Question

A portfolio of $ 100,000 is composed of two assets: A stock whose expected annual return is 10% with an annual standard deviation of 20%; A bond whose expected annual return is 5% with an annual standard deviation of 12%. The coefficient of correlation between their returns is 0.3. An investor puts 60% in the stock and 40% in bonds.

1. What is the expected annual return, standard deviation of the portfolio?           
2. What is the 1-year 95% VaR? Explain in non-technical terms the meaning of the number you calculated.                                                                                                 
3. What is the 1-year 99% VaR? Explain in non-technical terms the meaning of the number you calculated.        

Answer 1

1.
Annual return=60%*10%+40%*5%=8.00%

Standard deviation=sqrt((60%*20%)^2+(40%*12%)^2+2*60%*20%*40%*12%*0.3)=14.20%

2.
=-(8%-1.65*14.20%)*100000=15430.00

This means that in 5 out of the 100 cases, the portfolio will lose more than 15430. In other words, in 95 out of the 100 cases, the portfolio will lose less than 15430

3.
=-(8%-2.33*14.20%)*100000=25086.0000

This means that in 1 out of the 100 cases, the portfolio will lose more than 25086. In other words, in 99 out of the 100 cases, the portfolio will lose less than 25086