## What is the fixed asset pricing model?

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

Fixed asset pricing model – CAPM

## Understanding the Capital Asset Pricing Model (CAPM)

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



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or:

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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+??I(ERmRF)or:ERI=expected return on investmentRF=risk free rate??I=investment beta(ERmRF)=market risk premium

Investors expect to be compensated for the 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 taking by the investor.

The beta of a potential investment is a measure of the risk that the investment will add to a portfolio that looks like the market. 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 that it will reduce the risk of a portfolio.

The beta of a stock 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 he can use to find the value of an asset.

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

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

## Problems with the CAPM

There are several assumptions behind the CAPM formula that have turned out not to hold true in reality. Modern financial theory is based on two assumptions: (1) securities markets are highly competitive and efficient (ie, relevant information about companies is quickly and universally disseminated and absorbed); (2) these markets are dominated by rational and risk averse investors, who seek to maximize the satisfaction of the 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 both directions are not equally risky. The period of analysis for determining the volatility of a stock is not standard because the returns (and risk) of stocks 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 increased to 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 security appear to be overvalued.

The market portfolio that is used to find the market risk premium is only a notional value and is not an asset that can be bought 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 the CAPM is the assumption that future cash flows can be estimated for the discounting process. If an investor could estimate the future return of a stock with a high level of precision, the CAPM would not be necessary.

## The CAPM and the efficient border

Using the CAPM to build a portfolio is believed to help an investor manage their risk. If an investor could use the CAPM to perfectly optimize a portfolio’s return against 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 starting with the risk-free rate, the expected return on 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 notional portfolio can be built on the CML with the best return for the amount of risk. taken .

The CML and efficient frontier can be difficult to define, but it illustrates an important concept for investors: there is a trade-off between increased return and increased risk. Because it is not possible to perfectly build a portfolio that fits the CML, it is more common for investors to take too much risk when looking for additional return.

In the following graphic, you can see two portfolios that were built to fit along the efficient frontier. Portfolio A should earn 8% per year and have a standard deviation or risk level of 10%. Portfolio B is expected to yield 10% per year but has a standard deviation of 16%. The risk of portfolio B 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 on 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 the CAPM and the efficient frontier chart can be rearranged to illustrate the trade-off for individual assets. In the following graphic, 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 beta increases from one to two, so does the expected return.

The CAPM and the SML establish a link between the beta of a stock and its expected risk. A 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 these two models is diminished by assumptions about beta and market participants that are not true in actual markets. For example, beta does not take into account the relative 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 the CAPM

Given the criticisms of the CAPM and the assumptions underlying its use in portfolio construction, it might be difficult 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 share price of \$ 100. The advisor uses the CAPM to justify the price with a 13% discount rate. 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.

Suppose in this example that the performance of the peer group over the past few years was a little better than 10% while this stock had consistently underperformed with returns of 9%. The investment manager should not accept the adviser’s recommendation without a rationale for the expected increase in return.

An investor can also use the concepts of CAPM and the efficient frontier to assess the performance of their portfolio or individual stocks against the rest of the market. For example, suppose an investor’s portfolio has returned 10% per annum over 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 an 8% risk.

The investor could use this observation to reassess how their portfolio is constructed and which positions may not appear on the SML. This could explain why the investor’s portfolio sits to the right of the CML. If securities which weigh on returns or which have increased the risk of the portfolio disproportionately can be identified, the investor can make changes to improve returns.

## The bottom line

The CAPM uses the principles of modern portfolio theory to determine whether a security is measured at fair value. It is based on assumptions about investor behavior, 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 as they make better decisions about adding securities to a portfolio.

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