Question

Expected Return Standard Deviation         

Stocks, S 14                                           30          

Bonds, B 6 15          

The correlation between stocks and bonds is ρ(S,B) = 0.05

Note: I've entered the expected returns and standard deviations as whole numbers (not decimals)   

Treat the risk-free rate as the number 2 not 0.02 or 2%.

The risk-free rate is 2 percent. The CAL that is tangent to the portfolio frontier of stock and bonds has an expected return equal to 9.5 percent.

You wish to construct an efficient portfolio with an expected return equal to 8 percent. What are the asset weights in the portfolio? That is, what are the weight of stocks, bonds and bills in the portfolio? Please show your work.

Answer 1

The combination of stocks and bonds is expected to have a return of 9.5%

Let x be thw weight in stocks , the 1-x is the weight in bonds

x*14% + (1-x)*6% = 9.5%

0.14x +0.06 -0.06x = 0.095

0.08x = 0.035

x = 0.035/0.08 = 0.4375

1 - x = 0.5625

Stock = 0.4375 and Bonds = 0.5625

Next, we consider y to be invested in the above portfolio and 1-y to be invested in t-bills(risk free) to get a total of 8%

y*9.5% + (1-y)*2% = 8%

0.095y + 0.02-0.02y = 0.08

0.075y = 0.08-0.02 =0.06

y = 0.06/0.075 = 0.8

Portfolio = 0.8 and Risk free bills = 0.2

Weight of Stocks = 0.8*0.4375 = 0.35 or 35%

Weight of Bonds = 0.8*0.5625 = 0.45 or 45%

Weight of bills = 0.2 or 20%

To conclude,

Weight of Stocks = 35%

Weight of Bonds = 45%

Weight of Bills = 20%