Question

Critically evaluate the use of the duration approximation of VaR

Answer 1

Use of the duration approximation of VaR

VaR Approximation Methods:

Study of various approximations to the full revaluation method of computing value at risk using the historical simulation approach reveals alternatives that can significantly reduce processing resources — but at the acceptable expense of accuracy

Assessing Risk Assessment :

Value at risk, or VaR as it is widely known, has emerged as a popular method to measure financial market risk. In its most general form,VaR measures the maximum potential loss in the value of an asset or portfolio over a defined period, for a given confidence level. From a statistical point of view, VaR measures a particular quantile (confidence level) of the return distribution of a particular period. Of all the methods available for calculating VaR of a portfolio — parametric, historical simulation and Monte Carlo simulation — the historical simulation approach (HsVaR) alone doesn’t assume any distribution for returns and directly employs actual past data to generate possible future scenarios and determine the required quantile.

1. Identify the distribution of interest rate changes

2. Map distribution onto bond prices

Computed the VAR of a $100 million portfolio invested in a 5-year note. At the 95% level over one month, the portfolio VAR was found to be $1.7 million. Can we relate this number to the portfolio duration? The typical duration for a 5-year note is 4.5 years. Assume now that the current yield y is 5%. From historical data, we find that the worst increase in yields over a month at the 95% is 0.40%. The worst loss, or VAR, is then given by

Worst Dollar Loss = Duration x 1/(1+y) x Portfolio Value x Worst Yield Increase

VAR = 4.5 Years x (1/1.05) x $100m x 0.4%

which is also $1.7 million! Thus the value at risk is directly related to the concept of duration.
The VAR approach, however, is more general, because it allows investors to include many assets such as foreign currencies, commodities and equities, which are exposed to other sources of risk than interest rate movements.