Probability Problem and Question on Identifying Decision Models - Assignment Example

PROBABILITY PROBLEM AND QUESTION ON IDENTIFYING DECISION MODELS By [Name] Course: Professor’s Name: College: City: Date: Answers to Question 1: a. Given the following expected returns and standard deviations of assets B, M, Q, and D, which asset should the prudent financial manager select? Making investment decision involves proper assessment of risks and return profiles of the existing portfolios. The relationship between the expected return and standard deviation for all the asset portfolios can be used to determine whether or not the portfolio(s) is(are) fit to warrant an investment decision. Even though the risk of investing in a single asset may seem high, such a risk may become substantially lower or zero when assets are combined or analyzed collectively. Therefore, when analyzing different assets as a set of securities, it is always necessary to have a good knowledge on how the assets relate to each other. While the expected return measures the amount of profit that the manager expects to generate from the assets, the standard deviation measures the risk associated with each asset. The larger the standard deviation, the higher the risk associated with that particular asset. However, where the expected return and standard deviation are different, it is always advisable for managers to consider making a tradeoff decision between the expected return and standard deviation. Considering the table above, the financial manager should consider selecting asset B because it has the lowest coefficient of variation. The lower standard deviation means that the risk of investing in asset B is lower compared to the risk of investing in all the other three assets. Similarly, the lowest coefficient of variation means that asset B is less volatile compared to assets M, Q, and D. Calculations: For asset B, the coefficient of variation is equal to = 50% For asset M, the coefficient of variation is equal to = 62.5% For asset Q, the coefficient of variation is equal to = 64.3% For asset D, the coefficient of variation is equal to = 66.7% b. Which asset would the risk-averse financial manager prefer? When determining the best asset for investment, the first fundamental consideration is that all the assets offer equal amounts of initial investment, which in this case is $15,000 for assets A, B, C, and D [Table above]. Since the percentages represent the annual rate of return, we can use them to calculate the percentage standard deviation or volatility of return from each asset. The calculations are as shown below: For asset A, the average rate of return will be (8 + 12 + 14)/3 = 11.33% For asset B, the average rate of return will be (5 + 12 + 13)/3 = 10% For asset C, the average rate of return will be (3 + 12 + 15)/3 = 10% For asset D, the average rate of return will be (11 + 12 + 14)/3 = 12.33% Based on the calculated average rate of returns, it is evident that asset D would be most favorable. However, if we factor in other factors such as risks associated with each asset, the whole scenario may become different. For asset A, the standard deviation will be {(11.33 – 8)2 + (11.33 - 12)2 + (11.33 - 14)2}/3 = (11.09 + 0.45 + 7.13)/3 = = 2.49%. For asset B, the standard deviation will be {(10 - 5)2 + (10 - 12)2 + (10 - 13)2}/3 = (25 + 4 + 9)/3 = = 6.16%. For asset C, the standard deviation will be {(10 - 3)2 + (10 – 12)2 + (10 - 15)2}/3 = (49+ 4 + 25)/3 = = 8.83% For asset D, the standard deviation will be {(12.33 - 11)2 + (12.33 - 12)2 + (12.33 - 14)2}/3 = (1.77 + 0.11 + 2.79)/3 = = 2.16% Apart from the standard deviation, we may as well use the coefficient of variation to measure the assets’ volatility as follows: For asset A, the coefficient of variation will be equal to = 21.98% For asset B, the coefficient of variation will be equal to = 61.6% For asset C, the coefficient of variation will be equal to = 88.3% For asset D, the coefficient of variation will be equal to = 17.52% Assets A B C D Average Rate of Return 11.33% 10% 10% 12.33% Standard Deviation 2.49% 6.16% 8.83% 2.16% Coefficient of Variation 21.98% 61.6% 88.3% 17.52% From the calculations and table above, we can conclude that a risk-averse financial manager would prefer asset D because in addition to having the highest average annual return, the asset has the lowest standard deviation and coefficient of variation. While the standard variation for asset D is a reflection of lower risks, the lower coefficient of variation means that asset D has the lowest volatility rate compared to all the other three assets. c. Mohammed is hoping to buy 100 shares of Emaar shares for AED 24.00 per share on January 1, 2018. He hopes to receive a dividend of AED 2.00 per share at the end of 2018 and AED 3.00 per share at the end of 2019. At the end of 2020, Mohammed hopes to collect a dividend of AED 4.00 per share and will sell his stock for AED 18.00 per