What Is Mean-Variance Analysis?
I'm going to explain mean-variance analysis directly to you as an investor looking to evaluate your options. This method lets you measure both the risk and reward of different investments by focusing on the expected return, which is the mean, and the risk, represented by variance. You can use it to find the highest reward for a specific level of risk or the lowest risk for a desired return. It's a fundamental part of Modern Portfolio Theory, or MPT, where the strategy is to maximize your expected return based on how much risk you're willing to take. This tool aligns perfectly with your personal risk tolerance, making it essential for sound decision-making.
Key Takeaways
- Mean-variance analysis is a tool you use to weigh your investment decisions.
- The analysis helps you determine the biggest reward at a given level of risk or the least risk at a given level of return.
- It is part of Modern Portfolio Theory and is considered an important decision-making tool.
Understanding Mean-Variance Analysis
Let me break this down for you. Mean-variance analysis fits into modern portfolio theory, which operates on the idea that you'll make rational investment choices when you have all the facts. A key assumption here is that you, as an investor, want low risk paired with high rewards. The two core elements are variance and expected return. Variance is simply a figure showing how spread out or varied the numbers in a dataset are.
For instance, it can show you how much the returns on a particular security fluctuate daily or weekly. Expected return, on the other hand, is a probability-based estimate of what you might gain from investing in that security. If you're comparing two securities with the same expected return but different variances, pick the one with lower variance—it's the smarter choice. Likewise, if variances are similar, go for the one with the higher return.
In modern portfolio theory, you'd select a mix of securities with varying levels of variance and expected returns. The point is to diversify your holdings, which cuts down the risk of major losses when market conditions shift suddenly.
Example of Mean-Variance Analysis
You can calculate which investments offer the best variance and expected return—let me walk you through a straightforward example. Suppose your portfolio includes these investments: Investment A with $100,000 and an expected return of 5%, and Investment B with $300,000 and an expected return of 10%.
With a total portfolio value of $400,000, the weights are: Investment A at $100,000 / $400,000 = 25%, and Investment B at $300,000 / $400,000 = 75%. The total expected return for the portfolio is then (25% x 5%) + (75% x 10%) = 8.75%.
Portfolio variance isn't just a weighted average—it's more involved. Assume a correlation of 0.65 between the investments, with standard deviations of 7% for A and 14% for B. The variance calculates as (25%^2 x 7%^2) + (75%^2 x 14%^2) + (2 x 25% x 75% x 7% x 14% x 0.65) = 0.0137. The portfolio standard deviation is the square root of that: 11.71%.
Other articles for you
An open market is an economic system with minimal barriers allowing free-market activity driven by supply and demand.
Counterparty risk is the chance that one party in a financial transaction defaults on its obligations, affecting credit, investments, and trades.
Bilateral trade is the exchange of goods and services between two countries, facilitated by agreements that reduce trade barriers to promote economic growth.
Gold options are derivative contracts allowing the right, but not obligation, to buy or sell gold at a preset price using physical gold or futures as the underlying asset.
This text explains the role of dealers in securities trading, distinguishing them from brokers and highlighting their importance in market making and regulation.
UST refers to the United States Treasury, which manages federal finances and issues low-risk debt securities used as benchmarks in finance.
A common size income statement expresses each line item as a percentage of revenue to enable better analysis and comparisons of financial performance.
MCF is an abbreviation for thousand cubic feet, used to measure natural gas in the United States.
The Nordic model is a socio-economic system in Scandinavian countries that blends capitalism with extensive social welfare funded by high taxes.
An instrument refers to tools for transferring value in finance, controllable variables in economics, or legal documents like contracts.