What is The Capital Asset Pricing Model: CAPM Formula, Assumptions & Application

The Capital Asset Pricing Model (CAPM) helps investors estimate the return they should expect for the risk taken. They can compare investments in terms of fairness and structure.

For example, Arjun has ₹2,00,000 and wants to invest. He compared a few of the options in the table given below.
 

Here, company shares give ₹16,000 more than the government bonds. However, considering their risk factors, no one can say for sure is this is a good decision or not.

To solve this issue, Capital Asset Pricing Model (CAPM) is used. It will help in evaluating whether the risk is worth taking or not. So, let’s see how this model works, and more in this blog. 

How is The Capital Asset Pricing Model Calculated?

I am not a finance-geek, but you should know that approximately 73.5% of chief financial officers (CFOs) use CAPM. They estimate the cost of equity for capital budgeting purposes using the Capital Asset Pricing Model. 

Cost of equity is the profit investors expect when they buy a company’s shares. Around 75% of finance experts recommend CAPM to calculate it.

So, let’s see how the Capital Asset Pricing Model (CAPM) is calculated. 

Formula for CAPM,

E(Ri​)=Rf​+βi​×(E(Rm​)−Rf​)

Where:
 

• E(R₁): Expected return on the asset.
   
• Rf: Risk-free rate (e.g., government bond yield).
   
• βᵢ: Beta of the asset. It is a measure of how risky the asset is compared to the market
   
• E(Rₘ): Expected return of the overall market.

This formula shows that expected return includes both the ‘returns on paper’ and the ‘risks mentioned nowhere’.

For example, in Arjun’s case, CAPM will be calculated as follows:

Step 1: Collect the Data
 

• Risk-free rate (Rf): Government Bonds = 5%
   
• Expected market return (E(Rₘ)): Stock Market Average = 12%
   
• Beta (β): Let’s assume the company shares are riskier than the market. So, β = 1.2, which is a moderately high risk.

Step 2: Apply the CAPM Formula

E(Ri​)=Rf​+βi​×(E(Rm​)−Rf​)

E(Ri​)=5%+1.2 × (12%−5%)

E(Ri​)=5%+1.2 × 7%=5%+8.4%

E(Ri)=13.4%

Here, the expected returns for the company shares are 13.4%. It is 0.4% less than the actual return (13%). This means that the risk Arun is taking is bigger than the return he is getting. 

‘Matlab’, he is getting ₹26,000 on paper, but compared to the risks associated with this option, he should get ₹26,800

What is Market Risk Premium?

While surfing the net, you might have encountered the term market risk premium. Basically, it represents the extra return investors expect for bearing market risk. It is calculated as:

Market Risk Premium = E(Rm​)−Rf​

Where, 

• Rf: Risk-free rate (e.g., government bond yield).
• E(Rₘ): Expected return of the overall market.

It’s the extra return you get from the market compared to a completely safe investment. So, in Arun’s case, the market risk premium will be 7% (12% - 5%).

What are the Assumptions of CAPM?

Do you remember what Ohm’s Law stated? It gave us the formula for calculating resistance, ASSUMING the temperature and all other physical conditions are normal. That is a simple and strict assumption. In the same way, the Capital Asset Pricing Model works by certain assumptions that create the “ideal world” in which the formula works. 

1. Investors are Rational and Risk-Averse

The model assumes investors think logically and avoid unnecessary risks. They only take risks when they expect higher rewards. For example, if we talk about the direct plans in India, then around 5% of SIP accounts have been active for over 5 years. This shows long-term investment habits and diversification in today’s investors.

2. Borrow and Lend at the Risk-Free Rate

It assumes everyone can borrow or lend money freely at the same safe rate. This way, no one has an unfair advantage. In reality, banks charge more. For instance, Axis Bank’s personal loan rates range from 9.99% to 21.55%, while the risk-free rate (like a 10-year government bond) is much lower. That means borrowing is significantly more expensive than CAPM assumes.

3. Perfect and Smooth Markets

The model believes markets have no taxes, transaction costs, or delays in information. Everyone can trade easily without extra costs. However, transaction charges on NSE equity trades are about 0.00325%, with BSE even charging 0.00375%. 

4. Single-Period Investment Horizon

CAPM assumes investors plan for one fixed period at a time. They think about today’s choice and its return in that period. But many Indian investors invest long-term. About 5% of SIP accounts have been active for more than 5 years. 

The table given below summarises the assumptions discussed above.
 

CAPM is a simple and easy-to-use to use and understand model. But real markets are messy. They have fees, access to information varies, borrowing isn’t free, and people don’t always act rationally. 

Applications of CAPM

Despite some assumptions that make the Capital Asset Pricing Model (CAPM) an Ideal case, it is used every day. From investing, corporate finance, to portfolio decisions, you name it, and you will see CAPM being used there. Let’s see some of the areas where CAPM is used.

With the formulas mentioned for each of the applications, you can make great use of CAPM. With this, both individuals and companies can make investment and valuation decisions far better than just any assumption.

Conclusion 

The Capital Asset Pricing Model shows how much returns you can expect by considering profits and well as risks associated. This makes investing look easier and doable for beginners. With the right data, you can navigate between different investments without assuming anything wild. It works wonders for investors, fund managers, and even companies. 

Frequently Asked Questions

What is the Security Market Line (SML)?
The SML is a graph that plots expected return against beta, helping investors identify whether a stock is undervalued or overvalued.
 

How does CAPM differ from the Arbitrage Pricing Theory (APT)?
CAPM uses a single factor, that is market risk, to estimate return, while APT uses multiple macroeconomic factors like inflation, GDP growth, or interest rates.
 

What is the difference between historical and implied market risk premium
Historical premium uses past data Implied premium backs out expected returns from current market prices Each approach has different estimates and pros and cons
 

Why use multi factor models instead of CAPM
Multi factor models like size value and momentum capture additional sources of return and often fit historical data better than single factor CAPM
 

How do corporate finance teams adjust CAPM for practical use
Teams often smooth beta use industry betas or blend historical and fundamental betas They may also use an adjusted Blume beta for stability
 

What are behavioral critiques of CAPM
Behavioral finance highlights investor biases and limits to arbitrage questioning CAPM rational agent foundation and suggesting some anomalies may persist
 

How does inflation affect CAPM results?
Inflation influences both the risk-free rate and market returns. If not adjusted for inflation, CAPM may give misleading expected return estimates.
 

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