Investment Risk and Return: Concept Analysis - Essay Example

? CAPM ANALYSIS By Investment risk and return: Concept Analysis In 1929 stock market crash, investors in today’s money, lost $319 billion dollars (Time U.S. 2008). The Black Monday of 1987 was the largest one-day market crash in the history. On October 19, 1987, Dow lost 22.6 % of its value or $500 billion dollars (Stock Market Crash n.d.). On September 28, 2008 CNN reported, “The day's loss knocked out approximately $1.2 trillion in market value, the first post-$1 trillion day ever (CNN Money 2008 p. 1).” The above facts explain that investment in the security market is associated with the risk; sometime its magnitude is no less than the worst volcanic eruption or earthquake. The consequences of financial crashes create enormous damage in individuals’ plus country’s economic condition. Nevertheless, people keep investing in the security market. The primary reason is the opportunity of getting a good return from the security market. For example, during 1992 – 2011, the average of returns of the S&P was 9.6 % (Forbes 2012). Regardless of stock market crashes many investors believe that leaving money in the high-yield saving accounts is not an investment at all. Nevertheless, investing money in the security market involves a significant amount of risks. The return of an investment is a function of risks; lower the risks lower the return, and higher the risks higher the return. Return (y) y = a + mx a Risk (x) Figure1. Conceptual equation of Risk-Return, y =a +mx Return and risk relationship at the conceptual level can be represented through a straight line shown in figure 1. The algebraic equation of this line is y = b + mx … ………..Equation 1, where, “y” – is return and “x: – risk; “a” is the intercept, which shows return at zero risk, and “m” is the slope, which represents risk premium return. An investment may encounter market risk, default risk, interest rate risks, liquidity risk, and political risks (Forbes 2012). These risks make an impact on the return of an investment. The capital asset pricing model studies the impact of risks on the return of an investment. CAPM: Concept analysis Markowitz used the asset-pricing concept as an investment instrument. Investment instrument is an asset that can be can be bought and sold (Washington.edu n.d.). Markowitz also developed the concept of security portfolio. William Sharpe and John Lintner are the authors of the capital asset pricing model (CAPM); the model is based on the asset-pricing theory (Fama & French 2004), and Markowitz’s portfolio selection concept. Morkowitz model assumed that all investors were risk averse, and they chose mean variance efficient portfolios (Washington.edu n.d.). That is why; his approach is called mean variance model. Sharpe added two assumptions to this model to determine a mean-variance efficient portfolio from the security market. To understand the concept of mean-variance efficient portfolio, first we need to understand the concept of capital market line (CML). We use the graphical display of figure 1 to demonstrate the CML concept. We change the x-y axis plane to ? – E (r) plane. Figure 2. CML equation, E (r i) = r f + [{E(rM ) – rf } / ?M] x ? (Fama & French 2004). The axis ? is the level of risk or standard deviation of the portfolio, and E (r) is the expected return of the portfolio. The equation y = a + mx is changed according to the new coordinate system and expressed as E (r i) = r f + [{E(rM) – rf } / ?M] x ? ……………………………………. Equation 2. In the equation 2, the intercept rf denotes risk free return, and the slope [{E(rM – rf) / ?M] denotes market price of risk. On the ? – E ( r) plane, a curve is drawn (See Figure 2), which is called minimum variance frontier (Fama & French 2004). A tangent to this curve is drawn from the intercept rf. This straight line is called capital market line (CML), which is the mean-variance frontier with the risk less assets (Fama & French 2004). The point, where CML touches the curve is called the market portfolio, and on the ? – E (r) plane it is denoted with M (The Capital Asset Pricing Model n.d.). Thus; ?M is the market portfolio standard deviation, and rM its corresponding return. The curve is also called as efficient frontier, and the straight line is called the efficient frontier with risk less assets. The CML depicts the risk-return relationship of a portfolio, and its risk is measured in terms of standard deviation on the portfolio (Fama & French 2004). How this concept can be transferred to a single asset? In figure 2, the tangent to the curve is denoted as the market portfolio, M. If this portfolio is efficient, then expected return of an asset ri satisfies the equation ri – rf = ? x [E(rM-rf)], which gives a new equation ri = rf + ? x [E(rM-rf)] …………………………. …………………………… Equation 3. The equation 3 resembles the straight-line equation y = a + mx. Thus, equation 3 can be plotted on r – ? plane. The parameter ? of the equation is expressed as ?i = ?iM/ ?2M = Cov (ri, rM)/ ?2M. It should be noted that ? indicates volatility, and ?2 variance. The straight line represented by the equation E(ri) = rf + [E(rM) – rf] x ? is called security market line or SML (See Figure 3). This straight line illustrates the market risk versus return of the entire market at a certain time (The Capital Asset Pricing Model n.d.). Conceptually the SML equation demonstrates the relationship between expected return and covariance of asset i. For CAPM equilibrium condition, any asset should appear on the SML. The model emphasizes that expected return of an asset is a function of its covariance with the market portfolio. The above discussion states (The Capital Asset Pricing Model n.d.): Figure 3. SML equation, E(ri) = rf + [E(rM) – rf] x ? In the CML, risk is measured by ? In the SML, risk is measured by ? CML relates to a diversified portfolio SML relates to single asset CAPM : Application analysis The aforementioned study established that CAPM originated from Markowitz’s portfolio theory. The portfolio theory served as the base for the CAPM that enhanced Markowitz concept of the efficient frontier with portfolio diversification (Washington.edu n.d.). The practical application of the CAPM is presented in the following explanation. On can restrict to low-risk securities; however, such an investment will produce low profit. On the other hand, one can make a smart combination of high risk and low-risk securities in the portfolio so that some of the securities fluctuations cancel each other out. In the statistical term, this indicates searching for combined standard deviation that is low relative to the individual securities’ standard deviations. The application of this method should produce a high average rate of return, with less harmful fluctuations. The figure 4 Figure 4: Efficient Frontier ( Moneychimp a n.d.) illustrates the above description through the efficient frontier curve (Moneychimp a n.d.). The efficient frontier curve defines a region, which is bounded by an upward sloping curve. Based on historical data, for example, S & P 500 stocks, return rates and standard deviations can be obtained, which can be plotted to achieve efficient frontier like of figure 4. It is clear that one would like to choose securities those lie up along the efficient frontier, rather than lower down of the interior region. Portfolios those lie below the efficient frontier line and cluster to the right of the efficient frontier line are called sub-optimal (Investopedia n.d.). Those securities lie below do not provide enough profit for level of the risk, and those securities cluster to the right have a higher level of risks for the rate of return (Fama & French 2004). Thus, securities those rest up along the efficient frontier are the best for the portfolio. At the same time, the curved shape of the efficient frontier allows to imply diversification. Investor develops a portfolio that consists of the highest possible distribution of securities those exist on the efficient frontier in combination with the risk free security. This can be obtained using the Sharpe ratio (Moneychimp b n.d.). The concept of the Sharpe ratio is illustrated in figure 5. Sharpe ratio is a slope, represented by the equation, S(x) = (rx - Rf) / ? (x). In this equation, x – is an investment, and rx is the average annual return; Rf is the return of the risk free security. Graphically the Sharpe ratio is the slope of the straight line drawn from the Rf, which is a tangent to the Figure 5. Sharpe ratio ( Moneychimp b n.d.). efficient frontier. Now, the figure displays that a portfolio with some investment “x” along with a risk free investment is a straight line, and the highest slope of the straight line is a tangent to the efficient frontier curve (Moneychimp b n.d.). The practical application of this concept rests in finding of an investment that evaluates the highest possible Sharpe ratio. After that applying liner combination of this investment and risk free investment desired standard deviation value is achieved. The result offers the portfolio with highest possible return (Moneychimp b n.d.). The practical application of the efficient frontier and Sharpe ratio expresses asset prices in the market through a liners relationship (Moneychimp b n.d.); Expected rate of return on a security = Rate of risk free investment + (Volatility of a security, relative to the asset class) x (market premium) = ri = rf + ? (rm-rf) ………………………………………………………………Equation 