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Merrill Finch Incorporated is a large financial services corporation. As a newly hired financial planner for the company, I have been assigned the task of investing $100,000 for a client. The investment alternatives have been restricted to five options: T-Bills, High Tech, Collections, U.S. Rubber, Market portfolio, and a 2-Stock portfolio.
The economic forecasting staff for Merrill Finch developed probability estimates for the state of the economy, and the security analysts have developed software to estimate the rate of return on each of these alternatives under each state of the economy. A chart showing the results of the analysis is in Appendix A of this report.
Section 1 of this report begins with a discussion on the concept of Return. The calculations of each of the alternatives expected rate of return are also calculated and discussed. Section 1 then continues with the concept of Risk. Three different measurements of risk are discussed and calculated for each of the investment alternatives. The risk measurements discussed are the Standard Deviation, Coefficient of Variance, and Beta Coefficient.
Section 2 discusses some scenarios of different investment options. The first is of a 2-stock portfolio consisting of the investment of $50,000 into both High Tech and Collections. The expected return, standard deviation, and coefficient of variance are then calculated and discussed for this option. The second scenario is of a portfolio consisting of randomly selected stocks. The section concludes with a discussion of the risk involved with this random portfolio and how the addition of more random stocks to the portfolio would affect the risk.
Section 3 discusses the Security Market Line (SML) Equation and how the SML would be affected if inflation expectations were to rise by 3 percentage points. Appendix B shows this equation and its use to calculate the required returns of each of the investment alternatives. The section is then concluded with a discussion of these calculations and how they compare to the expected returns calculated in section 1.
Due to time constraints, probability distribution graphs for High Tech, U.S. Rubber, T-bills, and a portfolio of randomly selected stocks has been omitted from this report.
Return is defined as the income that an investment provides in a year. When deciding on what type of market to invest in, it is wise to first look at each markets expected rate of return. The expected rate of return of an investment is the weighted average of the probability of all possible results. The expected rate of return of various investment options are shown in Appendix A of this report on page 6. For each option, the expected rate of return is calculated by multiplying the probability of the state of the economy by the corresponding estimated rate of return for that market, then taking the sum of these values.
One of the invested alternatives for Merrill Finch’s client is Treasury Bills, or T-bills. These are a form of treasury securities issued by the United States Treasury. T-bills are said to be a risk-free investment, but in realty, there are no true risk-free securities. In regards to default risk, T-bills are risk-free because the Treasury must redeem them. Being that they must be redeemed, also shows that they are independent of the state of the economy. They are, however, susceptible to other forms of risk. If the rates were to increase or decrease, T-bills would then be susceptible to reinvestment rate risk, the risk that they might not be able to be reinvested at the same rate. For this investment, the expected rate of return on T-bills is calculated to be 5.5% .
High Tech and Collections are two other investment alternatives for the client. The expected rate of return is 12.4% for investing in High Tech and 1.0% for Collections. Investors might choose to invest in one of these two depending on how well they predict the economy will do. High Tech has a direct relationship with the movement of the economy. If the market is expected to increase, then this would be a good investment. Collections, however, moves in the opposite direction of the economy. If a decline is expected, then investors would use this as a hedge against the negative movement of the economy.
The remaining alternatives for this client are to invest in U.S. Rubber, a market portfolio, and a 2-stock portfolio of High Tech and Collections. The expected rates of return are 9.8% in U.S. Rubber, 10.5% in a market portfolio, and 6.7% in the 2-stock portfolio.
RiskAs we have already discussed above, no securities are truly risk-free. Depending on the nature of the investment, the type of investment risk will vary. The following sections discuss some of the different types of measurements that can be used to determine the amount of risk in an investment.
•Standard Deviation. The standard deviation (σ) is defined as a statistical measure of the variability of a set of observations. The smaller the standard deviation, the lower the risk of the investment. It is calculated by taking the weighted average of the deviations from the expected value. This provides an idea of how far above or below the expected return the actual return is likely to be. The type of risk measured by the standard deviation is Stand-Alone Risk, which measures the undiversified risk of holding an individual asset. For this investment analysis, the standard deviation for T-bills is 0% , 20% for High Tech, 13.2% for Collections, 18.8% for U.S. Rubber, 15.2% for a market portfolio, and 3.4% for the 2-stock portfolio.
