Walker Is A Successful Businesswoman Who Has Achieved A S

Walker Is A Successful Businesswoman Who Has Accumulated A Subst

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 Return Correlations 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) ï³p 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)?

Paper For Above instruction

The assessment of PJ Walker’s investment strategy, especially concerning the restriction on the number of stocks held in her portfolio with Black Asset Management (BAM), requires a nuanced understanding of portfolio diversification and risk management principles. The core question is whether limiting BAM’s stock selection to 20 stocks will affect the risk profile of her portfolio. It is fundamental to recognize that diversification benefits stem from holding assets with low or negative correlations. As BAM has been successful due to its skillful stock picking, restricting its selection to 20 stocks could concentrate risk within the portfolio, potentially increasing its overall volatility. This narrowing of the stock universe may reduce the diversification benefits and increase systematic risk, especially if the selected stocks are highly correlated or if the stocks picked have similar risk factors.

Research indicates that concentration risk typically increases as the number of holdings decreases, especially when the selected stocks do not diversify across sectors or industries fully (Elton & Gruber, 1995). By limiting her portfolio to 20 stocks, PJ might inadvertently increase unsystematic risk if the stocks are not chosen with sufficient sector and industry diversification in mind. The size of individual positions, doubled from 3% to 6%, further exacerbates exposure to company-specific risk. Therefore, restricting BAM to 20 stocks likely increases the overall risk of the portfolio, particularly if the stocks are not carefully selected to maintain cross-sector diversification.

Assessing her friend’s suggestion to reduce the stock count further to 10 stocks presents additional risk considerations. A portfolio concentrated in only 10 stocks dramatically heightens the risk of poor performance due to company-specific events, amplifying unsystematic risk (Markowitz, 1952). While concentration can sometimes lead to higher returns if the stocks are exceptionally well chosen, it generally increases volatility and risk. Investor preferences for diversification and risk appetite usually favor broader, more diversified portfolios, which minimize the impact of poor-performing individual stocks.

Beyond individual stock selection, analyzing the impact on her total fund reveals critical insights. Adjustments to the stock holdings within BAM affect the overall risk-return profile of the $30 million fund. If BAM’s stock selection is skillful—capturing high returns with manageable risk—reducing the number of stocks may distort this balance, possibly diminishing the performance and increasing the volatility of the total fund. Modern portfolio theory underscores that diversification across uncorrelated or negatively correlated assets enhances risk-adjusted returns (Sharpe, 1966). Therefore, limiting stock selection must be aligned with the broader goal of optimizing portfolio efficiency.

In the context of asset class diversification, the data on small-cap stocks, corporate bonds, and international equities provide further insights into optimal portfolio construction. The Sharpe ratio, a measure of risk-adjusted return, favors asset classes like corporate bonds with a higher ratio of 0.70, indicating better reward per unit of risk. The correlations reveal that corporate bonds have a zero correlation with international equities, and a moderate -0.50 correlation with small caps, suggesting they can provide meaningful diversification benefits when combined with other assets.

When constructing a balanced portfolio, an investor might weigh these assets based on their risk profiles and expected returns to minimize risk while maximizing returns. For example, a portfolio combining 50% in bonds and 50% in small-cap stocks would have a composite expected return of approximately 8.5%, assuming linear combinations, with standard deviation dependent on the weights and correlations. Such a portfolio would benefit from diversification advantages from the low correlation coefficients, notably zero correlation between bonds and international stocks, enhancing overall risk-adjusted performance.

Investors rationally include small-cap and international stocks despite their higher risks because they offer higher expected returns, which can improve the efficiency of the portfolio when combined with assets like bonds. The Sharpe ratios further support this, as equities tend to offer higher returns relative to their risk (Mehra & Prescott, 1985). Consequently, diversification through combining multiple asset classes—especially those with low or zero correlation—serves to optimize risk-return trade-offs.

Turning to the portfolio construction for Azarinka Nadal, using the data on three risky assets and a risk-free rate, we analyze various portfolios to decide on the efficient frontier, optimal portfolio, and allocation strategies. The Sharpe ratio calculation involves subtracting the risk-free rate from the portfolio's expected return and dividing by its standard deviation. Completing these calculations reveals which portfolios maximize the Sharpe ratio, thus lying on the efficient frontier. Portfolio 2, with an expected return of 12.60%, risk of approximately 0.25, and a Sharpe ratio of 1.08, appears to be optimal, balancing return and risk efficiently.

The portfolio not on the efficient frontier is Portfolio 3, with a similar return but significantly lower Sharpe ratio, indicating less efficiency. The best risky portfolio is the one with a maximum Sharpe ratio, which in this case is portfolio 2. Applying her risk aversion parameter, Azarinka’s optimal allocation can be derived from the utility maximization framework, leading to an investment proportion in the risky portfolio and risk-free assets that aligns with her risk preferences (Luenberger, 1998). Her risk aversion coefficient of 3 suggests a conservative stance, favoring a significant allocation to the risk-free asset, which results in a diversified and balanced overall portfolio.

In conclusion, the analysis highlights that restricting stock holdings in mutual funds impacts diversification and risk, while asset class combinations can optimize portfolio efficiency. Proper allocation based on risk-return profiles, risk aversion, and market conditions is vital in constructing portfolios that align with investor objectives. These principles underpin sound investment management strategies that emphasize diversification, efficient frontier positioning, and aligning allocations with individual risk tolerance.

References

• Elton, E. J., & Gruber, M. J. (1995). Modern Portfolio Theory and Investment Analysis (5th ed.). Wiley.
• Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77-91.
• Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(1), 119-138.
• Mehra, R., & Prescott, E. C. (1985). The Equity Premium: A Puzzle. Journal of Monetary Economics, 15(2), 145-161.
• Luenberger, D. G. (1998). Investment Science. Oxford University Press.