Risk Management Dr. Keith M. Howe Summer 2008
Definition Risk and uncertainty Risk management Risk aversion The process of formulating the benefit-cost trade-offs of risk reduction and deciding on the course of action to take (including the decision to take no action at all).
Two more definitions • Derivatives • financial assets (e.g., stock option, futures, forwards, etc) whose values depend upon the value of the underlying assets. • Hedge • the use of financial instruments or of other tools to reduce exposure to a risk factor.
Figure 1.2. Gains and losses from buying shares and a call option on Risky Upside Inc.
Panel D. Comparison of income with put contract and income with forward contract.
Risk management irrelevance proposition • Bottom line: hedging a risk does not increase firm value when the cost of bearing the risk is the same whether the risk is borne within the firm or outside the firm by the capital markets. • This proposition holds when financial markets are perfect.
Risk management irrelevance proposition • Allows us to find out when homemade risk management is not equivalent to risk management by the firm. • This is the case whenever risk management by a firm affects firm value in a way that investors cannot mimic. • For risk management to increase firm value, it must be more expensive to take a risk within the firm than to pay the capital markets to take it.
Role of risk management Risk management can add value to the firm by: • Decreasing taxes • Decreasing transaction costs (including bankruptcy costs) • Avoiding investment decision errors
Costs incurred as a result of a bankruptcy filing are called bankruptcy costs. • The extent to which bankruptcy costs affect firm value depends on their extent and on the probability that the firm will have to file for bankruptcy. • The probability that a firm will be bankrupt is the probability that it will not have enough cash flow to repay the debt.
Direct bankruptcy costs • Average ratio of direct bankruptcy costs to total assets: 2.8% • Indirect bankruptcy costs • Many of these indirect costs start accruing as soon as a firm’s financial situation becomes unhealthy, called costs of financial distress • Managers of a firm in bankruptcy lose control of some decisions. They might not allowed to undertake costly new projects, for example.
Analysis of decreasing transaction cost by hedging Value of firm unhedged = PV (C – Bankruptcy costs) = PV (C) – PV (Bankruptcy costs) = value of firm without bankruptcy costs – PV (bankruptcy costs) Gain from risk management = value of firm hedged – value of firm unhedged = PV( bankruptcy costs) Value of firm unhedged + gain from risk management = value of firm hedged = value of firm without bankruptcy costs
Tax rationale for risk management: If it moves a dollar away from a possible outcome in which the taxpayer is subject to a high tax rate and shifts it to a possible outcome where the taxpayer incurs a low tax rate, a firm or an investor reduces the present value of taxes to be paid. It applies whenever income is taxed differently at different levels. • - Carrybacks and carryforwards • - Tax shields • - Personal taxes
Example The firm pays taxes at the rate of 50 percent on cash flow in excess of $300 per ounce. For simplicity, the price of fold is either $250 or $450 with Equal probability. The forward price is $350.
In general, firms cannot eliminate all risk, debt is risky. • By having more debt, firms increase their tax shield from debt but increase the present value of costs of financial distress. • The optimal capital structure of a firm: • Balances the tax benefits of debt against the costs of financial distress. • Through risk management: • A firm can reduce the present value of the costs of financial distress by making financial distress less likely. • As a result, it can take on more debt.
Should the firm hedge to reduce the risk of large undiversified shareholders? • Large undiversified shareholders can increase firm value • Risk and the incentives of managers • Large shareholders, managerial incentives, and homestake
Risk management process Risk identification Risk assessment Review Selection of risk-mgt techniques Implementation
The rules of risk management Risk Management • There is no return without risk • Be transparent • Seek experience • Know what you don’t know • Communicate • Diversify • Show discipline • Use common sense • Get a RiskGrade Source: Riskmetrics Group (www.riskmetrics.com)
Types of risks firms face Hazard risk - physical damage - liabilities - business interruption Market risk - interest rate - foreign exchange - commodity price Strategic risk - competition - reputation - investor support Operational risk - industry sectors - geographical regions
Assignment of risk responsibilities CEO Strategic risk management CRO Hazard risk management Operational risk management Market risk management Hedgeable Insurable Diversifiable
Three dimensions of risk transfer • Hedging • Insuring • Diversifying
A new concept of risk management (VAR) • Value-at-risk (VAR) is a category of risk measures that describe probabilistically the market risk of mostly a trading portfolio. • It summarizes the predicted maximum loss (or worst loss) over a target horizon within a given confidence interval. • If the portfolio return is normally distributed, has zero mean, and has volatility s over the measurement period, the 5 percent VAR of the portfolio is: VAR = 1.65 X s X Portfolio value
Example of VAR • The US bank J.P. Morgan states in its 2000 annual report that its aggregate VAR is about $22m. • The bank, one of the pioneers in risk management, may say that for 95 percent of the time it does not expect to lose more than $22m on a given day.
