# Capital Asset Pricing Model (CAPM) – definition, explanation, calculation

Return and risk are important parameters when assessing a security on the capital market. The “Capital Asset Pricing Model” (CAPM) or “Price Model for Capital Goods” provides a first indication of what risk / return ratio an investor can expect from a stock compared to the market as a whole.

## What is the Capital Asset Pricing Model (CAPM)?

CAPM was developed in the 1960s by Nobel Prize-winning economist William F. Sharpe, former Harvard professor of business administration John Lintner and Norwegian economist Jan Mossin.

The basis for CAPM is the portfolio theory developed by the American economist Harry Markowitz in 1952. CAPM assumes that return and risk are in balance in the capital market, ie. a higher return can only be achieved if more risk is accepted at the same time.

## How does CAPM work?

CAPM explains the relationship between return and risk in the capital market equilibrium using a securities index.

The expected return on a stock (µ, y-axis) is compared with the risk beta (ß, x-axis). Beta is the level of volatility relative to the overall market. The comparative value of the market as a whole is always 1. If the beta value of the stock in question is greater than 1, the return on the security fluctuates more than the market as a whole. If the value is less than 1, the return fluctuates less than the total market.

It is important that the beta value only describes the systematic risk that affects the stock – such as a war or a crisis like COVID-19, which affects all or at least a large group of securities. In contrast, unsystematic risk is only related to the issuer of the stock itself, such as a scandal in the company. The portfolio theory assumes that an investor can almost completely rule out the unsystematic risk by spreading (diversifying) his portfolio. Therefore, the unsystematic risk in CAPM is neglected.

The above-mentioned securities characteristic line, which follows from the securities’ expected return and risk in the overall market, starts on the y-axis at the level of the risk-free interest rate (rf), which is determined using government bonds with a good credit rating e.g. The risk-free interest rate can also be in the negative range, as is the case for a federal bond, for example.

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## Formula for calculating CAPM

In order to be able to calculate a securities’ expected return (µ) according to CAPM, the following key figures must be known: the risk-free interest rate (rf), the systematic risk beta (ß) and the expected return on the overall market. If µ is fixed, the value can be compared with the total market in the second step.

The CAPM uses the following formula to determine the expected return (µ) of a security:

r + ß * (µ – r) = µ

## CAPM calculation example: inventory of US sports equipment manufacturers

In this case, r is the yield on a ten-year US government bond (0.72%). The beta is displayed individually for each stock and can be viewed by investors at most online brokers. For example, the beta factor for our US sports equipment manufacturer is 1.1 over the last 12 months. The expected return for the S & P500 is 11.86% (subsequent 12-month return).

This results in:

0.72 + 1.1 * (11.86 – 0.72) = 12.97%

The expected return of 12.97% is above the return on the comparable market (11.86%) with the same risk. In relation to risk-return ratios, the share is above the securities index and therefore has higher potential returns than the comparable market. Security tends to be underestimated by investors, representing a possible buy signal.

## Conclusion: CAPM is not “laying Wollmichsau” – but still usable

CAPM allows investors to compare the expected return on a security with the development of the overall market using a simple calculation. Nevertheless, investors should be aware that such a model can only provide an indication of how a stock may develop. One criticism of CAPM is that the model is primarily based on historical values. Reliable conclusions about the future cannot always be drawn from the past in the capital market. The so-called market portfolio does not exist in reality either. The frequently used benchmarks, such as stock indices such as the DAX or S&P 500, do not meet the requirements set by the authors for a market portfolio. Empirical studies repeatedly show “anomalies” that cannot be explained by CAPM, such as the momentum effect and the value effect. CAPM is not a “jack of all trades”. However, CAPM can be useful for an initial indication of a stock’s performance.

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