Confidence Level
The confidence level is p = (1−α), which defines the probability of the expected maximum loss. The market risk surface can be analyzed by varying the level of confidence. While the most common confidence levels are between 95 % and 99 %, they can as well vary between 90 % and 99.9% (Hendricks , 1996). The Basel Committee requires the use of 99 % confidence level in official reporting (Basel Committee, 2006). Though it is high enough for capital requirement calculations, but a lower level of confidence (e.g. 95 %) is a good bet for use of internal reporting, I believe.
Forecast Horizon
The length of the period, for which the expected maximum loss is forecasted, is known as forecast horizon or holding period. As large deviations in the portfolio value are more probable over a long period than a short one, VaR is usually greater for a holding period of one month than for a day. The portfolio composition is assumed to remain static for VaR over the holding period. The adequate length of the holding period depends on many factors like the risk is measured from a private or a regulatory perspective (Christoffersen et al. , 1998) etc. It also has an impact on the adequate length of the holding period (Khindanova and Rachev , 2000). In practice, the holding period can vary from one trading day to years, but the Basel Committee requires the use of 10-day holding period for official reporting. They still permit the use of a shorter holding period and scaling of VaR to correspond 10-day holding period (Basel Committee, 2006). Khindanova and Rachev (2000) suggest that a 10-day holding period is inadequate for frequently traded assets and restrictive for illiquid assets, which I fully agree with Khindanove specially for bank's exposure to Hedge Funds, which I feel requires more research for regulatory purpose.
Historical Observation Period
The length of the data sample in VaR calculation is known as the historical observation period. This observation period relates VaR to the history of the market risk factors, as the volatility of the risk factors is determined based on the length of the historical observation period. While the Basel Committee sets a minimum length of one year for the historical observation period (Basel Committee , 2006), while the period may vary from a month to several years in practice. However, this is permitted only if short horizon returns are i.i.d., which is not always the case (Christoffersen et al. , 1998). The regulatory requirement of 250 trading days produces rather accurate VaR forecasts when used with the most common volatility models and Historical Simulation VaR (Hendricks , 1996). Longer historical observation periods provide the most accurate forecasts (Khindanova and Rachev , 2000). Hendricks (1996) reports the superiority of 1,250-day historical observation period on the basis of an analysis of several VaR models with 95 % and 99 % levels of confidence. He finds the stability of unconditional distribution of changes in portfolio value to support the use of long periods. His results highlight the Basel Committee requirement for a minimum historical observation period of 250 days, as he finds shorter periods to produce inaccurate VaR measures. I fully agree with him and strongly believe shorter period than 5 years is not a good candidate for VaR measures. Here factors in the main problem under reference, the data scarcity for VaR measures by banks.
Uniqueness of Bootstrapped Simulation VaR
In this context, I believe the Historical Simulation VaR method is a good candidate. This measure, as a historical simulation method, does not take any distributional assumption and the distribution of the future shifts in the risk factors of a portfolio is a treated as the same way as the prior period distribution of shits to simulate the value at risk. This measure, by bootstrapping, takes care of inadequacy of data points. The data point generation by bootstrapping implicitly takes the volatilities and correlations present in the historical data. We can draw any amount of large data which is essential for model validation that may be not be case in historical simulation with less historical data.
I have tried the Historical Simulation VaR,both with bootstrapping and without bootstrapping, on same data set. The empirical result for historical simulation VaR without bootstrapped comes as 49.935 while historical simulation VaR with bootstrapped comes as 51.2312. Regulators must be happy with bootstrapping!
What I have tried with Historical Simulation (without Bootstrapping)Download file
What I have tried with Historical Simuation (with Bootstrapping)Download file
The major advantage of this method is that it neither assumes returns are normally distributed nor it assumes returns are identically distributed over time .As a result, this measure can well accommodate the fat tail for VaR, the common feature in financial markets, computation unlike other simple approaches, even in face of data scarcity.
Though I strongly believe Extreme Value Theory driven VaR measures, mostly POT method - my all-time favorite, is the best candidate for VaR measures when it comes to capture the movement in the tail of the financial return series, where lies the real risk in the volatile financial markets.
