, a bond offered a nominal HPR of 80% per year. The inflation rate was 70% per year.

a. What was the real HPR on the bond over the year?

b. Compare this real HPR to the approximation r ~ R - i.

Suppose that the inflation rate is expected to be 3% in the near future. Using the historical data provided in this chapter, what would be your predictions for:

b. The expected rate of return on large stocks?

c. The risk premium on the stock market?

An economy is making a rapid recovery from steep recession, and businesses foresee a need for large amounts of capital investment. Why would this development affect real interest rates?

Given $100,000 to invest, what is the expected risk premium in dollars of investing in equities versus risk-free T-bills (U.S. Treasury bills) based on the following table?

Action

Probability

Expected Return

Invest in equities

- .6 -

- $50,000

---- -

--$30,000

Invest in risk-free T-bill

1.0

Based on the scenarios below, what is the expected return for a portfolio with the following return profile?

Market Condition

Bear

Normal

Bull

Probability

.2

.3

.5

Rate of return

-25%

10%

24%

Bodie-Kane-Marcus: I I. Introduction I 5. History of Interest Rates I I © The McGraw-Hill

Investments, Fifth Edition and Risk Premiums Companies, 2001

PART I Introduction

a.

4%.

b.

10%

c.

20%

d.

25%

Use the following expectations on Stocks X and Y to answer questions 13 through 15 (round to the nearest percent).

Bear Market

Normal Market

Bull Market

Probability

0.2

0.5

0.3

Stock X

-20%

18%

50%

Stock Y

-15%

20%

10%

13. What are the expected returns for Stocks X and Y?

Stock X

Stock Y

a.

18%

5%

b.

18%

12%

c.

20%

11%

d.

20%

10%

14. What are the standard deviations of returns on Stocks X and Y?

Stock X

Stock Y

a.

15%

26%

b.

20%

4%

c.

24%

13%

d.

28%

8%

15. Assume that of your $10,000 portfolio, you invest $9,000 in Stock X and $1,000 in Stock Y. What is the expected return on your portfolio?

Probabilities for three states of the economy, and probabilities for the returns on a particular stock in each state are shown in the table below.

State of Economy

Probability of Economic State

Stock

Performance

Probability of Stock Performance in Given Economic State

Good

.3

Good

.6

Neutral

.3

Poor

.1

Neutral

.5

Good

.4

Neutral

.3

Poor

.3

Poor

.2

Good

.2

Neutral

.3

Poor

.5

Bodie-Kane-Marcus: Investments, Fifth Edition

I. Introduction

5. History of Interest Rates and Risk Premiums

© The McGraw-Hill Companies, 2001

CHAPTER 5 History of Interest Rates and Risk Premiums

The probability that the economy will be neutral and the stock will experience poor performance is a. .06.

17. An analyst estimates that a stock has the following probabilities of return depending on the state of the economy:

State of Economy

Probability

Return

Good

.1

15%

Normal

.6

13

Poor

.3

7

The expected return of the stock is:

Problems 18-19 represent a greater challenge. You may need to review the definitions of call and put options in Chapter 2.

18. You are faced with the probability distribution of the HPR on the stock market index fund given in Table 5.1 of the text. Suppose the price of a put option on a share of the index fund with exercise price of $110 and maturity of one year is $12.

a. What is the probability distribution of the HPR on the put option?

b. What is the probability distribution of the HPR on a portfolio consisting of one share of the index fund and a put option?

c. In what sense does buying the put option constitute a purchase of insurance in this case?

19. Take as given the conditions described in the previous question, and suppose the risk-free interest rate is 6% per year. You are contemplating investing $107.55 in a one-year CD and simultaneously buying a call option on the stock market index fund with an exercise price of $110 and a maturity of one year. What is the probability distribution of your dollar return at the end of the year?

Lessons From The Intelligent Investor

Lessons From The Intelligent Investor

If you're like a lot of people watching the recession unfold, you have likely started to look at your finances under a microscope. Perhaps you have started saving the annual savings rate by people has started to recover a bit.

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Responses

  • owen
    What is your estimate of the expected annual hpr?
    7 years ago

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