Abigail Grace has a $$900,000$ fully diversified portfolio. She subsequently inherits ABC Company common stock worth $$100,000.$ Her financial adviser provided her with the following estimates:

Risk and Return Characteristics

The correlation coefficient of ABC stock returns with the original portfolio returns is $\mathrm{.}40.$

a$.$ The inheritance changes Grace's overall portfolio, and she is deciding whether to keep the ABC stock. Assuming Grace keeps the ABC stock, calculate the:

i$.$ Expected return of her new portfolio, which includes the ABC stock.

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

iii. Standard deviation of her new portfolio, which includes the ABC stock.

$b.$ If Grace sells the ABC stock, she will invest the proceeds in risk$-$free government securities yielding $\mathrm{.}42\%$ monthly. Assuming Grace sells the ABC stock and replaces it with the government securities$,$ calculate the

i$.$ Expected return of her new portfolio, which includes the government securities$.$

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

iii. Standard deviation of her new portfolio, which includes the government securities$.$

c$.$ Determine whether the systematic risk of her new portfolio, which includes the government securities$,$ will be higher or lower than that of her original portfolio.

d$.$ On the basis of conversations with her husband, Grace 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. Her husband comments, $"$It doesn't matter whether you keep all of the ABC stock or replace it with $$100,000$ of XYZ stock." State whether her husband's comment is correct or incorrect.

Justify your response.

$e.$ In a recent discussion with her financial adviser, Grace commented, $"$If I just don't lose money in my portfolio, I will be satisfied." She went on to say, "I am more afraid of losing money than I am concerned about achieving high returns."

i$.$ Describe one weakness of using standard deviation of returns as a risk measure for Grace.

ii$.$ Identify an alternate risk measure that is more appropriate under the circumstances.