1.Suppose there are three portfolios being considered.Portfolio A has an expected return of 11.5% and volatility of 18%.Portfolio B has an expected return of 8% and volatility of 14%.Portfolio C has an expected return of 6% and volatility of 10%.

The correlation between portfolio A and B is 0.40.The correlation between portfolio A and C is 0.30.The correlation between portfolio B and C is 0.50.

Combinations of portfolios are not being considered.

a) Which portfolio would a highly risk averse investor choose?

A) Portfolio A

B) Portfolio B

C) Portfolio C

D) Not sure, no clue, or no idea

b) An investor wants to minimize the probability of returns falling below 3.5%.Which portfolio has the lowest probability of producing a return less than 3.5%?

A) Portfolio A

B) Portfolio B

C) Portfolio C

D) Not sure, no clue, or no idea

2.Suppose that an investor chooses according to mean-standard deviation criterion.The investor is faced with the following 4 investment choices:

Expected ReturnStandard Deviation

Portfolio P10%5%

Portfolio Q21%11%

Portfolio R18%23%

Portfolio S24%16%

Which of the statements below is correct?

A) Investor chooses Q over P

B) Investor chooses Q over R

C) Investor chooses S over all of the others

D Investor chooses S over Q

E) Investor chooses R over P

3. A wealthy investor has no other source of income beyond her investments.Her investment advisor recommends that she tilt her portfolio to cyclical stocks and high-yield bonds because the average investor holds a job and is recession sensitive.Explain the advisor's advice.

4.A formerly wealthy Silicon Valley executive is currently reassessing his financial portfolio.His portfolio consists of an S&P 500 index fund, stock options in his company, some 5-year US Treasury bonds, and some cash in money market accounts.His other assets include a condo in Palo Alto, a convertible Porsche, and himself (that is, his education and skills to be used to generate future income).

You have been hired by the executive to recommend an additional asset class to invest in.Using the knowledge of mean-variance optimization you learned in class, which of the following investment vehicle is the best choice to consider for this executive.

A)A house in Palo Alto (and sell the condo).

B)Russell 2000 iShares (a fund that tracks an index of small-cap stocks).

C)A global mutual fund investing in Europe and Asia.

D)Technology stocks other than that of his own company.

E)Stocks in his own company.

5.An investor sells his soul to the devil and discovers with absolute certainty that a stock (stock XXX) has the highest expected return among all the stocks in his universe.Assume that every stock in this universe has the same volatility.There is also a risk-free asset in this universe.Since he already knows which stock has the highest expected return (and the highest Sharpe Ratio), there is no point in buying any other stock in his portfolio.

A)True

B)False

6.The correlation coefficient between pairs of stocks are as follows: corr(A,B) = .85, corr(A,C) = .60, corr(A,D) = .45, corr(A,E) = .50, corr(B,C)= .65, corr(B,D) =.35, corr(B,E)=.80, corr (C,D)= .40, corr (C,E)=.35, corr(D,E) = .40. Each stock has an expected excess return of 8% and volatility of 20%. If your entire portfolio is now composed of stock A and you can add some of only one stock to your portfolio, which one would you choose?

A)Need more data

B)Stock B

C)Stock C

D)Stock D

E)Stock E

7.Suppose a large-cap stock index has an expected return of 15% and volatility of 15%.A government bond index has an expected return of 5%, volatility of 10%, and correlation with the large-cap stock index of 0.50.Calculate the expected return and standard deviation of return for a portfolio 75% invested in the stock index and 25% invested in the bond index.

8.Suppose a risk-free asset has a 5% return and a second asset has an expected return of 13% with a volatility of 23%.Calculate the expected return and standard deviation of return for a portfolio consisting 10% of the risk-free asset and 90% of the second asset.

9.We consider a risky asset with expected return of 14% and variance of the return of .0064. The risk-free rate is 7%. What is the volatility of a portfolio that is 60% invested in that risky and 40% in the risk-free asset?

10.Consider the MVE portfolio that consists of various risky assets from a universe of N assets.The MVE portfolio has a positive Sharpe Ratio.An investor allocates between the MVE portfolio and a risk-free asset according to her risk-aversion to come up with her final portfolio allocation.

It is optimal for her final portfolio allocation to be short the MVE portfolio.

A) True

B) False

C) Not sure, no clue, or no idea

11.Consider the same MVE portfolio as above, which consists of various risky assets from a universe of N assets.The MVE portfolio has a positive Sharpe Ratio.An investor allocates between the MVE portfolio and a risk-free asset according to her risk-aversion to come up with her final portfolio allocation.

It is possible (optimal) for her final portfolio allocation to be short some risky assets.

A) True

B) False

C) Not sure, no clue, or no idea

12.Suppose that you are managing a pension fund.The fund consists of risky investments, but the fund is not allowed to invest in the risk-free asset.However, the pensioners can invest in (or borrow) the risk-free asset themselves.Which of the following parameters do you not need in order to make your investment decisions?

A)Risk-aversion of your clients (pension fund shareholders).

B)Risk-free rate.

C)Expected returns of assets under management.

D)Volatilities of assets under management.

E)Correlations among the assets under management.

13.Suppose the S&P 500 has an expected return of 13.50% and volatility of 20%.The risk-free rate is 6.25%.If you believe that the S&P 500 is the mean-variance efficient portfolio, what is the highest rate of return you can achieve if you're willing to accept 12% standard deviation of risk?