Performance measurement and risk assessment in finance

This thesis is concerned with evaluating mutual fund performance and assessing market risk involved in the investment portfolios. It consists of four closely related chapters, two on mutual fund performance measurement and two on risk assessment.; Chapter 1 presents a systematic survey of the various econometric methods used in the literature of performance measurement. We summarize the statistical properties of various performance metrics such as the Sharpe Ratio, Jensen's Alpha and Treynor Index, and compare these metrics with Morningstar's Risk-Adjusted Rating. We emphasize the importance of studying the exact sample properties of these metrics, given the paucity of mutual fund returns data. This chapter also explores the relationship between performance measurement and portfolio efficiency in terms of multivariate analysis. It turns out that the test of portfolio efficiency is equivalent to the test that there is no outperformance for all funds. The test statistics of portfolio efficiency can be expressed in terms of Jensen's alpha, Sharpe ratio and other parameters. Finally, the various methods used to classify mutual funds' styles are outlined around the development of the constrained regression technique, and the empirical results of mutual fund from non-US nations are examined.; Chapter 2 applies the standard market timing models to an unexplored database of Canadian mutual funds, aiming to test the forecasting skills of Canadian mutual fund managers. If the standard univariate test procedure is performed on each fund separately, we find no evidence of forecasting skills except for dividend funds. Because the returns of funds belonging to the same group are highly correlated, we advocate the use of multivariate test procedure to simultaneously test funds' forecasting skills. The test results show that there are more funds exhibiting forecasting skills besides dividend funds. The better performance of dividend funds is explained by fund characteristics such as management fee, asset size and management tenure.; Chapter 3 extends the forecasting of Value-at-Risk (VaR) into an asymmetric loss framework. The so-called VARLINEX forecasting incorporates the linex loss function to allow asymmetric loss when underestimating or overestimating Value-at-Risk. Two procedures to estimate the parameters in the linex loss function are proposed, and the confidence intervals of Value-at-Risk are derived through the properties of order statistics. Using the S&P 500 and the TSE 300 index data, the linex VaR estimates are calculated and compared with those computed under RiskMetrics methodology. The empirical results provide evidence that the linex VaR estimates are more accurate than those from RiskMetrics.; Chapter 4 examines how sensitive the probability distributions of option prices are to the assumptions about the distribution of asset returns. We employ the framework of Grundy (1991) and Lo and Wang (1995) where two different models of asset returns have the same risk-neutral distribution and lead to the same (current) option price formula. As we forecast forward, however, the (future) option prices will reflect the differences in the distributions. As the Value-at-Risk is a quantile of the probability distribution function, we can calculate the sensitivity of the Value-at-Risk of a typical European option to the underlying asset return distributions. The Value-at-Risk of options turns out to be extremely sensitive to the specification of the true underlying distributions.