Question

Your client has $102.000 invested in stock A She would like to build a two-stock portfolio by investing another $102,000 in other lock Bor C She wants a portfolio with an expected return of at least 14.0% and as low a risk as possible, but the standard deviation must be no more than 40% What do you advise her lo do, and what will be the portfolio expected return and standard deviation? Expected Return Standard Deviation Correlation with A 50% 125 0.13 12% 0.25 The expected return of the portfolio with stock Bis % (Round to one decimal place)

Answer 1

As the Expected Return and Risk of both B and C are the same , the choice of selecting one stock from B or C boils down to their correlation coefficient with A.

Let us calculate Risk and Return in both cases (i.e. when A is selected and that when B is selected)

We know that Expected Return of a portfolio is the weighted average return of its individual stocks

Here Since the investment is $102000 in both A and the selected stock (B or C) , therefore their weights are equal

Therefore W_A =W_B= W_C = 0.5

So, the Expected Return from the portfolio of A and B is

= W_A *R_A + W_B* R_B where R_{A and} R_B are the expected returns of A and B

= 0.5* 16%+ 0.5*12% = 14%

Similarly, the Expected Return from the portfolio of A and C is

= W_A *R_A + W_C* R_C where R_{A and} R_C are the expected returns of A and C

= 0.5* 16%+ 0.5*12% = 14%

The Expected Standard Deviation of a portfolio comprising of two stocks A and B can be written as

= WA * o+W*0% + 2 * WA* W8*0A* OB * PAB

Where  σ_A and σ_B are the standard Deviations of A and B and $\rho _{AB}$ is the correlation coefficient between A and B

Therefore, the Standard Deviation (Risk) of the portfolio comprising of A and B

= sqrt(0.5²*50² + 0.5²*40² + 2* 0.5 *0.5 * 50 * 40 * 0.13)

=sqrt ( 625+ 400+ 130)  

=sqrt (1155) = 33.99% = 34% (rounded to one decimal place)

Similarly, the Standard Deviation (Risk) of the portfolio comprising of A and C

= sqrt(0.5²*50² + 0.5²*40² + 2* 0.5 *0.5 * 50 * 40 * 0.25)

=sqrt ( 625+ 400+ 250)  

=sqrt (1275) = 35.71% = 35.7% (rounded to one decimal place)

As, we can clearly see that the portfolio of A and B has the same return of 14% as that of portfolio of A and C

But the risk (standard deviation) of portfolio A and B is less (34%) only against risk (standard deviation) of portfolio A and C (35.7%)

Hence, your client should invest in B and make a portfolio of A and B