1. McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. 5-1 Chapter 5 History of Interest Rates and Risk Premiums

2. 5-2 Factors Influencing Rates Supply Households Demand Businesses Government’s Net Supply and/or Demand Federal Reserve Actions

3. 5-3 Q0Q0 Q1Q1 r0r0 r1r1 Funds Interest Rates Supply Demand Interest Rates Supply Q0Q0 Q1Q1 r0r0 r1r1 Funds Demand »Level of Interest Rates

4. 5-4 Fisher effect: Approximation nominal rate = real rate + inflation premium R = r + i or r = R - i Example r = 3%, i = 6% R = 9% = 3% + 6% or 3% = 9% - 6% Fisher effect: Exact r = (R - i) / (1 + i) 2.83% = (9%-6%) / (1.06) Empirical Relationship: Inflation and interest rates move closely together Real vs. Nominal Rates

5. 5-5 Financial Return Total return: the total gain or loss experienced on an investment over a given period of time Components of the total return Income stream from the investment Capital gain or loss due to changes in asset prices Total return can be expressed either in dollar terms or in percentage terms.

6. 5-6 Cash Flow Time Line P t-1 cash payments P t +-----------------------------------------------------+ Time t-1 Time t P t = Price at time t (today) Capital Gain = P t – P t-1 = Price today – Price last period Dollar Return = Cash Payments + Capital Gain = Cash Payments + P t – P t-1

7. 5-7 Example 5.1 You purchased a stock last year for $25. It has paid $1 in dividends and is not worth $21. What is your Dollar Return?

8. 5-8 Example 5.2 You bought an 11% coupon bond one year ago for $1125. You can sell that bond today for $1100. What is your Dollar Return?

9. 5-9 Holding Period Return (hpr) or Percentage Return This is the most common way to express the gains or losses over a period It is the $Return relative to the amount invested 1+hpr is often called the wealth relative

10. 5-10 Example 5.1 (Revised) You purchased a stock last year for $25. It has paid $1 in dividends and is not worth $21. What is your Dollar Return? What is your hpr?

11. 5-11 Example 5.2 Revised You bought an 11% coupon bond one year ago for $1125. You can sell that bond today for $1100. What is your Dollar Return? What is your hpr?

12. 5-12 Measuring Wealth over Time Yearhpr$1 Investment$1 Investment each year 115%1*(1.15) = 1.15 V t-1 (1+i t ) = V t 1*(1.15)=1.15 (1+V t-1 )(1+i t ) = V t 2-10%1.15*(0.90) =1.035(1+1.15)*(0.90) = 1.935 313%1.035*1.13 = 1.1696(1+1.935)*(1.13) = 3.3166

13. 5-13 Arithmetic Average Return Add the individual hpr’s and divide by the number of years

14. 5-14 Geometric Rate of Return Multiply by the wealth relatives, raise to the 1/N power and subtract 1 Is the constant rate of wealth building over time that results in the observed future value By Financial Calculator: P/YR=1 I/YR(FV=1.1696, PV=-1, N=3) = 5.36%

15. 5-15 IRR from a Constant Investment tCF 0 1 2 33.3166 P/YR=1 Press  IRR = 5.10%

16. 5-16 Value of $1 Invested in Equities, Treasury Bonds and Bills, 1900 - 2003 Year $ $148 61 $22 10,000 1,000 100 10 1 Equities Bonds Bills Inflation 1900 1920 1940 1960 1980 2000 2003 100,000 15,579

17. 5-17 Geometric Return Calculation A $1 investment in Large Stocks (with dividends reinvested) was worth 15579 after 103 years. The geometric mean return can be computed as (use P/Yr = 1) I/YR(FV=15579, PV=-1, N=103)=9.83% Stocks I/YR(FV=148, PV=-1, N=76)=4.97% Long US Bond I/YR(FV=61, PV=-1, N=76)=4.07% US TBill I/YR(FV=22, PV=-1, N=76)=3.05% Inflation

