The Markowitz Model Selecting an Efficient Investment Portfolio - Assignment Example

Interpretation of the Results AutoPower Company Distribution plan has the information about what amount of supplies they should make to each destination (Provided in the appendix). The distribution plan has enough supplies but needs to determine the number of motors to send from their harbours. The cost of sending motors from one harbour to specific destinations is given per motor. In any business operation, business managers in any department would want to utilize the minimum cost possible. In this distribution section, it will be part of cost of production of which if minimized, increases the chances of maximizing profit. The main aim therefore is to send the motors to their destinations by the most cost efficient way. The company can consider the cheapest way in terms of cost or the cheapest way in terms of the number of routes used in total. From the spread sheet model, there are five options from which the company can determine the number of motors to send from each harbour to specific destinations. Option A and Option D (£ 121450) give the cheapest way of sending the motors, followed by Option C (£ 124000), then option B (£ 124850) and lastly option E (£ 125 950). Recommendation The most cost efficient way of sending the motors is by use of the routes presented in option A and D in the spreadsheet. The two options give the lowest costs of sending the motors and do not involve a lot of routes. The models show that in each distribution plan, six routes are to be used except for option C which has seven routes. There are two possible distribution plans that the company can use, however the company has to choose one. From the two given possibilities, that is Option A and D, it is not easy to determine the best option. Both have only one route to Nancy from Antwerp making distribution easy. Option D has one route that completes the supply of what is required in Liege, Belgium and one route that supplies the demand in Tilburg unlike the option A which has Tilburg’s demand supplied through two routes. Option A also has one route that completes the supply of what is required in Liege, Belgium and one route that completes the supply required in Leipzeg, Germany. The company can therefore use either of the two options (A and D) considering the lower costs that the routes have as compared to the other supply routes. Selection of the best spread sheet model to use can further be determined by considering other factors that affect distribution from the harbours to the destination areas. All the data is given in the spread sheet model which also has graphs revealing the interpretation. Question 2 Markowitz asset features: According to Markowitz, assets are defined by mean variance parameters which define them as either risky of non risky. The mean variance produces the risks related to investment in a group of assets (Fabozzi & Markowitz, 2002). He formulated the formula of obtaining expected return for a portfolio which has another form as: w1μ1 + w2 μ2……wn μn = The portfolio’s expected return. Where w represents the weights of the assets and μ represents the expected rate of return (Fabozzi & Markowitz, 2002). According to this formula, the risks are obtained from the variance of each portfolio asset returns. The standard deviation gives the minimum risk and a plot of the expected returns against the standard deviation graph gives the optimal portfolio based on the expected return of the investor (Fabozzi & Markowitz, 2002). a). A comparative assessment of the expected return and the risk. The risk of a portfolio is obtained by the variance of the returns. Data is presented in the following worksheets: ‘Weighted sum’ which has given the weighted sum of each portfolio used in the other data analysis procedures ‘Variance W’ which gives the variance of Water portfolio ‘Variance B’ which gives the variance of Brewers portfolio ‘Variance T’ which gives the variance of Telecoms portfolio and ‘Variance P’ which gives the variance of property portfolio The variances represent the risks of each portfolio Below is a table showing the variances and expected returns obtained from the calculation. Analysis Water portfolio has the lowest risk but has a higher expected return than Telecoms which has the lowest expected return. Telecom has the second lowest risk. Brewers and property have high expected returns and high risks. ‘Brewers’ has the highest expected return with a risk level of 20.156 while Property has the highest risk and the second highest expected return. b). Risk Minimization According to (answer 2), investors can either select from efficient portfolio or optimal portfolio. Investors however are known to be averse and would prefer investing in portfolios with lower risks. If two portfolios are presented with the same expected return but different risks, the investors would select a portfolio with the lowest risk (Fabozzi & Markowitz, 2002). For a risk minimizer, the portfolio with the lowest risk would be the best choice, but there is a way