Question

Suppose there are only two possible future states of nature: Good and Bad. There is a 25% probability that the future will be Good. Suppose also that there are two stocks: A and B. Stock A will return 7% if the future is Good and will return 1% if the future is Bad. Stock B will return 3% if the future is Good and -5% if the future is Bad. If you have a portfolio that contains 60% of Stock A and 40% of Stock B, what will be the standard deviation of the portfolio? (hint: the portfolio expected return is 0.3%)

Select one: a. 8.67% b. 2.94% c. 12.35% d. 15.2% e. None of the above

Answer 1

Weight of Stock A = 0.60
Weight of Stock B = 0.40

Good:

Expected Return = 0.60 * 0.07 + 0.40 * 0.03
Expected Return = 0.0540 or 5.40%

Bad:

Expected Return = 0.60 * 0.01 + 0.40 * (-0.05)
Expected Return = -0.0140 or -1.40%

Probability of Good = 0.25
Probability of Bad = 0.75

Expected Return of Portfolio = 0.25 * 0.0540 + 0.75 * (-0.0140)
Expected Return of Portfolio = 0.0030 or 0.30%

Variance of Portfolio = 0.25 * (0.0540 - 0.0030)^2 + 0.75 * (-0.0140 - 0.0030)^2
Variance of Portfolio = 0.000867

Standard Deviation of Portfolio = (0.000867)^(1/2)
Standard Deviation of Portfolio = 0.0294 or 2.94%