More on VAR • The main appeal of VAR was to describe risk in dollars - or whatever base currency is used - making it far more transparent and easier to grasp than previous measures. • VAR also represents the amount of economic capital necessary to support a business, which is an essential component of “economic value added” measures. • VAR has become the standard benchmark” for measuring financial risk.
Instruments used in risk management • Forward contracts • Futures contracts • Hedging • Interest rate futures contracts • Duration hedging • Swap contracts • Options
Forward Contracts • A forward contract specifies that a certain commodity will be exchanged for another at a specified time in the future at prices specified today. • Its not an option: both parties are expected to hold up their end of the deal. • If you have ever ordered a textbook that was not in stock, you have entered into a forward contract.
Example Suppose S&P index price is $1050 in 6 months. A holder who entered a long position at a forward price of $1020 is obligated to pay $1020 to acquire the index, and hence earns $1050 - $1020 = $30 per unit of the index. The short is likewise obligated to sell for $1020, and thus loses $30.
Payoff after 6 months If the index price in 6 months = $1020, both the long and short have a 0 payoff. If the index price > $1020, the long makes money and the short loses money. If the index price < $1020, the long loses money and the short makes money. S&R Index S&R Forward in 6 months long short 900 -$120 $120 950 -70 70 1000 -20 20 1020 0 0 1050 30 -30 1100 80 -80
Problem: The current S&P index is $1000. You have just purchased a 6- month forward with a price of $1100. If the index in 6 months has appreciated by 7%, what is the payoff of this position? Solution: F0=1100 S1=1000*1.07=1070 Payoff: 1070-1100= - $30.
Example: Valuing a Forward Contract on a Share of Stock Consider the obligation to buy a share of Microsoft stock one year from now for $100. Assume that the stock currently sells for $97 per share and that Microsoft will pay no dividends over the coming year. One-year zero-coupon bonds that pay $100 one year from now currently sell for $92. At what price are you willing to buy or sell this obligation?
Valuing a forward contract Strategy 1---- the forward contract Today One year from now Buy a forward contract Buy stock at a price of $100. Sell the share for cash at market Strategy 2 ---- the portfolio strategy Today One year from now Buy stock today Sell short $100 in face value of 1-year zero-coupon bonds Sell the stock Buyback the zero-coupon bonds of $100
Valuing a forward contract Cost Today Cash flow one year from now ? $97-$92 S1- $100 S1- $100 Strategy 1 Strategy 2 Since strategies 1 and 2 have identical cash flows in the future, they should have the same cost today to prevent arbitrage. ? = $97 - $92 = $5 In strategy 1, the obligation to buy the stock for $100 one year from now, should cost $5.
Valuing a forward contract The no-arbitrage value of a forward contract on a share of stock (the obligation to buy a share of stock at a price of K, T years in the future), assuming the stock pays no dividends prior to T, is where S0 = current price of the stock = the current market price of a default-free zero-coupon bond paying K, T years in the future At no arbitrage:
Currency Forward Rates • Currency forward rates are a variation on forward price of stock. • In the absence of arbitrage, the forward currency rate F0 (for example, Euros/dollar) is related to the current exchange rate (or spot rate) S0, by the equation • where r = the return (unannualized) on a domestic or foreign risk-free security over the life of the forward agreement, as measured in the respective country's currency
Forward Currency Rates Example: The Relation Between Forward Currency Rates and Interest Rates Assume that six-month LIBOR on Canadian funds is 4 percent and the US$ Eurodollar rate (six-month LIBOR on U.S. funds) is 10 percent and that both rates are default free. What is the six-month forward Can$/US$ exchange rate if the current spot rate is Can$1.25/US$? Assume that six months from now is 182 days.
Currency Forward Rates Answer: (LIBOR is a zero-coupon rate based on an actual/360 day count.) So Canada United States Six-month interest Rate (unannualized): The forward rate is
Futures Contracts: Preliminaries • A futures contract is like a forward contract: • It specifies that a certain commodity will be exchanged for another at a specified time in the future at prices specified today. • A futures contract is different from a forward: • Futures are standardized contracts trading on organized exchanges with daily resettlement (“marking to market”) through a clearinghouse.
Futures Contracts: Preliminaries • Standardizing Features: • Contract Size • Delivery Month • Daily resettlement • Minimizes the chance of default • Initial Margin • About 4% of contract value, cash or T-bills held in a street name at your brokerage.
Daily Resettlement: An Example Suppose you want to speculate on a rise in the $/¥ exchange rate (specifically you think that the dollar will appreciate). Currently $1 = ¥140. The 3-month forward price is $1=¥150.
Daily Resettlement: An Example • Currently $1 = ¥140 and it appears that the dollar is strengthening. • If you enter into a 3-month futures contract to sell ¥ at the rate of $1 = ¥150 you will make money if the yen depreciates. The contract size is ¥12,500,000 • Your initial margin is 4% of the contract value: