The Capital Asset Pricing Model - Report Example

Corporate Investment Analysis CAPM: Apple and Microsoft The capital asset pricing model (CAPM) is a pioneering model of asset pricing under uncertainty. First developed by a financial economist, William Sharpe (1964), later a winner of the Nobel Prize in economics, and Lintner (1965), the model establishes the link between risk and return on assets based on Markowitzs fundamental portfolio framework The model predicts that the expected return on assets is equal to the sum of the return on risk-free assets and the product of the beta of the asset and the expected return on the market portfolio. In his book published in 1970, Mr. Sharpe stated that investment is subject to two types of risk: systematic risk and unsystematic risk. Unsystematic risks , otherwise known as “specific” risks are unique to individual stocks and can be lessened through diversification – that is, as the investor increases his holdings in his portfolio, his risks diminish. On the other hand, systematic risks are those that cannot be diversified away because all investments are affected - by such factors, for example, as interest rates, inflation and recession. It is the systematic risk that is correlated with the movement of the general market. Diversification does not solve the problem of systematic risk, so that during recessions the general market may move south and along with it the individual stocks that compose that market. The CAPM formula which describes the relationship between risk and expected returns, is expressed by the following formula: E(Ri) = Rf + im (E (Rm) – Rf) Where: E (Ri) is the expected return on lthe capital asset Rf is the risk-free rate of interest im (the beta coefficient) the sensitivity of the asset to market returns Cov (Ri, Rm)  = ------------------ Var (Rm) E (Rm) is the expected return of the market R (Rm) – Rf is sometimes known as the market or risk premium (the difference between expected market rate of return and the risk-free rate of return). Statement of the Problem: Using the data provided consisting of 37 monthly prices from Jan 2000 to January 2003 of Apple Computers Corporation, determine the company’s beta coefficient. Solution Procedure. Firstly, it was not necessary to work out the solution manually as the Excel spreadsheet has the built-in computational capability to derive the cross-sectional regression line and formula. The increase from a previous month to the current month is computed in percentage terms, for both the DJIA and Apple, which are then placed adjacent to each other on the worksheet. Using the chart icon, we obtain the scatter diagram, the chart, and finally the trendline and formula. The linear equation that comes out for Apple Computer is y =l.253 – 0.0544, and R Square is 0.1278, for that inclusive period. (See attached table and equation box). This means that the beta coefficient is 1.253, the y-intercept -0544, and coefficient of determination, which tells us about the amount of systematic risk (very minimal here) inherent in the price movements of Apple. The beta of 1.253 is greater than 1.00, the benchmark for the market index DJIA, and this means that the stock is moving more aggressively than the market as a whole. It is more sensitive than the market.- it drops 25% more than the DJIA during the down market, and it rises 25% more than the index during the down market. In other words the stock is more risky than the average stock. The website http://finance.yahoo.com/q/cq?d=v1&s=AAPL+beta , particularly the Profile thereof, states, unfortunately, that Apple’s beta is not available. Item 10 :”BETA N/A N/A 0.00 0.00% 0 Chart, , More” The Microsoft beta also is not available (http://finance.yahoo.com /q/pr?s=MSFT) The 10 year Treasury Note is at 3.75% and this can be assumed as the risk-free rate. If the market rate of return is 12%, it means that the premium is (12-3.75) or 8.25%. In the absence of sourced data, let us assume that Microsoft has a beta of 1 (unity), it will show the following results by using the linear equation: Y = 3.75 + 8.25(1) = 12.00 For Apple Computer which has a beta coefficient of 1.253, the equation will be: Y = 3.75 + 8.25(1.253) = 3.75 + 10.33725 = 14.09% Thus Apple Computer will yield 14.09 % return when the market as a whole makes 12%. Why are betas different? Betas differ to the extent that they are sensitive to the movements of the market index such as the Dow