Answer-first summary for fast verification
Answer: The actual returns, which correspond to the total return on the bank's trading portfolio, and the hypothetical returns, which represent the returns obtained from freezing the starting positions in the bank's trading portfolio
## Explanation **B is correct.** The two most appropriate sets of returns data for backtesting VaR models are: 1. **Actual returns** - These correspond to the total return on the bank's trading portfolio, including all intraday trading activities, fees, commissions, and other trading-related components. 2. **Hypothetical returns** - These represent the returns obtained from freezing the starting positions in the bank's trading portfolio, essentially showing what the returns would have been if no intraday trading occurred. ### Why This Approach is Optimal: - **Diagnostic Power**: Using both sets provides valuable diagnostic information: - If the model passes backtesting with hypothetical returns but fails with actual returns, the problem likely lies with intraday trading activities. - If the model fails backtesting with hypothetical returns, the modeling methodology itself needs re-examination. - **Regulatory Standards**: This approach aligns with best practices and regulatory requirements for VaR model validation. ### Why Other Options Are Incorrect: - **A is incorrect**: The description of "cleaned returns" is inaccurate, and these are not the correct two sets for comprehensive backtesting. - **C is incorrect**: These are not the optimal two sets, and the description of cleaned returns is incorrect. - **D is incorrect**: "Trading returns" is not a standard term in backtesting methodology. **Reference**: Phillipe Jorion, Value at Risk: The New Benchmark for Managing Financial Risk, Third Edition, Chapter 6: Backtesting VaR
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An analyst at bank LKS has been asked to validate the bank's VaR model through backtesting. The analyst uses two sets of returns data to generate results of predicted and actual losses that can be compared in the validation process. Which of the following correctly describes the two most appropriate sets of returns data to use in backtesting?
A
The cleaned returns, which are the actual returns minus any profit and loss from intraday trades, and the actual returns, which correspond to the total returns on the bank's trading portfolio
B
The actual returns, which correspond to the total return on the bank's trading portfolio, and the hypothetical returns, which represent the returns obtained from freezing the starting positions in the bank's trading portfolio
C
The hypothetical returns, which represent the returns obtained from freezing the starting positions in the bank's trading portfolio, and the cleaned returns, which are the actual returns minus any profit and loss from intraday trades
D
The trading returns, which are the actual returns minus any fees and commissions, and the hypothetical returns, which represent the actual returns obtained from freezing the starting positions in the bank's trading portfolio