Category: investments

Capital allocation line
When a riskfree asset exists in an economy, investors can add that asset to their portfolios if they wish so. In the riskreturn space, the combination of the riskfree asset and any risky asset is a straight line. This line is called the capital allocation line as it shows how an investor’s capital is allocated…

Security market line
The security market line depicts the linear relationship between expected return and systematic risk, which is measured by beta, according to the capital asset pricing model (CAPM). Specifically, the equation of the security market line is nothing but the CAPM formula: where E[Ri] is the expected return on asset i, E[Rm] is the expected return…

Market portfolio
We have so far learned how to calculate the risk and return of portfolios and how to trace an efficient frontier through meanvariance optimization. It is now time to introduce a special portfolio that will play a significant role when we discuss the CAPM: The market portfolio. What is the market portfolio? The market portfolio is the…

CAPM calculator, equation, assumptions
The capital asset pricing model (or CAPM) is among the most widelyused asset pricing models by stock analysts and portfolio managers. Its popularity arises from its simplicity and elegance. Analysts can use it to forecast returns or to estimate the cost of equity. In this post, we offer a CAPM calculator and discuss the model…

Minimum variance portfolio
In a market with multiple risky assets, the minimum variance portfolio is a particular combination of those assets that yields the minimum volatility. To be more specific, consider the market depicted in Figure 1. Here, the blue curve represents the efficient frontier. That is, all portfolios that lie on it are efficient portfolios (e.g., D…

Treynor ratio formula, calculator
Treynor ratio is a popular riskadjusted performance measure. It was developed by the American economist Jack Treynor in the mid1960s (you can find the reference for his seminal paper at the bottom of this page). It is a measure of how much “excess return” (i.e., return above the riskfree rate) a security (stock, bond, mutual fund,…

Sharpe ratio calculator, formula
Sharpe ratio is among the most widely used performance evaluation metrics in the fund management industry. It is a rewardtorisk ratio, such that it captures the (excess) return an asset (e.g., stock) generates per unit of (total) risk, which is measured by return volatility. It was developed by Nobel laureate William F. Sharpe, who is…

Efficient frontier calculator
In modern portfolio theory, the efficient frontier represents the collection of all efficient portfolios within a market. Efficient portfolios offer the best riskreturn tradeoff and, as such, are superior to inefficient portfolios, which are suboptimal. In this lesson, we explain how investors can trace the efficient frontier using meanvariance optimization (the topic of the previous…

Meanvariance optimization
According to modern portfolio theory, investors are concerned about the “mean” and “variance” of asset returns, where the former captures the “centrality” and the latter the “spread” (or “riskiness”) of potential returns. As such, investors engage in meanvariance optimization. That is, they seek the portfolios that offer the best tradeoff between risk and return. In…

Idiosyncratic risk
What is idiosyncratic risk? It is the type of risk that affects either a single security such as a stock or a small group of securities. This is in contrast to systematic risk, which affects all risky securities in a particular market. The word “idiosyncratic” does not commonly feature in daily language. Many people may…