Exercices (metrics in risk management) Exercice 1 ERMM1 Corp wants to know its weighted average cost of capital. Indeed, the CEO wishes to create a common risk-culture amongst business units and evaluate projects on a same basis. He gave you some informations : Actual Risk-free rate : 3% Risk premium applied for the same class of risk as ERMM1 : 1% Market portfolio return : 8% Bêta of the firm : 0,9 Historical interest rate applied on ERM1’s outstanding financial debts : 4,8% Balance sheet is as follow : Assets M€ Liabilities M€ Fixed assets 420 Shareholders’equity 450 Working capital 580 Financial debts 550 Total 1 000 Total 1 000 Financial debts are repayable in 2 years and tax rate is 30%. There is actually 10 000 000 outstanding shares listed on the stock-market at a 52 €. Recurring operating income is 77 M€ for the year. 1) Determine the WACC 2) Determine Economic Value Added Exercice 2 ERMM Corp is a distributor of consumer goods. It has to decide how many pieces to order every day. Three choices are available : small order, medium order and large order. The demand that can be low, moderate, or high depending on many factors. If it buys too little pieces, it will support opportunity costs and if it buys too many pieces it will support cost for storage and wastes. After studying revenues and costs, profit per day (in 000 $) for these situations and for small, medium or large order, company has stated profits as shown in table below. Table of profit (decision matrix). Order/Demand Low Moderate High Small 47 44 43 Medium 42 50 46 Large 36 45 55 1) Apply all decisions criterias you know and decide 2) If you can assign probability of 30%, 50% and 20% to demand Exercice 3 The risk manager of ERMM2 gave you an excell spreadsheet that contains 500 values simulated from an annual aggregate loss distribution. ERMM2’s total equities is 10 M€. 1) Determine mean and standard deviation of this loss distribution 2) Assuming that this loss distribution follow a Normal Law, find the 95% Value-atRisk of this loss distribution, based on the sample of 500 values. Is your answer different if you relax this assumption and take empirical data? 1 e. On a 10 years history. For well-diversified traded chemical companies. 4) The “Tail VaR” is defined as the average loss on claims which have a loss size greater than the VaR – i. confirm the correlation between the two businesses. Exercice 4 ERMM4 Corp. Board of directors has been mandated to found a less volatile but complementary business. Last shareholders’ annual meeting has adopted the resolution to proceed to an initial public offering at a 2-years horizon..010165. a small but promising chemical company actually wants to diversify its activities. Market conditions 1 2 3 Probability Estimated Return for ERM2 actual business 20% -25% 60% 20% 20% 60% Estimated return for new business 1% 15% -7% 1) On available data. They found in cosmetics market a potential use for ERMM2’s products.. the maximum unexpected loss for any individual risk should be less than 1% of total equities. Find the 95% Tail VaR. the average of the losses given that the loss is above the VaR threshold. return and standard deviation of return are expected to be 13% and 16% respectively. the estimated correlation between returns on the two markets is 0.3) Given that the company is exposed to other significant risks. Because of the cyclical nature of its business (painting). returns are highly volatile. 2) Determine the weight of this new business in the portfolio of ERM2 if the Board wants to achieve the targeted return and standard deviation? (help : you can use simulation on excel) 1 . Find the shortfall risk. PUT24.0% 13.0 % 32 5.0 % 34 4.0% 87. faces some technical problems with its furniture products.0% 100.0% 1. the risk manager collected statistical data on claims for the past two years.5% 0.5% 0. a €120 000 deductible and a €500 000 policy limit.Exercices (metrics in operational risk management) Exercice 1 ERM 1 Corp. Insurance contract include a €5 000 € premium.0% 4.0 % 37 1. manager has found a relation between operating margin and weather. the bank suggests PUT options (the right to receive in € x times the difference between (REFERENCE TEMPERATURE-observed average t°)) at the end of the summer season.5% 2.0% 0.0% 82.0% 95.0% 53.0% 9.0 % 36 3.0% 26 6.0% 77. he asks you to answer the four questions below.0% 91.0% 7. Different simulation scenarios leads to the following formula : Operating margin (€)= 100 000*(t°-23°)-200 000. A financial institution offered him two solutions. It operates in French South-coast market during the summer season.0% 47. Frequency Number of Frequency claims 0 50% 1 30% 2 20% 1) 2) 3) 4) Severity Size per claim 1 000 € 5 000 € 50% 50% Determine the expected claim frequency Determine the expected monthly aggregate Euros of loss Determine the maximum possible annual Euros of loss Determine the one-month 95% Value-at-risk aggregate Euros of loss Exercice 2 ERM 2 Corp. Due to actual climate change. is an ice-cream producer. For derivatives.0% 27.0 % 35 4.5% 0.5% 1.0 % 31 6.5% 3.0% 41. In order to know actual risk exposure on a monthly basis.0 % 1) Determine for each solution the outcome profile 2) Given the probability distribution and a risk-adjusted rate of 4% determine the actuarially fair insurance premium 3) Compare the different solutions 1 .0 % 27 6. On collected evidences. Based on empirical evidences.5% 0.0% 34.0 % 33 5.0% 99. is the right to receive €100 000 times (24°C-average observed temperature) for a €10000 premium.0 % 29 6.0 % 30 6.0% 9.0% 65.0% 5.0% 2.0% 4. Probability distribution of temperature Temperature (°C) probability cumulated Temperature (°C) probability cumulated 13 14 15 16 17 18 19 20 21 22 23 24 25 0.0% 7.5% 0.0% 5.0% 59.0 % 28 6.0% 98.0% 18.0% 71. The first one is to contract insurance for loss.5% 2. ERM2 manager is searching for alternative solutions to protect its revenues.0 % 38 1. 4) Compute VaR 95% with and without transferring risk. 1 . the market price was 23. Informations on Rhodia’s financial position are as follow.85 € with 101085957 outstanding shares listed in Euronext market. a leading chemical company to supply a fixed volume of products (12 000 000 €) per year on a 3-years agreement.Exercices (metrics in financial risk management) Exercice 1 ERMF1 is a raw materials retailer. At year end. It has been approached by Rhodia. Compute Altman Z-Score? Is this information enough to help you entering in this LTA? 1 . All four options are European options. have the same underlying asset. and sell for 10 € one PUT option with an exercise price of 70. You buy for 1€ one PUT option with an exercise price of 60. At the same time.Exercice 2 July 1st. and have a common expiration date. The main Bank of the company proposes two swaps : . 1 . invested 500 000 $ in floating-rate bonds (libor+3%). Exercice 3 ERMF1 buy one call option for 6 € with an exercise price of 40. and sell one call option for 5€ with an exercise price of 50.5% in December and will increase to 4% in july 2009. 2008.A $500 000 swap receiving floating rate (libor) and paying fixed 5% interest rate - $500 000 swap paying floating rate (libor) and receiving fixed 5% interest rate 1) Describe the main risk the company actually faces? What can be hedging objective? 2) Which solution would you recommend to the chief financial officer with respect to the above objective? 3) What will be the outcomes for the next two semesters if libor rate will decrease to 3. group’s main financial subsidiary. it borrowed $1 000 000 (floating rate : libor+1%). PARTNER FL. Libor annual rate is actually 4.5%. Determine the total net payoff from your option position.