Capital Asset Pricing Module

Question: Describe about arbitrage pricing theory, Inter-temporal CAPM and disadvantages and alternatives to CAPM. Answer: Introduction Thecapital asset pricing model isa model which is primarily used in determining a possible and appropriate required rate of returnof asecurity. This theory describes the connection between the expected return, unsystematic risks and the valuation of a security. This theory infers that a securitys cost of capital is lower for an investor holding an improved diversification of investments in comparison to an investor who is holding the entire market portfolio. The basic idea underlying the theory is that investors are compensated by multiple means:time value of moneyand risk. The former is represented by the opportunity of investment which is considered risk free and which provides a compensating avenue to the investors who have placed their money under an investment for a period of time while the later factor i.e. the risk factor is compensated by the market premium over the risk free opportunities. Founders The Capital Asset Pricing Model (CAPM) was pioneered by the four economists during the early 1960s. John Lintner, Jan Mossin, William Sharpe, and Jack Treynor developed the concept and thesis behind the model which was essentially used for describing security returns. The CAPM Equation and Assumptions The CAPM model comes at the expected return for an asset through the following equation: Expected Return (ER) = RF + beta [E(Rm) - RF ] Where, E(RM)= The return expected on the portfolio available in the market Beta = is the unit which measures the diversifiable risk of asset which is relative to the portfolio available in the market RF = Risk free rate of return As per CAPM, the expected return deriving from an asset would be the sum total of the risk-free rate combined with a risk premium. Risk premium in the model is represented by Beta [E(RM) RF] The CAPM has only one risk factor which is diversifiable, the risk represented by the movement of the overall related market. Beta measures the sensitivity which is inherent and related to the return which the asset provides to the return which is generated by the overall market portfolio. The other factor which comprise the risk premium in the model is the spread over the expected return provided by the market portfolio, E(R), and the return on risk-free investment. The risk premium is nothing but the incentive which an investor gets for assuming the risk prevalent in the market over and above the return which can be earned if an investor invests in an asset which provides a return which is risk-free. Taken as a whole, the premium of risk is the multiplication of the quantity measured as risk in market and the possible compensation for assuming the risk in the market. Assumptions of CAPM First Assumption: investment decisions are made by the investors on basis the return which is expected and deviation in these returns. Second Assumption: All the Investors investing are prudent and averse to risk. Third Assumption: All the Investors invest for an equal frame of time. Fourth Assumption: All the Investors have the expectations which are similar relating to return expected from the market and deviation of return on all these assets. Fifth Assumption: All the investors are capable of availing the risk free rate for lending and borrowing the fund in the market i.e. there is a presence of significant risk free rate which is free from risks. Sixth Assumption: All the Capital markets in the economy are perfectly competitive and runs smoothly First four assumptions represents the behaviour which an investor portray while making investing decisions while the remaining assumptions are related to the features prevalent in the capital market. Arbitrage Pricing Theory The (APT) model, suggests that there are multiple risk factors which influence an assets expected return. The APT model does not mention about the various risk factors which are present, however it assumes that their is a linear relationship among the returns generated by asset and the risk factors attached to it. Principle behind APT Arbitrage, simply speaking is the process where an asset is simultaneously bought and sold from two different markets at two different prices so as to generate gains by buying at a price which is lower in one market and simultaneously selling the same asset at a price which is higher than the price prevailing in the other market. This arbitrage rests on a basic principle of  nance which is known as the law of one price, which states that the payoff generated from an asset which could be created as a pack of assets should be equal to the payoff from the individual assets which forms the pack of assets and the price of individual assets combined together which forms the pack. And where there is a situation prevalent in the market which shows that the price of the pack of assets differs from that of individual asset which forms the pack with the same price, a prudent investors would transact in these assets in such a manner which would restore the price back to equilibrium. This mechanism in the market serves as the basic idea behind the APT model, and is discovered on the fact that a transaction of arbitrage does not show off the investor to any movement which is adverse in relation to the price which is present in the market for the assets transacted. Equation R = E(Rm) + Bi,1F1 + Bi,2F2 + + Bi,HFH + Ei where R = the return provided by the asset in question E(Rm)= the return which is expected on the asset Fh = the h-th factor that is common to the returns of all assets (h = 1, ..., H) i,h = the sensitivity of the i-th asset to the h-th factor Ei = the return which is unsystematic for the asset Consumption based Capital Asset Pricing Model (CCAPM) Consumption based Capital Asset Pricing Model is a model which determines expected asset returns. Robert Lucas and Douglas Breeden laid the foundations of this concept. As per this model, the return premium which is expected that an asset provides in relation to the risk-free investment is in sync to the covariance of the return which is linked with consumption. Instead of market beta which was used in the standard CAPM model, this model uses the consumption beta which is derived by the coefficient from a regression of an assets return on consumption growth. Thus, the central prediction of the CCAPM is that the premiums that assets offer are proportional to their consumption betas. The CCAPM equation (ER) = Rf + Beta [E(Rn) - Rf ] Where, ER= return which is expected on security E(RM)= The market return Beta = beta of consumption Rf = Risk free return Basic difference between CAPM and CCAP Under the CAPM model the investors, the factors which concerns the investor were the amount and uncertainty which is over the money they would get in future.The wealth of each investor is basically in perfect correlation with the return which is provided by the portfolio in the market, thus the demand for securities and other risky assets is arrived by the risk which is there in the market. While In the