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ST-1
a.) The average rate of return for each stock is calculated by simply averaging the
returns over the 5-year period. The average return for Stock A is
Avg A =

(-18% + 44% - 22% + 22% + 34%)/5
= 12%

The realized rate of return on a portfolio made up of Stock A and Stock B would
be calculated by finding the average rate of return in each year as
A,t

(% of Stock A) + B,t (% of Stock B)

Then average these annual returns:
Year
2009
2010
2011
2012
2013

Portfolio AB’s Return, AB
-21%
34
-13
15
45
Avg AB =12

b.) The standard deviation od returns is estimated as follows:
T- 1
For Stock A, the estimated is about 30%
(-0.18 – 0.12) 2 + (0.44 – 0.12)2 + (-0.22 – 0.12)2 + (0.22 – 0.12)2 +
(0.34 – 0.12)2
A=
A

= 0.30265

5–1
30%

The standard deviations of returns for Stock B and for the portfolio are similarly
determined, and they are as follows:

Standard deviation

Stock A
30%

Stock B
30%

Portfolio AB
29%

c.) Because the risk reduction from diversification is small (AB falls only from 30% to
29%), the most likely value of the correlation coefficient is 0.80. If the correlation
coefficient were -0.8, then the risk reduction would be much larger. In fact, the
correlation between Stocks A and B is 0.8.
d.) If more randomly selected stocks were added to a portfolio, p would decline to
somewhere in the vicinity of 20%. The value of p would remain constant only if the
correlation coefficient were + 1.0, which is most unlikely. The value of p would decline to
zero only if p = -1.0 for some pair of stocks or some pair of portfolios.
ST-2
a.) b = (0.60) (0.70) + (0.25) (0.90) + (0.1) (1.30) + (0.05) (1.50)
= 0.42 + 0.225 + 0.13 + 0.075 = 0.85
b.) rRF = 6%; RPM = 5%; b = 0.85
rp = 6% +; (5%)(0.85)
= 10.25%
c.) bN = (0.5)(0.70) + (0.25)(0.90) + (0.1)(1.30) + (0.15)(1.50)
= 0.35 + 0.225 + 0.13 + 0.225
= 0.93
r = 6% + (5%)(0.93)
= 10.65%

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