Abigail Grace has a $$900,000$ fully diversified portfolio. She subsequently inherits ABC Com$-$

pany common stock worth $$100,000.$ Her financial adviser provided her with the following

forecast information:

Risk and Return Characteristics

The correlation coefficient of ABC stock returns with the original portfolio returns is $.40.$

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 $.42\%$ monthly. Assuming Grace sells the ABC stock and replaces it with the gov$-$

ernment 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$.$