# CAPITAL ASSET PRICING MODEL

A fundamental task for a corporate financial manager is to estimate the company’s cost of equity capital. But computing that cost is a rigorous task and quite often the results are subjective and therefore questionable as credible benchmarks.

The Capital Asset Pricing Model (CAPM) is a model that depicts the relationship between the expected return and the risk of investing in security. The model was formulated by a famous American financial economist (and later, Nobel laureate) William Sharpe, set out in his 1970 book Portfolio Theory and Capital Markets. It is an idealized portrayal of how financial markets price securities and thereby, determine anticipated returns on capital investments. The model furnishes a methodology for quantifying risk and translating that risk into estimates of expected return on equity.

A primary advantage of CAPM is the factual nature of the estimated costs of equity that the model can yield. CAPM cannot be used in isolation because it streamlines the world of financial markets. However, the financial managers can utilize it to supplement other techniques and facilitate judgment in their attempts to formulate a realistic cost of equity calculations.

**Assumptions : **

The modern financial theory rests on two assumptions:

(1) The securities markets are very competitive and efficient (that is, appropriate knowledge about the companies is rapidly and universally disseminated and absorbed);

(2) These markets are influenced by rational, risk-averse investors, who seek to maximize satisfaction from returns on their investments.

Further, more specialized limiting assumptions include frictionless markets without imperfections such as taxes, transaction costs, and restrictions on borrowing and short selling. The model also requires limiting assumptions concerning the investors’ preferences and the statistical nature of securities returns. Ultimately, investors are assumed to agree on the probable performance and risk of securities, based on a common time horizon.

Although CAPM’s assumptions are unrealistic, such simplification of reality is often a necessity to develop useful models. An experienced financial executive may have difficulty perceiving the world postulated by this theory and the research conducted to date has focused on relaxing these restrictive assumptions.

**CAPM FORMULA : **

The model is based on the notion that investors should gain higher yields whilst investing in more high-risk investments, thus defining the presence of the market risk premium in the model’s formula.

*Anticipated return = Risk-free rate + (beta x market risk premium)*

1. Using the capital asset pricing model, the anticipated return is what an investor can expect to earn on investment over the life of that investment.

2. A risk-free rate is a discount rate an investor can use in determining the value of an investment. It is the equivalent of the yield of a 10-year government bond.

3. Beta is the representation of a stock’s risk. It is a numerical value that quantifies how susceptible the stock is to changes in the market. Regression analysis is required to calculate β, This enables to value assets when comparing multiple variables.

*β = Covariance/Variance*

To calculate β, obtain the closing prices for your stock as well as for the index that you are employing as your benchmark over a said period. Then, separately calculate the price change for your stock and the index using the following formula:

*[(Today’s price – Price yesterday)/Yesterday’s price] x 100*

Next, compare the stock and the index to see how they move with each other as compared to how the index moves by itself. The result that you will attain is βi. The formula is as follows:

*Covariance ÷ Variance which is the stock’s daily change and index’s daily change ÷ Index’s daily change*

- If a stock’s risk outpaces the market, then its beta is more than one.
- If its beta is less than one, the security is less volatile than the market. It can reduce the risk within a diversified portfolio.
- For instance, if a company’s beta is equal to 1.3 the security has 130% of the volatility of the market average. However, if the beta is equal to 1, the anticipated return on a security is equal to the average market return. A beta of -1 implies that the security has a perfect negative correlation with the market.

4. Lastly, the market risk premium represents an asset’s return beyond just the risk-free rate. The market risk premium is the additional return that can entice investors to put capital into riskier investments.

Risky investments can often be worthwhile to investors if the return rewards them owing to their time and risk tolerance. *CAPM analyzes whether or not a stock’s value is worth the risk.*

**CAPM in Action : **

For example, say you’re looking at a stock worth Rs. 3500 per share today that pays a 3% annual dividend. The stock’s beta is 1.5, making it riskier than the overall market. Also, assume that the risk-free rate is 3% and this investor expects the market to rise in value by 5% per year.

Then,

CAPM =3%+1.5×(5%−3%)

The expected return of the stock based on CAPM is 6%.

This expected return discounts the stock’s expected dividends and appreciation of the stock over the expected holding period. If the discounted value of future cash flows is equal to Rs. 3500, then CAPM says the stock has a fair price for its risk.

**Illustration of CAPM : **

The security market line is a characteristic line that appears on a chart that illustrates the CAPM. It shows the systematic (market) risk of various securities compared to the whole market’s expected return at a point in time. You can use the following formula to determine the required return:

*Required Return = Risk-Free Rate of Return + β(Market Return – Risk-Free Rate of Return)*

Image: CFI’s Math for Corporate Finance Course.

The X-axis is the risk or β, and the Y-axis is the expected return. The market risk premium is where it is on the security mark line.

**The utility of the model **

Although the application of this model continues to provoke a vigorous debate, investment managers widely apply the simple CAPM and its more refined extensions. Its prime advantage is that it quantifies risk and delivers a widely applicable, relatively objective routine for translating risk measures into estimates of expected return.

Due to its shortcomings, financial executives should not rely on CAPM as a precise algorithm for estimating the cost of equity capital. Nevertheless, given the intrinsic complication in measuring the cost of equity, CAPM’s deficiencies appear no worse than those of other approaches.

CAPM’s application to corporate finance is a current development. Although it has been employed in several utility rate-setting proceedings, it has yet to gain substantial use in corporate circles for estimating companies’ costs of equity. The model certainly represents a fresh approach to an important task. Financial decision-makers can use the model in conjunction with conventional techniques and sound judgment to develop realistic and useful estimates of the costs of equity capital.

Despite all the limitations, the model can be a useful addition to the financial manager’s analytical tool kit.

**References: **

*1.)CAPM: theory, advantages, and disadvantages -Written by a member of the Financial Management examining team.*

*2.)capital-asset-pricing-model by M1 Finance LLC.(2017)*

*3.)Sharpe, William F. (1964). “Capital asset prices: A theory of market equilibrium under conditions of risk”. Journal of Finance.*

*4.) Doeswijk, Ronald; Lam, Trevin; Swinkels, Laurens (2019). “Historical returns of the market portfolio”. Review of Asset Pricing Studies.*