The Capital Asset Pricing Model - a Common Model to Measure an Assets Risk - Term Paper Example

PART A Relevant data/ information sources 1.0 Risk and return relationship and the portfolio return Executive Summary This report provides an overview of the expected return and risk of portfolios consisting of stocks for health sector industry listed on ASX, which are run from 2001 to 2014 as depicted in the excel. Firstly, the risk and return of the combined portfolio will be examined by applying Mean-Variance approach, followed by the portfolio analysis using the CAPM approach including the justification of data selection, information of the rationale and calculated results. Then, the recommendation will be provided with consideration of assumptions and limitations under the two approaches and analysing the results of the calculations. 1.1 Introduction Under perfect market, every signal investor have totally same information, capital for investment, and technological judgment, there is no arbitrage opportunity. The market equilibrium makes every investor has same market portfolio. Generally, the market portfolio is considered to be an effective portfolio. However, the estimation of systematic risk will be wrong, when the incorrect portfolio and market index are chosen (Roll, R, 1977). Also, the behaviour of market participant as the more important role affects market prices to be informationally inefficient .Risk and return of the combined portfolio is assessed by applying mean-variance approach, followed by the portfolio analysis using the CAPM approach including the justification of data selection, information of the rationale and calculated results. then, the recommendation will be provided with consideration of assumptions and limitations under the two approaches and analysing the results of the calculations. The relation between risk and return is that of an inverse proportion since, the higher the risk of a return, the high the returns and consequently, to capitalize on this and at the same time reduce the risk from the investment, an investor should consider holding a portfolio of securities. Component cost of capital is ideal in ascertaining the value of the firm since, cost of capital provides guideline o calculating the cost of equity as well as cost of debt and consequently the weighted average cost of capital. By doing so, it will be easier in concluding on whether to invest or not an investment project. CAPM A portfolio under Markowitz’s mean-variance framework] is characterized by the reward, measured by the expected return, and the risk, measured by the variance of return the expected return, which determines the reward of a portfolio, would be more likely to be maximized by investors. Historical data is collected as the basic information for further calculation The Capital Asset Pricing Model (CAPM) is a common model in modern finance as a measure of an asset’s risk. CAPM indicates that the expected return for a security is related to its beta. Beta is a measure of the systematic risk. This risk cannot be reduced and be avoided under any circumstances. In terms of CAPM, beta is simply the covariance of a security’s return with the return from the market portfolio. Their relationship can be normalized by dividing the covariance to the market variance PART B Literature Review on risk (beta) and return analysis 1. Calculation of Beta (β) Beta (β) is a measure of the sensitivity of the stock price relative to the change in the whole market. It measures the systematic (non-diversifiable) risk of a company relative to the market index (Manickaraj and Loganathan 2004). In calculating the beta, the company monthly historical data since January 2001 to 2014 are used. The specific time is chosen as to avoid any dramatic fluctuations in the company’s historical data because of Global Financial Crisis in 2008- 2009. A 51 months period of monthly data is believed to be sufficient to provide a reliable result that will represent beta (β). 1.2 Market Index All Ordinaries Accumulated Index is used as the market index represents 500 largest companies. Moreover, accumulation index is being used instead of the non-accumulated because it takes into account both price and return growth and assumes that dividends are reinvested back. The detailed monthly All Ordinaries Accumulated Index can be found in the excel workbook. 2.1 CAPM (Capital Asset Pricing Model) Analysis The capital asset pricing model can be defined as ‘a model for ascertaining the risk premium on a security. The model discloses that returns, which match to risks, are gained under the situation that the capital market upholds balance. 