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Question

Suppose you have invested only in two stocks, A and B. The returns on the two stocks depend on the following three states of the economy, which are equally likely to happen:
State of Economy                      Return on Stock A (%)                               Return on Stock B (%)
Bear                                                               6.30                                                              &nbs p;    -3.70
Normal                                        &nbs p;               10.50                         &nb sp;                                        6.40
Bull                                                              15.60                      ;                                         &nb sp; 25.30

a.) Calculate the expected return on each stock.
b.) Calculate the standard deviation of returns on each stock.
c.) Calculate the covariance and correlation between the returns on the two stocks.


Optional Information:
Orlando, Florida

Submitted: 1532 days and 13 hours ago.
Category: Finance
Value: $5
Status: CLOSED

Accepted Answer

Let A and B be stochastic variables where A denotes the return on stock A and B denotes the return on stock B.

a)
E[A] = (6.3+10.5+15.6)/3 = 10.8 %

E = (-3.7+6.4+25.30)/3 = 9.3 %

b)
SD(A) = sqrt([(0.063 - 0.108)² + (0.105 - 0.108)² + (0.156 - 0.108)²]/3) = 0.038026

SD(B) = sqrt([(-0.037 - 0.093)² + (0.064 - 0.093)² + (0.253 - 0.093)²]/3) = 0.1201196

c)
Cov(A, B) = [(0.063 - 0.108)(-0.037 - 0.093) + (0.105 - 0.108)(0.064 - 0.093) + (0.156 - 0.108)(0.253 - 0.093)]/3 = 0.00453996

Corr(A, B) = 0.004539/(0.038026*0.1201196)
Sk1llz38727.4724021643

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Expert: Sk1llz
Pos. Feedback: 90.0 %
Accepts: 34
Answered: 1/10/2006

Mastermind

Mathematics, Statistics and Physics

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