Question

6. Portfolio expected return and risk A collection of financial assets and securities is referred to as a portfolio. Most individuals and institutions invest in a portfolio, making portfolio risk analysis an integral part of the field of finance. Just like stand-alone assets and securities, portfolios are also exposed to risk. Portfolio risk refers to the possibility that an investment portfolio will not generate the investor's expected rate of return. Analyzing portfolio risk and return involves the understanding of expected returns from a portfolio Consider the following case: Sophia is an amateur investor who holds a small portfolio consisting of only four stocks. The stock holdings in her portfolio are shown in the following table: Stock Artemis Inc. Babish & Co. Percentage of Portfolio 20% 30% 35% 15% Expected Return 8.00% 14.00% 11.00% 3.00% Standard Devicon 24.00% 28.00% 31.00% Cornell Industries Danforth Motors 33.00% What is the expected return on Sophia's stock portfolio? 10.10% 15.15% 7.58% 13.64%

Answer 1

The return of a portfolio is the weighted return of the constituent stocks

So Return of this portfolio = 0.20 * 8% +0.30 *14%+0.35*11%+0.15*3%= 10.1% (1st option)

As the correlation coefficient is less than 1, the portfolio standard deviation is less than the weighted average standard deviation of 29%. We can actually measure the standard deviation of the portfolio as follows:

The standard deviation of a portfolio is given by

Where Wi is the weight of the security i,

Op = W;*W, *0; * 0;* Pij

$\sigma _{i}$ is the standard deviation of returns of security i.

and $\rho _{i,j}$ is the correlation coefficient between returns of security i and security j

So, standard deviation of portfolio =sqrt (0.20^2*0.24^2+0.30^2*0.28^2+0.35^2*0.31^2 + 0.15^2*0.33^2+ 2*0.2*0.3*0.24*0.28*0.4+ 2*0.2*0.35*0.24*0.31*0.4+ 2*0.2*0.15*0.24*0.33*0.4+ 2*0.3*0.35*0.28*0.31*0.4+ 2*0.3*0.15*0.28*0.33*0.4+ 2*0.35*0.15*0.31*0.33*0.4)

where sqrt stands for square root

=sqrt(0.0477895)

=0.2186 =21.86% which is less than 29%, the weighted average standard deviation of portfolio stocks