1. The standard deviation of return on investment A is 9%, while the standard de

Question

1. The standard deviation of return on investment A is 9%, while the standard deviation of return on investment B is 7%. If the covariance between the returns on A and B is 0.0025, the correlation of returns on A and B is _________?

Recall that the correlation is the covariance scaled by the two standard deviations. Be sure to express everything in decimal form.

2. A project will double your investment in one year with probability 0.4, and a complementary chance of losing half your money otherwise. What is the standard deviation of this investment?

First, find the expected (mean) return, which is the probability-weighted average of returns.

Then, find the variance, which is the probability-weighted average of squared differences from the mean.

Then take square root of variance to find standard deviation.

Explanation / Answer

1

Cov(A,B) = StdDev(A)*StdDev(B)*Corr(A,B)
0.0025 = 0.09*0.07*Corr(A,B)
Corr(A,B) = 0.3968

2

P[100%] = 0.4
P[-50%] = 0.6

E[X] = 1*0.4 + (-0.5)*0.6 = 0.1
E[X2] = 12*0.4 + (-0.5)2*0.6 = 0.55

Var[X] = E[X2] - E[X]2 = 0.55

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