The problem with derivatives

If a bank extends a floating rate loan to a customer then it will generally say that it has an asset of 100 on its books and 100 at risk, or being pernickety 100 plus the value of interest from time to time, or being even more pernickety the principal amount and the amount of interest payable at the next interest payment date discounted to the present at a relevant short term interest rate (i.e. the value a 3^rd party would pay for the loan), but in any event the value on the books and the value at risk is pretty close to 100.

When the same bank lends money at a fixed rate, the analysis is similar except that if the prevailing long term interest rates change the value at risk will also change.  If interest rates drop, then the loan becomes more valuable (or to put it another way, the bank has more value at risk), and if interest rates increase the loan becomes less valuable. Some accounting methods would record the loan at 100, whilst more modern “mark-to-market” approaches would insist that the loan is accounted for at its market price.  This approach would seem to give a better view of the likely value of the asset on redemption or sale, but it fails to give any indication of the inherent riskiness of the fixed price loan compared to the floating rate loan.

This is a simple example but it shows clearly that two assets with similar initial values may differ over time, and it is the understanding and management of this type of risk that is at the heart of the problem of managing the risk in derivatives.

Consider a simple 5 year interest rate swap where a bank agrees to receive a fixed rate of 6% on a notional principal of 100 and pay a floating rate of interest.  The bank would account for this at 0 at inception, but what is the maximum loss?  Well if LIBOR jumps overnight to 1000% (not likely, but let’s not worry about likelihood for the moment), the bank would be paying 1,000 per year and receiving 6, so it would pay out 4,980 over 5 years.  Fortunately the bank could discount its payments at the prevailing interest rate of 1000% so that the discounted value of its loss would be 99.4, and if we repeat the calculation with higher rates of interest we will see that the amount of that loss rises asymptotically to 100 as the interest rate tends to infinity.  In other words the maximum value at risk is 100. 

Now the bullish swaps dealer will say that it is wrong to treat the swap as a potential loss of 100, because the risk of that loss is low and in any event the bank is just as likely to see the market move the other way and make a profit.  So the accountants give way and say, OK so long as you book the mark-to-market value of your swap book in your accounts we will be happy.  The problem is that they are recognising the discounted value of the assets, but not the risk that that valuation will change with a change in underlying conditions.  Banks measure this sort of risk with their value-at-risk systems but the extent to which it is reported is variable.

Now consider how this relates to various derivatives such as options which operate when certain triggering events occur.  An option is in the money if the strike price and price of the underlying make it economically worthwhile to exercise the option and out of the money if not.  An out-of-the-money option is not worthless, but has a value related to the expectation of the extent to which it may become in-the-money.  An in-the-money option has an intrinsic value related to the difference between the strike price and the underlying price and a further value related to expectations of increase in the intrinsic value before expiry.  An option that is close to being in-the-money will show the greatest variation in value with underlying conditions.  And this effect can be even more pronounced for various exotic options such as barrier options and knock in options. 

One of the problems is that there is no consistency in recognising the risk inherent in each type of instrument.  A mechanism that works effectively for loans does not work for swaps, one that works for swaps does not work for options, one that works for simple options does not work for exotic options.  At each stage risk is assessed in terms of a measurable value, but that measure does not record the first derivative of that value with respect to some variable property.  A financial product may show little value at risk under current market conditions, but that value may change with a change in market conditions.

What is the solution?  Hard to tell but one lesson from earlier regulatory regimes is the effectiveness of arbitrariness.  In a less scientific world, banks were required to allocate risk capital to financial transactions in a way that at times seemed inappropriate and in many cases seemed to be excessive.  In order to “modernise” markets bank regulators became more amenable to risk capital allocations that followed value at risk models.  The net result was that banks lowered their use of capital per unit of risk and arguably arbitraged risk/return against their allocated risk capital.  Banks might say they didn’t do this deliberately but the assumption has to be that is a natural consequence of the banks being totally flexible in the structuring of financial products whilst risk capital is allocated to those products using fixed, albeit sophisticated, methodologies. 

Imposing a more heavy handed and somewhat arbitrary allocation of risk capital will reduce the banks capacity to undertake trades and will force them to concentrate on trades that provide the highest reward for the capital at risk.