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Answer: The stock price would be HKD 89.05, and the interest rate would be 3.90%
A is correct. In a historical simulation with a 500-day historical reference period, the 500 historical daily changes (from Day 0 through Day 500) are used to create 500 scenarios for what might happen between today and tomorrow (on Day 501). In practice, the risk factors that may be used in a historical simulation are divided into two categories: those where the percentage change in the past is used to define a percentage change in the future, and those where the actual change in the past is used to define an actual change in the future. Stock prices are usually considered to be in the first category, while interest rates are usually considered to be in the second category. The historical change in the stock price from Day 0 to Day 1 should therefore be measured as 72 / 76 − 1 = −5.263% change, while the change in the interest rate should be measured as 2.60% − 2.50% = 0.10% change. Applying these changes to the current stock price and interest rate of HKD 94 and 3.8%, respectively, produces a scenario for the historical simulation with a stock price of 94 * (1 − 0.05263) = HKD 89.05263, and an interest rate of 3.80% + 0.10% = 3.90%.
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2. A risk analyst at a hedge fund is conducting a historical simulation to estimate the ES of a portfolio.
The value of the portfolio at market close of any given day depends on the price of a stock and the level of an interest rate at the close of that day. The analyst uses closing values of these variables on the most recent 501 trading days as the historical dataset for the simulation and collects the following data, with Day 0 representing the first data point and Day 500 representing the last data point of the historical period:
| Day | Stock price (HKD) | Interest rate (%) |
|---|---|---|
| 0 | 76.00 | 2.50% |
| 1 | 72.00 | 2.60% |
| ... | ... | ... |
| 500 | 94.00 | 3.80% |
What stock price and interest rate would be most appropriate for the analyst to use in the scenario of the historical simulation for Day 501?
A
The stock price would be HKD 89.05, and the interest rate would be 3.90%
B
The stock price would be HKD 89.05, and the interest rate would be 3.95%
C
The stock price would be HKD 92.00, and the interest rate would be 3.90%
D
The stock price would be HKD 92.00, and the interest rate would be 3.95%