in which the risks can be minimized. According to (Beste et al, 2002), risk minimization has the following formula: Minimization = 1/2xTVx = ½ Var (P) (). Resulting to the equation xT µ = µp = E (P) xT1 = 1 µp = is the desired level of expected return for the portfolio X = a column vector of portfolio weights for each security [x1, x2,…….xn]T µ = The vector of expected returns [µ1…. µn 1 =[1,1,…..,1]T From the spreadsheet model, minimization is given by (Σx²/n)½ Minimization of the risks is therefore ½ of the variances of each portfolio. From the spreadsheet model on portfolios, each portfolio’s risk has been calculated and minimized risks shown. In order to obtain an optimal strategy, the investor has to find a portfolio with an x (portfolio) value that can produce his/her expected return. The x that produces a solution to the system for an expected return for example 12% is the frontier portfolio (Beste et al, 2002). c). Description The curves represented in the figure below are the indifference curves. In portfolio theory, investors are faced with a set of choices. Different portfolios have different levels of risks as well as different levels of expected return. The investors have to select the best from the various portfolios. When the expected return is high, the risk is also high. Entities or investors are forced to select from the portfolios therefore get different utility levels from different return/risk combinations. The level of utility is articulated by the utility function and the utility function expresses the preferences made by the entities or the investors over the returns and risks of each portfolio. Utility function is represented graphically by use of indifference curves as above. In the case above, there are four portfolios with different risks and expected returns as illustrated in the table. Expression in the indifference curves shows the graph above. This graph represents a set of efficient and optimal portfolios. The different colours represent different portfolios as referenced below the graph. The vertical axis measures the expected return while the horizontal axis measures the risk. The two lines on Telecoms portfolio represent two different risk and expected return levels. Let the first line be A and the second be B. The second point has a higher expected return that the first point but also has a higher risk. This shows that the investor has an equal preference over both points. Points A and B are both on the same curve which means if the investor selects point A, both the risk and the expected return will be low. If the investor selects position B, both the risk and the expected return will be high. The investor therefore has equal chances in the selection any position in the curve. Given a variety of portfolios to choose from with different levels of expected returns and risks an investor would obtain more utility if the indifference curve was further from the horizontal axis. This shows that the returns are high for the same level of risks. To get the risks of 10%, the returns are plotted against the variance. Optimal values are obtained where the Iso mean values meet the iso-variance. In this case, the expected return is 10%. The plot against the risk under various portfolios reveals several risk levels giving the investor a variety of choices to make from each portfolio. From the ‘Optimal Portfolio Graph’ 10% gives the following approximate risks levels under the four portfolios Brewers: 0.5, 4.8, 10.5, 18.7 and 22.1 all -/+ 0.05 Water: 1, 5.9 and 14.9 Telecoms: 2, 7.8, 13.9, 18 and 22.4 -+ 0.05 Property: 8.4, 16.9 and 21.2 Based on the minimized risks below: Water Brewers Telecoms Property Minimized Risk 1.64 4.49 3.108 4.67 Weighted Sum 9.71 10.97 9.24 9.765 If the investor expects 10% return, then there are various levels of risks to choose from. The investor can chose to invest on the Brewers portfolio at 0.5 or 4.8 -/+0.5 risk levels which are closer to the minimized risk. The investor could also invest on water since it has a risk of 1 which is also lower that risk after minimization (1.64). Telecoms has also a risk level two, which the investor can decide to operate on since it is also lower that the minimized risk levels. Property has the lowest risk level at 8.4 which is 3.73 more that the minimized risk. References List Beste, A., Leventhal, D., Williams, J., Lu, Q. (2002). The Markowitz Model Selecting an Efficient Investment Portfolio. Fabozzi, F. J. and Markowitz, H. (2002). Vol. 94. The Theory and Practice of Investment Management. John Wiley and Sons. Appendices Appendix 1 The Demand at Destinations ASSEMBLY PLANT NUMBER OF MOTORS REQUIRED (1) Leipzig, Germany 400 (2) Nancy, France 900 (3) Liege, Belgium 200 (4) Tilburg, the Netherlands 500 Appendix 2 Numbers of Motors at Respective Harbours HARBOUR NUMBER OF MOTORS AVAILBLE (A) Amsterdam 500 (B) Antwerp 700 (C) Le Havre 800 Appendix 3 The Cost per Motor TO DESTINATION Leipzig Nancy Liege Tilburg From Origin (1) (2) (3) (4) (A) Amsterdam 120 130 41 59.50 (B) Antwerp 61 40 100 110 (C) Le Havre 102.50 90 122 42 Read More