The Key Aspects of Evaluating Risk Management in Agribusiness - Assignment Example

RISK MANAGEMENT IN AGRIBUSINESS NAME: COURSE TITLE LECTURER: DATE OF SUBMISSION: Question One: a. Estimation of Joint, marginal and posterior probabilities, and Bayes’ theorem i. Joint probability; The joint probability measures likelihood of two events occurring at the same time. The calculation below shows risk exposure by the famers as a result of potato late blight fungus (PLBF); Unlikely scenario P (Z1S1) = 0.4 X 0.7= 0.28 P (Z1S2) = 0.4 X 0.6= 0.24 P (Z1S3) = 0.4 X 0.2= 0.08 Possible Scenario P (Z2S1) = 0.4 X 0.2= 0.08 P (Z2S2) = 0.4 X 0.2= 0.08 P (Z2S3) = 0.4 X 0.3= 0.12 Probable Scenario P (Z3S1) = 0.2 X 0.1= 0.02 P (Z3S2) = 0.2 X 0.2= 0.04 P (Z3S3) = 0.2 X 0.5= 0.10 ii. Marginal probability; The marginal probability shows the likelihood of PLBF from subsets of randomly collected variables of unlikely, possible and probable occurrence. The Marginal probability of PLBF is given by (PZ1) =P (S1 and Z1) + P (S2 and Z1) + P (S3 and Z1) P (Z1) = (0.4 X 0.7) + (0.4 X 0.6) + (0.2 X 0.2) = 0.56 P (Z2) = (0.4X0.2) + (0.4X0.2) + (0.2X0.3) = 0.22 P (Z3) = (0.4X0.1) + (0.4X0.2) + (0.2X0.5) = 0.22 iii. Posterior probability; The probability shows probability of event (A) occurring because another event (B) has occurred. The calculation below shows posterior probability; P (SiǀZk) = P (Zk and Si) / P(Zk) P (S1/Z1) = =0.500 P (S2/Z1) = = 0.429 P (S3/Z1) = = 0.143 P (S1/Z2) = =0.364 P (S2/Z2) = = 0.364 P (S3/Z2) = = 0.545 P (S1/Z3) = =0.091 P (S2/Z3) = = 0.182 P (S3/Z3) = = 0.455 iv. Bayes’ Theorem; A B C D E F G H I 1 State Prior Likelihoods P(Zk/Si) Joint Probabilities P(Si and Zk) 2 Sn P(Sn) Z1 Z2 Z3 Z1 Z2 Z3 3 S1 0.4 0.7 0.2 0.1 0.28 0.08 0.04 4 S2 0.4 0.6 0.2 0.2 0.24 0.08 0.08 5 S3 0.2 0.2 0.3 0.5 0.04 0.06 0.1 6 Check 1.0 Marginal P(Zk) 0.56 0.22 0.22 7 Posterior P(S1/Zk) 0.500 0.429 0.143 8 P(S2/Zk) 0.364 0.364 0.545 9 P(S3/Zk) 0.091 0.182 0.455 10 Check 1.0 1.0 1.0 b. Probability tree Posterior probability; Joint probability; Question Two a. The return of the three alternatives i. Alternative 1: Safe Money Market Fund Assume I choose safe money market fund with compounding interest rate of 2% quarterly. Therefore, income earned as interest from compounded fund is calculated as shown below; Income earned (Interest) = P (1+r/n) nt - P P is principal invested R is compounding rate N is compounded times in a year T is number of years. = 500,000 (1+0.02) 3*3 – 500,000 = $97,546.284 ii. Alternative 2: Tomato and Safe money market fund Safe money market income: Compounding rate = 5% Remaining fund after investing on tomato = 500,000 – 30,000 = 470,000 Income earned from interest = 470,000 (1+0.05) 3 – 470,000 = $74,083.75 Tomato income Revenue Dry * P (10,500*0.6) 6,300 6,300 6,300 Revenue Wet * P (13,300*0.4) 5,320 5,320 5,320 Total 11,620 11,620 11,620 Total income = 11,620*3 – 10,000*3 = $4,860 Total income for alternative 2 = Safe money market fund return + Tomato return = 74,083.75 + 4,860 = $78,943.75 iii. Alternative 3: Wheat and Safe money market fund Safe money market income: Compounding rate = 5% Remaining fund after investing on tomato = 500,000 – 6,500*3 = 480,500 Income earned from interest = 480,500 (1+0.05) 3 – 480,500 = $75,738.81 Wheat income Revenue Dry * P (7,500*0.6) 4,500 4,500 4,500 Revenue Wet * P (6,800*0.4) 2,720 2,720 2,720 Total 7,220 7,220 7,220 Total income = 7,220*3 – 6,500*3 = $2,160 Total income for alternative 3 = Safe money market fund return + Wheat return = 