Gloria Gomez has a portfolio worth $80,000. She subsequently inherits ABC Company common stock worth $20,000. Her financial advisor provided her with the following forecasted information:

The correlation coefficient of ABC stock returns with the original portfolio returns is 0.40. The risk- free rate Gloria can earn by investing in government securities is 4% per year.

a) The inheritance changes Glorias overall portfolio and she is deciding whether to keep the ABC stock. Assuming Gloria keeps the ABC stock, calculate:

a.1) the expected return of Glorias new portfolio (which includes the ABC stock). a.2) the standard deviation of Glorias new portfolio (which includes the ABC stock).

b) Based on conversations with her husband, Gloria is considering selling the $20,000 of ABC stock and acquiring $20,000 of XYZ Company common stock instead. XYZ stock has the same expected return and standard deviation as ABC stock BUT DIFFERENT correlation with the original portfolio. The correlation coefficient of ABC stock returns with the original portfolio returns is 0. Her husband comments, It does not matter whether you keep all the ABC stock or replace it with $20,000 of XYZ stock. State whether her husbands comment is correct or incorrect. Justify your response.

c) Assuming Gloria sells the ABC stock and invests all the proceeds from ABC stock with the risk- free asset, calculate:

c.1) the expected return of Glorias new portfolio (which includes the risk-free asset). c.2) the standard deviation of Glorias new portfolio (which includes the risk-free asset).

d) Gloria has a utility function of the form U=E(rC) 12 A (C)2 with risk aversion A=3. Is she better off keeping stock ABC (item a) or replacing it by the risk-free asset (item c)? Justify your answer.

e) Gloria has a utility function of the form U=E(rC) 12 A (C)2 with risk aversion A=3. Suppose she decides to allocate her total wealth (i.e., her original wealth plus the inheritance) optimally between her original portfolio and the risk-free asset (so, having zero in ABC stock). How much money should she have in the risk-free asset

Original Portfolio ABC Company Expected Return 8% 12% Standard Deviation of Return 15% 40%