2.2 Hypothesis of this model The original capital asset pricing model is the hypothetical model in finance, which developed from Markowitz’s Mean-variance structure and hypothesis of market symmetry (Steinbach, 2001). It is predictable that model share the most of hypothesis of the original MV approach; together with the CAPM own assumptions. The assumption of the CAPM model is as follows a. Can provide and have a loan of infinite amounts under the risk free rate of interest. b. Have similar analysis of the best likely capital allotment line. c. Have similar and only one time horizon. d. There are no transaction costs. e. Accessibility of information on a timely manner. f. Deal with securities that are all highly separable into little correspondence. The assumptions above point to: firstly, investors are coherent and generally diversified across a variety of venture. Secondly, the capital market works completely with no market resistance. Thirdly, there is equability in interest rates of lending and borrowing. 4.1Time horizon of sample For the capital asset pricing model, in the frequent observation of judgment beta, 5-year data is employed. The study point out that capital asset pricing model executes is better over short periods in relation long periods.( T Bos, P Newbold, 1984), since adjustment of managerial plans and business over 10 years cycle may lead to an unrelated and imprecise beta (Bradfield 2003). Consequently, a 5-year-period from April 2008 to March 2013 is preferred. 4.1.2. Interval of sample The monthly data are suggested when approximating beta based on CAPM (Bartholdy and Peare, 2001). As explained previously in MV part, employing monthly data over a long period (2001-2014) will reduce the unfairness and provide an extra precise universal image of the entire venture assortment. 4.1.3. Market index All Ordinaries Index that are usually recognized as market index and entails roughly 97.7% of market capitalisation, covers a parcel of 500 stocks (Frino 2009). Even though, there is additional market alternative, such as the S&P/ASX 200 accumulation Index as well as S&P/ASX 200 Index, which are extremely accepted. The entire Ordinaries Index does not overlook the dividends paid through not taking the dividends into contemplation when giving the index. Consequently, the All Ordinaries Index corresponds to market index. 4.1.4. Risk-free rate For ascertainment of beta of capital asset pricing model, the risk-free rate ought to be firstly concluded. Normally, the government bond is constantly chosen as implicit zero risk asset when scheming beta and pricing capital (Frino, 2009). There are numerous diverse classes of bonds, such as 5-year, 10-year, and 30-year. On the other hand, the 10-year government bond rate is the majority and as well suitable since it is less sensitivity to unanticipated change in price rises (Campbell & Viceira, 1998). Bowman (2001) also said that “the most frequently used assessment in Australia is based upon the ten-year risk free rate of Government bonds, which depicts a small risk venture.” consequently, 10-year government bonds are employed as a appraisal of the risk-free rate. Calculation of beta There are two distinct kinds of risks acknowledged in the CAPM. The unsystematic risk and systematic risk According to Frino, Hill and Chen (2009, p.173), unsystematic risk is ‘the change in the value of a security which consequential from an occurrence explicit to the security. Systematic risk is ‘the change in the value of a security which is determined by extensive market connected factors’. It therefore implies that, unsystematic risk can be eradicated by an adequate diversified venture; therefore, investors cannot be acceptable a risk premium for the risk. In dissimilarity, systematic risk can be get rid of by an enough diversified speculation; consequently, some risk premium can be provided for investors as reimbursement. Beta coefficient is the tool of appraisal for the systematic risk of securities, which determines the volatility of an entity share or stock portfolio. Beta coefficient is a regression coefficient that can be computed from past data. Essential prescription: = = Which means the coefficient a=0, beta is given by: Where: =the dividend over the holding every 6 months \ = closing price at month t; Pt-1 = closing price at month t-1 = index level at month t; It-1 = index level at month t-1 = the return on stock I, earned over period t = the risk-free rate of return = the market rate of return =the number of periods (n = 60 in this case) PART C Discussion on the results in the light of literature on the issue Interpreting the Beta of individual stock return Graph of Portfolio Combination The graph below shows a positive relationship between portfolio beta and the expected return in a growing market, where beta indicates the relationship