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: 104107). 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

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