Measuring Market Risk - Reserve Bank of India

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10 RESERVE BANK OF INDIA OCCASIONAL PAPERS extreme value theory (EVT) - modeling either the distribution of extreme return or only the tails of return distribution. 3.2.1 Non-Parametric Approach - Historical Simulation The non-parametric approach, such as, historical simulation (HS), possess some specific advantages over the normal method, as it is not model based, although it is a statistical measure of potential loss. The main benefit is that it can cope with all portfolios that are either linear or non-linear. The method does not assume any specific form of the distribution of price change/return. The method captures the characteristics of the price change distribution of the portfolio, as it estimates VaR based on the distribution actually observed. But one has to be careful in selecting past data. If the past data do not contain highly volatile periods, then HS method would not be able to capture the same. Hence, HS should be applied when one has very large data points to take into account all possible cyclical events. HS method takes a portfolio at a point of time and then revalues the same using the historical price series. Daily returns, calculated based on the price series, are then sorted in an ascending order and find out the required data point at desired percentiles. Linear interpolation can be used to estimate required percentile if it falls in between two data points. Another variant of HS method is a hybrid approach put forward by Boudhoukh, et al. (1997), that takes into account the exponentially weighing approach in HS for estimating the percentiles of the return directly. As described by Boudhoukh et al. (1997, pp. 3), “the approach starts with ordering the returns over the observation period just like the HS approach. While the HS approach attributes equal weights to each observation in building the conditional empirical distribution, the hybrid approach attributes exponentially declining weights to historical returns”. The process is simplified as follows: Calculate the return series of past price data of the security or the portfolio. Fix a value δ from the interval (0,1). Usually δ is fixed at =0.98. To each most recent k returns: R(t), R(t-1), …R(t-k+1) assign a
MEASURING MARKET RISK 11 weight proportional to 1, δ, δ 2 , …., δ k-1 , respectively. In order to make total weights sum to 1, the weights for R(t), R(t-1), …..,R(t-k+1) would be , respectively 4 . Sort the returns in ascending order. In order to obtain VaR of the portfolio for probability ‘p’, 0
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