share. If the probability of his expectations being realized are .9, what will be Mohammed’s expected holding period return be? In finance management, “holding period return (HPR)” refers to the rate of return on an investment or asset over the period of investment. In most cases, organizations and individual investors use HPR to measure their investment performance. The standard formula for calculating HPR is given as follows: HPR = x Probability The calculations below relate to the case of Mohammed: Beginning Value = (100 shares x AED 24.00 per share) = AED 2,400. Return/Profit = (100 shares x AED 2 per share) + (100 shares x AED 3 per share) + (100 shares x 4 per share). Return/Profit = AED 200 + AED 300 + AED 400 = AED 900. Ending Value = (100 shares x 18 AED) = AED 1,800. Therefore, HPR = = 11.25% According to the calculations, Mohammed’s expected holding period return will be 11.25% Answers to Question 2 Champion Breweries must choose between two asset purchases. The annual rate of return and related probabilities given below summarize the firm's analysis. For each asset, compute (a) The expected rate of return on Asset B (the expected return for Asset A is calculated below. (b) The standard deviation of the expected return. (c) The coefficient of variation of the return. (d) Which asset should Champion select? Calculation of Expected Return for Asset A: Expected Return = 15% (10% - 15%)2 × 0.30 = 7.5% (15% - 15%)2 × 0.40 = 0% (20% - 15%)2 × 0.30 = 7.5% Expected Rate of Return = 15% Calculation of Expected Return for Asset B: Expected Return = 15% (5% - 15%)2 x 0.40 = 40% (15% - 15%)2 x 0.20 = 0% (25% - 15%)2 x 0.40 = 40% Expected Rate of Rerun = 80% Calculation of the Standard Deviation of the Expected Return for Asset A: Variance (SA2) = = 16.67 Standard Deviation (SA) = = 4.08% Calculation of the Standard Deviation of the Expected Return for Asset B: Variance (SB2) = = 4291.67 Standard Deviation (SB) = = 65.51% Calculating the Coefficient of Variation: The general formula for determining the coefficient of variation is given as: Coefficient of Variation (CV) =, where “s” is the symbol for sample standard deviation and is the symbol for standard deviation. Therefore: For asset A, the coefficient of variation will be equal to = 27.2% For asset B, the coefficient of variation will be equal to = 81.89% Based on the calculations and the coefficient of variation, Champion should select asset A since it has the lowest coefficient of variation. The coefficient of variation is this case has been used as measure of volatility or the amount of risk associated with each asset. The higher the coefficient of variation, the higher the risk associated with an asset. It is riskier to invest in asset B than in asset A. Answers to Question 3 Apart from the expected value and standard deviation, an organization may decide to use a decision tree model when making an investment decision. The decision tree is valued by organizations because it gives a systematic representation of a decision process and focuses entirely on the investment outcomes. The decision tree can as well be used to incorporate the range of factors that make one investment decision to be risker than other investment decisions. As probabilistic approach to decision-making, the application of a decision tree requires proper identification of choices and chances or state of nature, which must then be represented in terms of square nodes and circular nodes respectively. This trait makes the process tedious and time consuming. Any error made at the beginning or in the course of analysis may compromise the entire decision. Furthermore, the construction of the tree revolves around the use of logic while the calculation of the expected payoffs begin by rolling the decision tree backwards. Such a process at times become confusing, especially when the decision analysis involves large data. Similarly, organizations use influence diagrams to describe the risks associated with investment decisions and determine whether or not it is possible to mitigate the risks. Organizations that use influence diagrams recognize the fact that tree diagram and other probability methods do not give the exact relationships that can be used to facilitate the decision processes. Through influence diagrams, it becomes possible for organizations to maintain information validity and monitor the complex changes in recursive structures that often lead to huge losses. The only challenge is that influence diagrams consume large space and may not be appropriate for large data. The primary aim of an investment decision is to come up with a model that can be used to maximize benefits. Therefore, organizations can use deterministic models to determine the outcomes of investment decision. However, organizations using deterministic models find it hard quantifying the amount of risks associated with each projects and the impacts on overall performance. Read More