Lecture 06

Summary

This lesson explores portfolio management, focusing on expected returns and risk computation in portfolios with multiple securities. It discusses portfolio construction, risk diversification, and the benefits of investing in mutual funds and indexes for diversification. The script also explains how diversification reduces stock-specific risk and the concept of market risk.

Takeaways

• 📈 **Portfolio Management Basics**: The lesson introduces the concept of portfolio management, focusing on the computation of expected returns and risk for portfolios with multiple securities.
• 🔍 **Expected Returns Calculation**: Expected returns for a portfolio are calculated as the weighted average of the expected returns of individual securities, with weights representing the proportion of investment in each security.
• 💡 **Diversification Benefits**: Diversification in a portfolio reduces risk by spreading investments across multiple securities, which can help mitigate the impact of poor performance by any single security.
• 🔄 **Risk and Correlation**: The risk of a two-security portfolio is influenced by the correlation between the securities. A correlation of 1 indicates perfect movement in lockstep, reducing diversification benefits, while a correlation of -1 theoretically eliminates portfolio risk.
• 🌐 **Portfolio Risk Components**: Portfolio risk consists of idiosyncratic (stock-specific) risk and systematic (market) risk. Idiosyncratic risk can be diversified away by adding more securities, but systematic risk remains.
• 📊 **Variance and Covariance**: The risk of a portfolio is calculated using variance (σ²) and covariance terms. Variance terms represent the risk of individual securities, while covariance terms capture the risk associated with the correlation between securities.
• 🤔 **Investment in Mutual Funds**: Mutual funds and indexes provide diversification by pooling investments across many securities, reducing the impact of individual security performance on the overall portfolio.
• 🌟 **Risk Diversification**: As the number of securities in a portfolio increases, the specific risk (variance terms) tends to zero, and the portfolio risk converges towards the average covariance, highlighting the importance of diversification.
• 💼 **Practical Portfolio Construction**: The lesson discusses practical examples of portfolio construction, including how to compute expected returns and risk for portfolios with different securities and varying correlation coefficients.
• 🏦 **Market Risk Understanding**: Investors and fund managers are primarily rewarded for bearing market risk, which is non-diversifiable. This understanding is crucial for asset pricing models that only price market risk.

Q & A

What is the fundamental concept introduced in the lesson?

The lesson introduces the concept of portfolio management, including the computation of expected returns and risk of a portfolio, portfolio construction with two and multiple securities, and the concept of risk diversification.

What is the significance of expected returns in portfolio management?

Expected returns are crucial in portfolio management as they represent the anticipated earnings from the securities in the portfolio, which helps investors make informed decisions about where to allocate their funds.

How is the expected return of a two-security portfolio calculated?

The expected return of a two-security portfolio is calculated as the weighted average of the expected returns of the individual securities, using the formula \( ER_p = w_1 imes ER_1 + w_2 imes ER_2 \), where \( w_1 \) and \( w_2 \) are the proportionate weights of the securities and \( ER_1 \), \( ER_2 \) are their respective expected returns.

What is the role of diversification in portfolio management?

Diversification plays a key role in portfolio management by spreading risk across various securities, potentially reducing the overall risk of the portfolio without significantly affecting the expected return.

How does the correlation between securities impact the risk of a portfolio?

The correlation between securities affects the risk of a portfolio by influencing the covariance terms in the portfolio's variance calculation. A lower correlation between securities can lead to greater diversification and lower portfolio risk.

What is the difference between systematic and unsystematic risk in the context of a portfolio?

Systematic risk, also known as market risk, is the risk inherent to the entire market and cannot be diversified away. Unsystematic risk, on the other hand, is specific to individual securities and can be mitigated through diversification by including more securities in the portfolio.

How does the risk of a portfolio change as more securities are added?

As more securities are added to a portfolio, the idiosyncratic or stock-specific risk (unsystematic risk) tends to decrease due to diversification. However, the systematic risk, which is the market risk, remains constant and cannot be diversified away.

What is the formula for calculating the risk of a two-security portfolio?

The risk of a two-security portfolio is calculated using the formula \( \sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 \cdot w_1 \cdot w_2 \cdot \sigma_1 \cdot \sigma_2 \cdot \rho_{1,2} \), where \( \sigma_1 \) and \( \sigma_2 \) are the standard deviations of the individual securities, \( w_1 \) and \( w_2 \) are their weights, and \( \rho_{1,2} \) is the correlation coefficient between the securities.

Can the risk of a portfolio ever be completely eliminated through diversification?

No, the risk of a portfolio can never be completely eliminated through diversification. While diversification can reduce the unsystematic risk to near zero by adding a large number of securities, the systematic risk, which is related to market movements, remains.

Why do investors choose to invest in mutual funds and indexes?

Investors choose to invest in mutual funds and indexes as these investment vehicles provide instant diversification by spreading investments across a wide range of securities, reducing the risk associated with individual stock selection.

How does the risk and return profile of a portfolio compare to investing in a single stock?

A portfolio generally offers a more balanced risk and return profile compared to investing in a single stock. While a single stock investment may offer high returns but comes with higher risk, a portfolio diversifies this risk and can provide more stable returns.