The Capital Asset Pricing Model - Coursework Example

The Capital Asset Pricing Model Question 1 Return on investment is defined as the financial result for the amount of money invested. For example, if an investor decides to buys or invests in an asset costing $100 and later sells it for $120, the return on investment is $20. The rate of dollar return is often converted to ‘rate of return’ by finding the percentage or proportion represented by the return. In the example indicated above, a return of $20 on $100 invested will have a return rate of $20/$100, which is 20% or 0.2. Return is generally used to mean the ‘rate of return.’ Risks arise when the investors are not sure of the outcomes the investments will produce. Supposing that the investors are able to link a chance (probability) to every possible return that may arise, they can illustrate a distribution for the return on investment. Probability return is defined as the list of possible returns on investment in addition to the probability of every return. The expected return (Expected value of return) can be found by weighting the average of all possible returns on investment, using probability as the weights. That is, expected value of return E(R) is: Choose of a risk is not obvious in the case of probability of the value of return because any of the outcome might occur. Supposing that the investor is good forecasting, a single outcome would result from the share value. That means the case of probability distribution would not be needed. Risks are connected to the pattern of dispersion on the probability distribution. Greater risks are noticed when the distribution if more widespread and dispersed. Variance, absolute deviation, mean, and range are measures that have been introduced to represent the dispersion of the return or risks. The most accepted measure among the listed items is the variance. However, it is noted by many statisticians that standard deviation (the square root of variance) is a good platform when finding solutions for dispersion. Variance in the distribution of returns is defined as the measured average of squares of every return’s deviation in relation to the expected value of dollar return. The probability weights should also be applied in this instance. The formula below can be used to calculate variance: The importance of return and risks is that it allows the investors to note the investment that is risk averse using the portfolios with the same ‘values of expected return. After comparison and a proper analysis, investors can identify the investments that are risky but with high values of expected returns. In addition they decide to take on lee risky investments depending on the portfolio values. The following data can be used to understand the portfolio value and minim return and maximum risks in an investment. Changing in cells Transpose Solution Share (Solution) Share A B C D E F G H I J A 5% 5% 4% 0% 18% 0% 20% 0% 18% 6% 28% B 4% C 0% D 18% E 0% F 20% G 0% H 18% I 6% Portfolio portfolio Portfolio J 28% Variance SD Return SUM 100% 1.83% 13.51% 10%   Minimum Return   10%   Maximum Risk     Diversification can be used to reduce portfolio risks. Diversification involves holding groups (combinations) of instruments that do not correlate. These instruments should not be perfectly positively correlated. In simple terms, the investors may reduce the exposure to single risky shares (assets) by holding portfolio of shares that are diverse. The correlation coefficient is: Diversification may also help in indicating the same portfolio of expected return using a reduced risk instrument. Perfectly uncorrelated assets have pairs with 0 correlations. Portfolio return variance refers to the sum of all the assets of the held square fraction in an asset times the return variance of that asset. Question 2 Firstly, the calculations indicated in the excel spreadsheet has the following values that will help in analyzing this section: Portfolio Variance = 1.83% Portfolio Standard Deviation = 13.51% Portfolio Return = 10% Minimum Return = 10% In this model, Solver has been used to calculate the portfolio that will help the investors to maximize their expected return on shares invested. The condition that applies in this case is that the constraint is placed at the level where the standard deviation for the portfolio does not exceed 13.52%. The diagram below shows the effect of introducing a risk free asset. From the graph, possible combinations of risky shares, without any holds of risky-free shares have been plotted in the space indicating the risk-expected return. The correlation of possible frontiers has been defined in the free space. The hyperbola is indicated on the left boundary while the upper edge of the graph is known as the efficient frontier. The best possible returns can be found on the portfolios found in the efficient frontier space. Question 3 With the introduction of a risk free share in the model (graph) above, there will be changes in the efficient frontier space. More risks will be the outcome, thus the relation of shares that the investors should not invest in. The risk premium over SD will be 70.40% while the risk premium is 9.51% the efficient frontier line will shift to the left while the space will be smaller. The following table shows how the shares will be affected by introducing risk free asset. SD Rrturn 7.21% 1% 7.21% 2% 7.21% 3% 7.21% 4% 7.39% 5% 7.99% 6% 8.86% 7% Prop. In Prop. In 10.03% 8% Risk Free Portfolio 11.61% 9% 1 0.00% 4% 0% 13.51% 10% 0 100.00% 10% 13.51% 15.72% 11% -1 200.00% 16% 27% 18.14% 12% 74% 26% 6% 4% 20.71% 13% 23.40% 14% 26.17% 15% 29.38% 16% 33.15% 17% 37.30% 18% 42.73% 19% risk premium Risk premium over SD 51.42% 20% 9.51% 70.40% 61% 21% Question 4 Typical risk adverse investors tend to seek low risks while eying high returns on their invested assets. For risk adverse investors holding well-diversified portfolios, beta emerges the effective measure for individual risks in a security. Beta value is found at the efficient frontier point (in this case it is at 15% and 10% of the corresponding y and x axes respectively). Looking at the values of the variance and standard deviation of two stocks, risk adverse investors tend to go for portfolios that are less risky. Risk aversion does not necessarily mean that the investors will not accept to bear the risks. It means that they will regard risks as elements that are undesirable. However, the risks can be tolerated supposing that the expected value of return is worthwhile. That, is the expected return will be able to compensate the risks incurred. Question 5 The Limitations of the Approach There are three main limitations that relate to the approach used in this analysis. Firstly, there is the case of parameter stability. Parameter instability refers to the tendency of relationships between the variables to change with time depending on the market economies. There are other certainties that may also affect the stability of the parameter. For example, supposing that a mutual fund has been producing good expected returns in the history of the market, and technology was being used to steer the good returns, the model may not be relevant for small-cap and foreign markets. Secondly, public perception of the relationship may also be a step back in the efficiency of the model used in this report. Public dissemination may limit or reduce market effectives in efficient markets. The effective markets of future periods may also be affected by the effect of public dissemination on the model. Finally, relationships between the chosen parameters may be violated during the analysis. The variables used in the models are not realistic in their application in the real world. References Business Finance (nd). Risk and Return. Retrieved March 22, 2014, from http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CDkQFjAC&url=http%3A%2F%2Fhighered.mcgraw-hill.com%2Fsites%2Fdl%2Ffree%2F0070997594%2F918724%2FPeirson11e_Ch07.pdf&ei=5LktU7vWNaTT0QX2y4CoCw&usg=AFQjCNHHadgezKdMRC_iLJknxJlHl791rg&sig2=upypIY0vWL0NY4r3vsRQxA&bvm=bv.62922401,d.d2k Chambers, R., Donald (2014). The limitations of diversification return. Retrieved March 22, 2014, from http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10&cad=rja&uact=8&ved=0CHkQFjAJ&url=http%3A%2F%2Fwww.hec.ca%2Ffinance%2FFichier%2FChambers2014.pdf&ei=5LktU7vWNaTT0QX2y4CoCw&usg=AFQjCNFBxoh__-xCTPrGsonONF_ArKqAtg&sig2=c50akZBB0Tkm-K4zCJgfyg&bvm=bv.62922401,d.d2k Fama, E. F., & French, K. R. (2004). The capital asset pricing model: theory and evidence. Journal of Economic Perspectives, 25-46. Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (1988). A capital asset pricing model with time-varying covariances. The Journal of Political Economy, 116-131. Hansen, L. P., & Singleton, K. J. (1983). Stochastic consumption, risk aversion, and the temporal behavior of asset returns. The Journal of Political Economy, 91(2), 249. Read More