75,738.81+ 2,160 = $77,898.81 b. The best alternative The suitable alternative is the one that gives high utility based on utility function of W0.5. Therefore, utility for the alternative is as shown below; Alternative 1 = 97,546.2840.5 = 312.32 Alternative 2 = 78,943.750.5 = 280.97 Alternative 3 = 77,898.810.5 = 275.21 Therefore, investing the whole amount in the safe money market fund will yield high utility (312.32) as compared to splitting the amount and investing in farming. Question Three State of nature Dry Mild Wet Alternative 1 – Barley 500 200 -200 Alternative 2 – Corn 200 300 -200 Alternative 3 – Potato 300 100 -100 Alternative 4 – Wheat -200 100 300 a. Maximin Minimum -200,-200, -100, -200 Maximum -100 The farmer who uses Maximin criteria will choose Alternative 3 – Potato- Wet (-100) since it maximum of minimum. b. Maximax Maximum 500, 300, 300,300 Maximum= 500 The famer Using Maximax criteria for risk prediction will choose Alternative 1 – Barley - Dry (500) since it is maximum of maximum outcome predicted (Dunis, Laws & Naïm, 2003). c. Minimax The calculation of regret matrix; State of nature Dry Mild Wet Alternative 1 – Barely 500-500 200-300 -200-300 Alternative 2 – Corn 200-500 300-300 -200-300 Alternative 3 – Potato 300-500 100-300 -100-200 Alternative 4 – Wheat -200-500 100-300 300-300 Regret matrix State of nature Dry Mild Wet Alternative 1 – Barley 0 -100 -500 Alternative 2 – Corn -300 0 -500 Alternative 3 – Potato -200 -200 -400 Alternative 4 – Wheat -700 -200 0 The table above shows the calculation of regret and the follow are results of minimum values; Minimum = -500, -500, -400, -700 (The alternative is chosen from the maximum of minimums) Maximum -400 The famer using the Minimax regret criteria will choose alternative 3 – Potato- at wet state because it gives the maximum regret of -400. d. Hurwitz alpha criteria Ii = αXi + (1 - α) Yi Alternative 1 – Barley: (0.4)500 - (0.6)200 = 80 Alternative 2 – Corn: (0.4)300 - (0.6)200 = 0 Alternative 3 – Potato: (0.4)300 - (0.6)100 = 60 Alternative 4 – Wheat: (0.4)300 - (0.6)200 = 0 The farmer should choose Alternative 1 – Barley with 80 since it is the highest compared to other alternatives. e. Principle of insufficient reason: State of nature Dry Mild Wet Average Alternative 1 – Barley 500 200 -200 166.67 Alternative 2 – Corn 200 300 -200 100 Alternative 3 – Potato 300 100 -100 100 Alternative 4 – Wheat -200 100 300 66.67 The principle of insufficient reason shows that the farmer should choose Alternative 1 – Barley with an average of 166.67. Question Four a. Minimum acceptable return level (R min) The minimum acceptable return level must pay off the loan borrowed before compensating personal funds. Invested fund =$600,000 Loan =$30,000 R min = x100% = 5% b. Safety-first ratio The safety-first ratio enables the investor to choose crop that yields optimal return (Tetenov, 2012; Hanf, 2005). This is achieved by calculation of safety-first ratio then selecting crop with the highest ratio. This is shown below; SFRatio = Banana = = 1.059 Capsicum = = 1.051 Corn = = 1.818 Potato = = 0.943 Tomato = = 1.183 According to Roy’s rule, the crop with optimal return is the one with highest ratio. Therefore, the crop with highest ratio is corn with SFRatio of 1.818. c. Telser’s rule Telser’s rule enables the farmer to choose crop with the probability of ruin less than the predetermined percentage (Dudley, 2002). α is obtained from the z table for K values. The analysis of crop return using Telser’s rule is applied as