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Optimizing Risk-Return: Portfolio Diversification Strategies

Understand the key concepts in investing, such as risk management through standard deviation, diversification for risk control, the Capital Allocation Line, the Sharpe Ratio, and optimal portfolio construction. Learn about the mean-variance criterion, the optimal risky portfolio, and the minimum variance portfolio. Explore the benefits of diversification in reducing standard deviation and optimizing returns in portfolio construction.

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Optimizing Risk-Return: Portfolio Diversification Strategies

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  1. Summary to Date • Investing is about measuring and understanding the risk/return relationship • Risk • Measured through the use of standard deviation • Controlled through diversification • The Capital Allocation Line • The Sharpe Ratio (reward to volatility) • The mean-variance criterion • The optimal risky portfolio • The minimum variance portfolio Intermediate Investments F303

  2. Summary to Date • While the return of a portfolio made up of two assets is simply the weighted average, the standard deviation is only a weighted average if the assets are perfectly correlated • Otherwise, the standard deviation is something less than the weighted average, showing the benefits of diversification! Intermediate Investments F303

  3. The Optimal Risky Portfolio • Optimal Risky Portfolio (p. 200 has an error) WA = (RPA) * (VARZ) – (RPZ)(SDA)(SDB)(RhoAZ) --------------------------------------------------------------------------- (RPA)*(VARZ) + (RPZ)*(VARA) -(RPA+RPZ)(SDA)(SDZ)(RhoAZ) Intermediate Investments F303

  4. The Minimum Variance Portfolio • Minimum Variance Portfolio (p. 197) WA = (VARZ) – (SDA)(SDZ)(RhoAZ) ------------------------------------------------------ (VARZ) + (VARA) – 2(SDA)(SDZ)(RhoAZ) Intermediate Investments F303

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