Value at risk (VaR) has become an essential component in the toolkit of risk managers because it provides a quantitative measure of downside risk. In practice, the objective should be to provide a reasonable accurate estimate of risk at a reasonable cost. This involves choosing among the various industry standards a method that is most appropriate for the portfolio at hand. Generally VAR tell us how much loss a company can absorb or how much value is at risk of any company.
There are many existing value at risk (VaR) models both in theory and practice. Of course, each method has its own merits under different circumstances. Therefore, it is of vital importance to compare and to evaluate all these different models. Many methods have been proposed in the literature to carry out these tasks. In this thesis, we shall propose several other nonparametric approaches to evaluate VaR models. In particular, we shall propose to use the Owen's empirical likelihood method to evaluate VaR models. The advantages of the empirical likelihood method has been well known in the literature. It should be noted, however, that the empirical likelihood method has typically been studied under the independent setting although it has also been extended to cover the weak dependent data under very general setting. In our VaR models, however, we can explore the special dependence structure (e.g., martingale differences) to develop the empirical likelihood methods.
Discussion
Value at risk in government bonds
Government bonds used to be a safe asset class until very recently. Now investors not only ponder the interest rate risk of government bonds, but also the credit risk. Simply investing in AAA government bonds, what many institutional investors have opted for, is perhaps a safe solution in the short-run. But it will also provide low yields on the bond portfolio and little diversification. In this project we would like to model both the value and the risk of government bonds. And then decide on which bonds have an attractive value-to-risk trade-off, and which bonds we should not invest in.
Value
The yield on a bond tells an investor the expected return when keeping the bond until maturity. In asset management bonds are seldom kept to maturity. Hence we need to be smarter than simply look at yields. For example we can also consider the steepness of the curve which is a good predictor of future bond returns (see e.g. Ilmanen, 1996). And we can use the curve to compute the carry of the government bond index: what is the return if the curve does not change? Objective: A good value measure.
Risk
On the risk side we can look at market variables like volatilities and correlations with other bond returns. But also fiscal sustainability indicators (e.g. debt-to-GDP), ratings, credit spreads and governance scores.
Value-to-risk
In the final step we need to find the right trade-off between value and risk. For example if the risk of a country is twice as large: ...