Question

1. Consider information regarding the following two stocks. The probability of each state of the economy is 1/3. No dividends are paid.

STOCK. Initial Price. Boom. Normal Bust

A. 40 60 50 25

B. 25 20 25 35

(a) What is the expected value and the standard deviation of the rate of return of each stock?

(b) Which stock is the better investment for you? Why?

Answer 1

Return of Stock A in boom period = (Price in Boom period - Initial price) / Initial price

Return of Stock A in boom period = (60 - 40) / 40

Return of Stock A in boom period = 50%

Return of Stock A in normal period = (Price in Boom period - Initial price) / Initial price

Return of Stock A in normal period = (50 - 40) / 40

Return of Stock A in normal period = 25%

Return of Stock A in bust period = (Price in Boom period - Initial price) / Initial price

Return of Stock A in bust period = (25 - 40) / 40

Return of Stock A in bust period = -37.5%

Return of Stock B in boom period = (Price in Boom period - Initial price) / Initial price

Return of Stock B in boom period = (20 - 25) / 25

Return of Stock B in boom period = -20%

Return of Stock B in normal period = (Price in Boom period - Initial price) / Initial price

Return of Stock B in normal period = (25 - 25) / 25

Return of Stock B in normal period = 0%

Return of Stock B in bust period = (Price in Boom period - Initial price) / Initial price

Return of Stock B in bust period = (35 - 25) / 25

Return of Stock B in bust period = 40%

1)

Expected Return of Stock A = Probability * Return of Stock A

Expected Return of Stock A = ((1 / 3) * 50% + (1 / 3) * 25% + (1 / 3) * (-37.5%))

Expected Return of Stock A = 12.5%

Expected Return of Stock B = Probability * Return of Stock B

Expected Return of Stock B = ((1 / 3) * (-20%) + (1 / 3) * 0% + (1 / 3) * 40%)

Expected Return of Stock B = 6.67%

Variance of Stock A = Probability * (Return on Stock A - Expected Return of Stock A)²

Variance of Stock A = (1 / 3) * (50% - 12.5%)² + (1 / 3) * (25% - 12.5%)² + (1 / 3) * (-37.5% - 12.5%)²

Variance of Stock A = 13.54%

Standard Deviation of Stock A = Variance of Stock A

Standard Deviation of Stock A = 13.54%

Standard Deviation of Stock A = 36.80%

Variance of Stock B = Probability * (Return on Stock B - Expected Return of Stock B)²

Variance of Stock B = (1 / 3) * (-20% - 6.67%)² + (1 / 3) * (0% - 6.67%)² + (1 / 3) * (40% - 6.67%)²

Variance of Stock B = 6.22%

Standard Deviation of Stock B = Variance of Stock B

Standard Deviation of Stock B = 6.22%

Standard Deviation of Stock B = 24.94%

2)

Coefficient of Variation of Stock A = Standard Deviation of Stock A / Expected Return of Stock A

Coefficient of Variation of Stock A = 36.80% / 12.5%

Coefficient of Variation of Stock A = 2.94

Coefficient of Variation of Stock B = Standard Deviation of Stock B / Expected Return of Stock B

Coefficient of Variation of Stock B = 24.94% / 6.67%

Coefficient of Variation of Stock B = 3.74

Coefficient of Variation of Stock B > Coefficient of Variation of Stock A which implies that the returns on Stock B are more volatile from the mean than Stock A. I would prefer Stock A over Stock B