Intro to Finance: Risk and Return - Diversification Benefits, Systematic vs. Unsystematic Risk

What This Is

Diversification is a risk management strategy that involves spreading investments across different asset classes, sectors, or geographic regions to reduce exposure to any one particular risk factor. By doing so, investors can potentially lower their overall portfolio risk and increase expected returns. For example, consider an investor who allocates 60% of their portfolio to Apple (AAPL) and 40% to Tesla (TSLA). If the tech sector experiences a downturn, the investor's exposure to this risk is reduced, as Tesla's performance is less correlated with Apple's.

Key Formulas & Symbols

• Beta (?): measures the systematic risk of an asset relative to the market.-= Cov(Ri, Rm) / ?i^2, where Ri = asset return, Rm = market return, and ?i = asset volatility.
• Systematic Risk (?m): the risk that affects the entire market. ?m = ?(?(Ri - Rm)^2 / (n - 1)), where Ri = asset return, Rm = market return, and n = number of observations.
• Unsystematic Risk (?i): the risk specific to an individual asset. ?i = ?(?(Ri - Rm)^2 / (n - 1)), where Ri = asset return, Rm = market return, and n = number of observations.
• Portfolio Beta (?p): the weighted average of individual asset betas. ?p = ?(wi * ?i), where wi = weight of asset i, and ?i = beta of asset i.
• Diversification Ratio (DR): measures the reduction in portfolio risk due to diversification. DR = (?p^2 - ?(wi^2 * ?i^2)) / ?p^2, where ?p = portfolio volatility, wi = weight of asset i, and ?i = volatility of asset i.
• Correlation Coefficient (?): measures the linear relationship between two assets.-= Cov(Ri, Rj) / (?i * ?j), where Ri = return of asset i, Rj = return of asset j, and ?i = volatility of asset i.
• Portfolio Standard Deviation (?p): the square root of the portfolio variance. ?p = ?(?(wi^2 * ?i^2) + ?(wi * wi' * ?i * ?j * ?)), where wi = weight of asset i, wi' = weight of asset j, ?i = volatility of asset i, ?j = volatility of asset j, and-= correlation coefficient between assets i and j.

Step-by-Step Calculation

1. Calculate the individual asset betas using historical return data.
2. Calculate the portfolio beta using the weighted average of individual asset betas.
3. Calculate the portfolio standard deviation using the portfolio variance formula.
4. Calculate the diversification ratio using the portfolio standard deviation and individual asset volatilities.
5. Interpret the results: a higher diversification ratio indicates a greater reduction in portfolio risk due to diversification.

Common Mistakes

• Mistake: Confusing systematic and unsystematic risk.
• Correction: Systematic risk affects the entire market, while unsystematic risk is specific to an individual asset. For example, a downturn in the tech sector affects both Apple and Tesla, but a fire at a Tesla factory only affects Tesla.
• Mistake: Failing to account for correlation between assets.
• Correction: Correlation affects the portfolio standard deviation, and ignoring it can lead to incorrect risk assessments. For example, if Apple and Tesla have a high correlation, diversifying between the two may not reduce portfolio risk as much as diversifying between Apple and a non-tech company.
• Mistake: Using beta as a measure of expected return.
• Correction: Beta measures systematic risk, not expected return. Expected return is influenced by other factors, such as dividend yield, growth rate, and risk-free rate.

Exam / CFA Tips

• Tip: Be prepared to calculate portfolio beta and standard deviation using historical return data.
• Tip: Understand the difference between systematic and unsystematic risk, and how they affect portfolio risk.
• Tip: Be aware of correlation between assets and its impact on portfolio risk.

Quick Practice Problem

Scenario: An investor allocates 60% of their portfolio to Apple (AAPL) and 40% to Tesla (TSLA). If the tech sector experiences a downturn, and Apple's return is -10%, while Tesla's return is -5%, what is the portfolio return?

Answer: Portfolio return = 0.6 * (-10%) + 0.4 * (-5%) = -7%

Explanation: The investor's exposure to the tech sector downturn is reduced due to diversification between Apple and Tesla.

Last-Minute Cram Sheet

• Beta (?): measures systematic risk, not expected return.
• Systematic Risk (?m): affects the entire market.
• Unsystematic Risk (?i): specific to an individual asset.
• Portfolio Beta (?p): weighted average of individual asset betas.
• Diversification Ratio (DR): measures reduction in portfolio risk due to diversification.
• Correlation Coefficient (?): measures linear relationship between two assets.
• Portfolio Standard Deviation (?p): square root of portfolio variance.
• The diversification ratio is not a measure of expected return.
• Correlation affects portfolio risk, but not expected return.
• Beta is not a measure of risk-free rate.