18. 5-18 Geometric Real Rates of Return To compute the long run real rate of return one can divide the ending value of the investment by the ending value of the inflation figure to determine the purchasing power of the investment. Then compute the return using “Real Dollars” Real value of the Large Stocks at end of period is 15579/22 = 708.14 I/YR(FV=708.14, PV=-1, N=103)=6.58% I/YR(FV=6.73, PV=-1, N=103)=1.87% Long US Bond I/YR(FV=2.73, PV=-1, N=103)=1.00% TBill

19. 5-19 Arithmetic versus Geometric Returns (1900-2003) StocksBondsBills Nominal Returns Arithmetic Avg 11.75.24.1 Nominal Returns Geometric 9.85.04.1 Real Returns Arithmetic Avg 8.52.31.1 Real Returns Geometric 6.61.91.0

20. 5-20 Geom.Arith.Stan. SeriesMean%Mean%Dev.% Sm Stk11.617.739.3 Lg Stk10.012.020.6 LT Gov 5.4 5.7 8.2 T-Bills 3.8 3.8 3.2 Inflation 3.1 3.1 4.4 Annual Holding Period Returns (1926-2002)

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26. 5-26 Take home message If you have a short holding period, stocks are very risky, but from a longer term perspective they have provided the best returns both recently and historically Investment is not about saving money for the future, its about earning money from the money you invested so that most of your portfolio is from the earning of that portfolio and not from your deposits into that fund

27. 5-27 Percentage Returns on Bills, Bonds, and Stocks, 1900 - 2003 Difference between average return of stocks and bills = 7.6% Difference between average return of stocks and bonds = 6.5% Risk premium: the difference in returns offered by a risky asset relative to the risk-free return available

28. 5-28 Why are Treasury Bills considered risk free? If the government default on Treasury Bills, your last concern will be the money you might have earned on the TB When you buy a Treasury Bill, you purchase it at a discount and redeem it at par, so you know when you buy it, what your return will be If you buy a stock, you don’t know what you will sell it for, or what dividends it will pay; thus, it is risky The yield on Treasury Bills, is generally taken to be the risk free return

29. 5-29 Distribution of Historical Stock Returns, 1900 - 2003 50 -20-1001020304050 Percent return in a given year Probability distribution for future stock returns is unknown. We can approximate the unknown distribution by assuming a normal distribution.

30. 5-30 Variability of Stock Returns Normal distribution can be described by its mean and its variance. A Normal Distribution is symmetric around the mean Variance (  2 ) - the expected value of squared deviations from the mean Units of variance (%-squared) - hard to interpret, so calculate standard deviation, a measure of volatility equal to square root of  2

31. 5-31 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is fully characterized by its mean and standard deviation Characteristics of Probability Distributions

32. 5-32 The Normal Distribution

33. 5-33 Volatility of Asset Returns Asset classes with greater volatility pay higher average returns. Average return on stocks is more than double the average return on bonds, but stocks are 2.5 times more volatile.

34. 5-34 Risk Real SeriesPremiums%Returns% Sm Stk 13.914.6 Lg Stk 9.3 8.9 LT Gov 1.9 2.6 T-Bills --- 0.7 Inflation --- --- Risk Premiums and Real Returns (1926-2002)

35. 5-35 Subjective returns p s = probability of a state r s = return if a state occurs 1 to s states Mean Scenario or Subjective Returns

36. 5-36 StateProb. of Stater in State 1.1-.05 2.2.05 3.4.15 4.2.25 5.1.35 E(r) = (.1)(-.05) + (.2)(.05) +...+ (.1)(.35) E(r) =.15 Scenario or Subjective Returns: Example

37. 5-37 Standard deviation = [variance] 1/2 Subjective or Scenario Var =[(.1)(-.05-.15) 2 +(.2)(.05-.15) 2 +...+.1(.35-.15) 2 ] Var=.01199 S.D.= sqrt[.01199] =.1095 Using Our Example : Variance or Dispersion of Returns