Problem $8$ An investor has a $$900,000$ fully diversified portfolio. He subsequently inherits ABC

Company common stock worth $$100,000.$ His financial advisor provided him with the following

forecast information: the expected monthly returns and the standard deviation of monthly returns

for the original portfolio are $0\mathrm{.}67\%$ and $2\mathrm{.}37\%,$ respectively; the corresponding estimates for the

ABC Company stock are $1\mathrm{.}25\%$ and $2\mathrm{.}95\%,$ respectively. The correlation coefficient of ABC stock

returns with the original portfolio returns is $0\mathrm{.}40.$

a$.$ The inheritance changes the investor$$s overall portfolio and he is deciding whether to keep

the ABC stock. Assuming he keeps the ABC stock, calculate the:

$($i$)$ Expected return of his new portfolio that includes the ABC stock.

$($ii$)$ Covariance of ABC stock returns with the original portfolio returns.

$($iii$)$ Standard deviation of his new portfolio that includes the ABC stock.

b$.$ If the investor sells the ABC stock, he will invest the proceeds in risk free government securities

yielding $0\mathrm{.}42\%$ monthly. Assuming he sells the ABC stock and replaces it with the government

securities$,$ calculate the

$($i$)$ Expected return of his new portfolio, that includes the government securities$.$

$($ii$)$ Covariance of the government security returns with the original portfolio returns.

$($iii$)$ Standard deviation of his new portfolio, that includes the government securities$.$

c$.$ Determine whether the systematic risk of his new portfolio, which includes the government

securities$,$ will be higher or lower than that of his original portfolio.

d$.$ Based on conversations with his friend, the investor is considering selling the $$100,000$ of

ABC stock and acquiring $$100,000$ of XYZ Company common stock instead. XYZ stock has

the same expected return and standard deviation as ABC stock. His friend comments, $$It

doesn$$t matter whether you keep all of the ABC stock or replace it with $$100,000$ of XYZ

stock.$$ State whether the friend?s comment is correct or incorrect. Justify your response.

e$.$ In a recent discussion with his financial advisor, the investor commented, $$If I just don$$t los

money in my portfolio, I will be satisfied.$$ He went on to say, $$I am more afraid of losing

money than I am concerned about achieving high returns.$$ Describe one weakness of using

standard deviation of returns as a risk measure for this investor.