consumption CAPM, the uncertainty which is related to returns on security is in direct connection to the uncertainty which is related to consumption. Inter temporal Capital Asset Pricing Model (ICAPM) Inter temporal Capital Asset Pricing Model was founded by Nobel laureate Robert Merton in 1973. In this model the expected return of an asset is dependent upon its covariance with the portfolio which is present in the market and with static variables which act as a proxy for deviation which occurs in the set of opportunities in investment. This model is derived from the behaviour which is used by a random number of investors while making the selection of portfolio which as a result will maximize the utility which is expected over the consumption over the life and which can be traded consequently in a period of time. Exclusive functions of demand for each asset is formed, and it is depicted that, unlike the single-period model, the present demands are influenced by the probability of changes which are uncertain in the investment opportunities in the future. After the summation of demands and after the required clearing in the market, the relationships of equilibrium which is probable among the expected returns are arrived at, and in contrast to the standard CAPM, the returns which are expected from the assets which are risky might vary from the riskfree rate even when there is no market risk Dividend discount Model It is a model of valuation which arrives at the value of shares through the discounting of the dividend payments which would occur in future. This model derives the price which is also called the intrinsic value of the security. The model derived price of a security is the total of cash flows generated in future and which is discounted at the required rate of return which is demanded by the investor for the risk which he owns while investing in the stock. Future cash flows comprises of dividend payments and the proceeds of the security during its sale. The price derived is referred as intrinsic value. When the stock does not pay dividend, in that case the cash flows expected in future cash comprises the proceeds during sale of the stock. Stock Intrinsic Value = D1 / (1+Ke)1 + D1 / (1+Ke)2 + D1 / (1+Ke)3 +...... D1 / (1+Ke)n +Pn / (1+Ke)n Where, Pn = Proceeds from stock at the end of year n D1 = Dividend payment each year Ke = discounting rate n = Number of years until stock is disposed off There are 3 models used in the dividend discount model: a. No growth : this assumes a constant dividend payment for a stock. As there is no growth, the model has an assumption that the dividend payment always remain constant; the price of stock would be the dividends paid each year divided by the discounting rate or the required rate of return Securitys Intrinsic value = Dividend payments each year / discouting rate. b. Stable growth model :it assumes that dividends grow by a specific rate each year, the growth rate is presented as g and the discounting rate is denoted by k. Securitys Intrinsic value = D1/k-g D1 = dividend to be paid next year K = discounting rate g = rate at which dividend grows c. Variable growth model : This basically spreads the growth into different phases: a initial phase which is fast, followed by a transitional phase which is slower and finally ends with even a lower sustainable rate which sustains over a long time. Primarily, this is an extension of stable growth model where each phase of growth is calculated by the stable growth medium while using 3 varied growth rates for each phase. The present values for every phase are summed to arrive at the intrinsic value of the security. Equation (assuming growth rate becomes constant after 4 years) Stock Intrinsic Value = D1 / (1+Ke)1 + D2 / (1+Ke)2 + D3 / (1+Ke)3 + D4 / (1+Ke)4 + 1 / (1+Ke)4 x D5 / (Ke-g) Where, D1...D5 are variable annual dividend payments Ke = Capitalization rate g = constant growth rate Disadvantages and alternatives to CAPM Following are the points illustrating the disadvantages of Capital Asset Pricing Model: Beta as a measure of risk: As it uses standard deviation and variance as a measure which determines the risk, these measures do not take into account the factors which are regarded as the influencing factors for spreading the returns on the asset. It is basically a attack on the idea that the spread of return over asset returns shows a distribution which is normal. Reliability of Beta value: Beta which is arrived through statistic calculations might not be present for securities of many companies in the market. It might not be possible to estimate the cost of equity of those firms using this model. All limitation that is related to beta value also applies to the model. Limitation of assumptions: The behavioural assumptions underlying the model are not practical and this is not how an investor decides about the portfolio in the practical world. There are proofs that multiple risk factors affecting returns on assets are prevalent. Availability of Information: It is very difficult to collect significant information on prevailing risk free rates and the return which is expected from the portfolio in the market as there are various risk free rates in the market for a particular asset while for other asset, as the market is volatile, the risk free rate differs over frame of time. Other risks: By emphasizing only on market risk, it ignores other risks. While these ignored risks are also significant to stake holders who possess a portfolio which is not diversified Alternatives to CAPM Arbitrage Pricing Theory model: The pricing theory is framed basically from arguments revolving over the arbitrage. It portrays that the return which is expected on a stock or a portfolio is derived through the various factors. This theory substitutes the difficulty of discovering the market portfolio in the CAPM with the difficulty of selecting and computing the factors which are relevant. Accounting based measure of risk: This approach can be concluded as a model which derives beta of an asset from the flows of cash that are underlying or those which are linked to a particular security. To do so it demands an estimation of structure of cost flows and cash flows. The result will be a collection of inputs into the below equation, which like CAPM takes a rate which is risk free along with the factor which demands adjustments Equation Ri = Rf + [Em Rf] Y Where: Ri = rate of return which is required for a particular firm Rf = Risk free rate of return Em = Expected mean rate of return for all firms.. Y = The rate of return deviating factor for a particular firm in relation to all the firms. References com, (2016). ACCA global official website. [online] Available at: https://www.accaglobal.com/in/en/student/exam-support-resources/fundamentals-exams-study-resources/f9/technical-articles/CAPM-theory.html [Accessed 16 Mar. 2016].edu, (2016). American.edu website [online] Available at: https://www1.american.edu/academic.depts/ksb/finance_realestate/mrobe/Library/capm_Perold_JEP04.pdf [Accessed 16 Mar. 2016] us, (2016). 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