Mean-variance analysis is the art of balancing risk, represented as variance, against the anticipated return. Investors leverage this analysis to make informed investment choices, determining the level of risk they are willing to accept for varying levels of reward. This analytical approach helps investors ascertain the highest reward possible for a specific risk level or the minimal risk for a given return threshold.
Key Takeaways:
- Investment Tool: Mean-variance analysis assists in making investment decisions.
- Risk-Return Balance: Facilitates determination of the highest reward at a particular risk level or the least risk at a certain return level.
- Variance Insight: Reveals the spread of returns over periods (daily, weekly, etc.).
- Expected Return Understanding: Estimates the probable returns of an investment.
- Preference in Investments: Among securities with identical expected returns, the one with lower variance is preferred. Conversely, with similar variance, the higher return option is more favorable.
Unlocking the Basics of Mean-Variance Analysis
Mean-variance analysis is integral to modern portfolio theory, which posits that investors make rational investment decisions when provided with comprehensive information. This theory assumes a preference for low-risk, high-reward investments. The core components of this analysis are variance and expected return.
Variance measures the dispersion of returns in a particular set, such as the daily or weekly returns of a security. Expected return, on the other hand, is a probabilistic estimation of the returns one anticipates from an investment.
When comparing two securities with the same expected return, the one with the lower variance is the better choice. Similarly, with equal variances, the security offering higher returns is preferable.
In modern portfolio theory, an investor diversifies by selecting various securities with differing variances and expected returns, aiming to mitigate catastrophic losses amidst volatile market conditions.
Practical Example of Mean-Variance Analysis
Consider an investor holding the following assets:
- Investment A: Amount = $100,000, expected return = 5%
- Investment B: Amount = $300,000, expected return = 10%
With a total portfolio worth $400,000, the asset weights are:
- Investment A weight: $100,000 / $400,000 = 25%
- Investment B weight: $300,000 / $400,000 = 75%
Subsequently, the portfolio’s expected return is calculated as:
Portfolio expected return = (25% * 5%) + (75% * 10%) = 8.75%
Calculating portfolio variance is complex and not simply the weighted average of individual investment variances. Consider the correlation between two investments as 0.65, with standard deviations of 7% for Investment A and 14% for Investment B.
In this scenario, the portfolio variance is computed as:
Portfolio variance = (25%^2 * 7%^2) + (75%^2 * 14%^2) + (2 * 25% * 75% * 7% * 14% * 0.65) = 0.0137
Taking the square root of this variance gives the portfolio’s standard deviation:
Portfolio standard deviation = sqrt(0.0137) = 11.71%
Thus, mean-variance analysis equips investors to make strategic decisions with a nuanced understanding of risk and reward, aligning their investments in a way that harmonizes these critical factors.
Related Terms: Portfolio Optimization, Modern Portfolio Theory, Expected Return, Variance, Investment Risk.
