Question

security	beta	Standard deviation	Expected return
S&P 500	1.0	20%	10%
Risk free security	0	0	4%
Stock d	( )	30%	13%
Stock e	0.8	15%	( )
Stock f	1.2	25%	( )

4) You form a complete portfolio by investing $8000 in S&P 500 and $2000 in the risk free security. Given the information about S&P 500 and the risk free security on the table, figure out expected return, standard deviation, and a beta for the complete portfolio.

Answer 1

Given about complete portfolio,

Investment in S&P 500 = $8000

required return on S&P 500 Rm = 10%

Standard deviation of S&P 500 SD(m) = 20%

Beta of S&P 500 = 1

Investment in risk free security = $2000

Risk free rate Rf = 4%

So, weight of S%P 500 wm in this portfolio is

wm = 8000/(8000 + 2000) = 0.8

weight of risk free security wf = 2000/(8000 + 2000) = 0.2

So, expected return on complete portfolio E(r) = wm*Rm + wf*Rf = 0.8*10 + 0.2*4 = 8.8%

Standard deviation of this portfolio SD(r) = wm*sd(m) = 0.8*20 = 16%

Beta of this portfolio = wm*Beta of S&P 500 = 0.8*1 = 0.8