Larry Hickey, Principal Advisor, Risk Limited Corp.

Culling through 57 publicly reported instances of unauthorized trading and/or improper trade valuation between 1974 and 2009, recurring, actionable themes jump off the page. Your ETRM system may not be able to remedy a star trader culture, or 'independent' prices sourced from a buddy or trades that haven't been entered. But in many cases, all the information necessary to detect the problem has been properly captured in the system. The key is knowing what to look for.

Men

The English language has no word meaning 'he or she' and the phrase itself is clumsy and distracting to the reader. Many writers work around this by alternating the use of 'he' or 'she' when the person being discussed could be a man or a woman. But that compromise doesn't seem quite fair in this case. In reviewing published reports of 57 instances of rogue trading, I could find only one case where a female created the losses (Citibank – 2003). There are two other cases in China where female supervisors were held accountable for their male underlings' misdeeds (Hunan Zhuzhou Smelting Plant – 1997, China State Reserves Bureau – 2005). We'll omit consideration of the male Morgan Grenfell fund manager who showed up in court dressed as a woman. Rogue trading, it seems, is very much a guy thing. So 'he' is used throughout this article.

High delta options

High delta options, which have a high likelihood of being exercised, have featured in several rogue trading episodes. For example, in the AIB incident, John Rusnak would enter offsetting deep in-the-money currency options. He sold the long-dated option and bought the short-dated one. In a bit of financial alchemy that went unquestioned, the premiums were identical. The back office was told that confirmations were unnecessary. He would then fail to exercise the fictitious long option. Rusnak went on to lose $691 million before being uncovered in 2002.

High delta options arise most often when there has been a significant move in the underlying price. Of more particular interest to the risk manager are options that had a high delta when they were traded.

The curious risk manager might run a report to see all open options with a time to expiration greater than a week and a delta above 80. We won't look at short-dated options because all options eventually have a delta of 100 or 0 at expiration and we we're not looking for routine options expiring in-the-money. The report should include the counterparty, trade date, expiration date, delta, trade P&L and value. The risk manager's local knowledge of what is normal is critical if we're to spot trades that seem to break the pattern. Does anything on the report strike you? Is a lot of value concentrated in a few trades? Do you see any pattern in the counterparties? Focus on the bought options. Are those counterparties real? They weren't at Barings in 1995 or at West LB in 2007.

If a hole is to be discovered in your accounts tomorrow, it will look like a receivable today.

Now, for each open high delta option, rerun the report as of the option trade date. We're looking for two things – evidence of an off-market trade price which will show up as a large P&L number and/or a high delta.

Options with a high delta when traded merit a closer look. With rare exception, at-the-money or out-of-the-money options are traded. When a broker goes out to market makers for a price, only the expiration date and strike - the price at which the underlying will be bought or sold if the option is exercised - is mentioned. Unless specified up front, strikes above the forward price are calls and strikes below are puts. The implied volatility price for a strike applies equally to the put and call. There may be a legitimate reason for trading a high delta option, such as closing out a specific position to reduce a credit exposure, but that reason should be clarified.

Related transactions

What about instances where the trade date P&L is large? Did prices move that day? If not, were there other related transactions, possibly with the same counterparty? Is there evidence that a gain on one trade was offset by a loss on another? Follow the money.

If there is a disconnect between realized and unrealized P&L for the purposes of bonus or budget calculations, the possibility of gaming must be considered.

Do these related transactions have the effect of moving P&L from one reporting period to another? Is P&L being moved into or out of the period used to determine bonuses? Both would be problematic, but 'into' is more so. Robbing Peter to pay Paul is one thing. Robbing Peter to pay the traders is another. 'Out of' may be sandbagging. Are bonuses capped in any way? Is P&L in the next reporting period worth more to the traders than P&L this period?

The snowball

Really big losses don't usually start out that way. They start small and the trader tries to trade his way out. As positions expire, the losses will have to be rolled forward to avoid detection. As the losses mount, the positions being rolled forward grow ever larger. We saw this in the China Aviation Oil fiasco of 2004, for example.

Run a report of your P&L on open trades grouped by counterparty. Look for 'unlucky' counterparties; the counterparties to your profitable trades. Do one or two stand out? If so, pull up all trades with these counterparties over the past year. Is there any evidence of trades regularly being rolled over into bigger positions? Pull up all versions of these trades to see changes since inception. Has the quantity or delivery date ever been changed?

