Performance Measurement in Finance

74 Performance Measurement in Finance

In the case of simple discrete exposure(s), the distribution of the

uncertain cash flow can be worked out ex ante using analytical results

independent of the underlying markets. We show that incorporating

such information drastically improves Value at Risk calculations.

3.1 INTRODUCTION

When market risk is calculated, it gives the loss in value of a portfolio over a

given holding period with a given confidence level. This calculation assumes

that the composition of the portfolio does not change during the holding

period. However, variable exposures are frequent in the world of finance

and real life examples can be found within corporations, banking or asset

management. Corporate companies are faced with uncertain cash flows in a

tendering situation. Imagine a company that plans to make a bid of a specified

amount of units in a foreign currency to acquire another firm domiciled in the

foreign country. It may not be desirable for the takeover company to hedge

the potential currency exposure. Indeed if the takeover is not accepted the

optimal strategy retrospectively was to do nothing. However, if the takeover

was certain full hedging should have been recommended. Takeover-contingent

foreign exchange call options have been priced (Kwok, 1998: 104–107). A

more general problem consists in modelling the uncertain cash flows such

that an optimal hedging strategy can be designed ex ante.BrownandToft

(2001) derive optimal hedging strategies using vanilla derivatives (forwards

and options) and custom ‘exotic’ derivative contracts for a value-maximizing

firm that faces both price and quantity risks. They find that optimal hedges

depend critically on price and quantity volatilities, the correlation between

price and quantity, and profit margin.

Within banking, Jorion (2001) notes that traders change positions actively

during the trading day whereas Value at Risk (VaR) is measured over a one-

day horizon assuming that the current positions are ‘frozen’ over that time

span. Despite this, he observes that empirical results for eight large banks

indicate that on a quarterly basis VaR measures offer strongly significant pre-

dictions of the variability of trading revenues. Berkowitz and O’Brien (2001)

independently compare, for a sample of six large dealer banks, daily VaR

data as reported to regulators against subsequent trading profits. They find

that VaR estimates tend to be conservative; that is, too high. The problem

acknowledged in both papers is that the profits and losses refer to broad trad-

ing income including both the revenues generated by market-making activities

and proprietary trading. The income generated by the purchase and sales of

trading instruments on behalf of clients tends to be smoother than proprietary