•Coefficient of Variance. The Coefficient of Variance (CV) is a standardized measure of the amount of risk per unit of return. It is calculated by dividing the standard deviation by the expected return. The larger the CV, the riskier the investment. It is a better measurement of Stand-Alone risk than the standard deviation. This is because it includes the effects of both risk and return and allows for a closer evaluation of situations where investments have substantially different expected returns. This investment analysis shows the CV for T-bills to 0, 1.6 for High Tech, 13.2 for Collections, 1.9 for U.S. Rubber, 1.4 for a market portfolio, and 0.5 for the 2-stock portfolio.
•Beta Coefficient. The Beta Coefficient a measurement of Market Risk. It shows the extent to which a given stock’s returns move up and down with the stock market. The Beta of an average stock is 1.0, but most have betas in the range of 0.5 to 1.5. Beta coefficients are calculated as the slope of a “regression line”, which represents the difference between a given stock and the stock market in general. The expected returns of a market are directly related to each alternatives market risk. In other words, the higher the rate of return of the alternative, the higher its beta coefficient. The estimated betas for each of the clients investment alternatives are shown in the chart in Appendix A. Considering the beta coefficients provided in this chart along with the other information that we have calculated, we do not yet have enough information to choose among the various alternativesWhen considering whether or not to invest in a particular alternative, one thing to consider is portfolio diversification.
An investors view of risk in an investment can be greatly affected by the diversification of their portfolio. The risks that can affect an undiversified portfolio may not be the same as those of a diversified portfolio. An undiversified investor may need to be more aware of the stand-alone risk and, therefore, closely monitor the alternatives Coefficient of Variance or standard deviation. These, however, may not be as relevant to a diversified investor because they are more concerned with the impact that a stock may have on the riskiness of their entire portfolio rather than on its stand-alone risk. Aside from having higher risk, another drawback to having a portfolio containing only an individual stock is that you would not be compensated for your higher degree of risk.
SECTION 2: Investment Alternatives2-Stock PortfolioOne of the investment alternatives for the client is a 2-stock portfolio. An option with this alternative would be to invest $50,000 into both High Tech and Collections. The chart in Appendix A contains the calculations of the various measurements of risk. The expected return on the 2-stock portfolio is 6.7%, the standard deviation is 3.4%, and the CV is 0.5. The riskiness of this alternative is different than that of the individual stocks if they were apart from one another. A major difference is in the measurement of the stand-alone risk. The stand-alone risk of the individual stocks is greater than that of a stock portfolio. This is because the two stocks have opposite reactions to the market. As the risk of one alternative increases, the risk of the other decreases, reducing the overall risk of the portfolio.
Random Stock SelectionAnother investment alternative to consider might be to start a portfolio with one randomly selected stock, then randomly adding more and more stocks to this portfolio. Initially, the portfolio would have significant risk because it only contains one individual stock. As more stocks are added, the expected rate of return would remain the same, but the risk would be reduced due to the diversification of the risk through the various stocks.
SECTION 3: Security Market LineThe Security Market Line (SML) equation shows the relationship between risk as measured by beta and the required rates of return on individual securities. Appendix B shows this equation and the calculations of the required returns for our various investment alternatives. Given an estimated risk-free rate of 5.5% and market return of 10.5%, the required rates of return were calculated at 5.5% for T-bills, 12.1% for High Tech, 1.15% for Collections, 9.9% for U.S. Rubber, and 10.5% for a market portfolio. These returns compare closely to the estimated returns in the chart in Appendix A. The required returns are equal to the estimated returns for the Market Portfolio and T-Bills, showing that they are fairly valued. Required returns are greater for U.S. Rubber and Collections, showing that they are overvalued. The required return is lower for High Tech, showing that it is undervalued.
The required return of a portfolio with 50-50 High Tech and Collections is calculated at 6.63%. For a 50-50 portfolio of High Tech and U.S. Rubber, the required return is 11%.
If investors raised their inflation expectation by 3 percentage points over current estimates as reflected in the 5.5% risk-free rate, the SML would result in an upward shift of 3 percentage points. The required returns of both high and low-risk securities would also result in an increase of 3 percentage points. If investors risk aversion increased enough to cause the market risk premium to increase by 3 percentage points, the SML would then result in an upward rotation about the y-axis and the required returns of high-risk securities would increase.