Concentrated business

Run a report of your trading volumes by broker. Is your business highly concentrated? Are any of your 'independent' prices sourced from brokers with whom you are doing a large amount of business? In particular, does your portfolio contain a large, non-standard OTC trade? Who is providing the market price used to value this position?

High Sharpe Ratio

The Sharpe Ratio is a measure of excess return per unit of risk taken. Bernie Madoff's Sharpe Ratio of 2.55 was red flag # 28 in Harry Markopolos' now famous November 2005 letter to the SEC. By comparison, the Sharpe Ratio of the S&P 500 is around .4.

How are your traders doing by this measure?

Run a report of daily P&L by trader. Store these results. At the period of your choosing, select an appropriate risk free benchmark and calculate the ratio of excess return to the standard deviation of the time series. You're interested in traders with high Sharpe Ratios. Run a report showing both sides of all internal trades for these traders. The total P&L of the internal trades must be 0. Is there evidence that P&L is being systematically moved to the high Sharpe Ratio traders through off-market transfer prices? If not, where is the 'free' money coming from?

Sandbagging

Sandbagging, as used here, is hiding P&L for recognition in a later reporting period. Look closely at your time series of daily P&L by trader. Does P&L arrive either very early or very late in the reporting period? Can money be hidden anywhere? Has there been any change in reserve assumptions? If not, compare volatilities before and after the P&L arrival.

Unlucky?

Are all rogue traders unlucky? An unscientific survey of 57 publicly reported cases of rogue trading between 1974 and 2009 only turned up one instance* where the trades were profitable. If you were to bravely assume that companies will report ALL cases of rogue trading and, less bravely, that rogue trades amount to 50/50 bets, you would have expected roughly 23 instances of winning rogue traders. Let's see how your theory stands up to the data using a statistical tool called the t distribution. Well, it turns out that your theory can be rejected with less than a 1 in 20,000 chance of being wrong. A review of the cases shows that the vast majority amount to coin flips gone wrong, as you assumed. So winning rogue trades are simply not being reported. Is the root of the problem rogue trading or rogue management?

*After a liquid lunch, a Morgan Stanley oil trader went short 5,395 oil futures on May 9th of this year. They were closed out at a profit the next day.

Off market prices

Over time, trade and market prices may diverge. That's normal. What's not normal is for them to be materially different on the trade date. Each day, run an exception report that flags any new trades where the trade price differs from the market price by some threshold. Who are the counterparties? What else have you done with those counterparties?

A daily blackout

Does your system have a defined cut-off point when no new trades are entered and reports are generated? This kind of daily snapshot instead of real-time monitoring is particularly susceptible to gaming.

Run a report of all cancelled trades. Are there a lot of them? Is there any evidence that trades are being entered for the snapshot and then quickly cancelled before they can be confirmed? Fake trades have featured several incidents including Daiwa Bank in 1995.

Short dated options

Are short-dated options being sold? These can be particularly pernicious. If there is a reporting cut-off, the option may be sold afterwards and may expire before the next day's reporting. Or the dealer may delay entering the sale to achieve this same end.

But even if the option is entered into the system and properly reported, the incremental risk may not be clear.

Let's say a Value-at-Risk (VaR) report is run for a holding period of one day and 95% confidence level. This is based on price changes being normally distributed, essentially ruling out really big moves. But every now and then really big moves do happen. On Oct 19, 1987, the Dow fell 22.6%. Using a 20% volatility, that was an astounding 18 standard deviation move. That shouldn't happen even once in the history of the universe times the number of grains of sand on earth. So if a low delta overnight option is sold, VaR may only rise slightly. Remember that VaR is a measure of the loss at the 95% confidence point. It tells us nothing about what lies beyond. To get the full story, you need to run stress tests that show what happens when the 'impossible' happens.

Run a report of all sold options where the difference between the trade date and the expiration date is less than a week. Compare when the options were entered in the system with the trade date.

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The smile

The smile is a subset of improper valuation issues. Variants of this were seen Natwest in 1997, NAB in 2004 and BMO in 2007.

