Questions Risk Management Workshop 1 Chapter 10 10.1, 10.2, 10.3, 10.5, 10.7, 10.8, 10.9, 10.10, 10.11, 10.12, 10.15, 10.19. 10.1 The volatility of an asset is 2% per day. What is the standard deviation of the percentage price change in three days? 10.2 The volatility of an asset is 25% per annum. What is the standard deviation of the percentage price change in one trading day? Assuming a normal distribution 10.3 Why do traders assume 252 rather than 365 days in a year when using volatilities? 10.5 Suppose that observations on an exchange rate at the end of the past 11 days have been 0.7000, 0.7010, 0.7070, 0.6999, 0.6970, 0.7003, 0.6951, 0.6953, 0.6934, 0.6923, and 0.6922. Estimate the daily volatility using both approaches in Section 10.5. 10.7 Explain the exponentially weighted moving average (EWMA) model for esti- mating volatility from historical data. 10.8 What is the difference between the exponentially weighted moving average model and the GARCH(1,1) model for updating volatilities? of the asset at the close of trading yesterday was $30.00. The parameter in the EWMA model is 0.94. Suppose that the price of the asset at the close of trading todayis $30.50. How will this cause the volatility to be updated by the EWMA model? 10.10 A company uses an EWMA model for forecasting volatility. It decides to change the parameter from 0.95 to 0.85. Explain the likely impact on the forecasts. λ λ 10.11 Assume that an index at close of trading yesterday was 1,040 and the daily volatility of the index was estimated as 1% per day at that time. The parame- ters in a GARCH(1,1) model are = 0ω.000002, = 0α.06, and = 0β.92. If the level of the index at close of trading today is 1,060, what is the new volatility estimate? 10.12 The most recent estimate of the daily volatility of the dollar–sterling exchangerate is 0.6% and the exchange rate at 4:00 p.m. yesterday was 1.5000. The parameterin the EWMA model is 0.9. Suppose that the exchange rate at 4:00 p.m. today proves to be 1.4950. How would the estimate of the daily volatility be updated? λ
10.15 Suppose that the daily volatility of the FTSE 100 stock index (measured in pounds sterling) is 1.8% and the daily volatility of the dollar–sterling ex- change rateis 0.9%. Suppose further that the correlation between the FTSE 100 and the dollar–sterling exchange rate is 0.4. What is the volatility of the FTSE 100 when it is translated to U.S. dollars? Assume that the dollar–sterling exchange rate is expressedas the number of U.S. dollars per pound sterling. (Hint: When Z = XY, the percentage daily change in Z is approximately equal to the percentage daily change in X plus the percentage daily change in Y.) 10.19 Suppose that the price of an asset at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price at the close of trading today is $298. Update the volatility estimate using(a) The EWMA model with = 0λ.94(b) TheGARCH(1,1) model with = 0ω.000002, = 0α.04, and = 0 β . 94 Chapter 12 12.3, 12.4, 12.5 , 12.6, 12.7, 12.8, 12.9
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- Fall '16
- Exchange Rate, Portfolio Manager, Risk in finance, Operational risk, Value at risk