Category: calculators

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…

Risk premium definition, calculator
Different stocks offer different levels of expected return. What causes stock A’s expected return to be higher than stock B’s expected return? How does the expected return on a risky asset relate to the riskfree rate of return? In this post, we answer both questions by introducing the concept of risk premium. Jump to: Risk…

Return volatility formula and calculator
We start this lesson by discussing what is meant by (stock) return volatility. Then, we explain the return volatility formula. Finally, a simple return volatility calculator is provided for your convenience. What is (stock) return volatility? Imagine an investor who bought shares of a stock three years ago. According to the investor’s calculations, her annual…

Arithmetic average return calculator and formula
In this lesson, we introduce a simple yet really useful measure of investment performance. In particular, we discuss the arithmetic average return formula and provide a practical arithmetic average return calculator. It is really important for investors to be able to accurately assess the performance of their investments. In that sense, arithmetic average (or mean)…

Geometric average return calculator and formula
In this post, we explain the geometric average return formula using numerical examples and discuss how it differs from the arithmetic average return. We provide a practical geometric average return calculator as well. Geometric average return formula The geometric average return formula (or the geometric mean return formula) can be written as follows: While the…

Jensen’s alpha formula and calculator
Jensen’s alpha is a popular performance evaluation metric, which was developed by the American financial economist Michael Jensen in the late 60s. It is a riskadjusted performance measure (other examples include the Sharpe ratio and Treynor ratio) and is theoretically linked to the capital asset pricing model (or the CAPM). Jensen’s alpha formula We can…

The risk of a portfolio – Calculator and formula
We often say that risk and return are two sides of the same coin. You can’t discuss one without the other. In the previous post, we showed you how to calculate the return on a portfolio of assets. In this post, we explain the formula for portfolio risk. We also offer an easytouse portfolio risk…