Question

9. Portfolio risk and return

Ariel holds a $10,000 portfolio that consists of four stocks. Her investment in each stock, as well as each stock's beta, is listed in the following table:

Stock	Investment	Beta	Standard Deviation
Andalusian Limited (AL)	$3,500	0.80	15.00%
Kulatsu Motors Co. (KMC)	$2,000	1.50	12.00%
Western Gas & Electric Co. (WGC)	$1,500	1.20	16.00%
Makissi Corp. (MC)	$3,000	0.50	22.50%

Suppose all stocks in Ariel's portfolio were equally weighted. Which of these stocks would contribute the least market risk to the portfolio?

• Western Gas & Electric Co.

• Andalusian Limited

• Kulatsu Motors Co.

• Makissi Corp.

If the risk-free rate is 4% and the market risk premium is 6%, what is Ariel's portfolio's beta and required return? Fill in the following table:

Answer 1

Least market risk - Makissi Corp. (MC)

Least market risk is one where the stock will have lowest beta. Beta indicates market risk of portfolio.

Least standalone risk - Kulatsu Motors Co.

Least standalone risk is one where the stock will have lowest standard deviation. Standard deviation of a stock represents total risk it has on standalone basis.

Based on CAPM,

Expected return on security = Risk free rate + Beta * Market risk premium

Beta of portfolio is weighted average of beta of individual constituents.

Beta of portfolio = ($3500/$10000) * 0.80 + ($2000/$10000) * 1.50 + ($1500/$10000) * 1.20 + ($3000/$10000) * 0.50

Beta of portfolio = 0.28 + 0.30 + 0.18 + 0.15 = 0.91

Expected return = 4% + 0.91 * 6% = 9.46%