Diversification and Risky Asset Allocation

Learning Objectives

• Understand how to calculate expected returns and variances for a security and a portfolio.

• Grasp the significance of portfolio diversification and its impact on risk.

• Explore the concept of the efficient frontier and the importance of proper asset allocation.

Diversification

• Holding multiple investments can mitigate risk as not all investments will rise or fall in value simultaneously.

• Diversification can greatly enhance portfolio return while minimizing risk.

• Key questions: How does diversification work, and what are its effects on returns and risks?

Role of Diversification and Asset Allocation

• First explored by Professor Harry Markowitz in the 1950s.

• An efficiently diversified portfolio maximizes expected return for a given level of risk.

• Important to understand how diversification relates to expected returns.

Expected Returns

• The expected return is the weighted average of potential returns from the investment over time.

• To calculate:

  1. Define possible economic scenarios.

  2. Estimate performance of securities in each scenario.

  3. Assign probabilities to scenarios.

  

Factors Influencing Stock Choices

• Example:

  • Starcents had an expected return of 25%.

  • Jpod had an expected return of 20%.

• Investors may choose Jpod for lower risk despite a lower expected return.

Expected Risk Premium

• Calculated as:
  Expected Risk Premium=Expected Return -Riskfree Rate

  

• For example, if the risk-free rate is 8%:

  • Jpod has a premium of 12% (20% - 8%).

  • Starcents has a premium of 17% (25% - 8%).

Calculating Variance of Expected Returns

• Variance measures the dispersion of returns around the expected return.

• Formula:

  

• Standard deviation is the square root of variance.

Portfolio Composition

• Portfolios consist of multiple assets, and their respective weights indicate the proportion of investment in each.

• Expected return of a portfolio is calculated as a weighted average of individual asset expected returns:

  

Portfolio Variance Calculations

• Variance of a portfolio is not a straightforward weighted average of individual variances.

• The formula considers the covariance between asset returns as well.

Diversification and Risk Reduction

• Adding more assets reduces diversifiable risk; the portfolio standard deviation decreases with the number of stocks.

• Correlation is crucial: less than perfect correlation among assets helps lower overall risk.

The Fallacy of Time Diversification

• Misconception that long-term holding of stocks cancels volatility effects.

• Historical data shows that volatility of wealth increases over longer periods, contrary to the common belief.

Why Diversification Works

• Key factors include the correlation of asset returns; imperfect correlation helps reduce risk.

• Correlation coefficients range from -1 (perfect negative) to +1 (perfect positive).

Markowitz Efficient Frontier

• Represents the set of portfolios that offer the highest expected return for a given level of risk.

• Portfolios below this frontier are considered inefficient as they provide lower returns for the same risk or higher risk for the same return.

Importance of Asset Allocation

• Strategic asset allocation involves diversifying investments across different asset classes to optimize returns while managing risk.

• Understanding the risk-return profiles of assets is key to constructing an efficient portfolio.