shown below; Crop E(Ri) K α Banana 14 1.059 14.46% Capsicum 12 1.051 14.69% Corn 9 1.818 3.44% Potato 10 0.943 17.36% Tomato 16 1.183 11.90% According to the table above, corn is the best crop since it has a very low probability of ruin (3.44) compared to the three crops which recorded probability less than 15%. d. Expected return of Corn The expected return for corn is as shown below; SFRatio = 1.818 = = 3.9996 + 5 = 8.9996% = 9% Corn gives optimum return using the two methods; Roy’s and Telser’s rule. Therefore, expected return of corn remains at 9%. Question Five a. Decision basing on E-V Rule EV (Corn) = [200x0.2+ 400x0.3 + 600x0.4 + 800x0.1] = 480 EV (Potato) = [200x0.2 + 400x0.4 + 600x0.2 + 800x0.2] = 480 EV (Wheat) = [200x0.1 + 400x0.3 + 600x0.2 + 800x0.2] = 420 The corn and potato provides the best alternative since they yield higher and same return as per EV rule of 480. a. First Stochastic Dominance According to Lombardi & Calzolari (2009), the formula of first stochastic dominance is given by; F(x) = P (A< x) Outcome Corn: (x) Potato: (x) Wheat: (x) 200 40 40 20 400 120 160 120 600 240 120 120 800 80 160 160 Variance calculation; Var(X) = Σx2p − μ2 Corn = 2002x0.2 + 4002x0.3 + 6002x0.4 + 8002x0.1 - 4802 = 33,600 Potato = 2002x0.2 + 4002x0.4 + 6002x0.2 + 8002x0.2 - 4802 = 41,600 Wheat =2002x0.1 + 4002x0.3 + 6002x0.2 + 8002x0.2 - 4802 = 21,600 The weight of each variance is given by; Corn = = 0.347 Potato = =0.430 Wheat = = 0.223 Where; X= Expected return for each outcome The second stochastic dominance function is given as; Potato; F(x) =0.347x Tomato; F(x) =0.43x Corn; F(x) =0.223x Therefore, from the table above we can get the following outcomes for second stochastic dominance; Outcome Corn: F(x) Potato: F(x) Wheat: F(x) 200 13.88 17.20 4.46 400 41.64 68.80 26.76 600 83.28 51.60 26.76 800 27.76 68.80 35.68 The CDF’s Graph The graph above shows the variation of outcome of the three crops using second stochastic dominance. The wheat shows little variation while potato showing high variation but with a predictable movement. The corn crop is the preferred alternative since it has the highest peak as compared to potato and wheat (Azencott, Beri & Timofeyev, 2011). Reference: Azencott, R., Beri, A., & Timofeyev, I. (2011). Parametric Estimation of Stationary Stochastic Processes Under Indirect Observability. Journal Of Statistical Physics, 144(1), 150-170. DeFusco, R., Ivanov, S., & Karels, G. (2009). The exchange traded funds’ pricing deviation: analysis and forecasts. Journal Of Economics And Finance, 35(2), 181-197. Dudley, R. (2002). Real analysis and probability. Cambridge: Cambridge University Press. Dunis, C., Laws, J., & Naïm, P. (2003). Applied quantitative methods for trading and investment. Chichester, England: John Wiley. Hanf, C. (2005). Coping with Risk in Agriculture, 2nd Edition. European Review Of Agricultural Economics, 32(2), 294-296. Hardaker, J. (2004). Coping with risk in agriculture. Wallingford, Oxfordshire [u.a.]: CABI Pub. Kharasch, E., & Rosow, C. (2013). Assessing the Utility of the Utility Function. Anesthesiology, 119(3), 504-506. Lombardi, M., & Calzolari, G. (2009). Indirect estimation of -stable stochastic volatility models. Computational Statistics & Data Analysis, 53(6), 2298-2308. Pindyck, R.S. and Rubinfeld, D.L. (2013). Microeconomics. Eigth Edition. Pearson Prentice Hall, New Jersey. Tetenov, A. (2012). Statistical treatment choice based on asymmetric minimax regret criteria. Journal Of Econometrics, 166(1), 157-165. Read More