Filtering Historical Simulation. Backtest Analysis

1 Filtered Historical Simulation1 Filtering Historical simulation . Backtest Analysis1By Giovanni Barone-Adesi, Kostas Giannopoulos and Les VosperMarch 2000A new generation of VaR models, based on Historical simulation (boot-strapping), is being increasingly used in the risk management indus-try. It consists of generating scenarios, based on Historical pricechanges, for all the variables in the portfolio. Since the estimatedVaR is based on the empirical distribution of asset returns it re-flects a more realistic picture of the portfolio s risk. Unfortu-nately this methodology has a number of disadvantages. To overcomesome of them Barone-Adesi, Bourgoin and Giannopoulos(1998) and Bar-one-Adesi, Giannopoulos and Vosper (1999) introduce filtered histori-cal simulation (FHS hereafter).

2 They take into account the changes inpast and current volatilities of Historical returns and make theleast number of assumptions about the statistical properties of fu-ture price this paper we Backtest the FHS VaR model on three types of portfo-lios invested over a period of two years. The first set of backtestsconsists of LIFFE financial futures and options contracts traded onLIFFE. In the second set of backtests we examine the suitability ofthe FHS model on interest rate swaps. Finally, we Backtest a set ofmixed portfolios consisting of LIFFE interest rate futures and op-tions as well as plain vanilla go beyond the strict criteria of the BIS recommendations by evalu-ating daily risk at four different confidence levels and five differ-ent trading horizons for a large number of realistic portfolios2 ofderivative the first section we describe the backtesting methodology and re-port the results for the LIFFE portfolios.

3 To enable us to appraisethe different components of risk measurements on each of the threetypes of portfolios we run three sets of backtests, relaxing the fol-lowing assumptions in each test: in the first Backtest we keep con-stant implied volatilities and FX rates. Our Analysis focuses on howwell FHS predicts losses due to futures and options market pricechanges. In our second Backtest we simulate implied volatilitieswhile in the third Backtest we also take into account the portfolios FX exposure. Our results show that fixed implied volatility performsbetter at short VaR horizons, while at longer ones (5 to 10 days) ourstochastic implied volatility performs better. 1 Universita della Svizzera Italiana and City University Business School, Westminster BusinessSchool and London Clearing House.

4 We are grateful to The London Clearing House for providing usthe data and financing the For Backtest 1, a total of 75,835 daily portfolios; backtests 2 and 3 have a total of 75,985 portfolios. Filtered Historical Simulation2In the second series of backtests we investigate the performance ofFHS on books of interest rate swaps. We compare each book s dailyvalues with the FHS lower forecasted value. For each book we producetwo types of forecast; an aggregate market value risk expressed inGBP and a set of currency components (plain vanilla swaps in USD,JPY, DEM, and GBP are used). In the swap portfolios we find that ourmethodology is too conservative at longer the final set of backtests we investigate the performance of theFHS model on diversified portfolios across plain vanilla swaps andfutures and options traded on LIFFE.

5 This study shares the same datawith the separate LIFFE and Swaps backtests but restricts the numberof portfolios to 20 among the largest members on LIFFE. By adding toeach LIFFE portfolio one of the four swap books3 used in the swapsbacktest we form 20 combined (combo) Analysis is based on two criteria: statistical and economic. Theformer examine the frequency and the pattern of losses exceeding theVaR predicted by FHS (breaks); the latter examine the implications ofthese breaks in economic terms, with reference to the total VaR allo-cated. Overall our findings sustain the validity of FHS as a riskmeasurement model. Furthermore, we find that diversification reducesrisk effectively across the markets we study.

6 3 Four SWAP books consisting of 500 Swaps each were formed for the SWAP Backtest . Details of theportfolios are available from the authors. Filtered Historical Simulation31 Overview of VaR models play a core role in the risk management of today s financial institutions. A number ofVaR models are in use. All of them have the same aim, to measure the size of possible future losses ata predetermined probability. There are a variety of approaches used by VaR models to estimate thepotential losses. Models differ in fact in the way they calculate the density function of future profitsand losses of current positions, as well as the assumptions they rely on.

7 Although VaR Analysis hasbeen used since early 1980 s by some departments of few large financial institutions it wasn t until themiddle 1990 s that it became widely accepted by banks and also imposed by the regulators. The cor-nerstone behind this wide acceptance was a linear VaR model, based on the variance-covariance ofpast security returns, introduced by JP Morgan, RiskMetrics (1993). The variance-covariance ap-proach to calculate risk can be traced back to the early days of Markowitz s (1959) Modern PortfolioTheory, which is now common knowledge among today s risk VaR models, however, impose strong assumptions about the underlying data. For example, thedensity function of daily returns follows a theoretical distribution (usually normal) and has constantmean and variance4.

8 The empirical evidence about the distributional properties of speculative pricechanges provides evidence against these assumptions5, Kendall (1953) and Mandelbrot (1963).Risk managers have also seen their daily portfolio s profits and losses to be much larger than thosepredicted by the normal distribution. The RiskMetrics VaR method has two additional major limita-tions. It linearises derivative positions and it does not take into account expiring contracts. Theseshortcomings may result in large biases, particularly for longer VaR horizons and for portfoliosweighed with short out-of-the money overcome problems of linearising derivative positions and to account for expiring contracts, riskmanagers have begun to look at simulation techniques.

9 Pathways are simulated for scenarios for lin-ear positions, interest rate factors and currency exchange rate and are then used to value all positionsfor each scenario. The VaR is estimated from the distribution ( 1st percentile) of the simulatedportfolio values. Monte-Carlo simulation is widely used by financial institutions around the , this method can attract severe criticisms. First, the generation of the scenarios is basedon random numbers drawn from a theoretical distribution, often normal, which not only does notconform to the empirical distribution of most asset returns, but also limits the losses to around three orfour standard deviations when a very large number of simulation runs is carried out.

10 Second, tomaintain the multivariate properties of the risk factors when generating scenarios, Historical correla-tions are used; during market crises, when most correlations tend to increase rapidly, a Monte Carlosystem is likely to underestimate the possible losses. Third, Historical simulation tends to be slow, be-cause a large number of scenarios which has to be and Giannopoulos (1996) argue that the covariances (and correlations) are unnecessaryin calculating portfolio risk7. They suggested the creation of a synthetic security by multiplying cur-rent portfolio weights by the Historical returns of all assets in the portfolio. They fit a conditionalvolatility model on these Historical returns to estimate the last trading day s volatility and then calcu-late the portfolio s VaR as in RiskMetrics (1993).