Value at Risk of a Lehman Bond

Abstract

One fine day Scilla, a person who wants to be very cautious, invests the savings of a lifetime on a bond. Scilla feels quit safe, because the bond, issued by the Lehman Brothers bank, is part of a list of bonds declared low risk/return by a consortium of banks called Patti Chiari. The next day she turns on the radio and discovers that the bank has failed. Along with Scilla there are several thousand small and medium-sized investors, for a total notional amount of several billion euros, both simple buyers of Lehman bonds and underwriters of insurance policies in which Lehman bonds were included as a guarantee of capital. Many of them are in dispute with their banks and with the Patti Chiari consortium which was responsible for drafting the list. One of the requirement for a bond to be in the list was to have a low Value at Risk, not above a certain threshold, that was set at 0.3125% for the one-day 99% VaR. The investors argue that the VaR of their bonds had exceeded, from some months, the maximum threshold and therefore that those bonds would have to come out of the list. A simple and direct backtesting unequivocally shows that those cases have a foundation, in particular for the bond XS0189741001 which this document deals with. That is, that any measure of one-day 99% VaR that falls within the maximum limit of 0.3125% can be declared wrong with a margin of error close to zero.