
Treynor ratio formula and calculator
As part of our free investments course, we have already covered two important investment performance measures: Jensen’s alpha and Sharpe ratio. In this post, we focus on the Treynor ratio, which is another popular riskadjusted performance measure. In particular, we explain the Treynor ratio formula and offer an easytouse Treynor ratio calculator as well. Jump […]

Risk aversion coefficient – meaning and formula
When we discussed investors’ risk preferences, we distinguished between riskaverse, riskneutral, and riskseeking behavior. We also explained that riskaverse investors expect compensation for bearing risk, which is called a risk premium. But, how do measure risk aversion? The answer is the risk aversion coefficient. It quantifies the degree to which an individual dislikes risk. In […]

Jensen’s alpha formula and calculator
When evaluating the performance of mutual funds, ETFs, or your own portfolio, it is vital to do that on a riskadjusted basis. That is, it would be misleading to compare investment opportunities on the basis of returns only as higher returns normally require bearing more risk. In this post, we discuss one of the most […]

Sharpe ratio calculator, formula, examples
The Sharpe ratio is a popular tool used in performance evaluation. In this post, we offer a Sharpe ratio calculator as well as explain the formula with examples. Jump to The Sharpe ratio formula Using the Sharpe ratio to evaluate performance – an example Exante vs expost Sharpe ratio The Sharpe ratio vs the Treynor […]

Investments quiz – Test your knowledge!
This investments quiz aims to test your knowledge of the material covered in our free investments course. The quiz is a multiplechoice test. It consists of three sections: Section A: Return calculations. Section B: Portfolio theory. Section C: CAPM and APT. The answers and solutions are provided at the bottom of this page. Section A: […]

Arbitrage pricing theory (APT)
In the previous lesson, we learned about the capital asset pricing model (CAPM). According to the CAPM, any risky asset’s expected return depends on its exposure to the market risk. So, CAPM is based on the idea that market risk is the sole systematic risk factor. Because systematic risk can’t be eliminated via diversification, riskaverse […]

Capital asset pricing model (CAPM)
The capital asset pricing model (or the CAPM) is probably one of the most commonly taught topics in finance. This is not because it is a perfect model. In fact, it is far from it. However, the CAPM is built upon some of the most fundamental concepts in finance. Furthermore, CAPM is widely used in […]

Systematic risk and unsystematic risk
When we talk about the risk of investing in stocks, corporate bonds, etc., we can distinguish between two main sources of risk: Systematic risk and unsystematic risk. The former relates to sources of risk that affect the entire market whereas the latter is risk specific to individual securities. Learning objectives Understand the distinction between systematic […]

What is the market portfolio?
The market portfolio is the market valueweighted portfolio of all risky assets in an economy. In this post, we show how the market portfolio is equivalent to the optimal risky portfolio when all investors behave according to the modern portfolio theory. Learning objectives Understand the link between the optimal risky portfolio and the market portfolio. […]

What is the optimal risky portfolio?
In the previous post, we explained that when there is no riskfree asset in an economy, investors should invest in one of the efficient portfolios that lie on the efficient frontier based on their risk tolerance. We added that, if a riskfree asset exists, then there is a unique efficient portfolio that all investors should […]