Risk and Return in Stocks

STOCKS A AND B
The data that follow (and in file STOCK AB) give the rates of return over a 50-year period
for two stocks, which we'll call stock A and stock B. The rate of return is defined
as the increase in value of the portfolio (including any dividends or other distributions)
during the year divided by its value at the beginning of the year. That's the fraction by
which your wealth would have changed had it been invested in that particular combination
of securities. The rate of return may be either positive or negative.
What was the average return for stock A? Stock B? In the theory of finance, the
standard deviation of the return is often used as a measure of the risk associated with
investing in a given security. What are the standard deviations of the returns for stocks
A and B?

Assume that the history of stocks A and B is a useful guide to what may be expected
of them in the foreseeable future. (That may seem like a big assumption, but assume it
anyway.) Suppose you want to use this history as a guide to making an investment decision
for the long run. Based on this history, and assuming that standard deviation of return
is the appropriate measure of risk, does it make any difference whether you invest
wholly in stock A, wholly in stock B, or half in stock Aand half in stock B? Assume that
average return is to be maximized and risk is to be minimized, if that is jointly possible.

Cases 6.
Stocks A and B
Companies, 2003
DATA SET
YEAR A B YEAR A B YEAR A B YEAR A B
1 0.215 0.199 14 0.122 0.122 27 0.001 0.112 40 0.215 0.045
2 0.194 0.017 15 0.265 0.103 28 0.122 0.294 41 0.315 0.419
3 0.130 0.112 16 0.237 0.218 29 0.230 0.055 42 0.008 0.199
4 0.337 0.218 17 0.151 0.055 30 -0.013 0.179 43 0.058 0.055
5 0.165 0.246 18 0.201 0.294 31 0.044 0.132 44 -0.035 0.151
6 0.115 0.160 19 0.230 0.304 32 0.258 0.112 45 0.265 0.227
7 0.308 0.218 20 0.194 0.246 33 0.280 0.218 46 0.215 0.151
8 0.130 0.294 21 0.008 0.112 34 0.122 0.246 47 0.211 0.093
9 0.330 0.170 22 0.265 0.313 35 0.072 0.227 48 0.230 0.221
10 0.294 0.103 23 0.222 0.017 36 0.187 0.266 49 0.115 0.218
11 0.244 0.055 24 0.144 0.333 37 0.130 0.294 50 0.106 0.025
12 0.401 0.179 25 0.108 0.103 38 0.101 0.074
13 0.251 0.428 26 0.194 0.122 39 0.308 0.246
I-18 CASE 6 STOCKS A AND B