Question

Use this info to answer the problem

State Probability Return on C Return on D

Boom .25 10% 5%

Norm .40 6% 10%

Bust .35 2% 5%

What is the standard deviation of a portfolio with 40% of the funds invested in C and the rest in D?

Please show work and formulas used, Thanks.

Answer 1

Portfolio Return=40%*return of C+60%*return of D
State Portfolio Return
Boom =40%*10%+60%*5%=7.00%

Norm =40%*6%+60%*10%=8.40%

Bust =40%*2%+60%*5%=3.80%

Expected Return=Sum(probability*returns)=0.25*7%+0.40*8.4%+0.35*3.8%=6.440%

Standard Deviation=Sqrt(Sum(probability*(returns-expected returns)^2))=Sqrt(0.25*(7%-6.44%)^2+0.40*(8.40%-6.44%)^2+0.35*(3.80%-6.44%)^2)=2.014%