Question

The following data are the returns for 1980 through 1986 on five types of capital-market instruments: common stocks, small-capitilzation stocks, long-term corporate bonds, long-term U.S. government bonds, and U.S. Treasury Bills. You may wish to use a spreadsheet program to make your calculations. Year Common Stock Small Stocks Long-term Corporate Bonds Long-term Government Bonds U.S. Treasury Bills 1980 0.3242 0.3988 -0.0262 -0.0395 0.1124 1981 -0.0491 0.1388 -0.0096 0.0185 0.1471 1982 0.2141 0.2801 0.4379 0.4035 0.1054 1983 0.2251 0.3967 0.0470 0.0068 0.0880 1984 0.0627 -0.0667 0.1639 0.1543 0.0985 1985 0.3216 0.2466 0.3090 0.3097 0.0772 1986 0.1847 0.0685 0.1985 0.2444 0.0616 For the average return problems, enter your answers in percentage format (e.g. enter 12.5% as 12.50 rather than .125) For the holding period return problems, enter your answers as percentage values; in other words, convert your decimal format of holding period return to percentage return format (e.g. a formula result of 2.25 should be converted to 225%) For the expected return problems, enter your answers as percentage values (e.g. enter 7.50% as 7.50 and not as 0.075) What was the average return during the period for all Common Stocks? Calculate the average return for Small Company Stocks. What was the average return during the period for Long Term Corporate Bonds? What was the average return during the period for Long Term Government Bonds? What was the average return during the period for US Treasury Bills? Calculate the holding period return for common stocks for the 7-year holding period of 1980 through 1986. Calculate the holding period return for Long Term Corporate Bonds for the 7-year holding period of 1980 through 1986. Calculate the holding period return for US Treasury Bills for the 7-year holding period of 1980 through 1986. Using the Average US Treasury Bill Rate as a proxy for the risk-free rate, what was the average risk premium for Small Company Common Stocks for the 7-year period? Using the Average US Treasury Bill Rate as a proxy for the risk-free rate, what was the average risk premium for Long Term Corporate Bonds for the 7-year period?

Answer 1

Average Return = Total/n

n = No. of Years

Year	Common Stock	Small Stocks	Long-term Corporate Bonds	Long-term Government Bonds	U.S. Treasury Bills
1980	0.3242	0.3988	-0.0262	-0.0395	0.1124
1981	-0.0491	0.1388	-0.0096	0.0185	0.1471
1982	0.2141	0.2801	0.4379	0.4035	0.1054
1983	0.2251	0.3967	0.047	0.0068	0.088
1984	0.0627	-0.0667	0.1639	0.1543	0.0985
1985	0.3216	0.2466	0.309	0.3097	0.0772
1986	0.1847	0.0685	0.1985	0.2444	0.0616
Average	18.33%	20.90%	16.01%	15.68%	9.86%

Holding Period from 1980 to 1986

No. of periods to grow = 6 (80-81, 81-82, .. ,85-86)

Holding Period Return =

Year	Common Stock	in $	Long-term Corporate Bonds	in $	Long-term Government Bonds	in $
1980	0.3242	100.0000	-0.0262	100.0000	-0.0395	100.0000
1981	-0.0491	95.0900	-0.0096	99.0400	0.0185	101.8500
1982	0.2141	115.4488	0.4379	142.4096	0.4035	142.9465
1983	0.2251	141.4363	0.047	149.1029	0.0068	143.9185
1984	0.0627	150.3043	0.1639	173.5408	0.1543	166.1251
1985	0.3216	198.6422	0.309	227.1649	0.3097	217.5741
1986	0.1847	235.3314	0.1985	272.2572	0.2444	270.7492
Holding Period Return		105.17%		109.49%		109.33%

Average US T-bill Rate = 9.86%

Risk Premium of Small Company Common Stock = Average Risk-Free Rate + Average Small Stock Return

= 9.86% + 20.90% = 30.76%

Risk Premium of Long Term Corporate Bond = Average Risk-Free Rate + Average LT Corp Bond Return

= 25.87%