Assume you bought 100 shares of X-Corp on January 1 for $43.75 a share and held

Question

Assume you bought 100 shares of X-Corp on January 1 for $43.75 a share and held the stock for one year. During that period of time you received $1.22 a share in dividends and sold the stock for $47 a share.

Assume you are now considering investing some money in 2 companies that you think will generate the following returns:

Company A

State of the economy

Probability of occurrence

% return given that state

Recession

30%

12%

Stable

60%

18%

Boom

10%

25%

Company B

State of the economy

Probability of occurrence

% return given that state

Recession

30%

9%

Stable

60%

14%

Boom

10%

16%

Which Stock provides the best investment based on the risk? Is there a reward tradeoff?

What is the expected return and standard deviation of a portfolio consisting of 40% invested in Stock A and 60% invested in Stock B given a correlation coefficient of .61?

State of the economy

Probability of occurrence

% return given that state

Recession

30%

12%

Stable

60%

18%

Boom

10%

25%

Explanation / Answer

1) Expected Return (Company A) = w1R1 + w2R2 + w3R3

                                             = (0.30) * (0.12) + (0.60) * (0.18) + (0.10) * (0.25)

                                             = 0.036 + 0.108 + 0.025 = 0.169 or 16.9%

Expected Return (Company B) = w1R1 + w2R2 + w3R3

                                             = (0.30) * (0.09) + (0.60) * (0.14) + (0.10) * (0.16)

                                             = 0.027 + 0.084 + 0.016 = 0.127 or 12.7%

Therefore, Stock A provides the best investment based on the risk, since the Expected return of stock A is high.

There is no reward tradeoff, since if the risk remain the same, reward should be the same. But it is different in both the stocks.

2) Expected return of Company A = 16.9% * 40% = 0.0676 or 6.76%

Expected return of Company B = 12.7% * 60% = 0.0762 or 7.62%

Correlation coefficient rxy = sxy / sx sy

                               0.61 = [(0.0676 - 0.0719) (0.0762 - 0.0719) / 2 - 1] / sx sy

                               0.61 = [-0.0043 * 0.0043 / 1] / sx sy

                                          sx sy = 3.03

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