## Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is a mathematical model that describes the relationship between systematic risk and expected return for assets, especially equities. The CAPM model is widely used in finance to price risky securities and generate expected returns for assets based on their risk and cost of capital.

## Understanding the Capital Asset Pricing Model (CAPM)

The following is the formula for estimating an asset’s expected return given its risk:

Risk and the time value of money are expected to be compensated for by investors. The time value of money is taken into consideration by the risk-free rate in the CAPM formula. The CAPM formula’s other components account for the investor’s willingness to take on greater risk.

A potential investment’s beta is a measure of how much risk it will contribute to a portfolio that resembles the market. A beta greater than one indicates that a stock is riskier than the market. The calculation posits that a stock with a beta of less than one will minimize a portfolio’s risk.

The market risk premium, which is the projected return from the market above the risk-free rate, is then multiplied by a stock’s beta. The risk-free rate is then multiplied by the stock’s beta multiplied by the market risk premium. The outcome should provide an investor with the required return or discount rate to determine the asset’s value.

When risk and time value of money are compared to predicted return, the CAPM method is used to determine if a stock is properly valued.

Consider an investor who is considering a stock that is currently worth $100 per share and offers a 3% yearly dividend. When compared to the market, the stock has a beta of 1.3, indicating that it is riskier than a market portfolio. Assume that the risk-free rate is 3% and that the investor anticipates the market to grow at an annual rate of 8%.

According to the CAPM model, the stock’s predicted return is 9.5 percent:

9.5% = 3% + 1.3 × (8% − 3%)

The CAPM formula’s projected return is used to discount the stock’s expected dividends and capital appreciation over the expected holding term. The CAPM method suggests that the stock is reasonably valued relative to risk if the discounted value of those future cash flows equals $100.

## Problems With the Capital Asset Pricing Model

Several assumptions underlying the CAPM formula have been demonstrated to be false in practice. Two assumptions underpin modern financial theory: One, securities markets are highly competitive and efficient (that is, important information about firms is widely transmitted and absorbed fast), and two, these markets are dominated by rational, risk-averse investors seeking to maximum satisfaction from their investments.

Despite these flaws, the CAPM formula remains popular because it is straightforward and allows for quick comparisons of investment options.

The inclusion of beta in the calculation assumes that a stock’s price volatility may be used to measure risk. Price movements in both directions, on the other hand, are not equally dangerous. Because stock returns (and risk) are not normally distributed, the look-back period used to measure a stock’s volatility is not conventional.

The CAPM also implies that over the discounting period, the risk-free rate would remain constant. Assume that the interest rate on US Treasury bonds grew to 5% or 6% throughout the 10-year holding period in the previous scenario. An increase in the risk-free rate raises the cost of capital utilized in the investment, thereby overvaluing the stock.

The market portfolio used to calculate the market risk premium is merely a theoretical value; it is not a real-world asset that can be bought or invested in instead of stocks. Typically, investors will substitute a prominent stock index, such as the S&P 500, for the market, which is an imprecise comparison.

The premise that future cash flows can be forecast for the discounting process is the most serious criticism of the CAPM. The CAPM would be unnecessary if an investor could predict a stock’s future return with a high degree of precision.

## The CAPM and the Efficient Frontier

Using the CAPM to construct a portfolio is designed to assist an investor in risk management. If a portfolio’s return relative to risk could be perfectly optimized using the CAPM, it would exist on a curve known as the efficient frontier, as depicted in the graph below.

The graph illustrates how higher expected profits (y-axis) necessitate higher expected risk (x-axis). According to Modern Portfolio Theory (MPT), a portfolio’s expected return increases as risk increases, starting with the risk-free rate. Any investment that fits on the Capital Market Line (CML) is superior than any portfolio that fits to the right of that line, but at some point on the CML, a theoretical portfolio with the best return for the amount of risk taken can be formed.

Although the CML and efficient frontier are difficult to define, they demonstrate a crucial notion for investors: more yield comes at the expense of increased risk.

Because it’s impossible to construct a portfolio that exactly meets the CML, investors are more likely to take on too much risk in the pursuit of higher returns.

Two portfolios that have been built to fit along the efficient frontier are shown in the chart below. Portfolio A is predicted to return 8% per year and has a risk level of 10% standard deviation. Portfolio B is predicted to return 10% per year, but has a standard deviation of 16%. Portfolio B’s risk increased quicker than its predicted returns.

The efficient frontier is based on the same assumptions as the CAPM, but it can only be determined theoretically. If a portfolio were to reside on the efficient frontier, it would offer the best return for the risk it entails. However, because future returns cannot be forecast, it is impossible to determine whether a portfolio is on the efficient frontier or not.

The CAPM exhibits this risk-return trade-off, and the efficient frontier graph can be reconfigured to show the trade-off for individual assets. The CML is currently known as the Security Market Line, as shown in the chart below (SML). The stock’s beta is used instead of predicted risk on the x-axis.

## Practical Value of the CAPM

Given the CAPM’s detractors and the assumptions that underpin its application in portfolio development, it’s difficult to see how it may be effective. However, the CAPM can still be useful for evaluating the reasonableness of future expectations or conducting comparisons.

Consider an advisor who suggests adding a $100-per-share stock to a client’s portfolio. With a discount rate of 13%, the advisor applies the CAPM to explain the pricing. This information can be compared to the company’s past performance and its peers by the advisor’s investment manager to evaluate if a 13 percent return is a reasonable expectation.

Assume that the peer group’s performance over the last few years has been somewhat better than 10%, whereas this stock has consistently underperformed with returns of 9%. The investment manager should not follow the advisor’s advice unless the enhanced expected return can be justified.

An investor can also utilize the CAPM and efficient frontier principles to compare the performance of their portfolio or individual stocks to the rest of the market. Consider an investor’s portfolio, which has returned 10% each year for the last three years with a 10% standard deviation of returns (risk). The market averages, on the other hand, have returned 10% over the last three years with an 8% risk.

This observation could be used by the investor to rethink how their portfolio is put together and which holdings may not be on the SML. This may explain why the portfolio of the investor is to the right of the CML. If the investor can identify the holdings that are driving down returns or have increased the portfolio’s risk unduly, he or she can make changes to boost returns.

## The Bottom Line

To establish if a security is properly priced, the CAPM employs Modern Portfolio Theory principles. It is based on unrealistic assumptions about investor behavior, risk and return distributions, and market fundamentals. The basic concepts of CAPM and the related efficient frontier, on the other hand, can assist investors better grasp the link between expected risk and return when deciding which assets to add to a portfolio.