The Right Choice When Investing - Term Paper Example

Expected utility model and possible investment advice Student name University Course Lecturer TABLE OF CONTENTS 1.0 Introduction 3 2.0 Expected utility computation 3 3.0 Expected money value 6 4.0 Crop with greatest utility 7 5.0 Certainty equivalence 8 6.0 Risk premium for the crops 10 7.0 Choice of insurance with government subsidy 11 8.0 Disease insurance 11 9.0 Hedging table 13 List of References 15 1.0 Introduction Making the right choices during investments is very key. This is because risk is real and could quickly reduce a person’s investments without warning (Bolton, Chen, and Wang, 2013). However, Pattillo (2016) affirms thattaking risks is also part of investment since fear of risk is also fear of prosperity. Careful investors according to the advice of Rubaltelli, et al. (2015) can therefore only minimize risk levels or avoid obvious risks when they plan through an assessment of all possible alternatives and their scales of risk. This paper provides an expert advice on risk management and decisions for investment in an Agricultural setup. 2.0 Expected utility computation In economics, expected utility is a term that summarizes the expected utility that an entity should probably reach under certain circumstances and is calculated by computing weighted averages of all probable outcomes under specific circumstances (Fishburn, 2013). The weights, Cerreia‐Vioglio, Dillenberger, and Ortoleva (2015) intimates, are assigned as likelihood to occur or the value of probability of a certain event occurring. Fishburn (2013) argues that the expected utility model teaches that the all possible utility levels’ weighted average, under a level of uncertainty, will be equal to utility at a given time.The utility of the farmer at different income levels is as follows: Utility of farmer Sally Whitwell at different income levels Expected income (AUD' 000) Sally Whitwell's utility $0 0 $100 20 $200 35 $300 48 $400 60 $500 71 $600 81 $700 89 $800 94 $900 96 From the table, the expected utility is computed with regression analysis as follows: Regression Statistics Multiple R 0.978778329 R Square 0.958007018 Adjusted R Square 0.952757895 Standard Error 65.80673409 The r-square value is 0.958 implying about 95.8% perfection in the model used. The standard error is quite high at 65.80 implying that the risk value for the expected utility is also high. However, the significance of this is estimated using ANOVA shown below. ANOVA   df SS MS F Significance F Regression 1 790355.79 790355.79 182.5080242 8.64955E-07 Residual 8 34644.21001 4330.526251 Total 9 825000       The ANOVA data shows a very significant relationship for the standard error with a high F-value of 182 significant at 99% confidence interval. Regression coefficients are shown below:   Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -82.884607 44.597783 -1.85849 0.1001623 -185.7272 19.958066 Sally Whitwell's utility 8.97112133 0.6640575 13.50955 8.6495E-7 7.439801 10.502440 The regression data shown above leads to a computation of the utility line plot shown below. The y intercept is presented by -82.885 i.e. expected income against the expected utility of 8.9711. this means that at estimated utility of 8.9711, Sally would get a loss of $82.885 implying a high risk. Sally therefore needs a utility value of at least 10.50 to earn an estimated $19.95. The advice is that Sally should consider heavy investment, more than $100 to have substantial utility. At expected income of $600, risk aversion, absolute and relative is given as follows; Absolute risk aversion (600) = 8.9711x - 82.885 682.885=8.9711(x) x=76.1205426 Relative risk aversion = absolute risk±standard error = $76.1205426±44.597783 =31-5223 or 120.7182 3.0 Expected money value Expected money value is computed for each of the following crops Investment options Very dry (20%) Dry (25%) Mild (30%) Wet (25%) Carrot 200 500 700 -200 Corn 100 300 400 -300 Kale 300 400 500 -100 Lettuce -300 -100 400 500 Tomato 100 300 600 -100 1. Carrot=20(200)+25(500)+30(700)+25(-200) =4000+12500+21000-5000 =$32500 2. Corn =2000+7500+12000-7500 =$14000 3. Kale = 6000+10000+15000-2500 =$28500 4. Lettuce=-6000 – 2500+12000+12500 =$16000 5. Tomato=2000+7500+18000-2500 =$25000 4.0 Crop with greatest utility Expected utility is given by the function  Expected utility (x) is given by: EU(x)=. The carrot produceshighest money hence, since it is a directly proportional function, the highest utility is from the carrot crop: substituting EU(x)=  with the carrot expected income is given as=  =32582.885/8.9711 = 3631.98. 5.0 Certainty equivalence The certainty equivalence was ascertained from the 95% confidence interval of each of the crops as shown with the descriptive statistics below. Carrot  Corn Kale Lettuce Tomato Mean 300 125 275 125 225 Standard Error 195.789002 154.784796 131.497782 193.1105038 149.303940 Median 350 200 350 150 200 Standard Deviation 391.578004 309.569593 262.995564 386.2210075 298.607881 Sample Variance 153333.333 95833.3333 69166.6666 149166.6667 89166.6666 Kurtosis -0.7684310 0.757655955 2.23486718 -4.40922568 -0.4161062 Skewness -0.5995806 -1.13762436 -1.4430588 -0.1692376 0.42252141 Range 900 700 600 800 700 Minimum -200 -300 -100 -300 -100 Maximum 700 400 500 500 600 Sum 1200 500 1100 500 900 Count 4 4 4 4 4 Confidence Level(95.0%) 623.087986 492.594304 418.484630 614.563809 475.15177 The certainty for each crop i.e. what ought to be invested to yield income at 95% confidence interval is as follows: a. Carrot = 623.0879863 b. Corn = 492.5943048 c. Kale = 418.4846304 d. Lettuce = 614.5638092 e. Tomato = 475.151774 Certainty level for carrot is best of all the crops while kale crop remains the most uncertain based on the computations shown above. Insurance is therefore recommended for the high risk crops i.e. kale, corn and tomato. 