Financial Risk Manager Part 1
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A hedge fund's risk analyst is carrying out a historical simulation to determine the Expected Shortfall (ES) of a portfolio. This portfolio's daily valuation depends on the stock price and the interest rate recorded at the market's close. The analyst has gathered closing values for these variables over the last 501 trading days to create a comprehensive historical dataset necessary for the simulation exercise. Day 0 represents the initial data point, and Day 500 marks the end of the historical period. Below is a snippet of the dataset:
Day Stock price (HKD) Interest rate (%) 1 76.00 2.50% 2 72.00 2.60% 500 94.00 3.80%
Based on this dataset, what are the most appropriate stock price and interest rate values that the analyst should use for the historical simulation scenario on Day 501?
A hedge fund's risk analyst is carrying out a historical simulation to determine the Expected Shortfall (ES) of a portfolio. This portfolio's daily valuation depends on the stock price and the interest rate recorded at the market's close. The analyst has gathered closing values for these variables over the last 501 trading days to create a comprehensive historical dataset necessary for the simulation exercise. Day 0 represents the initial data point, and Day 500 marks the end of the historical period. Below is a snippet of the dataset:
| Day | Stock price (HKD) | Interest rate (%) |
|---|---|---|
| 1 | 76.00 | 2.50% |
| 2 | 72.00 | 2.60% |
| 500 | 94.00 | 3.80% |
Based on this dataset, what are the most appropriate stock price and interest rate values that the analyst should use for the historical simulation scenario on Day 501?
Explanation:
The correct answer is A. In a historical simulation with a 500-day historical reference period, the 500 historical daily changes (from Day 0 through Day 500) are used to create 500 scenarios for what might happen between today and tomorrow (on Day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). The risk factors are divided into two categories: those where the percentage change in the past is used to define a percentage change in the future (such as stock prices), and those where the actual change in the past is used to define an actual change in the future (such as interest rates).
For the stock price, the historical change from Day 0 to Day 1 is calculated as a percentage change: . Applying this percentage change to the current stock price of HKD 94 gives us the simulated stock price for Day 501: , which is rounded to HKD 89.05.
For the interest rate, the historical change from Day 0 to Day 1 is calculated as an actual change: . Applying this actual change to the current interest rate of 3.80% results in the simulated interest rate for Day 501: .
Option B incorrectly applies the percentage change to the interest rate, option C incorrectly applies the actual change to the stock price, and option D is incorrect for both stock price and interest rate. Therefore, the most appropriate values for the historical simulation for Day 501 are the stock price of HKD 89.05 and the interest rate of 3.90%, as indicated in option A.