4. The equation 4 demonstrates that investors are risk averse, and that is why they seek risk premium to invest in risk assets. Total risk consists of systematic and unsystematic risk; however, diversification in the portfolio may help in avoiding unsystematic risk. Since the systematic risk is unavoidable, market tends to compensate it. The level of systematic risk is compensated with the use of ? coefficient. CAPM: Practical application The CAPM has implications for (Tutors on Net n.d.): 1. Risk-return relationship for efficient portfolios 2. Risk-return relationship for an individual asset or security 3. Identification of under and over-valued assets 4. Pricing of assets yet to be traded in the market 5. Effect of leverage on cost of equity 6. Capital budgeting decisions and cost of capital, and 7. Risk of the firm through diversification of project portfolio. The practical application of the model is influenced by the value of the ?, which is derived using regression analysis of the market portfolio and a single security. It depicts tendency of security’s return responding to market swing. The value of ? may be 1, more than 1 and less than 1. The ? value 1 indicates that the individual security price will move with the market portfolio. The security with ? value less than 1 implies that it is less volatile than the market while ? value more than 1 implies it is more volatile than the market. If the ? value of a particular stock is 2, it indicates that when market moves by 1%, the average return of that particular stock rises 2%, but when market falls 1%, that stock falls 2% (UK Essays n.d). Hence, this stock is more volatile compared to the market portfolio. On the contrary, when ? is 0.5, this security is 50 % less volatile than the market portfolio (UK Essays n.d.). The securities with ? > 1 are called aggressive assets, and ? < 1 are called defensive assets (UK Essays n.d.). Examples 1 (Fu-berlin-de n.d p 3 ): Given: Market portfolio = 13 % Risk free rate = 5 % ? = 1.2 Equilibrium return = 5% + 1.2 (13% - 5%) = 14.6 % This security lies on the SML, and it is overpriced Example 2 (Fu-berlin-de n.d p 6 ): Given: Portfolio consists of 40 % of R1, 60 % of R2. The ? of R1 = 1.2, and the ? of R2 = 1.8. The portfolio ? is defined from the following equation. O.4 R1 + 06.6 R2 = 0.4[Rf + 1.2 (Rm-Rf)] + 0.6[Rf + 1.8 (Rm-Rf)]= Rf + 1.56 (Rm-Rf). The ? of the portfolio is 1.56. Example 3: Company ? = 1.4 Rf = 5 % E[rM] = 13 % E[r project] = 5 % + 1.4 (13 % - 4 %) = 16.2 % = Cost of capital The project NPV and IRR will be calculated using 16.2 % cost of capital. Reference List CNN Money 2008, Stock Crushed, cnn.com., viewed on 12 April 2013, http://money.cnn.com/2008/09/29/markets/markets_newyork/ Fama, E.f., & French, K.R. 2004, The Capital Asset Pricing Model: Theory and Evidence, Journal of Economic Prospective, volume 18, number 3, pages 25 – 46, umich.edu., viewed on 12 April, 2013, http://www-personal.umich.edu/~kathrynd/JEP.FamaandFrench.pdf Forbes 2012, Four Risks of Investing. forbes.com., viewed on 12 April 2013, http://www.forbes.com/sites/moneybuilder/2012/06/15/four-risks-of-investing/ Fu-berlin-de n.d. Risk, Return, and Capital Asset Pricing Model, .fu-berlin.de., viewed on April 12 2013, http://userpage.fu-berlin.de/~ballou/cofi/mctest/test07.pdf Investopedia n.d., Definition of Efficient Frontier, investopedia.com., viewed on 12 April 2013, http://www.investopedia.com/terms/e/efficientfrontier.asp Moneychimp a n.d., The Efficient Frontier and Portfolio Diversification, moneychimp.com., viewed on 12 April 2013,http://www.moneychimp.com/articles/risk/efficient_frontier.htm Moneychimp b n.d., The Sharpe Ratio, moneychimp.com. viewed on 12 April 2013, http://www.moneychimp.com/articles/risk/sharpe_ratio.htm Stock Market Crash n.d., Black Monday – The Stock Market Crash of 1987, stock-market-crash-net., viewed on 12 April 2013 http://www.stock-market-crash.net/1987-crash/ The Capital Asset Pricing Model n.d., nyu.edu., viewed on 12 April 2013, http://pages.stern.nyu.edu/~ashapiro/courses/B01.231103/FFL09.pdf Time U.S. 2008, The Crash of 1929, times.com., viewed on 12 April2013, http://www.time.com/time/nation/article/0,8599,1854569,00.html Tutors on Net n.d., Capital Asset Pricing Model (CAPM), tutorsonnet.com., viewed on 12 April2013, http://www.tutorsonnet.com/homework_help/risk_and_return/capm_assignment_help_online_tutoring.htm UK Essays n.d., The Capital Asset Pricing Model, ukessays.co.uk., viewed on 12 April 2013, http://www.ukessays.co.uk/essays/accounting/capm.php Washington.edu n.d., Markowitz Mean-Variance Portfolio Theory, whashington.edu. viewed on 12 April 2013, http://www.math.washington.edu/~burke/crs/408/fin-proj/mark1.pdf Read More