6.0 Risk premium for the crops According to Damodaran (2016), risk premium is defined as the risk free rate less the return on an investment that is expected to be yielded. The form of compensation that investors can tolerate in case of extra risk, argues Peng and Wang(2016), is called an asset risk premium while a risk free asset is one that demonstrates no risk in case of an investment. The risk premium for each crop is given by the function Y= 8.9711x - 82.885 from the regression analysis where y is the sum of expected crop investment. Thus . The risk premium for the crops is therefore as follows: Carrot = 143.002 Corn x =  = 64.97 Kale x =  = 131.86 Lettuce x =  = 64.97 Tomato x =  = 109.56 7.0 Choice of insurance with government subsidy The risk premium less the $30 government subsidy for weather is given as follows: Carrot = 113.002 Corn = 34.97 Kale = 101.86 Lettuce = 34.97 Tomato = 79.56 The data indicates that without the whether risk using government subsidy, the risk is still significant for kales, carrots and tomato. Insurance is therefore still advised for these three crops but can be foregone for corn and lettuce crops. 8.0 Disease insurance Expected profit per crop is 70% while the probability of the disease risk is 30%. This has the implication that the expected profits for each crop is as follows (refer back to expected money value. Carrot = 70% of $32500 = $22750 Corn = 70% x $14000 = $9800 Kale = 70% of $28500 = $19950 Lettuce = 70% of $16000 = $11200 Tomato = 70% of $25000 = $17500 Insurance value is therefore given by Disease risk of 30% of money value for crop multiplied by the cost per dollar. The computations per crop is as follows: I. Carrot = 30% of 22750*35 cents =$2388.75 II. Corn = 30% x $9800 x 35 cents =$1029 III. Kale = 30% x $19950 x 35 cents =$2094.75 IV. Lettuce = 30% x $11200 x 35 cents =$1176 V. Tomato = 30% x $17500 x 35 cents =$1837.5 9.0 Hedging table In finance and insurance, hedging is a strategy that investors use to reduce the risk of a peril hence the price of asset movements risk (Moschini, and Hennessy, 2001). As Conlon, Cotter and Gençay (2016) posit, hedging could involve taking things such as security for example a futures contract. Other scholars refer to hedging as the same thing as an insurance policy hence hedging is confined to taking an insurance policy for the specific risks that are prone in a particular area of investment (Turcic, Kouvelis, and Bolandifar, 2014). In this case probable insurance policies would be crop disease policy and weather insurance policy. Hedging also is considerate of risk-reward tradeoffwhich is meant to reduce the risk potentially though it may also chip away probable gains. Hedging’s shouldn’t be though as free in the end because some gains are lost in an equal manner as potential risks. For example, when an insurance policy is meant to cover weather conditions such as floods, whereas the monthly bills goes up,in case there is no flood, the holder of the policy gets no payout. However, a perfect hedge helps an investor to eliminate a portfolio of risks in a position hence referred to as 100% inverse correlation in relation to the investment thought to be vulnerable (Conlon, Cotter and Gençay, 2016). The table below refers to the hedging for the case study preparing hedge with options (constant cash and future prices) where the basis is held constant. Cash and futures Options price Today 1st Nov: Cash $5.10 per bushel (wheat) Futures 1st Jan: $5.40 bushel Purchase $5.50/bushel put at $0.20 bushel (pay $1,000 plus commission) Later 1st Dec: Sell wheat locally at $5.00 per bushel Futures 1st Jan $5.10 per bushel Sell $5.40/bushel put at $0/bushel (receive $0) Option expires worthless Results Cash price paid $5.00/bushel Less commission $0.03/bushel Less option premium loss $0.20/bushel Net selling price $5.23/bushel List of References Bolton, P., Chen, H. and Wang, N., 2013. Market timing, investment, and risk management. Journal of Financial Economics, 109(1), pp.40-62. Cerreia‐Vioglio, S., Dillenberger, D. and Ortoleva, P., 2015. Cautious expected utility and the certainty effect. Econometrica, 83(2), pp.693-728. Conlon, T., Cotter, J. and Gençay, R., 2016. Commodity futures hedging, risk aversion and the hedging horizon. The European Journal of Finance, 22(15), pp.1534-1560. Damodaran, A., 2016. Equity risk premiums (ERP): Determinants, estimation and implications–The 2016 Edition. Fishburn, P.C., 2013. The foundations of expected utility (Vol. 31). Springer Science & Business Media. Moschini, G. and Hennessy, D.A., 2001. Uncertainty, risk aversion, and risk management for agricultural producers. Handbook of agricultural economics, 1, pp.87-153. Pattillo, C., 2016. 4 Risk, Financial Constraints and Equipment Investment. Investment and Risk in Africa, p.96. Peng, X. and Wang, W., 2016. Optimal investment and risk control for an insurer under inside information. Insurance: Mathematics and Economics, 69, pp.104-116. Rubaltelli, E., Agnoli, S., Rancan, M. and Pozzoli, T., 2015. Emotional Intelligence and risk taking in investment decision-making (No. 15107). Universita di Modena e Reggio Emilia, Dipartimento di Economia" Marco Biagi". Turcic, D., Kouvelis, P. and Bolandifar, E., 2014. Risk-Aversion Happens: Hedging Commodity Material Purchases in a Bilateral Supply Chain. Read More