between stock and market. The analysis is concluded at by using the Mean Variance Analysis. The analysis is developed by Markowitz (1952). It is recognized that every rational investor, at a certain level of risk, will accept only the largest expected return, or the lowest level of risk with a certain expected rate of return. Under this approach, expected returns and risks is calculated based on the historical returns. The calculated results of the portfolio return and standard deviation represent the investment return and risk (Ross, Westerfield, and Jordan 2008).The assumption of the model holds that Assumptions: Based on the rules and principles of Mean Variance Analysis, there are several assumptions. a. The return and risk is calculated using historical performance, therefore, the historical data could correctly reflect the future performance of the assets (Frino, Hill and Chen 2009). b. Frino, Hill and Chen (2009, p160) also state that the sample collection of historical returns represents a random draw from ‘an underlying distribution of returns’. c. Investors are rational and risk-averse. They would choose a portfolio asset traded effectively to maximize returns or minimize risks (Franco and Gerald 1974). d. There is also a ‘homogeneous expectation assumption’ (Markowitz 1952). It is assumed that all investors are holding similar expectations in respect to return, variance and covariance. e. Investors are price takers. f. The capital market is a perfect market where conditions are assumed to meet perfect competition. Analysis of the expected return and portfolio beta In terms of mean-variance approach, portfolio investment with low Beta and high return is recommended by the calculated results as depicted by the above graphic presentation. Under this weight, the investment expected return is 0.38% per month and the risk is 0.156%. According to Markowitz (1952), portfolio theory assumes that a portfolio, which gives both maximum, expected return and minimum variance, is commended to the investor. However, in practice application, the portfolio with maximum expected return is not necessarily the one with minimum variance. There is a rate at which the investor can gain expected return by taking on variance, or reduce variance by giving up expected return. Based on the assumption which is that investors are rational and risk averse, it is recommended that investors should choose the portfolio with the minimum variance and relatively higher return as observed from the excel work attached This could be seen in the figure in which the curve reaches the point with smallest level of risk. The equally weighted average beta and equally weighted average return Table: Risk-Return Matrix     Based on Mean Security Return   Mean =     High Low Total Based on Mean High 0.63 0.3714 1.0014 Security Risk (Beta) Mean= Low 0.3714 0.63 1.0014   Total 1.0014 1.0014       Based on Market index return =       High Low Total Based on Market Risk (Beta) =1 High 0.8346 0.1534 0.988 Low 0.1534 0.8346 0.988   Total 0.988 0.988   From the above risk-return matrix, it can be depicted that the security risk (Beta) has an high value of 0.63 which below the industrial market Beta of 0.83.In this regards under high risk of the individual companies returns the weighted risk for the companies is minimal in relation to market implying therefore investment in health sector will be an ideal investment as depicted by high risk situation. At the same time, under a low risky situation of the firm, it depict 0.37 while the market risk is 0.15.in this regards, the market risk provides a suitable risk measure implying that risky situation of the firm underflow risky situation is highly. It implies therefore that investment in health sector is risky since; many companies are investing heavily and spending huge capital in form of investment hence implying that investors are risk averse. Under CAPM rule, a rational investor wills investment in venture that will provide maximum returns inform of profit with low risk on return. Comparison of the portfolio beta and returns and individual companies’ beta and returns based three different times Market returns Individual stock Returns Total Weighted Beta 12/1/2007 39.36 23.670 153.49 12/1/2009 29.20 83 35.33 12/1/2014 63.15 66.14 113.93 From the above comparison of stock return as beta for market and individual return depict that individual stock returns is much as higher as compared to returns of the market. The interpretation is that investment in healthy sector is a viable venture since investors will realize returns inform of profit much as compared to market returns and performance. The beta of the individual company’s return is high as compared to market beta hence implying