Question

Consider the following information:

Bear Market Normal Market Bull Market
Probability 0.3 0.5 0.2
Return on Stock A -10% 0% 40%
Return on Stock B -5% 5% 50%

Calculate and comment upon the expected return and standard deviation of A and B.

Answer 1

Answer on Question #83961 - Economics - Finance

Question:

Consider the following information:

Calculate and comment upon the expected return and standard deviation of A and B.

Answer

1) We can calculate expected return by the following formula:

$$ERR = \sum_{i=1}^{n} R_i P_i$$

Where

R – return expected in a given scenario;

P – probability of the return being achieved in the scenario;

n – number of scenario.

$$ERR_A = 10\% \times 0.3 + 0\% \times 0.5 + 40\% \times 0.2 = 11\%$$ $$ERR_B = 5\% \times 0.3 + 5\% \times 0.5 + 50\% \times 0.2 = 14\%$$

2) Then we find standard deviation for stocks A and B:

$$\sigma_A = \sqrt{\sum_{i=1}^{n} (R_i - ERR_i)^2 * P_i}$$ $$\sigma_A = \sqrt{(10 - 11)^2 * 0.3 + (0 - 11)^2 * 0.5 + (40 - 11)^2 * 0.2} = 15\%$$ $$\sigma_B = \sqrt{(5 - 14)^2 * 0.3 + (5 - 14)^2 * 0.5 + (50 - 14)^2 * 0.2} = 18\%$$

Standard deviation reflects volatility of return. As we can see the stock A has the lower expected return and lower volatility, the stock B has higher expected return and higher level of volatility.

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