# Category: investments

• ## Capital asset pricing model (CAPM)

The capital asset pricing model (or CAPM) is among the most widely-used asset pricing models by stock analysts and portfolio managers. Its popularity arises from its simplicity and elegance. Analysts and investors can use it to forecast returns or to estimate the cost of equity. In this lesson, we explain this model and its assumptions.…

• ## Minimum variance portfolio

In this lesson, we explain what is meant by the minimum variance portfolio (MVP), derive its formula for the two-asset case, and provide an online calculator as well. You can also check out our video tutorial to learn how to find the position of the MVP on the efficient frontier using Excel’s solver tool. And,…

• ## Treynor ratio formula, calculator

Treynor ratio is a popular risk-adjusted performance measure. It gets its name from the American economist Jack Treynor who came up with this measure in the mid-1960s (see the full reference at the end). It is a measure of how much “excess return” (i.e., return above the risk-free rate) a security (stock, bond, mutual fund, etc.)…

• ## Sharpe ratio calculator, formula

Sharpe ratio is among the most widely used performance evaluation metrics in the fund management industry. It is a reward-to-risk 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 risk-return 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 mean-variance optimization (the topic of the previous…

• ## Mean-variance 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 mean-variance optimization. That is, they seek the portfolios that offer the best tradeoff between risk and return. In…

• ## Idiosyncratic risk

Idiosyncratic risk 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” is not commonly used in daily language. ln fact, idiosyncratic risk is often…

• ## What is risk premium?

Risk premium definition The risk premium for a security (e.g., stock, bond, etc.) can be defined as the return the security generates over the risk-free rate of return. For example, if the yields on government bonds are 3%, and a stock is expected to return 8%, then this stock’s risk premium is 8% − 3% =…

• ## Risk preferences: What’s the opposite of risk averse?

As humans, we have a natural tendency to avoid taking risks when we can, a notion that we refer to as risk aversion. Specifically, when faced with a choice between a safe payoff and a risky one, we’d opt for the latter only if it entails a sufficient risk premium, which is our reward for…

• ## Fair game meaning

In daily language, “fair game” can be used to suggest that something or someone can be an object of criticism (perhaps because of their behavior or nature). But, what about the meaning of fair game in an economic or financial context? In such a context, a fair game can be defined as a game in…