EN$-$US

Stock Selection Case Study

Markowitz won the Nobel Prize for his work in stock portfolio theory. He was the first to measure portfolio risk using the variance of returns

$.$

$1$

$$He introduced stock selection based on an

$$

efficient frontier

$$

$,$

$$namely$,$ by picking the stocks that give the portfolio

$$

with minimum variance for a given return" and

$$

maximum return for a given variance."

An investor is considering buying a combination of

$3$

$$stocks

$$

$$

Alpha

$,$

$"$

$$

Bravo

$,$

$"$

$$and

$$

Charlie

$"$

$-$

$$using Markowitz's portfolio optimization method. The expected returns and risk of these stocks are given in Table

$1$

$.$

Table

$1$

$.$

$$Return and Risk Data for

$3$

$$stocks

Stock Alpha Bravo Charlie

Expected Return

Risk

$($

variance of returns

$)$

$0$

$.$

$0$

$6$

$2$

$0$

$.$

$0$

$1$

$4$

$6$

$0$

$.$

$1$

$4$

$6$

$0$

$.$

$0$

$8$

$5$

$4$

$0$

$.$

$1$

$2$

$8$

$0$

$.$

$0$

$2$

$8$

$9$

An investor would like to purchase some combination of the

$3$

$$stocks to build a

$$portfolio that gives at least a

$1$

$0$

$\%$

$$return at the lowest possible risk

$($

i

$.$

e

$.$

$,$

$$at

$$A portfolio's variance depends on how each individual stock's price fluctuations are correlated with every other stock's, known as the

covariance of returns. The covariances are given in the variance

$-$

covariance matrix in Table

$2$

$.$

$$For example, the covariance between Alpha and Bravo is

$0$

$.$

$0$

$1$

$8$

$7$

$.$

$2$

Table

$2$

$.$

$$Variance

$-$

Covariance Matrix of Returns

Alpha Bravo Charlie Al