that the venture proposal is risky in terms of volatility as a result, an investor considering investing in this risky venture with high returns should consider holding a portfolio of returns in order to diversify the risk. The capital asset pricing model provides that a rational investor should consider investing in that risky venture with high return as well as low component cost of capital in order to maximize the investment opportunity. The above comparison depict that investment in healthcare is a risky venture with high returns and thus it is a good opportunity for investors. In contrast with the risk free rate, which is 3.51% annually in 2013, the portfolio return exceeds the risk free assets’ with minimized risk, therefore it is still recommended. However, with the consideration of rationale and limitation of this approach, the return calculated fail to consider systematic risk and the measure of risk is also questionable. As a result, it is suggested to use CAPM analysis to decide portfolio investing. As shown in excel, the weighted expected return of Market and individual fir57.6 and ms 43.9 respectively. The betas of Market and individual firms are 0.113 and 0.153 respectively. As shown in graph of portfolio combinations, there is a positive linear relationship between beta of the portfolio and its expected return. After calculating with CAPM approach in excel, the expected returns of Market and individual firms become 0.024% and 0.0276%. As the average risk premium is positive (0.0418%) and the average risk free rate is 0.0089%, the individual firms, which have a higher beta (0.153) gives a higher expected, return (0.0276%). According to the CAPM theory, the relationship between beta and market sensitivity is positive. This indicates that a higher beta gives a higher risk. When choosing an optimal portfolio in this report, the one with the lowest standard deviation should be considered. Therefore, portfolio with the lowest standard deviation/risk (0.0576326) is the one we considered as the optimal one. There are two reasons why we choose the portfolio as an ideal investment strategy. Firstly, as the expected return of market is 0.024% ,the expected return of market after using CAPM formula in excel is 0.0276% This indicates that the true value of market stock is underestimated; hence the weight of market in a recommended portfolio should be relatively higher, which is 60% above average to minimize investment risk. Secondly, the fluctuation of the expected return of different portfolios is very small. The maximum expected return is 0.000500479 and the minimum one is 0.000488942. Therefore, we can consider the expected returns are almost the same in different portfolios. So at a given level of return, the minimized risk investment in this report should be recommended Conclusion In CAPM, beta is an important indicator that measures the systematically risk of stock. But is beta accurate enough to explain expected return? In early stage, most the empirical research can support CAPM. Sharpe (1972) would be the first one who showed the expected return and beta are followed by liner relationship. Black, Jensen and Scholes (1972) also provided the same conclusion. In the real world, investment happens not only in one period, it can be affected by many time horizons. According to Merton’s (1973) statement, investing behaviour should be an inter-temporal capital allocation. CAPM approach normally measures only in one time horizon, so the result accuracy will be affected. Reference List Anagnostopoulos, K. and Mamanis, G. 2013, ‘Using Multiobjective Algorithms to Solve the WEsDiscrete Mean-Variance Portfolio Selection’, International Journal of Economics and Finance, Vol. 2, No. 3, viewed 27 April 2013, Questia Trusted online search. Arnold, Glen (2005). Corporate financial management (3. ed. ed.). Harlow [u.a.]: Financial Times/Prentice Hall Ltd, pp. 354. Black, Fischer, Michael C. Jensen and Myron Scholes, 1972, The Capital Asset Pricing Model: Some Empirical Tests, in Studies in the Theory of Capital Markets, Michael C. Jensen, ed, New York: Praeger, 79-121. Blake, T. 2005,The Bootstrap Theorem: Creating Empirical Distributions, Fundamentalfinance.com, viewed 26 April 2013, Blume M. 1971, ‘On the Assessment of Risk’, The Journal of Finance, Vol. 26, No.1, pp1-10. Bos, P. and Newbold, J. 1984, An empirical investigation of the possibility of stochastic systematic risk in the market model, Business, vol 57, pp. 43-41 Bowman, R.,2001, Estimating the Market Risk Premium: The Difficulty with Historical Evidence and an Alternative Approach, JASSA, 3, pp. 10-13. Bradfield D. 2003, Investment basics on estimating the beta coefficient. Investment Analysts Journal. , vol 57, pp. 47-53 Read More