Financial Eco and Asset Pricing - Essay Example

The assumptions of preference in economics and finance suggest the typical ordering of different choices according to the relative utility offered by each of the alternative. It is however, important to note that these preferences follow certain axioms based on which the decisions of each individual area measured or evaluated. The violation of any of the assumptions therefore can suggest that the preferences are not valid. Three basic axioms based on which the decisions or choices made by the consumers are: 1. Completeness 2. Transitivity 3. Reflexive Completeness of the preferences suggests that the consumer can make a choice between the two alternatives whereas reflexivity of the choices suggests that each choice or preference is as good as itself. Transitivity of preferences suggests that consumer is able to make a choice between different alternatives and these choices are transitivite i.e. if choice A is preferred over choice B and B is preferred over C than A is preferred over C. The choices made by the investors therefore need to follow these axioms in order to make them rational. The assumptions of expected utility hypothesis suggest that out of different choices available to the individual investor, only those choices will be preferred which can offer the highest expected value. The use of the expected utility hypothesis is specially more meaningful under the uncertain risk environment because investors tend to chose those investments which offer the higher expected values. However, higher expected values are often associated with the higher risk also. Considering the above discussion, the different assumptions of the mean variance theory under the simple decision problem as well as on the market equilibrium model suggest that that at the given mean values, lower variance is preferred whereas at the given variance levels, higher mean values are preferred. Thus the assumptions of mean variance theory and analysis suggest that in any case the investor will be concerned with the mean and variance of his portfolio over the given period of time. The overall shape of the opportunity set however, depends upon the covariance of different assets in the portfolio. Properties of the indifference curve under the mean variance analysis are based on the assumption that the returns are elliptically distributed. Based on this, the optimal portfolio is constructed when the asset returns are tangential to the capital market line. Portfolios with higher returns will be tangential on the upper part of the capital market line suggesting that the higher indifference curves will lie where the overall standard deviation of the portfolio is lower and mean returns are higher. It is also implied from this analysis that for an individual investor, the optimal portfolio will lie on the CML in such a manner that his total wealth will be divided between the tangency portfolio and the risk free assets. The optimal portfolio however, is achieved where the slope i.e. the sharpe ratio is at the highest. In order to understand as to how the mean variance assumptions help to generate the market equilibrium, it is important to assume the homogeneity of the expectations held by all the investors. According to the two fund separation theorem, all the investors actually held the efficient portfolios and that the holding of risky securities is always done in the same proportion thus in order to generate the market equilibrium, it is important that the market portfolio is constructed by having the same portfolio weights. Under these assumptions the CAPM will therefore generate the market equilibrium in such a manner that the above equation provide the equilibrium relationship between the risk and return under the assumptions made under mean variance analysis and CAPM. 2) A model is always considered as good if it attempt to provide answers to the different emerging problems and help to sort them out. However, every model is based on certain assumptions under which the different propositions of the model work and if these assumptions are violated, it may become difficult for the model to accurately predict the behaviour as outlined in the model. The situation becomes more interesting when two models attempt to provide answer to the same problem or address the same issue. In such situation, the model with the simpler assumptions and more practical approach to solving the underlying problems is preferred over the model which is not so good. The Capital Asset Pricing Model was developed by taking into account the mean variance theory of Markowitz and attempted to address the problem of portfolio construction under the risk and uncertainty. The basic assumptions of this model are: 1. All investors are rational and risk averse with the sole aim of maximizing utility. 2. No investor can influence the price and all investors are price takers. 3. Returns are normally distributed. 4. Lending and borrowing can take place at the risk free rate. 5. There will be no transaction costs and taxation 6. Information is available to all investors at same time. The above assumptions therefore formulate the core of the model along with the assumptions of mean variance analysis. However, under certain conditions, these assumptions often fail to provide the desired outcomes and therefore can be misleading. The model assumes that the returns are normally distributed and only take the quadratic utilities into account. However, historically, it has been shown that the returns in the stock and other markets are not normally distributed. The large swings in the market i.e. where the returns show standard deviation of more than 3 from the mean, occur more frequently against the assumption that the returns are normally distributed. One of the key criticisms of the model lies in the assumption that investors can borrow and lend at the risk free rate of returns. This assumption is easily violated in the real world application as it is always almost impossible to borrow at the risk free rates in the market. This is often due to the fact that there are differences between the risk profiles of an individual borrower and the government and therefore lenders have to be compensated for the extra risk they assume