The Capital Asset Pricing Model (CAPM) is one out of many models that describes the relationship between systematic risk and expected return for assets, particularly stocks and is often used as a method to calculate the expected rate of return of stocks (also called discount rate).

**The Formula and What It Means**

The formula for calculating the expected return of an asset given its risk is as follows:

*ER _{i }*=

*R*+

_{f }*β**(

*ER*−

_{m }*R*)

_{f}**where:**

*ER _{i} *= expected return of investment

*R _{f} *= risk-free rate

*β *= systematic risk (of the potential investment)

*ER _{m }*= expected return of the market

(*ER _{m }*−

*R*) = market risk premium

_{f}In the stock market, investors are compensated for the risk they take and the time value of money. In the CAPM formula, risk-free rate *R _{f}* accounts for the time value of money. In other words, it’s the rate of return one would earn on an investment that has 0 risk.

In practice, a representation of the risk-free rate is given by the yield on 10-year government bonds. They are considered risk-free because the probability that the Indian government defaults and is not able to pay the return is very small.

*R _{m}*

_{ }is the expected return of the stock market. It is what you can expect to earn on an average if you invest in a broad market index. The market risk premium is the difference between the expected return of the market and the risk-free rate. So, it’s like an expected reward for taking the extra risk. Using an estimate of the expected market return (

*R*) gives an estimate of the return of the stock (

_{m}*R*).

_{i}The *β *of a potential investment measures how much the stock moves when the market index moves up or down. The market, by definition, has a *β* of 1. A *β* of 1 means that the stock moves exactly like the market in both directions. A *β* greater than 1 means that the stock moves more aggressively with respect to the market so it gives you more upside potential when the markets are in bullish territory but it also carries a higher risk of money loss in a market downturn. Finally, a *β* smaller than 1 indicates that the stock is more defensive than the market, so there’s a lower risk but it also results in a lower return when things go well.

The market risk premium multiplied by the factor *β *[*β**(*ER _{m }*−

*R*)] is termed as ‘securities risk premium’.

_{f}So, for example, if the risk-free rate *R _{f}* is 5%, the expected return of the market

*ER*is 13% and the systematic risk

_{m}*β*of the security is 1.2. Then the expected return will be:

*ER _{i }*=

*R*+

_{f }*β**(

*ER*−

_{m }*R*) = 5% + 1.2*(13%−5%) = 14.6%

_{f}Now, what does this mean to a potential investor? If the expected return they are looking for is equal to or more than 14.6%, then this asset is a decent option to invest in.

**What the CAPM Implies**

The CAPM depicts that the expected rate of return of an investment is fully determined by two factors: the risk free rate *Rf* and the securities risk premium i.e. the market risk premium multiplied by the factor of *β *[ *β**(*ER _{m }*−

*R*) ].

_{f}**Greater Expected Returns require Greater Risk**

The graph shows how greater expected returns from an investment(y-axis) require a greater expected risk(x-axis). Starting with the risk-free rate, the expected return increases as the risk increases.

**Assumptions that don’t match reality**

The CAPM is based on several critical assumptions. Some assumptions which potentially have some issues include:

- Markets are efficient and all investors have equal access to information captured in the market. Now this generally won’t hold because institutional investors (a professional investor or organization that trades in large quantities) may have much better access to information, i.e., they have analysis, reports and other tools which make them more adept at evaluating securities than a retail investor (an individual or a non-professional investor). Also, different institutional investors are going to have different access to information.

- Moving on to investor behaviour, markets are assumed to be dominated by risk-averse and rational investors which doesn’t generally hold because all investors do not act rationally all the time. They might invest emotionally or they might invest in things that particularly interest them.

- Markets are frictionless i.e., there are no transaction costs, taxes or any kind of restraints in the market and one can buy and sell assets without incurring any kind of additional costs. Now, obviously this assumption doesn’t hold up in real life. While trading, there are a number of consequences that can’t be avoided. If you just think about when you trade shares, you incur a fee while buying or selling. You will also incur a bid-ask spread (the difference between the highest price that a buyer is willing to pay for an asset and the lowest price that a seller is willing to accept). Institutional investors, when they trade significant blocks of shares, also incur market impact costs i.e., the impact their trade has on share prices. Which means if they sell a lot of shares, they might depress the price. And, of course, taxes are a real concern. For example, Securities Transaction Tax (STT) is one such tax payable in India.

- Under CAPM, it is also assumed that all investors invest in the same time horizon. Investment horizon is the term used to describe the total length of time that an investor expects to hold a security before selling it off. This assumption also normally doesn’t hold in markets because all investors usually have different time horizons which varies according to their investment goals.

The CAPM is a very useful tool to calculate a discount rate or expected return rate but it’s not the only one. There are other modern approaches such as Arbitrage Pricing Theory and Merton’s Portfolio Problem. There are also a few Multi-Factor Models at work as well. But the CAPM still remains popular due to its simplicity and utility in numerous situations.

### References:

- Bleve, M. (2020).
*Capital Asset Pricing Model (CAPM) Explained*. The Finbox Blog. https://finbox.com/blog/capital-asset-pricing-model-capm-explained/ *Capital Asset Pricing Model.*University of South Wales. http://research.economics.unsw.edu.au/jmorley/econ487/CAPM_lecture.pdf- Kenton, W. (2021).
*Capital Asset Pricing Model (CAPM)*. Investopedia. https://www.investopedia.com/terms/c/capm.asp