### What is the capital pricing model?

The fixed asset pricing (CAPM) model describes the relationship between systematic risk and the expected return on assets, particularly equities. CAPM is widely used throughout finance to assess risky securities and generate expected returns on assets, given the risk of these assets and the cost of capital.

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Fixed asset pricing model – CAPM

### Understanding the Capital Pricing Model (CAPM)

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

The

$begin {aligned} & ER_i = R_f + beta_i (ER_m – R_f) \ & textbf {where:} \ & ER_i = text {expected return on investment} \ & R_f = text {rate risk-free} & beta_i = text {investment beta} \ & (ER_m – R_f) = text {market risk premium} \ end {aligned}$TheERIThe=RFThe+βIThe(ERmThe–RFThe)or:ERIThe=expected return on investmentRFThe=risk-free rateβIThe=investment beta(ERmThe–RFThe)=market risk premiumTheThe

Investors expect to be compensated for the risk and the time value of money. the risk-free rate in the CAPM formula represents the time value of money. The other components of the CAPM formula allow the investor to take additional risk.

the beta of a potential investment is a measure of the level of risk that 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 security has a beta lower than one, the formula assumes that it will reduce the risk of a portfolio.

The beta of a title 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 share beta product and the market risk premium. The result should give an investor return required or discount rate they can use to find the value of an asset.

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

For example, imagine that an investor is now considering a stock worth $ 100 per share that pays an annual dividend of 3%. The stock has a beta relative to the market of 1.3, which means it is more risky than a market portfolio. Suppose also that the risk-free rate is 3% and this investor expects the market to increase by 8% per year.

The expected yield of the stock based on the CAPM formula is 9.5%:

The

$begin {aligned} & 9.5 % = 3 % + 1,3 times (8 % – 3 %) \ end {aligned}$The9.5%=3%+1.3×(8%–3%)TheThe

The expected return on the CAPM formula is used to update the expected dividends and the appreciation of the share capital over the expected holding period. If the present value of these future cash flows is equal to $ 100, the CAPM formula indicates that the stock is correctly evaluated in relation to the risk.

### CAPM issues

There are several hypotheses behind the CAPM formula which have proven not to hold true. 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 price of a share. volatility. However, two-way price movements are not equally risky. The retrospective period for determining the volatility of a stock is not standard because the returns (and risk) of the stocks are not normally distributed.

CAPM also assumes that the risk-free rate will remain constant during the discount period. Suppose in the previous example that the interest rate on US Treasury bonds has 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 give the stock an appearance overvalued.

The market portfolio that is used to find the market risk premium is only a theoretical value and is not an asset that can be bought or invested as an alternative to the stock. Most of the time, investors will use a major stock index, like the S&P 500, to replace 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 return of a security with a high level of precision, the CAPM would not be necessary.

### CAPM and the efficient border

Using CAPM to build a portfolio is supposed to help an investor manage his risk. If an investor could use CAPM to perfectly optimize a portfolio’s return on risk, it would exist on a curve called effective border, as shown in the following graph.

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

CML and the effective border 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 build a portfolio that matches the CML, it is more common for investors to take too much risk when looking for an additional return.

In the following table, you can see two wallets that have been built to fit along the effective border. Portfolio A is expected to generate a return of 8% per year and a rate of 10% standard deviation or the level of risk. Portfolio B is expected to return 10% per year, but has a standard deviation of 16%. The risk of Portfolio B increased faster than its expected returns.

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

This trade-off between risk and return applies to CAPM and the effective border graph can be reorganized to illustrate the trade-off for individual assets. In the following graphic, you can see that the CML is now called Security market line (SML). Instead of the expected risk on the x-axis, the action beta is used. As you can see in the illustration, when the beta version goes from one to two, the expected performance also increases.

CAPM and SML link the beta of an action to its expected risk. A higher beta means more risk, but a portfolio of high beta stocks may exist somewhere on the CML where the compromise is acceptable, if not the theoretical ideal.

The value of these two 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 risk of a security which is more volatile than the market with a high frequency of downward shocks compared to another security with an equally high beta which does not undergo the same kind downward price movements.

### CAPM practical value

Given the criticism of CAPM and the assumptions behind its use in portfolio construction, it might be difficult to see how it could be useful. However, using 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 price of $ 100. The advisor uses 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 company’s past performance and to peers to see if a 13% return is a reasonable expectation.

Let us assume in this example that the performance of the peer group in recent years has been a little better than 10% whereas this security had constantly underperformed with 9% of returns. The investment manager should not follow the advisor’s recommendation without justifying the increase in expected return.

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

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

### Capital Pricing Model (CAPM) Summary

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