while lending to the more risky investors. The behavioural portfolio theory suggests that individual investors tend to held many portfolios as against the assumption of holding one portfolio under CAPM. In reality, investors tend to hold the fragmented portfolios rather than holding just one portfolio. Further, CAPM assumes that all the investors held all the assets in all the markets and therefore there is a no particular preference for any market. This assumption is easily violated and also being explained by the Arbitrage Pricing Theory which tend to assume that the investors tend to prefer investing in such markets where the probability of gaining higher returns is more. Thus CAPM does not assume that the assets are inherently mispriced therefore all the investors tend to hold the same portfolio in the market equilibrium condition. It is however, important to note that APM is itself an inspiration of the CAPM and borrows heavily from the underlying assumptions of the CAPM. Some of the assumptions of CAPM and their practical implication however are critical for making portfolio decisions under the assumptions of uncertainty. Further, the critical difference between the two approaches also lies in the fact that APT is a supply side model whereas CAPM is a demand side model. 3) Capital Asset Pricing model is considered as an equilibrium model for asset pricing suggesting that the returns on a security are positively and linearly related with the sensitivity of the security’s returns with that of the market. It is an ex-ante cross sectional equilibrium model can only be defined at the equilibrium level. It is also important to note that CAPM is based on the assumptions of the mean variance analysis and the resulting market portfolio is always actually a deduction of the model. CAPM is a utility based model and builds on the expected utilities and the framework underlined in the mean variance analysis. It is a valuation model suggesting a linear relationship between the returns of the assets and the market risk premium. Essentially it measures the systematic risk i.e. the risk which cannot be diversified and is based on the risk inherent in the market itself. It is also important to understand that the CAPM attempts to measure the sensitivity of the individual security with respect to the whole market therefore standardized the covariance between the returns on an individual security and the market returns. Probably the greatest strength of the model is its ability to be forward looking model and also inculcate the future expectations in the returns. Essentially, CAPM suggests that the investors will be evaluating their portfolios based on the expectations of the returns and the standard deviation of the portfolio over one horizon period. This is however, can also be considered as one of the limitations of the model as it focuses on the one horizon period and ignores the multi-period holding. Another important weakness of this model is the fact that markets are relatively imperfect and not all the investors have access to the same information at the same time. Further, all the investors are not fully diversified and therefore the construction of an optimal portfolio for all the investors may not seem to be a realistic assumption under the model. Another important weakness of this model is that the beta of the security can change radically even during the same period therefore the valuation of the securities can be misleading. Further, the beta values are often sensitive to the historical time period used and therefore can significantly affect the decision making of the individual investors. Arbitrage Pricing Model however, is relatively different model and takes into account different factors. The asset returns are therefore the result of the different sources or influences into account in order to measure and define the returns on the assets. The key factors which outline the returns on the assets include the business cycle, overall time horizon, market timing risk, inflation and confidence. These five key variables combine together to influence the returns of the individual securities. In fact this model is also considered as the multi index model because it is applied to different market equilibrium conditions to the multi-index returns. The key difference between the two models is therefore based upon the assumption that the market portfolio plays no part in APM whereas in CAPM it is one of the central assumptions on which the model is based. CAPM assumes that returns follow a particular distribution i.e. normal distribution however, APM is not restricted to any particular type of distribution thus allowing it to suit the real world more appropriately as compared to CAPM. What is also significant to note that APM takes into account the arbitrage which is a realistic phenomenon in markets. Due to imperfection of the information, individual securities tend to be under and overpriced within same or different markets thus allowing the investors to take advantage of such opportunities. It is also important to understand that the APM deals with both the single factor and multi factor model and therefore is considered as effective in terms of ensuring that the asset returns capture the different risks associated with each of the factor while valuing the investments. The basic structure of the equation identifying the linear pricing equation under both the models is same outlining that both the models also share some common characteristics. Further, both, CAMP as well as APM, interpret the risk and return in same manner thus ironing out the relative anomalies in terms of interpreting both the variables in terms of their importance to the investors. CAPM tend to indentify the risk factors in advance however, they cannot be observed however, under APM, risk factors can be observed but they cannot be identified. Based on this, individual investors arrive at the equilibrium points in different manner i.e. under CAPM, the investor chooses the optimum however, under APM, the investor has to exploit the arbitrage opportunities in order to arrive at the market equilibrium. References Bailey, Roy (2005). The economics of financial markets. Illustrated. ed. Cambridge: Cambridge University Press. Read More