Statistical Methods in Finance 2023

December 19 to 23, 2023



Non Parametric Estimation Of Parameters In Different Safety First Criteria

By Tushar Kanti Powdel
Tezpur University, India

The safety first criteria are well known risk management strategies used in finance. The safety first criteria proposed by Roy[32], Kataoka[24] and Telser[37] depend on the unknown return distribution. Dutta and Powdel[15] have shown that the distribution of long term returns(in logarithmic scale) can be well approximated by normal distribution. But Cont[10] reported that the distribution of short term returns seem to be heavy tailed and negatively skewed. Therefore, the normal distribution is not an appropriate model for the distribution of short term return in logarithmic scale. Using Monte Carlo (MC) simulations we compare the mean squared errors of different safety first criteria estimators for short term return data generated by a number of time series models. The MC simulations results suggest that the safety first criteria estimators obtained using empirical distribution function and sample quantile are not significantly improved by using other parametric or non parametric estimators of distribution function or quantiles of short term return distribution. For short term period we estimate the safety first criteria using empirical distribution function and sample quantile based on short term return data. We compare the safety first criteria for short and long term for six different assets/portfolios based on real data from April 2015 to March 2023. NIFTY 50 appears to be safer than Nasdaq, Bitcoin, Russell 2000, S&P 500 and Dow Jones Industrial Average based on all the three safety first criteria for both short term and long term.