Jones Industrial Average. Companies with a beta of greater than 1 are considered relatively aggressive, those with betas of less than 1 are defensive, while those than move in tandem with the market with 1 are considered neutral. As between two companies, their betas differ because they are subject to different unsystematic risks – risk that are specific to the company and its industry, the risks it faces as it operates as a going concern. A lot of events – such as the discovery of a new product that becomes popular with the consumers, a marketing program that fails, corporate fraud, and many others – are unique to particular company and does not partake of the macro factors that affect the economy as a whole, factors that move the general market as represented by the market index. It is only through diversification that the unsystematic risks are reduced, if not eliminated. A specific company may have different betas depending on the method used in computing it. For example, if the market proxy were the NASDAQ (which should be more appropriate here because both Microsoft and Apple are NASDAQ stocks), the beta figure will be different. Also different results would emerge if the NYSE Composite Index, or the S&P 500, or the Wilshire 5000 were used. Another reason is the length of historical data used as well as the time interval (weekly – used by Value Line, or monthly- used by Merrill Lynch). The adjusted tables and linear regression graph for the DJIA and Apple Computers are shown below: djia apple djia apple Date Adj. Close* Rtrn Adj. Close* Rtrn Adj.rtrn Adj.retrn 3-Jul 9,040.95 0.006178 19.09 0.001574 0.617777 0.157398 3-Jun 8,985.44 0.015274 19.06 0.061838 1.527413 6.183844 3-May 8,850.26 0.043652 17.95 0.262307 4.365166 26.23066 3-Apr 8,480.09 0.061055 14.22 0.005658 6.105506 0.565771 3-Mar 7,992.13 0.012806 14.14 -0.05796 1.28056 -5.79614 3-Feb 7,891.08 -0.02021 15.01 0.045265 -2.02053 4.526462 3-Jan 8,053.81 -0.0345 14.36 0.002094 -3.4504 0.209351 2-Dec 8,341.63 -0.06233 14.33 -0.07548 -6.23263 -7.54839 2-Nov 8,896.09 0.059433 15.5 -0.03547 5.943292 -3.54698 2-Oct 8,397.03 0.106047 16.07 0.108276 10.60468 10.82759 2-Sep 7,591.93 -0.12369 14.5 -0.01695 -12.3688 -1.69492 2-Aug 8,663.50 -0.00837 14.75 -0.03342 -0.83671 -3.34207 2-Jul 8,736.60 -0.05482 15.26 -0.13883 -5.48181 -13.8826 2-Jun 9,243.30 -0.06871 17.72 -0.23948 -6.87133 -23.9485 2-May 9,925.30 -0.0021 23.3 -0.03997 -0.21013 -3.9967 2-Apr 9,946.20 -0.04399 24.27 0.025349 -4.39931 2.534854 2-Mar 10,403.90 0.029467 23.67 0.090783 2.946735 9.078341 2-Feb 10,106.10 0.01876 21.7 -0.12217 1.876008 -12.2168 2-Jan 9,920.00 -0.01014 24.72 0.128767 -1.01381 12.87671 1-Dec 10,021.60 0.017256 21.9 0.028169 1.725608 2.816901 1-Nov 9,851.60 0.085564 21.3 0.212984 8.55638 21.29841 1-Oct 9,075.10 0.025713 17.56 0.132173 2.571319 13.21728 1-Sep 8,847.60 -0.11078 15.51 -0.16388 -11.0776 -16.3881 1-Aug 9,949.80 -0.05445 18.55 -0.01277 -5.44532 -1.27728 1-Jul 10,522.80 0.001942 18.79 -0.19183 0.194241 -19.1828 1-Jun 10,502.40 -0.03753 23.25 0.165414 -3.75278 16.54135 1-May 10,911.90 0.016479 19.95 -0.21734 1.647881 -21.734 1-Apr 10,735.00 0.08667 25.49 0.154961 8.667045 15.49615 1-Mar 9,878.80 -0.05874 22.07 0.209315 -5.87406 20.93151 1-Feb 10,495.30 -0.03601 18.25 -0.15587 -3.60141 -15.5874 1-Jan 10,887.40 0.009214 21.62 0.452957 0.921394 45.2957 Dec-00 10,788.00 0.035863 14.88 -0.09818 3.586346 -9.81818 Nov-00 10,414.50 -0.05073 16.5 -0.15644 -5.07333 -15.6442 Oct-00 10,971.10 0.030063 19.56 -0.24039 3.006319 -24.0388 Sep-00 10,650.90 -0.05031 25.75 -0.57745 -5.03072 -57.7453 Aug-00 11,215.10 0.065872 60.94 0.19937 6.587151 19.93702 Jul-00 10,522.00 0.007092 50.81 -0.02997 0.709233 -2.99733 Jun-00 10,447.90 -0.00707 52.38 0.247143 -0.70707 24.71429 May-00 10,522.30 -0.01971 42 -0.32291 -1.97132 -32.2908 Apr-00 10,733.90 -0.01721 62.03 -0.08659 -1.72131 -8.65852 Mar-00 10,921.90 0.078355 67.91 0.184959 7.835471 18.4959 Feb-00 10,128.30 -0.07424 57.31 0.104665 -7.42379 10.46646 Jan-00 10,940.50 51.88 REFERENCES Brealey, RA, Myers, SC & Marcus, AJ, (1995). Fundamentals of Corporate Finance, , Boston, Mass: McGraw-Hill Hirt, GA, & Block, SB (1987). Fundamentals of Investment Management, 2nd ed, Homewood IL: Irwin, Meir. S, “Betas compared: Merrill Lynch vs. Value Line,” Journal of Portfolio Management 7, no. 2, winter 1981, pp. 41-44. Van Horne, JC (1983). Financial management and policy, 2nd ednEnglewood Cliffs, NJ.: Prentice-Hall, Read More