An Overview of Risk Management

1. Chapter Ten An Overview of Risk Management

2. Chapter Outline • Risk, Uncertainty & Preferences to risk • Risk Management techniques • Hedging ( Forwards, Futures, Swap) • Option • Insurance • Diversification • Managing Exchange Rate Exposures • Risk Transfers and Economic Efficiency • The Probability Distribution : • Measuring the Expected Return • Measuring risk (the Variability of Returns): Variance & standard deviation • Calculating Risk premium • Calculating Variance and Standard Deviation for Historical Data

3. The difference between uncertainty and Risk • Uncertainty; don’t know what will occur in the future. • Risk: uncertainty that “matters” for you. • Same event • We can change risk to uncertainty by risk management • Ex: You invited 20 people for a party. How many will show up. Risk • Change risk to uncertainty : every one bring the food • Suppose you can’t ask everyone invited to bring his food. How can we risk? • Order 20: option to return surplus. Without extra costs. • Order 7: with option to order more last minute • But, in both cases the price would be higher. • So, Tradeoff (risk and costs(Return):

4. Preferncesto risk • Let us toss up a coin ( krona – klave) • Let us define the expected return as: • (1) • a game with 2 outcomes: • 1- 20% prob. that you gain 500 SEK • 2- 80% prob. that you gain zero • Then on average : E(R) = .20(500) + .80(0) = 100 • If I offer a 100 and asked to not play the game. • If you offered = 100 and you are indifferent neutral • If you offered < than 100 and accept  risk averse • If offered > 100 and still want to play the game lover. • Risk averse: You are willing to accept lower, but sure, E( R). • Or, you are willing to pay to  risk. • Generally most investors are risk aversion.

5. Risk Management • Financial risks: holding stock /bond in different currencies • How can we manage such risks?…. • Financial markets offer different techniques: • Risk transfers: sell risky asset, • insurance, • Diversification . • hedging (forwards, Futures,SWAP ), • options

6. Risk Transfers • If you don’t want to sell, 4 Methods of transferring Risk: • Insurance • Premium to eliminate the risk of loss but retain the gain. • Hedging the risk( Forward, Futures & Swap) : • Action to eliminate risk exposure by giving up the potential of Gain called hedging. • Forward: A contract, cost nothing, obligate(förpliktiga) you to buy (sell) an asset in the futureat a fixed P(förutbestämt) . Vara INTE med på uppgången • Ex: framer selling wheat forward. • EX: subscribe 3 years instead of 1 year. • Options: • Diversification

7. Managing Exchange Rate Exposures • Hedging (Forward), insurance or option. • A Swedish exporter will receive $100000 in 3 month time Et = 7Kr/1$ • Sell $ forward: eliminate the risk (↓$) by giving up(↑$) • Insurance: eliminate the risk (↓$)without giving up(↑$) • Buy a put Option: the right to sell $. without giving up if (↑$). • Diversification • Hold many risky assets risk that a single asset P . • Ex: You have $100 . 2 stocks (A and B) each costs 1$. • Should you buy one stock or 2? • Suppose 2 outcomes: if succeed = 4 times If fail = 0

8. Risk Transfers and EconomicEfficiency Reallocate risk to those who are willing to bear it. • A widow inherited stocks. Care about safety& low return • A student has $10000 deposited at the bank. • Both would be better by Swap • Everybody gets the combination of risk and return that fits him • Risk transfers increase efficiency : Risk sharing • Institutions for risk management. : • Innovations in risk management because D & S: • Supply • Demand: volatility • Two problems that limit the efficient allocation of risk: • Start up costs for banks & • asymmetric information.

9. Probability Theory, Quantitative analyzes for optimal risk management • Probability distribution; • The oldest • The probability distribution and volatility • E (R) : Mean • Volatility: Pr. & spread around the mean • What are the expected return for company A & for company B for the next year? You are given the following probability distribution. • E ( R)A , mean = .2(.30) + .6(.10)+.2(-.10) = 10% • E(R)B =.2(.50) + .6(.10)+.2(-.30) = 10%

10. MeasuringVolatility (TOTAL RISK) • Variance : • (2) • Variance (2) for (A) =(.20)(.30-.10)2 +(.60)(.10-.10)2 + (.20)(-.10-.10)2= 0.016 • Variance (2) for (B) = (.20)(.50-.10)2 +(.60)(.10-.10)2 + (.20)(-.30-.10)2= 0.064 • Standard deviation: (3) • SD () for (A)= • SD () for (B) =

11. Example – Calculating Returns & Risk Premiums • You bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40. • What is your dollar return? • Dollar return = 1.25 + (40 – 35) = $6.25 • What is your percentage return? • Dividend yield = 1.25 / 35 = 3.57% • Capital gains yield = (40 – 35) / 35 = 14.29% • Total percentage return = 3.57 + 14.29 = 17.86% • Risk Premiums (E(R) –RF) • The “extra” return earned for taking on risk • Treasury bills are considered to be risk-free • The risk premium is the return over the risk-free rate • Expected Return (average for historical date) – risk free

12. Example – Variance and Standard Deviation for Historical Data • Historical Data Variance = .0045 / 3 = 0,0015Standard Deviation = 0,03872