Portfolio Optimization Essay

424 WordsApr 1, 20092 Pages
Summarize result: Given a risk free rate, a market risk premium, and a portfolio of 30 DOW stocks, we found efficient frontiers and capital allocation lines for portfolios both with and without short-sale restrictions. Where short sales were allowed, the client’s utility function was maximized with a portfolio whose assets were weighted 18.8% in risk-free assets and 82.2% in a portfolio where the Sharpe Ratio was maximized. This allocation of assets will yield 2% monthly with 6.5% standard deviation. In the case where short sales are prohibited, utility was maximized with a portfolio whose assets are weighted -25% in risk-free assets and 125% in a portfolio whose Sharpe Ratio was maximized. This allocation of assets will yield 1.1% monthly with 4.7% standard deviation In order to achieve these weights, the client needs to borrow 20% of his total portfolio value. Differences between portfolios with and without short sale restrictions: Short sales are intrinsically more risky than holding a long position in an asset because they contradict historic market trends. Because they are more risky, they are often banned from use in portfolios, as was the case here. The optimized portfolios we found display the riskier nature of portfolios with short sales. The return in the portfolio without short sale restrictions was higher than the portfolio with short restrictions, while the standard deviation of the portfolio with short sales was greater than the short free portfolio. The optimal portfolio with short sales yields 1.57% more on a monthly basis than the portfolio without short sales, to compensate the investor for assuming 4.3% more risk on a monthly basis. Therefore, these optimal portfolios adhere to the basic principle that by assuming more risk you increase your returns. Insights and Weaknesses of the approach of the manager: The use of CAPM instead

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