resilience, not stability

Derivatives: The Negative Skewness in Dynamic Hedging and the Moral Hazard Problem

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In a recent article, John Kay discovered the temptations of negative skewness, even for non-bank investors. Although some may label this irrational or even a scam, seeking out negative skewness may be entirely rational in the presence of policies such as the Greenspan/Bernanke Put that seek to avoid tail outcomes at all costs. The product that John Kay describes is a equity reverse convertible bond with an auto-call feature and European barriers. A cursory internet search shows that atleast in Europe, these products are not uncommon and most are not dissimilar to the specific bond that he describes:

“If the FTSE index is higher in a year’s time than it is today, you receive a 10 per cent return and your money back (no doubt with an invitation to apply for a new kickout bond). If the FTSE has fallen, the bond runs for another year. If the index has then risen above its initial level, you receive your money back with a 20 per cent return. Otherwise the bond runs for another year. And so on. The race ends – sorry, the investment matures – after five years. If the FTSE index, having been below its initial level at the end of years one, two, three and four, now lies above it, then bingo! you get a 50 per cent bonus.

There is, of course, a catch. If you miss out on the five-year jackpot the manager will review whether or not the FTSE index ever closed at more than 50 per cent below its starting level. If it hasn’t, then you will get back your initial stake, without bonus or interest. If the index breached that 50 per cent barrier your capital will be scaled down, perhaps substantially.”

The distribution of returns of this bond is negatively skewed: In return for taking on a small probability of a significant loss (if equities fall by 50%), the investor is compensated via a highly probable but likely modest profit – it is probable that the investor only gets his principal back and the most probable profitable scenario is redemption in one year with a return of 10%.

But if the investor takes on a negatively skewed payoff, doesn’t the bank by definition take on a positively skewed payoff? And does that not invalidate my entire thesis on moral hazard? No – In fact, structured products which provide negatively skewed payoffs to bank clients frequently allow banks to take on negative skewness. Banks do not simply hold the other side of the bond – they dynamically hedge the risk exposure of the bond and it is this dynamically hedged exposure that has a negatively skewed payoff.

Dynamic hedging differs from static hedging in that the hedges put in place need to be continuously rebalanced throughout the life of the transaction. Most banks restrict their hedging to first-order and second-order risks such as delta, gamma, vega etc and only rarely hedge higher order risks. How often this rebalancing needs to be done depends on the stability of the risks themselves (how stable the risks are with regards to movements in the market and movements in time) and the realised movements in the market itself. At the extremes, a product with stable risks in a stable market environment will require only infrequent rebalancing of the hedge and a product with unstable risks in an unstable market environment will need to be rebalanced often. In a world without transaction costs and slippage, none of this matters. But in the real world, increased slippage costs dramatically reduce the profitability of a dynamically hedged structured product when markets are unstable and/or the tenor of the product increases.

For many structured products such as the auto-call reverse convertible, the risk exposure of the dynamically hedged position is as follows: a high probability of a stable and/or short lifespan combined with a small probability of an extremely unstable and long lifespan. Typically, the bank would hedge the delta and vega of the bond  sometimes utilising out-of-the-money puts and calls to replicate the skew exposure. In most probable scenarios, the risk exposure of the dynamically hedged position is fairly stable. If the market simply goes up and stays there, the bond redeems with a 10% return after one year and the hedge would have to be rebalanced very few times in a smooth manner. If the market simply goes down significantly, the risk exposure simplifies into one resembling a put option owned by a bank. But what if the market goes down a little bit and stays there? Or even worse, what if the market goes down dramatically and then reverses course in an equally swift manner but stops short of the redemption level? It is not difficult to visualise that in some scenarios, the losses due to slippage can quite easily swamp the profits and fees made at inception.

The losses are exacerbated as it is precisely in these unstable market conditions when hedges need to be rebalanced frequently that transactions costs and slippage spiral out of control – the bank then faces the option of running the risk of an unhedged position or locking in a certain and significant loss. Although many traders would argue that remaining unhedged is the more profitable strategy (sometimes correctly), senior managers almost always choose the option of locking in a known loss even if it wipes out the past profits of the business. Moreover, the oligopolistic nature of the market and the homogeneous “same-way” exposure of the banks implies that all market participants will need to hedge at the same time in the same manner. The execution of such hedging itself may also affect the fragile fundamentals of the related market in a reflexive feedback loop.

The simplistic argument against TBTF banks owning a derivatives business is as follows:  bankers accumulate large positions of a long tenor yet get paid bonuses based on annual performance. If the positions accumulated in this manner blow up afterwards, the bank and often the taxpayer is left holding the can. Banks counter this argument by pointing out that these positions are typically hedged. In a world of static hedging, this may be an acceptable argument. But in a derivative book that needs to be dynamically hedged, the argument falls apart. Most existing books of dynamically hedged derivative positions are a negative NPV asset if the likely slippage in future market disruptions is incorporated into their valuation, especially if these slippages are computed over the “real” distribution rather than a “normal” one. Warren Buffett found this out the hard way when Berkshire Hathaway lost $400 mio in the process of unwinding General Re’s derivatives book even though the unwind was executed in the benign market conditions of 2004-2005 and Gen Re was only a minor player in the derivatives market.

Even in a calm market environment, most long-tenor dynamically hedged positions are marked significantly above their true NPV net of expected future slippage. In the good times, this dynamic is hidden by the profits that flow in from new business. But sooner or later, the negative dynamics of the book (the “stock”) overwhelm the profits on the new business (the “flow”) especially as the flow of new deals dries up. And when the bank in question is too big to fail, it is not the stockholder or the retail investor but the taxpayer who will ultimately foot the bill.

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Written by Ashwin Parameswaran

November 18th, 2010 at 1:17 pm

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