Learning outcome (2007 FRM LO 55.2)

• Calculate and explain the payoff resulting from a TROR hedge of operational risk.

Does the TROR hedge operational risk? Depends on the operational-credit risk link.

Recall the protection given by a total rate of return swap (TRORS) is broader than a CDS or credit spread product. The TROR protects against default, credit deterioration and market risk. But this learning outcome asks about the ability of a TROR to hedge against operational risk.

Can a TROR hedge against operational risk. It's a matter of correlation: does an operational accident impact credit quality? The TROR hedges operational risk if operational damage impacts credit quality. This is sort of tautological and could apply generically to any risk. The TROR already hedges market value declines. So, if operational damage causes a decline in market value, the TROR therefore provides (at least a partial) hedge. This is, in fact, a cross-hedge.

This could be viewed as simple first derivative idea. Meissner defines specific operational-credit risk (page 68) as:

• The operational-credit risk (R) = (change in bond price as a %)/(change in company's outstanding equity as %).

In other words, assume bond price is a function of company equity:

• Bond price (B) = Function (company equity)

Then the specific operational-credit risk is given by a partial derivative of bond price with respect to equity: 

• Operational-credit risk (R) = change in bond price with respect to a change in company equity

Of course, this is merely a symbolic restatement of the idea "it hedges, if it in fact hedges." The fact we can use a bit of math gives us no additional insight on whether it hedges!

Total rate of return swap (TRORS)

As illustrated below:

• The notional is defined; e.g., notional = reference portfolio, notional < reference portfolio
• On coupon (swap) date, the TROR payer pays the coupon (interest) on the reference asset plus (+) the its change in value (capital appreciation/depreciation).
• On coupon (swap) date, the TROR receive pays LIBOR plus a spread

The TROR swap is a swap between the protection buyer (who transfers away the income and capital depreciation risk) and the protection seller (who is long the default risk, credit deterioration and market risk of the reference asset). But note the TROR payer is not without risk; she has sold default, deterioration and market risk, but replaced it with counterparty risk.

Meissner's example

Following Meissner's example, which is to show how the TROR swap can hedge operational risk, assume at start of period the investor implements the hedge:

Investor owns 10,000 bonds with current price of $100 per, for a $1 million investment.

Investor enters into a TROR swap for on 50% of her portfolio

 

Then the bond price drops:

• Then operational accident occurs and the bond price drops to $90.
• On revaluation, TROR receiver pays $10 reference depreciation x 50,000 bonds = $50,000. That's the capital appreciation/depreciation component; the TROR receiver continues to pay/receive the ongoing income component. In this case, it is the net difference between [LIBOR + spread - reference coupon].

This illustrates the fuzzy link between operational risk (which has a fuzzy definition) and default/deterioration/market risk (which is concretely represented by the bond price). There is only an "operational hedge" to the extent that the operational accident causes a price drop. Meissner's example is illustrative but it is a tenuous hedge. Further, if it depends on the idea that a decline in equity value is the nearest proxy for operational risk, a more direct route is to buy a put on the equity.

Reference:

Comments

1. Sarosh 17 Nov 2007

   I am a market maker and I would like a risk aversion model (hedge) in fast moving Forex market.

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