The value of a standard option is function of the underlying price, the strike price, time to expiration, interest rates and volatility. Four out of five of these valuation factors are transparent. The volatility, the annualized standard deviation of the underlying price, is the only unknown. For this reason, options are actually quoted in terms of volatility, say 10%. The idea being that all the variables can be plugged into an agreed formula to yield the dollar price.

The agreed formula assumes a normal distribution. But it turns out that markets behave somewhat differently than predicted by a normal price distribution. Markets tend to both sit still and undergo large moves more often than would be expected if the underlying process was normally distributed. Rather than adopt a more complex formula, the convention is to simply assign a different volatility to each strike. This is called the 'smile' because the lowest vol is typically for at-the-money options, where the strike is near the forward price. Strikes that are away from the forward price are usually assigned higher volatilities. Note that this is not always they case, in which case the 'smile' becomes the 'smirk'.

Offer

Would you like a spreadsheet to help price out-of-the-money options? Price any strike for any date. Inputs are at-the-money volatilities, butterfly and risk reversal prices, interest rates, holidays, and weekend and holiday variance factors. The input information is used to build the volatility surface. To price an option, type in the expiration date, put or call, strike and underlying price. The output is the implied volatility and delta. Results are not reliable below five delta. The spreadsheet assumes vanilla options, no dividends and out-of-the-money volatilities >= at-the-money volatilities. If you'd like to receive this free pricing tool, send an email to lhickey@riskltd.com.

What can go wrong? Well, if all strikes for a given expiration date are valued against a single volatility, there is an opportunity for gaming. By selling strikes away from the forward price an artificial profit appears if the sales are being marked against the lower at-the-money volatility. However, selling options will produce a short vega - the change in an option's price for a 1% increase in volatility - position and increase VaR. So the trader may buy in the cheaper at-the-money strikes, to flatten the vega exposure while still showing the artificial profit. This is called 'selling the wings' and can be accomplished using a vega neutral call spread, put spread or butterfly. Keep in mind, that at-the-money options have more vega than out-of-the money options. So the trader is selling more out-of-the-money options than he is buying at-the-money options. VaR is still going up.

Under certain market conditions, the fear is one direction only. Take stocks, for example. If conditions improve, markets may be relatively orderly and quiet as prices climb the proverbial wall of worry. Think of May to August of this year. If conditions worsen, markets are likely to be panicked and see violent price swings. Think of January to April of this year. The fear is down. Higher prices point to lower volatility and lower prices point to higher volatility. So out of-the-money puts trade at a higher price than out-of-the-money calls. The smile is now a smirk.

In this environment, the trader need not take a position in the at-the-money options at all. He can show an artificial profit by selling the put and buying the call. The trade is roughly vega neutral.

To determine if your portfolio is short the wings, run a report that shows your vega position by month. Now raise all volatilities by 1% and rerun the report. For each month, if your vega position went up or became less negative, you are long the wings. If it went down or became more negative, you are short the wings. If you are using a flat volatility and you are short the wings, your P&L is overstated.

If you are concerned that the position is systematically short wings on one side and long on the other, run the report showing your vega position by month with the underlying price down by 1% and then up by 1%. If you're long calls and short puts, the second vega will be higher. If this is an equity portfolio, your P&L may be overstated. Market prices for this trade, called a 'risk reversal' among other names, are readily available from brokers.

Rogue traders are proving to be a persistent lot. The most recent incident at PVM Oil Associates, the world's largest OTC oil brokerage, was reported in July of this year. But there doesn't seem to be a lot of innovation among them. We see the same old games played time and time again. A savvy risk manager asking the right questions of his ETRM system has to be favored in heads up play.

About the author

Larry Hickey started the first foreign exchange options business in Ireland for AIB in 1996. Hickey left the bank in 1998 for the deregulating US energy markets. One of his former colleagues at Allfirst Bank, then part of AIB Group in Baltimore, was John Rusnak, who was sentenced to 7-1/2 years in prison on Jan. 17, 2003, for hiding US$691 million in losses at the bank after bad bets snowballed in one of the largest ever cases of bank fraud. Rusnak was released from prison on Jan. 5, 2009, after serving less than six years of his sentence. For the past decade, Hickey has focused on risk management in an effort to prevent such behavior as Rusnak's. He has worked for several vendors in the ETRM space and continues to collect stories of how rogue traders exploit the very gaps those systems seek to fill.

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