# Capital Asset Pricing Model (CAPM) to determine stock value

Harry Markowitz’s Modern Portfolio Theory (MPT) is one of the most renowned theories on how risk-averse investors can construct an optimal portfolio for maximizing the financial returns on their investments with minimal risk. The theory received widespread acclaim and the Nobel Prize. However, over the years the theory has received criticism as it fails to take into consideration the asset or stock prices (Liu, 2017), instead only accounting for risk and return. Stock prices are important while calculating risk in stock and optimizing the portfolio value of an investor. The **Capital Asset Pricing Model (CAPM)** has emerged as a practical approach to calculating stock value (Fama & French, 2003).

## Understanding the concept of the Capital Asset Pricing Model

The capital Asset Pricing Model studies the relationship between the systematic risk of investing and the expected return. This model determines the expected return on investment by considering the risk attached to those assets and the cost of capital (CFI, 2020).

The above figure shows that as the risk associated with an investment increases, the return earned on it rises above the risk-free return. The risk premium amount of the asset is the proportion of the market risk borne by the investor. Thus, the expected return earned from an investment in a risky asset is a sum of the risk-free return and the proportion of the market risk premium.

Based on the above figure, the formula for the **CAPM** is

Wherein,

R_{i}: Expected return on the investment

R_{f}: Risk-free rate of return

R_{m}: Expected Market return on the security

(R_{m} – R_{f}): Market risk premium

β: Beta of the investment

## Pre-conditions or assumptions for the applicability of the Capital Asset Pricing Model

The usage of the CAPM is based on the existence of certain assumptions (Diksha, 2020; Rai, 2011). They are

- An investor does not aim at maximizing return or wealth but instead focuses on maximizing the utility derived from the wealth. This is because each investor has different preferences i.e. some prefer more risk while others value less risk. Thus, an investor aims at maximizing benefits, considering his preference for risk and return.
- Investors make their investment decisions based on the complete assessment of risk and return. By diversifying the risk, investors under the
**CAPM**consider the expected returns and variance (systematic risk measured by beta) before making any decision about an efficient portfolio. - There is the existence of perfect competition in the market i.e. free access to all information is available to all the investors wherein no extra cost or time is involved. Thus, the price of the stock is not influenced by any single investor’s decision.
- There is no limit on the borrowing or lending of assets by an investor. Thus, in order to reduce risk, an investor could either borrow at a risk-free rate or add risk-free assets to the portfolio.
- The investor has similar expectations for return as well as risk. This would lead to depicting a single efficient frontier or having homogeneity in the conception.
- There is an identical time horizon for all investors thus depicting that time has no relevance in influencing the rate of expected return.
- The total assets remain fixed. All the assets are divisible and even marketable. Thus, no new issues will be undertaken in the market and not much focus is on the investor’s requirement of liquidity.

## Terminologies related to Capital Asset Pricing Model

William Sharpe, the financial economist, while explaining the concept of **CAPM** has explained in his book Portfolio Theory and Capital Markets (1970) that investors have to face two types of risk (Chan, 2010; Mcclure, 2019) i.e.

### Systematic risk

Systematic risk represents the variability in the return that the investor has to bear due to market factors. As these risks are non-diversifiable thus investor has to bear them. Some of the factors which lead to systematic risk are recession, interest rate, boom conditions, or war.

### Unsystematic risk

This form of risk arises from firm-specific factors and is not due to movements in the market factors. Thus, unsystematic risks could be diversified by the investor. Some of the firm-specific factors which lead to the occurrence of such risks are management changes, strikes, or any specific export order.

Further, some of the terms used while implementing the Capital Asset Pricing Model are

### The expected return on investment

It represents the behaviour of the investment i.e. the assumption about the expected long-term return from investing in a particular asset (CFI, 2020).

### The risk-free rate of return

It represents the return earned from the asset having zero risk associated. It is the return that the investor would get over a specific time period. Treasury bills are mainly considered risk-free assets wherein the rate of return is adjusted to the inflation rate (Chen & Scott, 2020).

### Beta

Beta in the Capital Asset Pricing Model specifies the market volatility. Examining the fluctuations in the prices of the stocks, Beta measures the sensitivity of the stocks to systematic market risk. A company having a higher beta value tends to have more risk but also earn more return (Kenton & Westfall, 2020).

