# CAPM(capital assets pricing model)

The capital assets pricing model (CAPM) is a model the provides a framework to determine the required rate of return. Assets and indicates the relationship between return and risk of the assets. The required rate of return specified by CAPM helps in valuing an asset one can also compare the expected rate of return on an asset with its required rate of return and determine whether the assets are fairly valued As we explain in this section under CAPM, The security market line (SML) exemplifies the relationship between an assets risk and its required rate of return.
Assumption of CAPM
The CAPM rests on eight assumptions. The first five assumptions are those that underline the efficient market hypothesis and thus underline both modern portfolio theory(MPT) are the CAPM. The last three assumptions are necessary to create the CAPM from MPT. The eight assumptions is necessary to create the CAPM MPT.
The eight assumptions are the following
i)Market efficiency-For MPT and the CAPM the investor is maximizing the utility of wealth, a utility is a way of describing the difference in individual preferences. A diminishing marginal of utility for wealth is the most frequently described utility function. A risk-neutral investor would find each increment would have the utility. Given the investor wealth, the total utility he or she obtains will depend upon the combination of risk and return that are available.

ii)Risk aversion and mean-variance optimisation-Risk and return are measured by the variance and the mean of the portfolio returns. In using MPT and CAPM  we assume that portfolio variance is an appropriate measure of risk because it allows us to use two factors mean-variance is an appropriate measure of risk because it allows us to use two factors mean and variance to describe each assets relative attractiveness. In moving from MPT to the CAPM we presume that since rational investors diversify away diversifiable risk(on systematic risk), beta is a measure of the remaining risk (the variance) of the portfolio. Thus we presume that beta and return are directly and linearly related.

iii)Homogeneous expectation-This assumption simply states that all investor estimates of risk and return are the same. To have the single efficient frontier of modern portfolio theory, We must have consumed estimates of the mean and variance, and thus of the relative value of each investment varying preference could produce a number of investor specific efficient frontier instead of the single frontier of modern portfolio theory. We must have consensus estimates variance and thus of relative value of each investment. Thus MPT and CAPM and the efficiency of the market portfolio are inseparable.

iv)Time Horizon-This assumption suggests that investor from portfolio to achieve wealth at a single, common terminal horizon allows us the construct a single-period model. The model implies that investors the assets in the portfolio at one point in time and sell them at some undefined but common point in the future.
Continuous-time models have been developed, but they are more complex than the single-period models. We can see the single-period model to approximate multiperiod investor behavior but only if the following condition is true.
a)Return is independent overtime for the stock market .this is equivalent to saying that the weak form of the efficient market hypothesis holds.
b)Expectations are independent of past or current information for instance, we must b able to say that the return from a retail store chain is independent of such things as past and current inflation.

V)Information is finely and simultaneously available to investor-If group of investors were privy to special, not widely available information on which they could make superior decision ,markets would not be efficient and MPT and the CAPM would be affected without a set of common forecasts a single efficient frontier could not exist.

vi)There is a risk free assets and investors can borrow and lend unlimited amounts at the riskfree rate-this is may be the most crucial assumption of the CAPM . The risk-free assets are needed to simplify the complex pairwise covariance of marketwitz’s theory. The risk-free asset simplifies the curved efficient frontier of MPT to the linear efficient frontier of the CAPM and the investor has ceased to be concerned with the characteristics of individual assets. Risk is decreased or increased by adding a portion of the risk-preferred combination. Risk is decreased or increased by adding a portion of the risk free assets or by borrowing at the risk-free rate to invest additional funds in the market portfolio.

vii)There are no taxes transaction costs restrictions on short rates or other market imperfection -The assumption has several implications for the CAPM .first the assumption about short sale complements the assumption about a risk -free asset roll showed that these must be either a risk-free asset or a portfolio of short sold securities for the capital market line to be straight. If there were no risk-free assets. the investor could create one by short selling securities. If there are no-risk free assets and the investor could not create a  proxy risk fr asset, the capital market line would not be a linear and the direct linear realtionship between risk (beta)and the return would not exist, Second of the three assumptions specific to the CAPM, this one removes the real-world problem of transaction costs and taxes.The CAPM treats dividends and capital gains as equivalent and transaction cost as irrelevant. Assuming that all returns are equally desirable allows us to use the simple CAPM

viii)Total assets quantity is fixed, and all assets are marketable and divisible-This assumption suggests that we can ignore liquidity and new issues of securities.if such things can not be ignored, then the simple CAPM cannot capture all that is important in pricing securities. The fact is that liquidity is a serious concern for investors. Hence, some investors have begun to add liquidity as a factor in making their market estimates.The adaption produces multiple capital market lines -one line for each particular group of investors. Other firms have used the market value (the size) of the company as another factor in determining returns.