# Capital Asset Pricing Model (CAPM)

## What is the fixed asset pricing model?

The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and the expected return of assets, particularly stocks. CAPM is widely used in finance to price risky securities and generate expected returns for assets given the risk of those assets and the cost of capital.

Capital Pricing Model – CAPM

## Understanding the Capital Asset Pricing Model (CAPM)

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

Inasmuch as



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expected return on investment

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risk free rate

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investment beta

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begin{aligned} &ER_i = R_f + beta_i ( ER_m – R_f ) &textbf{where:} &ER_i = text{expected return on investment} &R_f = text{risk-free rate} &beta_i = text{investment beta} &(ER_m – R_f) = text{market risk premium} end{aligned}

ERI=RF+βI(ERmRF)or:ERI=expected return on investmentRF=risk free rateβI=investment beta(ERmRF)=market risk premiumInasmuch as

Investors expect to be compensated for risk and the time value of money. The risk-free rate in the CAPM formula takes into account the time value of money. The other components of the CAPM formula take into account the additional risk taken by the investor.

The beta of a potential investment is a measure of the risk the investment will add to a market-like portfolio. If a stock is riskier than the market, it will have a beta greater than one. If a stock has a beta of less than one, the formula assumes it will reduce a portfolio’s risk.

A stock’s beta is then multiplied by the market risk premium, which is the expected market return above the risk-free rate. The risk-free rate is then added to the product of the stock’s beta and the market risk premium. The result should give an investor the required rate of return or discount that they can use to find the value of an asset.

The objective of the CAPM formula is to assess whether a stock is correctly priced when its risk and time value of money are compared to its expected return.

For example, say an investor today is considering a stock worth 100 per share that pays an annual dividend of 3%. The stock has a market beta of 1.3, which means it is riskier than a market portfolio. Suppose also that the risk-free rate is 3% and that this investor expects the market value to increase by 8% per year. The expected return on the stock based on the CAPM formula is 9.5%: Inasmuch as  9 . 5 % = 3 % + 1 . 3 × ( 8 % 3 % ) begin{aligned} &9.5% = 3% + 1.3 times ( 8% – 3% ) end{aligned} 9.5%=3%+1.3×(8%3%)Inasmuch as The expected return from the CAPM formula is used to discount the expected dividends and capital appreciation of the stock over the expected holding period. If the present value of these future cash flows equals100, the CAPM formula indicates that the stock is fairly valued relative to risk.

## Problems with the CAPM

There are several assumptions behind the CAPM formula that have proven not to hold in reality. Modern financial theory is based on two assumptions: (1) securities markets are highly competitive and efficient (that is, relevant information about companies is rapidly and universally distributed and absorbed); (2) these markets are dominated by rational, risk-averse investors who seek to maximize the satisfaction of returns on their investments.

Despite these problems, the CAPM formula is still widely used because it is simple and makes it easy to compare investment alternatives.

The inclusion of beta in the formula assumes that risk can be measured by the volatility of a stock’s price. However, price movements in either direction are not as risky. The look-back period for determining a stock’s volatility is non-standard because stock returns (and risk) are not normally distributed.

The CAPM also assumes that the risk-free rate will remain constant over the discount period. Suppose, in the previous example, that the interest rate on US Treasury bonds reaches 5% or 6% during the 10-year holding period. An increase in the risk-free rate also increases the cost of capital used in the investment and could make the stock appear overvalued.

The market portfolio used to find the market risk premium is only a theoretical value and is not an asset that can be purchased or invested as an alternative to stock. Most of the time, investors will use a major stock index, like the S&P 500, to substitute for the market, which is an imperfect comparison.

The most serious criticism of CAPM is the assumption that future cash flows can be estimated for the discounting process. If an investor could estimate the future performance of a stock with a high level of accuracy, CAPM would not be necessary.

## The CAPM and the efficient frontier

Using CAPM to build a portfolio is meant to help an investor manage their risk. If an investor could use CAPM to perfectly optimize a portfolio’s return for risk, it would exist on a curve called the efficient frontier, as shown in the following chart.

The chart shows how higher expected returns (y-axis) require higher expected risk (x-axis). Modern portfolio theory suggests that from the risk-free rate, the expected return of a portfolio increases as risk increases. Any portfolio that matches the capital market line (CML) is better than any possible portfolio to the right of that line, but at some point a theoretical portfolio can be constructed on the CML with the best return for the amount of risk taken. .

The CML and the efficient frontier can be difficult to define, but they illustrate an important concept for investors: there is a trade-off between increased return and increased risk. Because it is not possible to perfectly construct a portfolio that matches the CML, it is more common for investors to take on too much risk as they seek additional yield.

In the following chart you can see two portfolios that have been constructed to fit along the efficient frontier. Portfolio A should generate a return of 8% per year and a standard deviation or level of risk of 10%. Portfolio B should generate a return of 10% per year, but its standard deviation is 16%. Portfolio B’s risk has increased faster than its expected returns.

The efficient frontier assumes the same things as the CAPM and can only be calculated in theory. If a portfolio existed at the efficient frontier, it would provide the maximum return for its level of risk. However, it is impossible to know whether or not a portfolio exists on the efficient frontier because future returns cannot be predicted.

This trade-off between risk and return applies to CAPM and the efficient frontier graph can be rearranged to illustrate the trade-off for individual assets. In the following table you can see that the CML is now called the Security Market Line (SML). Instead of the expected risk on the x-axis, the stock’s beta is used. As you can see in the illustration, as the beta increases from one to two, the expected return also increases.

CAPM and SML relate a stock’s beta to its expected risk. Higher beta means more risk, but a portfolio of high beta stocks could exist somewhere on the CML where the trade-off is acceptable, if not the theoretical ideal.

The value of both of these models is diminished by assumptions about beta and market players that are not true in real markets. For example, beta does not take into account the relative degree of risk of a stock that is more volatile than the market with a high frequency of downside shocks compared to another stock with an equally high beta that does not experience the same. type of downward price movements. .

## Practical value of CAPM

Given the criticisms of CAPM and the assumptions behind its use in portfolio construction, it might be hard to see how it could be useful. However, using the CAPM as a tool to assess the reasonableness of future expectations or to make comparisons may still have some value.

Imagine an advisor who offered to add a stock to a portfolio with a stock price of \$100. The advisor uses the CAPM to justify the price with a discount rate of 13%. The advisor’s investment manager can take this information and compare it to the past performance of the company and its peers to see if a 13% return is a reasonable expectation.

Assume in this example that the peer group’s performance over the past few years was slightly above 10% while that stock had consistently underperformed with returns of 9%. The investment manager should not follow the adviser’s recommendation without justifying the increase in expected return.

An investor can also use the concepts of CAPM and efficient frontier to assess the performance of their portfolio or individual stocks relative to the rest of the market. For example, suppose an investor’s portfolio has returned 10% per year for the past three years with a standard deviation of returns (risk) of 10%. However, market averages have returned 10% over the past three years with 8% risk.

The investor could use this observation to reevaluate how their portfolio is constructed and what holdings may not be on the SML. This could explain why the investor’s portfolio is to the right of the CML. If holdings that are slowing returns or have disproportionately increased portfolio risk can be identified, the investor can make changes to improve returns.

## The essential

The CAPM uses the principles of modern portfolio theory to determine whether a security is fair valued. It is based on assumptions about investor behaviors, risk and reward distributions and market fundamentals that do not correspond to reality. However, the underlying concepts of CAPM and the associated efficient frontier can help investors understand the relationship between expected risk and reward when making better decisions about adding securities to a portfolio. 