## Some of the challenges in using the Capital Asset Pricing Model analysis

Despite having the simple procedure of computation and providing the specification on the past performance of the stocks, CAPM analysis still faces some problems in its implementation (Rai, 2011) i.e.

**Unrealistic assumptions exist**:**CAPM**analysis is based on examining the investors’ behaviour over a single time horizon by considering that time does not have relevance in influencing the expected return. However, this assumption does not hold true as the past and current information about a stock does influence the decision of investors. Further, the assumption that there is a similar expectation of risk and return among investors, and that the existence of liquidity is not a matter of focus for investors is not true.**Expected return based on only Systematic risk**:**CAPM**analysis due to the diversifiable nature of firm-specific risk, does not include them in the return computation process. But factors like the dividend payout ratio or relative sensitivity to inflation of a firm also affect the investment decision. These firm-specific factors do need to be included in examining the impact of risk on expected return.**Unstable nature of the variables**: Government securities are considered as a proxy of risk-free securities and beta as a symbol of representing market risk. However, both of these variables change on a regular basis. Government securities return is affected by economic circumstances while beta value which represents the movement of prices changes over time. Thus, the expected return computed through the Capital Asset Pricing Model is less reliable.**Some of the variable costs are ignored**: Capital Asset Pricing Model assumes the market is perfectly competitive and no extra costs are required to be incurred. However, in reality, some of the costs like transaction cost, information cost, or brokerage need to be incurred for acquiring all information.

## Importance of Capital Asset Pricing Model for determining the stock value

**CAPM** analysis is the method that empirically helps in assessing the direct relationship between risk and return. Though the analysis is based on predicting the behaviour of investment based on the historical database, it is a simple way to assess the movements in price. Companies mainly use Capital Asset Pricing Model analysis because it not only helps in determining the cost of equity and estimating the required rate of return but also acts as a means to evaluate the performance of stocks in terms of return and cost. Further, by assessing the non-diversifiable risk, the Capital Asset Pricing Model analysis provides the method to construct an optimal portfolio with an adequate trade-off of risk and expected return (Rai, 2011).

For example, stocks having a beta value of 0.7 tends to bear less systematic risk as compared to stocks having a beta of 2.3. Thus, an investor would only choose the latter stock if the amount of market risk premium he is getting is enough to compensate for the associated risk. This comparison could be done by computing the expected return value using the Capital Asset Pricing Model.

Hence, despite having problems in the computation of the effective expected return, the Capital Asset Pricing Model is considered an optimal model for examining the investor behaviour and pricing mechanism of stocks. The process of conducting the **CAPM** analysis is stated here.

#### References

- CFI. (2020). Capital Asset Pricing Model. Retrieved July 4, 2020, from Corporate Finance Institute website: https://corporatefinanceinstitute.com/resources/ebooks/investment-banking/capital-asset-pricing-model-capm-guide/#:~:text=The Capital Asset Pricing Model,rate proportional to market risk
- Chan, S. (2010).
*Systematic and Unsystematic Risk-Capital Asset Pricing Model*. - Chen, J., & Scott, G. (2020). Risk-Free Rate Of Return. Retrieved July 4, 2020, from Investopedia website: https://www.investopedia.com/terms/r/risk-freerate.asp
- Diksha. (2020). CAPM: Assumptions and Limitations. Retrieved July 4, 2020, from Economics Discussion website: https://www.economicsdiscussion.net/portfolio-management/capm/capm-assumptions-and-limitations-securities-financial-economics/29904#:~:text=The CAPM has serious limitations,of the true risk involved.
- Fama, E., & French, K. (2003). The CAPM : Theory and Evidence.
*Journal of Economic Perspectives*,*18*(03), 25–46. - Kenton, W., & Westfall, P. (2020). Beta. Retrieved July 4, 2020, from Investopedia website: https://www.investopedia.com/terms/b/beta.asp
- Liu, W. (2017). Three Pricing Models in Modern Portfolio.
*2017 International Conference on Financial Management, Education and Social Science (FMESS 2017)*. - Mcclure, B. (2019). Explaining The Capital Asset Pricing Model (CAPM).
- Rai. (2011).
*Capital Asset Pricing Model (CAPM)*. 142–154.

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