Question

Q4) You are considering investing in stock S and you want to know how stock S is related to the market portfolio M. Given your research, you discovered the following information: Please provide full formulas instead of using Excel.

	Expected Return	Standard Deviation
Stock (S)	15%	25%
Market (M)	12%	20%
Risk-free	2%
Correlation of S and M	40%

1. What is the exposure of stock S to market risk? (3 points).
2. Discuss whether according to the CAPM, stock S is overvalued, undervalued or fairly valued. (2 points)
3. What is the level of systematic and idiosyncratic risk for stock S? (5 points)

Answer 1

Answer (a)

Exposure of Stock S to Market Risk : Beta of Stock S :

Beta = Correlation _{(S, market)} x σs / σ_market

= 0.40 x 0.25 / 0.20

= 0.5

Therefore, exposure of Stock S to market risk = Beta of Stock S = 0.50

Answer (b)

~ CAPM = Riskfree Rate + Beta (Expected Market Return - Rf Rate)

= 2% + 0.50 (12% - 2%)

= 7%

CAPM Return = 7%

Expected Return of S = 15%

~Since the Expected Return > CAPM Return, Stock is Undervalued.

Answer (c)

~  Systematic Risk of Stock S:

= Standard Deviation of Market x Beta of Stock S

= 20% x 0.50

= 10%

~ Idiosyncratic Risk of Stock S:

= Standard Deviation of Stock S - Systematic Risk of Stock S

= 25% - 10%

= 15%

~ Therefore, Systematic Risk = 10%, Idiosyncratic Risk = 15%