MIT OpenCourseWarehttp://ocw.mit.edu 15.997 Practice of Finance: Advanced Corporate Risk Management Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Measuring Risk – Part A: Exposure MIT Sloan School of Management 15. 997 Advanced Corporate Risk Management John E. Parsons Overview  Defining and Measuring Exposure  How Volatile are Companies?  Decomposing Risk to Factors  Modeling Exposure  Total Exposure  Economic Exposure  Cash Flow Exposure vs. Value Exposure 2 1Defining Exposure  When we talk about exposure, we are talking about risk. Variables that cause the value of an asset to change are called risk factors. If changes in the factor cause changes in the asset value, then the asset value is exposed to the factor.  The asset that is exposed could be, for example… ¾ the total market value of a company, ¾ the market value of a division or a project, ¾ the value of a supply contract, or ¾ the value of a security such as a stock or option or futures contract.  One set of risk factors are called market risks and include, ¾ exchange rates, ¾ general market movements, i.e., stock market indexes, ¾ the rate of inflation, ¾ interest rates, or ¾ the price of oil or other widely traded and quoted commodities. 3 Defining Exposure (cont.)  Many key risk factors don’t have a widely cited or even readily quotable index. ¾ The demand for your company’s product, product X, can wax and wane and is an important exposure. ¾ Technological progress may advantage or disadvantage your product or services.  And many key risk factors have to do with your own operations. ¾ Is your company able to implement an important new plant design? ¾ Can you train your staff to operate in a global environment? ¾ Is your R&D pipeline going to succeed in generating new, valuable drugs. 4 2An Aside  These are risks that you don’t want to hedge. Meaning you don’t want to just sell them away. If you do that, you might as well quit the business. If you think this is a business that you should be in, then these are the risks you claim to be able to master. You will profit by taking on these risks and winning at them. This is what you invest your capital in. In order to make a profit, this has to be the gamble you take on. 5 Exposure Measures  There are many ways to measure exposure or risk. ¾ A common measure of risk is volatility, i.e., the standard deviation of the value. We can speak interchangeably about volatility and variance, since variance is the square of the volatility. Therefore, exposure to factor X is the volatility in value due to movements in factor X. ¾ There are other measures of risk. A recently popularized measure is the value at risk or VAR. The VAR is the expected loss at a given confidence level, for example, the 5% confidence level. ¾ Why are there multiple measures of risk? Because risk is a complicated thing! ¾ Only in special cases, such as the normal distribution, can a random variable be summarized by just 2 parameters – expected return and variance. Many key risk factors are not well described by the normal distribution. For example, some have fat tails. And many asset exposures are asymmetric, creating a non-linear relationship between the factor and the asset value so that the distribution of the asset value is highly skewed. Therefore, variance is not a sufficient measure of risk. 6 3Exposure Measures (cont.)  A proper definition of exposure requires that we specify the horizon over which risk is measured. ¾ Is the exposure measured over a day, a week, a year? ¾ The size of the exposure may be sensitive to the horizon. For example, within a short horizon it may be impossible to close out a position. However, over a long horizon this is possible, and this puts a floor on the downside. The importance of horizon is even greater for analyzing risk at non-financial corporations than at financial corporations.  Exposures can also be conditioned on key variables. ¾ Market depth varies through time and can affect the volatility of a stock or other investment. ¾ General GARCH properties. Be careful about observing a simple average across all market conditions and then projecting that forward at a given time. 7 3 Examples of Exposure Calculations  Exposure of a receivable to a movement in the exchange rate.  Exposure of a call option to changes in the stock price.  Exposure of a company’s stock price to environmental legislation. 8 4Example #1: Exposure of a receivable to a movement in the exchange rate  An Italian aircraft parts manufacturer has made a sale to a US company. It has delivered a parts shipment invoiced at $3.20 million. The cost of goods sold is €1.95 million. Payment is due in 3 months. The €/$ rate is 0.6842.  Measured in Euros, the receipt on the transaction are risky. A 1% change in the exchange rate implies a €20,000 change in the Euro denominated value of the receivable.  The 3-month volatility in the Euro/Dollar exchange rate is 8.9%, i.e., ±8.9% is a one-standard deviation movement in the exchange rate over a 3-month horizon. 9 Example #1: Exposure of a receivable to a movement in the exchange rate (cont.) Standard Deviations Percentile Exchange Rate Receivable in Euros Gain or Loss +2 98% 0.8047 2.58 0.39 +1.65 95% .7831 2.51 0.32 +1 84% .7439 2.38 0.19 0 (Mean) 50% .6831 2.19 0 -1 16% .6223 1.99 -0.19 -1.65 5% .5831 1.87 -0.32 -2 2% .5615 1.80 -0.39 10 511 Example #2: Exposure of a call option to changes in the stock price  Using the Black-Scholes formula for a stock with a current price of $100, a strike price of $100, a time to maturityof 2 years, a volatility of 22%, andassuming the risk free rate is 5%: C($100) = $17.1.  There is significant upside and limited downside. It is a very non-linear exposure.  At the current price of $100, the option delta is 0.68331. Meaning that a $1change in the stock price yields an approximately $0.68 change in the call price.  But clearly for a large move in thestock price up, for example, $100, the change in the call price will be more than $68: C($200)-C($100) = $109.6-$17.1 = $92.5.  And for a large move down, the change in the call price will be much less. C($0)-C($100)= -$17.1. 0 20 40 60 80 100 120 0 50 100 150 200 Stock Price Call Price 12 Example #2: Exposure of