The Capital Asset Pricing Modelor CAPMis one of the most commonly used models for calculating the expected return on an asset and is used to price securities.

The CAPM requires 3 data inputs:. The reasons behind using a model such as the CAPM is that investors need to be compensated for taking risk. The model says that for any level of risk betathe return needs to exceed the return of a risk-free asset by a certain amount and that the more risk is assumed, the higher return is required. In the example above, the asset has a beta of 1. If a more stable industry such as a utility company is looked at, the required return is considerably lower. Although the CAPM should never be used to as a stand-alone tool for determining where to invest money, it is extremely useful in working out if you are being over or under-compensated for the amount of risk you are taking, although clearly there are a lot of variables involved, some of which cannot really be predicted with a great degree of accuracy.

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## Capital Asset Pricing Model

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CAPM assumes a particular form of utility functions in which only first and second moments matter, that is risk is measured by variance, for example a quadratic utility or alternatively asset returns whose probability distributions are completely described by the first two moments for example, the normal distribution and zero transaction costs necessary for diversification to get rid of all idiosyncratic risk.

Under these conditions, CAPM shows that the cost of equity capital is determined only by beta.

SharpeJohn Lintner a,b and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory. Sharpe, Markowitz and Merton Miller jointly received the Nobel Memorial Prize in Economics for this contribution to the field of financial economics. This version was more robust against empirical testing and was influential in the widespread adoption of the CAPM.

The CAPM is a model for pricing an individual security or portfolio. For individual securities, we make use of the security market line SML and its relation to expected return and systematic risk beta to show how the market must price individual securities in relation to their security risk class.

The SML enables us to calculate the reward-to-risk ratio for any security in relation to that of the overall market. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk ratio, thus:.

Note 1: the expected market rate of return is usually estimated by measuring the arithmetic average of the historical returns on a market portfolio e. Note 2: the risk free rate of return used for determining the risk premium is usually the arithmetic average of historical risk free rates of return and not the current risk free rate of return.

For the full derivation see Modern portfolio theory. There has also been research into a mean-reverting beta often referred to as the adjusted beta, as well as the consumption beta. However, in empirical tests the traditional CAPM has been found to do as well as or outperform the modified beta models.

The x -axis represents the risk betaand the y -axis represents the expected return. The market risk premium is determined from the slope of the SML. The equation of the SML is thus:.

### Capital Asset Pricing Model (CAPM)

It is a useful tool for determining if an asset being considered for a portfolio offers a reasonable expected return for its risk. Individual securities are plotted on the SML graph.

If the security's expected return versus risk is plotted above the SML, it is undervalued since the investor can expect a greater return for the inherent risk. And a security plotted below the SML is overvalued since the investor would be accepting less return for the amount of risk assumed. Assuming that the CAPM is correct, an asset is correctly priced when its estimated price is the same as the present value of future cash flows of the asset, discounted at the rate suggested by CAPM.

If the estimated price is higher than the CAPM valuation, then the asset is undervalued and overvalued when the estimated price is below the CAPM valuation. The CAPM returns the asset-appropriate required return or discount rate—i. Betas exceeding one signify more than average "riskiness"; betas below one indicate lower than average. Thus, a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate.

Given the accepted concave utility functionthe CAPM is consistent with intuition—investors should require a higher return for holding a more risky asset. Since beta reflects asset-specific sensitivity to non-diversifiable, i. Stock market indices are frequently used as local proxies for the market—and in that case by definition have a beta of one.

An investor in a large, diversified portfolio such as a mutual fundtherefore, expects performance in line with the market. The risk of a portfolio comprises systematic riskalso known as undiversifiable risk, and unsystematic risk which is also known as idiosyncratic risk or diversifiable risk. Systematic risk refers to the risk common to all securities—i. Unsystematic risk is the risk associated with individual assets. Unsystematic risk can be diversified away to smaller levels by including a greater number of assets in the portfolio specific risks "average out".

The same is not possible for systematic risk within one market. Depending on the market, a portfolio of approximately 30—40 securities in developed markets such as the UK or US will render the portfolio sufficiently diversified such that risk exposure is limited to systematic risk only.

In developing markets a larger number is required, due to the higher asset volatilities. A rational investor should not take on any diversifiable risk, as only non-diversifiable risks are rewarded within the scope of this model.Investors who have a portfolio of securities may like to add some more securities to the existing portfolio in order to diversify or reduce the risks.

So, it is appropriate to study the extent of risks of a security in terms of its contribution to the riskiness of a portfolio.

It considers the required rate of return of a security in the light of its contribution to total portfolio risk. The CAPM holds that only undiversifiable risk is relevant to the determination of expected return on any asset. Even though the CAPM is competent to examine the risk and return of any capital asset such as individual security, an investment project or a portfolio asset, we shall be discussing CAPM with reference to risk and return of a security only.

The investors are basically risk averse and diversification is necessary to reduce their risks. An investor aims at maximizing the utility of his wealth rather than the wealth or return. Each increment of wealth is enjoyed less than the last as each increment is less important in satisfying the basic needs of the individual.

Thus, the diminishing marginal utility is most applicable to wealth. There are also other forms of utility functions. Some investors showing a preference for larger risks are those who have increasing marginal utility for wealth. In such cases, each increase in wealth prompts the individual to acquire more wealth.

For a risk-neutral investor, each increment in wealth is equally attractive. In other words, each increment would have the same utility for him. Investors make investment decisions on the basis of risk and return.

Risk and return are measured by the variance and the mean of the portfolio returns. CAPM assumes that the rational investors put away their diversifiable risk, namely, unsystematic risk.

But only the systematic risk remains which varies with the Beta of the security. Some investors use the beta only to measure the risk while other investors use both beta and variance of returns as the sources of reward. As individuals have varying perceptions towards risk and reward, CAPM gives a series of efficient frontlines. All investors have similar expectations of risk and return. When the expectations of the investors differ, the estimates of mean and variance lead to different forecasts.

As a result, there will be innumerable efficient frontiers and the efficient portfolio of each will be different from that of the others. Varying preferences also imply that the price of an asset will be different for different investors. The CAPM is based on the assumption that all investors have identical time horizon. The core of this assumption is that investors buy all the assets in their portfolios at one point of time and sell them at some undefined but common point in future.

This assumption further implies that investors form portfolios to achieve wealth at a single common terminal rate. This single common horizon enables one to construct a single period model. This assumption is highly unrealistic as investors are short-term speculators. Further, the horizon is chosen on the basis of the characteristics of an asset.

So investors have different time horizons and their estimates of stock value vary even when the estimated earnings remain constant. Instead of single period model, investors generally adopt continuous time models as if they make a series of reinvestments. One of the important assumptions of the CAPM is that investors have free access to all the available information at no cost.Capital Asset pricing model CAPM is used to determine the current expected return of a specific security.

This model assumes that every stock moves in some way relative to the market in general, and that by knowing this relationship, and the required rate of return for the market, and the minimum required risk free rate of return, the required rate of return can be determined for any stock. Use the capital asset pricing model calculator below to solve the formula. Capital Asset Pricing Model is used to value a stocks required rate of return as a function of its volatility, and the relative risk and rate of return offered by the market.

The basic assumptions of this model give us insight into how it works. Investors are looking to generate a return on their funds by choosing assets to invest in with an expected rate of return.

When investing these funds, investors put their capital at risk. When deciding which asset to invest in, investors will look to compare the expected rates of return with the expected levels of risk. This means that all else being equal, investors will choose the asset that has the highest expected rate of return, and the asset that exposes them to the lowest level of risk possible. When talking of risk in capital assets, we are really talking about their volatility.

Volatility refers to the fluctuation in value of the asset, how much the price increases or decreases. A high degree of volatility means that a particular asset stock will increase and decrease in price to a higher degree than another asset with less volatility.

The relationship between the price of any one asset and the value of the market is known as Beta. An asset with a high Beta will increase in price more than the market when the market increases, and decrease more than the market when the market decreases.

A Beta with a value of 1 is expected to move to the same degree as the market, a Beta with a value lower than 1 will move to a lesser degree than the market, and a Beta of greater than 1 will move to a higher degree than the market when the market moves.

It is even possible to have a negative Beta. A negative Beta means that the price of the asset tends to decrease when the value of the market increases. As with the positive Beta, the greater the value of the negative Beta will indicate the degree to which the asset fluctuates inversely to the market.

The CAPM Capital Asset Pricing Model assumes that investors will never accept higher levels of risk volatility unless they are to be compensated with a higher expected rate of return.

This follows form the basic assumption that the value of the market in the long run will increase. An asset with a Beta greater than one will expose the investor to higher levels of volatility, but will also reward the investor as the value of the asset will grow at a higher rate than the market.

The CAPM Capital Asset Pricing Model also assumes that investors can always invest in a risk free asset, which will offer them the minimum possible rate of return for any investment. In the real world, this tends to be based on the rate offered by federal government short term treasury bills, as these are considered to be the closest possible to risk free investments. Since an investor will always want to expose themselves to the minimum level of risk, they must receive a premium rate of return relative to the amount of risk they are exposed to in any one asset.

This risk premium, which is over and above the risk free rate of return, is the required rate of return that an asset must generate in order for anyone to invest in it. If the asset does not produce the required rate of return, then the price is too high relative to the risk exposure.

Other models follow this theory, such as the Gordon Model Constant Dividend Growthwhich assumes that price can be determined by the rate of return received by an investor. The risk free rate of return in the CAPM Capital Asset Pricing Model refers to the rate of return an investor can receive without exposing their funds to any risk.

Typically based on the rate paid on short term federal treasury bills, this interest rate forms the basis for the required rate of return on all assets. No matter what the capital asset, the risk free rate of return will be included in the required rate of return. Any return over the risk free rate will be due to the risk premium required by investors to accept the higher level of risk in their portfolio.

The primary determinant of the required rate of return is the risk premium. Investors have a large selection of capital assets to invest in, which in aggregate compose the market.

If an investor invested in the entire market, then their required rate of return would be the rate of return that the entire market returns to investors.

The difference between this rate of return and the risk free rate would be the risk premium. Since the volatility each asset can be compared against the volatility of the market, then it follows that their risk premium would adjust by the same degree.Pro members can track their course progress and get access to exclusive downloads, quizzes and more!

Find out more. Already got an account? Log in here. The Capital Asset Pricing Model CAPM provides a way to calculate the expected return of an investment based on the time value of money and the systematic risk of the asset.

Put simply, CAPM estimates the price of a high-risk stock by linking the relationship between the risk of the stock, and the expected return.

CAPM is very commonly used in finance to price risky securities and calculating an expected return on those assets when considering the risk and cost of capital. The systematic risk and unsystematic risk are two kinds of risks that most investors face. When we talk about a risk that causes low or negative returns and risks of the financial system where the whole economy goes down, we are referring to systematic risk.

For example, an economic recession is a systematic risk. When we add additional investments to a portfolio, we are able to mitigate such risks. For instance, since there are particular events that may affect it, a portfolio of stocks is less prone to the negative performance of one company.

Risk specific to a particular investment, on the other hand, refers to unsystematic risk. By adding additional investments to a portfolio, you can still mitigate such risks.

The required return is measured based on the level of systematic risk inherent in a specific investment. You must first understand the risk of an investment to fully understand the capital asset, pricing model.

**How to Calculate Beta with Excel, Calculation of Beta**

A loss of investment to the investor is possible from individual securities since it carries a risk of depreciation. With additional risk, an investor expects to realize a higher return on their investment since some securities have more risk than others. The risk-free rate in the CAPM formula accounts for the time value of money — that money available at the present time is worth more than the same amount in the future due to its current earning capacity.

### The Capital Asset Pricing Model (CAPM), Explained

The other components of the formula focus on the additional risk taken on by the investor. The beta of the investment is a way to measure and account for how much risk this particular investment will add to the portfolio relative to the market. If a stock is riskier than the overall market, it will have a beta that is higher than 1 and a beta of less than 1 would assume that the investment will reduce the overall risk of the portfolio.

Once you have the beta, you multiply it by the market risk premium the return expected from the market that is above the risk-free rate. This value is then added to the risk-free rate to give you the final expected rate of return for the asset.With investing, the higher the risk, the more an investor expects to earn. The capital asset pricing model CAPM tries to estimate how much you can expect to earn given the amount of risk.

Investment professionals use the model in conjunction with fundamental analysistechnical analysis and other methods of sizing up securities when making investment decisions. Of course, individuals with the know-how can use CAPM, too. The capital asset pricing model CAPM is widely used within the financial industry, especially for riskier investments.

Using the capital asset pricing model, the expected return is what an investor can expect to earn on an investment over the life of that investment. It is a discount rate an investor can use in determining the value of an investment.

The risk-free rate is the equivalent of the yield of a year U. If its beta is less than one, it can reduce the risk within a diversified portfolio. The market risk premium is an added return that can entice investors to put capital into riskier investments.

Risky investments can be worthwhile to investors if the return rewards them for their time and risk tolerance.

Unsystematic risk, or specific risk is what modern portfolio theory targets when it suggests diversification of a portfolio. CAPM exists for measuring systematic risk. The capital asset pricing model is important in the world of financial modeling for a few key reasons.

Firstly, by helping investors calculate the expected return on an investment, it helps determine how appropriate a particular investment may be. Additionally, the CAPM is an important tool for investors when it comes to accessing both risk and reward.

That index could perform differently over time. The CAPM helps determine whether an investment is worth the risk. However, critics say the CAPM carries loads of inaccurate assumptions. Interest rates, recessions, and wars are examples of systematic risks.

Strikes, mismanagement or shortage of a necessary component in the manufacturing process all qualify as unsystematic risk.Definition: The capital asset pricing model or CAPM is a method of determining the fair value of an investment based on the time value of money and the risk incurred.

This model assumes that there are many investors with the same investment horizon and equal access to information and securities. All investors share homogenous beliefs about the investment opportunities offered in the market and are all price takers. They all borrow at a risk-free rate and pay no taxes or commissions.

CAPM calculates the expected rate of return and discounts the expected future cash flows to their present value. The model assumes that the expected rate of return is equal to the risk-free rate plus a risk premium. Therefore, if the actual return on investment is not equal or higher than the expected return, the investment should not be undertaken.

Pedro is an investment banking analyst at Lazard, and he wants to calculate the expected rate of return for a security. Pedro finds that the systematic risk b of the security is 1. Pedro uses the CAPM model to calculate the expected rate of return and determine if the investment should be undertaken.

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