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CHAPTER 11 The Management of Market Risk

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INTRODUCTION In the previous chapters, we spent a large amount of time describing how risks can be measured In this chapter, we discuss how risk measurement is used in risk management A bank's risk-management function is typically headed by the chief risk officer (CRO) Reporting to the CRO will be –the chief credit officer –the chief market risk officer –the chief operating risk officer Within the market-risk organization there are three groups –policies and procedures –risk measurement –risk management

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Setting VaR Limits the VaR limits would be set by starting with the total capital available to the trading operation and relating that to the maximum amount of VaR that can be supported by that capital For regulatory capital, the relationship is as follows:

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Setting VaR Limits This sets the VaR limit for the trading operation as a whole For the portfolios within the trading operation, the VaR limit (VaRL) should be set including the average correlation between each portfolio If there were only two portfolios, this would be as follows: VaRL 2 All = VaRL 2 1 + VaRL 2 2 + 2 ρ 1,2 VaRL 1 VaRL 2

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Setting VaR Limits we know the limit for all trading ( VaRL All ) and we know the average correlation between the two portfolios ( ρ 1,2 ) We can therefore use the quadratic equation to get VaRL 2 in terms of VaRL 1

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Setting VaR Limits The optimal amount to be allocated to each portfolio depends on the expected return per unit of stand-alone VaR Consider an example in which one business unit is expected to return $1.5 per dollar of VaR Another is expected to return $1.3 per dollar of VaR Let us assume that the correlation between them ( ρ 1,2 ) is 0.3, and that the VaR limit for the trading operation ( VaRL All ) is $100 Table 11-1 shows different values for VaRL 1 and the consequent values for VaRL 2 to ensure that the total VaR remains at $100 It also shows the expected revenue from each desk and the total revenue

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Setting VaR Limits For this example, the total revenue is expected to be maximized if VaRL1 equals $70 and VaRL2 equals $53

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Setting VaR Limits For strategic purposes, market-risk managers typically set the VaR limits for the major desks and allow the heads of the desks to set limits for the subordinate desks For subordinate desks, the limits may be translated from VaR into a measure that is more familiar to the trader, such as duration dollars or Greeks To translate from VaR to duration dollars we reverse the process used to calculate VaR from duration:

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