Question

Conceptual questions on portfolio and stand-alone risk

Latasha holds a $7,500 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
Perpetualcold Refrigeration Co. (PRC)	$2,625	0.90	9.00%
Kulatsu Motors Co. (KMC)	$1,500	1.70	11.00%
Three Waters Co. (TWC)	$1,125	1.10	18.00%
Mainway Toys Co. (MTC)	$2,250	0.30	25.50%

Suppose all stocks in Latasha’s portfolio were equally weighted. The stock that would contribute the least market risk to the portfolio is   . Further, if all of the stocks in the portfolio were equally weighted, the stock that would have the least amount of standalone risk is   .

If the risk-free rate is 4.00% and the market risk premium is 6.50%, then Latasha’s portfolio will exhibit a beta of     and a required return of     .

Answer 1

The stock that would contribute least market risk to the portfolio is the stock with lowest standard deviation i.e. Perpetual Cold Refrigeration Co. (PRC)

The stock with the lease amount of standalone risk is the stock with the lowest beta i.e. Mainway Toys Co.(MTC)

Portfolio beta is equal to the weighted average beta

= 0.9*2,625/7,500 +1.7*1,500/7,500 + 1.1*1,125/7,500 + 0.3*2,250/7,500

= 0.315+0.34+0.165+0.09

= 0.91

Required return = risk free rate + beta*market risk premium

= 4% + 0.91*6.5%

= 9.915%

Hence, portfolio would exhibit a beta of 0.91 and required return of 9.915%