In class, we have learned how to calculate the expected return and volatility of

Question

In class, we have learned how to calculate the expected return and volatility of a portfolio conssisting of two securities. Now let's try to calculate the expected return and volatility of a portfolio (call it target portfolio) consisting of three securities, one of which is treasury bill (i.e. risk-free debt). Assume the following: The procedure is to first form a portfolio (call it portfolio AB) consisting of only slock A and B (two securities), and then form our target portfolio based on portfolio AB and the Treasury Bill (again two securities). Calculate the expected return and volatility (i.e. standard deviation) of portfolio AB consisting of stock A and stock B. Note in portfolio AB. Mock A and stock B each has 50% weight. Now based on the expected return and volatility of portfolio AB calculated in step 1, calculate expected return and volatility of the target portfolio that consists of portfolio AB and Treasury Bill. Note in the target portfolio, portfolio AB will have weight of 80% (40% from stock A and 40% from stock B), and the Treasury Bill has weight of 20% Also note that since Treasury Bill 0% standard deviation, it will have zero correlation with portfolio AB.

Explanation / Answer

Computation of Expected return of portfolio =(12%+8%)/2                          
           ER   =   10%      
Stadard deviation formula =Square root of {{(WA*S.DA)^2+(WB*S.DB)^2+2*WA*S.DA*WB*S.DB* corrlation B/W A and B}                          
Where WA = weights of Stock A                          
   WB =weights of Stock B                      
   S.DA=Standard deviation of A                      
   S.DB=Standard deviation of B                      
                          
Then, Standard Deviation =Square root of {(12*0.5)^2+(18*0.5)^2+2*12*18*0.5*0.5*0.3}

=12.22%

Now Expected return of AB and Tresury bil = (10%+4%)/2

ER = 7%

Standard deviation =Square root of {{(WA*S.DA)^2+(WB*S.DB)^2}

Since Corrlation between AB and Tresury bill is ZERO

Standard deviation= square root of {(12.22*0.8)^2+(0*0.2)^2}

   =9.78%

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