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 risk-adjusted 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 Ex-ante vs ex-post 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 multiple-choice 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, risk-averse […]

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 value-weighted 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 risk-free 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 risk-free asset exists, then there is a unique efficient portfolio that all investors should […]

Efficient frontier – What is it?

The efficient frontier is the collection of all efficient portfolios in a market. But, what does that actually mean? How can investors distinguish between efficient portfolios and inefficient ones? Learning objectives Understand the concept of an efficient portfolio. Identify the main features of the efficient frontier. The mean-variance framework Not all portfolios of assets are […]