Section :3

Expected Return and Standard Deviation of a Two-Asset Portfolio


Now we calculate the expected returns and standard deviations of a two-stock portfolio. We have the following data for Stock 'C' and Stock 'S'.

 

Out of a total portfolio valuing SR 100,000, SR 40,000 is invested in stock 'C' and SR 60,000 in stock 'S'.

 

 

Stock C

Stock S

Expected Return

11%

25%

Standard Deviation

15%

20%

Correlation

0.3

 

First, we determine the weight of each stock relative to the entire portfolio:

 

WC

=

SR 40,000 / SR 100,000

=

0.40

WS

=

SR 60,000 / SR 100,000

=

0.60

 

 Next, we determine the weighted average return of the portfolio:

 

E(Rp ) 

=

(0.4)(11%)+(0.60)(25%)   

 =

19.4%

              

Finally, we calculate the standard deviation of the portfolio:


σp      =    [(0.4)(15%) + (0.6)(20%) + 2(0.4)(0.6)(0.3)(15%)(20%)]1/2
         
 =    (0.02232)1/2  =  14.94%

Using the same method of calculation, we calculate the expected returns and standard deviations under various portfolio allocations that are presented in the following table.

 

Weight Stock C

100%

80%

60%

40%

20%

0%

Weight Stock S

0%

20%

40%

60%

80%

100%

E(Rp)

11.0%

13.8%

16.6%

19.4%

22.2%

25.0%

σp

15.0%

13.7%

13.7%

14.9%

17.1%

20.0%

Coefficient of Variation

1.36%

0.99%

0.83%

0.77%

0.77%

0.80%

 

It can be seen from the above table that at some combinations, the risk per unit of return is less than others, and it is also less than if all the funds were invested in one stock. The reason for this is the correlation that is less than one. Whenever the correlation between two stocks is less than 1.0, there would be benefits of diversification. As the correlation between two assets decreases, there is less of a tendency for stock returns to move together. There separate movements of each stock serve to reduce the volatility of a portfolio to a level that is less than that of its individual components. By diversifying a portfolio across many stocks, it is possible to create portfolios with higher expected returns without increasing risk (standard deviation).


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