$7.$ 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:

Andre is an amateur investor who holds a small portfolio consisting of only four stocks. The stock holdings in his portfolio are shown in the following table:

Stock

Percentage of Portfolio

Expected Return

Standard Deviation

Artemis Inc. $20\%6\mathrm{.}00\%26\mathrm{.}00\%$

Babish & Co$.30\%14\mathrm{.}00\%30\mathrm{.}00\%$

Cornell Industries $35\%11\mathrm{.}00\%33\mathrm{.}00\%$

Danforth Motors $15\%5\mathrm{.}00\%35\mathrm{.}00\%$

What is the expected return on Andre$$s stock portfolio?

$13\mathrm{.}50\%$

$7\mathrm{.}50\%$

$15\mathrm{.}00\%$

$10\mathrm{.}00\%$

Suppose each stock in Andre$$s portfolio has a correlation coefficient of $0\mathrm{.}4(\backslash$rho $=0\mathrm{.}4)$ with each of the other stocks. If the weighted average of the risk of the individual securities $($as measured by their standard deviations$)$ included in the partially diversified four$-$stock portfolio is $31\%,$ the portfolio$$s standard deviation $(\backslash$sigma p

$)$ most likely is $31\%.$