Category: investments
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Security market line
The security market line (SML) 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…
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Market portfolio
We have so far learned how to calculate the risk and return of portfolios and how to trace an efficient frontier through mean-variance 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…
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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,…
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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.)…
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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…
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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…
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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…
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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…
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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% =…
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Risk preferences: What’s the opposite of risk averse?
in investmentsAs 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…
