Range value at risk (RVaR) is a quantile-based risk measure with two parameters. As special examples, the value at risk (VaR) and the expected shortfall (ES), two well-known but competing regulatory risk measures, are both members of the RVaR family. The estimation of RVaR is a critical issue in the financial sector. Several nonparametric RVaR estimators are described here. We examine these estimators’ accuracy in various scenarios using Monte Carlo simulations. Our simulations shed light on how changing p and q with respect to n affects the effectiveness of RVaR estimators that are nonparametric, with n representing the total number of samples. Finally, we perform a backtesting exercise of RVaR based on Acerbi and Szekely’s test.
An index fund is a mutual fund that aims to imitate a benchmark index. In India, there has been significant growth in the number of such funds since 2002. These funds are exposed mainly to market risk. The assessment and comparison of the market risk and the risk-adjusted returns of these funds are topics of interest to both researchers and investors. Value-at-risk and expected shortfall are wellknown measures of the market risk. The Sharpe ratio and the Treynor ratio measure risk-adjusted return earned in excess of average market return. For each fund, we estimate these measures. Most of the index funds exhibit similar market risk as the NIFTY or the SENSEX index, which they mimic. Moreover, the market risk of these funds seems to be unaffected by multiple-fund management by the respective fund managers. However, there exist significant differences among the risk-adjusted daily returns, earned in excess of the average daily index return, of the various Indian index funds. Ideally, an index fund is expected to exhibit similar risk and risk-adjusted return as the benchmark index. We identify some such Indian index funds.
Spectral risk measures (SRMs) belongs to the family of coherent risk measures. A natural estimator for the class of spectral risk measures (SRMs) has the form of L-statistics. We propose a kernel based estimator of SRM. We investigate the large sample properties of general L-statistics based on i.i.d cases and apply them to our kernel based estimator of SRM. We prove that the estimator is strongly consistent and asymptotically normal. We compare the finite sample performance of the kernel based estimator with that of empirical estimator of SRM using Monte Carlo simulation, where appropriate choice of smoothing parameter and the user's coefficient of risk aversion plays an important role. We estimate the exponential SRM of four future indices, namely, Nikkei 225, Dax, FTSE 100 and Hang Seng using our proposed kernel based estimator.
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