Introduction to Corporate Finance

6: The Trade-Off Between Risk and Return

a Plot a graph similar to Figure 6.7 showing the returns on Lilly and Merck each year.

b Fill in the blanks in the table above by calculating the 50–50 portfolio’s return each year from

Year 2 to Year 10, then plot this on the graph you created for part (a). How does the portfolio

return compare to the returns of the individual shares in the portfolio?

c Calculate the standard deviation of Lilly, Merck and the portfolio, and comment on what you find.

P6-25 In this problem, you will generate a graph similar to Figure 6.8. The table below shows the
standard deviation for various portfolios of shares listed in Table 6.6. Plot the relationship between
the number of shares in the portfolio and the portfolio’s standard deviation. Comment on how the
resulting graph is similar to and different from Figure 6.8.

Shares in the portfolio Std. deviation (%)

Exxon 16.6

Exxon + P&G 15.2

Exxon + P&G + Coke 15.4

Exxon + P&G + Coke + ADM 14.7

Exxon + P&G + Coke + ADM + Walmart 12.5

Exxon + P&G + Coke + ADM + Walmart + Wendy’s 14.5

Use the following information to compare the performance

of the S&P 500 Index, the Nasdaq Index and the Treasury

Bill Index from 1983–2003. Each of these index numbers

is calculated in a way that assumes that investors reinvest

any income they receive, so the total return equals the

percentage change in the index value each year. The last

column shows the level of the Consumer Price Index (CPI)

at the end of each year, so the percentage change in the

index indicates the rate of inflation for a particular year. Note

that, because the data start on 31 December 1983, it is not

possible to calculate returns or an inflation rate in 1983.

ASSIGNMENT

1 For the S&P 500, the Nasdaq and the T-bill series,

calculate: (a) the cumulative return over 20 years;

(b) the average annual return in nominal terms; (c) the

average annual return in real terms; and (d) the

standard deviation of the nominal return. Based on

these calculations, discuss the risk/return relationship

between these indexes. Which asset class earned the

highest average return? For which asset class were

returns most volatile? Plot your results on a graph

with the standard deviation of each asset class on

the horizontal axis and the average return on the

vertical axis.

2 Update this data using a more recent time period.

Conduct a similar analysis and compare the results

mini case

THE TRADE-OFF BETWEEN RISK AND RETURN

Date S&P 500 Nasdaq T-Bills CPI

31-12-1983 164.93 278.60 681.44 101.3

31-12-1984 167.24 247.35 748.88 105.3

31-12-1985 211.28 324.39 806.62 109.3

31-12-1986 242.17 348.81 855.73 110.5

31-12-1987 247.08 330.47 906.02 115.4

31-12-1988 277.72 381.38 968.89 120.5

31-12-1989 353.40 454.82 1,050.63 126.1

31-12-1990 330.22 373.84 1,131.42 133.8

31-12-1991 417.09 586.34 1,192.83 137.9

31-12-1992 435.71 676.95 1,234.36 141.9

31-12-1993 466.45 776.80 1,271.78 145.8

31-12-1994 459.27 751.96 1,327.55 149.7

31-12-1995 615.93 1,052.13 1,401.97 153.5

31-12-1996 740.74 1,291.03 1,473.98 158.6

31-12-1997 970.43 1,570.35 1,550.49 161.3

31-12-1998 1,229.23 2,192.68 1,625.77 163.9

31-12-1999 1,469.25 4,069.31 1,703.84 168.3

31-12-2000 1,320.28 2,470.52 1,805.75 174.0

31-12-2001 1,148.08 1,950.40 1,865.85 176.7

31-12-2002 879.82 1,335.51 1,895.83 180.9

31-12-2003 1,111.92 2,003.37 1,915.29 184.3