ECON 46205620
Homework 2
1.
The following table gives the anticipated 1year rates of return from a certain investment and
their probabilities.
ANTICIPATED 1YEAR RATE OF RETURN FROM A CERTAIN INVESTMENT
Rate of return (
X
)%
f(
X
)
20
0.10
10
0.15
10
0.45
25
0.25
30
0.05
Total 1.00
a.
What is the expected rate of return from this investment?
b.
Find the variance and standard deviation of the rate of return.
c.
Find the skewness and kurtosis coefficients.
d.
Find the cumulative distribution function (CDF) and obtain the probability that the rate of
return is 10 percent or less.
2.
Consider formulas (B.32) and (B.33)
B.32: var(X+Y) = var(X) + var(Y) + 2ρσ
X
σ
Y
B.33: var(X  Y) = var(X) + var(Y) 
2ρσ
X
σ
Y
Let
X
stand for the rate of return on a security, say IBM, and
Y
the rate of return on another
security, say, General Foods. Let s
2
(X) = 16, s
2
(Y) = 9, and r = 0.8. What is the variance of (X +
Y) in this case? Is it greater than or smaller than var(X)+var(Y)? In this instance, is it better to
invest equally in the two securities (i.e., diversify) than in either security exclusively? This
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 Spring '10
 Klein
 Econometrics, Standard Deviation, Variance, Probability theory, New Business Incorporations

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