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University of Southern California Individual Assignment #4 Note: This assignment is due at the beginning of Week #9 Live Session. This problem set is designed to give you practice applying portfolio management tools, such as the Sharpe Ratio analysis, computation of alpha’s, and historical anomalies. 1.As an investment advisor, you are approached by a very strange client. The client holds a fairly diverse portfolio of stocks, but all of the stocks are stocks found in the U.S. He is concerned that his portfolio allocations are not the best he can possibly have and he has come to you seeking advice. However, he refuses to reveal any information about precisely which stocks he holds – that would be bad luck. You look at the investment vehicles offered by your company. Shown in parenthesis are the notes you took at a recent marketing presentation you attended. Fund 1)US Small Cap Growth Fund (risky, but has high expected returns – all investments are in the US) Fund 2)US Convertible Bond Fund (mixture of stocks and bonds in the US) Fund 3)UK Index Fund (diverse mix of stocks in the UK; the correlation between US and UK Indices are about 0.50) Fund 4)UK Hedge Fund (special strategy fund in UK; high expected returns, but extremely high risk; the correlation between this Fund and UK Index is about 0.50, the correlation between this Fund and the US Index is about 0.0) Fund 5) US Real Estate Investment Trust (diverse mix of real estate properties located in the US, high expected returns and low risk, but has serious tax consequence -- correlation with the US Index of around 0.25.) Convince the client to invest in one of these funds (there is only one that makes sense for him). You must provide a good succinct argument (~5 sentences max). 2.A family friend of yours calls you up asking for financial advice. She works for Boing (a local aircraft manufacturer) and is offered, as an employee benefit, an opportunity to spend $10,000 to buy company stocks once a year at a 10% discount (employee stock plan). That is, if the stock price is $100/share, she can spend $10,000 and obtain 110 shares. This is a “take it or leave it” deal, and she will not be able to sell the stock for at least one year. Assume that she is an engineer who is not privy to any material inside information. She understands the concept of diversification, and understands that her own job security depends on the well-being of the company. Her rough analysis of her future job prospects and her assets estimates 50% of her wealth (from her job) to be in Boing, and 50% in the US market. Assume that the value of her job at Boing is perfectly reflected by the Boing stock. (So her portfolio is essentially 50% Boing stock and 50% US market). Assume also that, to her, $10,000 is fairly “small”. The US market has an expected return of 14%, standard deviation of 15%. The risk-free rate is 4%. Boing stock has an expected return of 12%, standard deviation of 25%. The correlation between Boing stock and the US market is 80%. Calculate the following and show your computations. a) Expected return on her current portfolio (including the value of her job): b) Sharpe Ratio of her current portfolio: c) If the US market portfolio is MVE, what should be the expected return of Boing stock? d) If the US market portfolio is MVE, what is the highest expected return that any portfolio can achieve, if that portfolio has a standard deviation of 9%? e) Assume that the expected return of Boing stock is 12%. Should she participate in the employee stock plan (at 10% discount)? Hint: you can treat the discount as an added return on holding the stock. 3.An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 18% and a standard deviation of 20%. Stock B has an expected return of 14% and a standard deviation of 5%. The correlation coefficient between the returns of A and B is 0.50. The risk-free rate is 10%. Based on these two stocks, what is the proportion of MVE (or tangency portfolio) that should be invested in stock A? (Hint: One the following is the correct answer.) A) 0% B) 50% C) 100% Show work and explain: 4.Suppose you evaluating an investment manager. Manager A has achieved a historical return of 20% per year with a beta (with respect to a benchmark) of 1.4, and volatility of 40%. Manager B has achieved a historical return of 15% per year, beta of 1.0 and volatility of 20% per year. The benchmark return has been 16% per year, and the risk-free rate is 6%. Volatility of the benchmark is 20% per year. a) According to Sharpe Ratio, which manager has produced superior returns? A) Manager A B) Manager B C) No idea b) According to , which manager has produced superior returns? A) Manager A B) Manager B C) No idea c) Draw the total risk (standard deviation) – reward (expected return) trade-off. Be sure to mark/draw the risk-free rate, the market portfolio, the mean-variance frontier, manager A and manager B. 5.A private investor manages her own portfolio by carefully analyzing various stocks to include or sell short in her portfolio (portfolio P). She maximizes the expected return of her portfolio while minimizing its standard deviation. She then invests some of her money into the portfolio and puts the rest in T-Bills. She is concerned that her portfolio is not the optimal portfolio among the stocks she has chosen to invest in. Her data on the securities she hold are as follows:: Security Expected Return Standard Deviation Correlation w/ Portfolio P Beta with the US Market Delta 18.0% 35.0% 0.90 1.50 Ford 10.0% 20.0% 0.60 1.15 LVMH 6.0% 25.0% 0.00 0.70 Portfolio P 13.0% 18.0% 1.00 0.90 T-Bills 4.0% 0.0% 0.00 0.00 She estimates the US Market to have an expected return of 12.0% and a standard deviation of 12.0%. Based on this data, indicate below, which direction this investor should adjust the portfolio weights for each of the three securities. a) DeltaIncreaseNo ChangeDecrease b) FordIncreaseNo ChangeDecrease c) LVMHIncreaseNo ChangeDecrease d)Now, suppose that a financial planner examines this investor’s portfolio. This financial planner uses the US Market as the benchmark. Using the investor’s estimates of expected return (18.0% for Delta, 10.0% for Ford, and 6.0% for LVMH), and other parameters given earlier. What would the financial planner estimate the alpha’s of these securities to be? e)Re-consider the investor. She now considers investing a part of her wealth into the US Market portfolio. She still currently holds portfolio P. What is the hurdle rate at which she would buy the US Market portfolio? Hint: you should begin by calculating the beta of the market with respect to portfolio P (this is NOT the beta of portfolio P with respect to the market). 6.A portfolio manager finds that stocks with high sales-to-price ratios tend to have low alpha’s relative to the US Market – especially when stocks have had a high run-up (increase) in price over that past 5 years. Which one of the following has she most likely replicated? (Hint: not all statements are true.) (Choose one. No explanation necessary) A) Small stocks tend to have low alphas. B) Low beta stocks tend to have low alphas. C) Low earnings stocks tend to have low alphas. D) Past 3-12 month loser stocks tend to have low alphas. E) Growth stocks tend to have low alphas. 7.Name an effect that have historically produced a positive alpha’s. What kinds of stocks have historically had higher returns than predicted by the Market Model in this effect (which ones have positive alphas). University of Southern California Individual Assignment #3 Note: This assignment is due at the beginning of Week #7 Live Session. This problem set is designed to help you develop intuition behind optimal asset allocation. 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).