1. PJ Walker is a successful businesswoman who has accumulated a substantial investment fund totaling $30 million made up of more than 150 individual stocks. She uses three separate investment advisory firms to manage the $30 million fund. Each advisor has $10 million of her money. There is no apparent conformity of strategy, tactics, or style among the three advisors.
Recently she was reviewing the performance of the overall fund, and of each separate advisor. She noted that one advisor, Black Asset Management (BAM), had consistently outperformed the other two advisors as well as the S&P 1500 index. BAM is a ‘bottom-up’ stock picking firm that avoids any attempts at market timing or asset allocation. It focuses exclusively on selecting individual stocks for PJ. It picks about 50 stocks for her, and invests no more than 3% of the $10 million in any one of these 50 stocks.
PJ correctly notes that the reason for BAMs consistent out- performance was because they have been able to identify and select 10-12 stocks each year that registered especially large gains.
PJ has an idea: tell BAM to pick no more than 20 stocks for her. Double the amounts to the stocks BAM really likes and forget the other 30 or so stocks!
A. Will the restriction to 20 stocks affect the risk of her BAM portfolio? Explain.
B. A friend of PJs liked her idea and said: “Look, why stop at 20 stocks? I think you should tell BAM to pick only 10 stocks for you.” Evaluate her friend’s idea.
C. Another friend suggested that instead of evaluating each investment advisor independently, it might be better to consider the effects of the change to 20 stocks in the BAM portfolio on her total $30 million fund. Evaluate PJs idea for BAM in light of her friend’s suggestion.
2. The following table provides data on three risky asset classes: small cap stocks as represented by the Russell 2000 Index; investment grade corporate bonds as represented by the Dow Jones Corporate Bond Index; and developed country equities as represented by the EAFE Stock Market Index.
The top part of the table presents information on expected returns, risks as measured by standard deviations and Sharpe ratios for each of the asset classes. The bottom part of the table presents information on the return correlations between the asset classes.
Russell 2000 DJ Corporate Bond EAFE
Expected Return 10.00% 7.00% 6.00%
Standard Deviation 21.00% 10.00% 35.00%
Sharpe Ratio 0 .48 0 .70 0 .17
Russell 2000 DJ Bonds EAFE
Russell 2000 1.00 – 0.50 + 0.80
DJ Bonds – 0.50 1.00 0.00 EAFE + 0.80 0.00 1.00
A. Suppose you have a portfolio currently 100 percent invested in investment grade corporate bonds. Which of the other two asset classes provides the greatest potential diversification benefits? Briefly explain.
B. What does the correlation coefficient of 0.00 between the Dow Jones Corporate Bond Index and EAFE Index mean? What does the correlation coefficient of +0.80 between the Russell 2000 and EAFE indices mean?
C. If you have a portfolio asset allocation of 50% in investment grade corporate bonds and 50% small capitalization stocks what will be its expected return and risk?
D. Given the data on expected returns, risks and the Sharpe Ratios from above why would any rational investor hold either US small capitalization stocks, as represented by the Russell 2000 index, or international developed country stocks as represented by the EAFE index?
1. Your firm, HiFee Investment Advisors, is building a portfolio for a client, Azarinka Nadal. After careful research you have decided that her portfolio should consist of three risky assets classes and a risk – free asset class. The three risky asset classes are mid-cap stocks as represented by the S&P 400 Index; U.S. Bonds as represented by the Barclays Aggregate U.S. Bond Index; and Emerging Market equities as represented by the S&P/IFCI index. The risk free asset class is represented by the yield on 1 year Treasury Bills.
The table below shows asset class weights, expected returns and risks on five (5) different portfolios of risky assets.
Risky Asset Portfolios
Risky Portfolio Asset Class Expected
Number Weights Return Risk____ Sharpe Ratio
S&P 400 BBI IFCI E(Rp) p
1 50% 30% 20% 12.00% 20.00%
2 30% 30% 40% 12.60% 25.00%
3 80% 10% 10% 12.00% 7.20%
4 60% 35% 5% 9.80% 16.60%
5 100% 0% 0% 9.00% 30.00%
The Treasury bill Rate is 3.60%.
A. Complete the column for the Sharpe Ratios in the table above.
B. Which of the above 5 portfolios of risky assets does not lie on the efficient frontier? Briefly Explain.
C. Which portfolio is the optimal/best risky portfolio? Briefly Explain.
D. Suppose that Azarinka’s degree of risk aversion, her “ A” is 3. What is the optimal allocation for her between the best risky portfolio and Treasury Bills?
E. What will be the expected return and risk on her complete portfolio (risky and risk free assets)?
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