Joakim Ahlinder och Magnus Hanson: Portfolio Risk Measures over Time

The main purpose of this master thesis, commissioned by Handelsbanken, is to provide a framework for estimation of Value-at-Risk in fixed income portfolios over time-horizons exceeding one day. We conduct a comparative study of various methods of scaling one day Value-at-Risk and their respective performance, focusing on time-horizons of ten days, three months and one year, taking into consideration the specific challenges of fixed income asset classes. We also investigate Value-at-Risk scaling in the setting of non-stationary portfolio weights, concentrating on the dynamic hedging strategy CPPI.

We find that the square-root-of-time rule performs relatively well in a majority of cases, both on simulated data and on real fixed income index data. Combined with other methods, such as bootstrap, and using a two-step method, scaling Value-at-Risk to three months and one year works well for low volatility assets, less so for more volatile assets with large jumps in price.

The implementation of CPPI shows an expected change in the distribution of the returns, where we see less large drops in the portfolio value accompanied by a decrease in the expected return; however, we also see an increase in complexity and assumptions which one has to address when deciding if the implementation of a so-called Management Action structure is appropriate.