Market volatility tends to fade and spike over time. Sharp corrections in financial markets occur more frequently than predicted by statistical theory. How do we explain these phenomena?

It seems to me that as a broad rule, and in particular where risk management is based on Value at Risk, that leverage is a function of underlying realized or historical volatility. In order for a portfolio to maintain a roughly constant level of risk, as represented by second moments, that is correlation and volatility, the level of leverage varies inversely with volatility. Intuitively this is prudent. Solvency requires that leverage is applied only to assets exhibiting low variability and that highly variable assets should not be highly levered.

Leverage is a function of the expected net excess returns and the volatility of the investment strategy pre leverage. As more arbitrageurs enter the market they reduce the level of mispricing between securities so that the return on capital employed in the trade is diminished and more leverage is required to produce the same return on equity. As arbitrageurs also enforce market efficiency they reduce price variation. Reduced volatility and reduced arbitrage encourage increased leverage. Increased leverage increases the probability that an unexpected data point violates the volatility assumptions leading to the need to reduce leverage.

Gross leverage is an important measure of systemic risk, both for individual participants as well as for regulators seeking to better understand system wide risk. However, delta adjusted notional exposure does not provide insight into second derivative effects which might accelerate or dampen any increase or decrease in leverage. To understand second order effects, it is useful to quantify the gamma. In a zero sum market, market net gamma is also zero. Gross gamma is the more interesting and useful quantity. Gamma concentrations at different market levels should be of interest to investors and regulators alike. These are analogous to the rapids, twists and turns along a river. Classifying gamma exposure according to the hedging activity of trader with the exposure is also important. Active delta hedgers are the target of scrutiny in the quantification of gamma since this is the source of feedback when markets begin to spiral out of control.

Realized volatility outside the expectations of historical volatility can trigger an increase or decrease in leverage. As volatility exhibits negative correlation with returns the likelihood is that a volatility breach is associated with fall in market levels. This is likely to trigger deleveraging. As markets trade to lower levels, negative gamma is likely to trigger further selling resulting in sharp corrections. At the same time, volatility rises further due to the market selling off implying a lower level of target leverage, the consequence of which is the need to deleverage. This negative feedback is likely responsible for most catastrophic market corrections.

Regulators should be mapping out gamma concentrations in addition to leverage to understand areas of unstable equilibria in markets. One would expect intelligent traders to seek and monitor the same information in their effort to avoid the landmines on the trading field, or to capitalize on them.

Unfortunately, mapping out gamma concentrations only identifies areas of unstable equilibria. What should regulators and traders do with this information? The answer to this is far away. A sharper definition of the general problem of managing systemic risk is also far away. The above is merely one facet of a vastly richer problem.

A corollary to the above characterization of gamma as a trigger for price movements is technical analysis. Often, technical analysis seems like the reading of tea leaves and other superstitions, but it is possible that investors’ desire to insure profits leads them to buy options at psychological strikes thus creating concentrations of gamma at key levels. This manifests as areas on a chart where prices cannot linger and must either retreat from (a resistance level), or bounce off (a support). A resistance once breached becomes a support, since the price cannot settle there. Maybe, there is a logic to chart reading after all, although one remains sceptical.

The SEC alleges that:

• GS failed to disclose that Paulson was involved in the portfolio construction of ABACUS 2007-AC1.
• GS misrepresented to ACA that Paulson was 200m long in the equity of ABACUS 2007-AC1.
• GS entered into CDS with Paulson that allowed Paulson to buy protection on tranches of ABACUS 2007-AC1s’ capital structure but did not disclose this to investors

The deal closed 2007 04 26. By 2007 10 24 83% of the RMBS had been downgraded and 17% were on negative watch. By 2008 01 29, 99% of the portfolio had been downgraded.

ABACUS 2007-AC1 was a synthetic CDO. Its assets consisted not of RMBS but of CDS referencing RMBS. In the construction of the collateral portfolio ABACUS 2007-AC1 would have to enter into these CDS with counterparties. Was Paulson a counterparty, the major or only counterparty?

It is going to be hard for the SEC to establish that GS defrauded investors by its failure to disclose Paulson’s role and intentions in ABACUS. Why? Paulson wanted to make a bet. A bet is not a sure thing. If Paulson or GS could affect the outcome of the bet then that is another matter. GS was effectively Paulson’s agent. GS got paid 15m to do the deal. GS job for which they were paid was to go find someone who would take the other side of the bet. GS is not bound to tell the other parties who their opposite number was. GS is indeed bound to provide full disclosure of the nature of the bet which they appear to have done. In fact, GS had a fiduciary duty to Paulson who was the paying client, a duty which includes confidentiality. One could argue that GS had a tortuous duty of care to the investors in ABACUS. Certainly there were conflicts. However, these are most certainly circumvented by the fact that IKB and ACA were market counterparties or expert and professional investors. If each party acted with due care as fiduciaries it is hard to obtain a fraud. Paulson acted for his investors. Goldman acted for Paulson and for its own shareholders. ACA and IKB all acted for their shareholders. But a bet was made and there would always be winners and losers. If anything, the quality of due diligence of ACA and IKB and the ratings agencies should be questioned.

ACA was engaged to provide an extra set of eyes on the deal. They were engaged by GS as portfolio selection agent, as well as to provide the credibility necessary to distribute the deal. It appears that ACA Capital, ACA’s parent turned up to effectively underwrite the deal as well. The SEC alleges that Paulson was involved in influencing the portfolio. This is trivially true by construction, however, things are not as clear cut as that. Paulson was specifying the bets he was willing to make. Out of the 123 underlying RMBS, ACA admitted 55. The final pool had circa 80 – 90 reference credits. ACA was not compelled to take the bets, and indeed only selected a subset of the Paulson portfolio. If we accept the SEC’s point of view we are accepting as logical behaviour the turning down or accepting of a bet based on the counterparty and not the information about the prospects, outcomes and probabilities of the bet itself.

The fact that the deal would not have placed without ACA as an independent portfolio selection agent, that Paulson had a hand in the portfolio selection, that Paulson made lots of money, are immaterial to the allegation. They are, however, the realities of the industry.

Did GS’s failure to disclose Paulson’s position long or short, constitute fraud, is the question before the courts.

There is the second allegation that is as important if not more. In my mind, this is the SEC’s stronger allegation since the misrepresentation leads to fraud. This is the allegation that GS represented to ACA that Paulson would invest 200m in the equity of ABACUS 2007-AC1. The SEC complaint does not present supporting evidence. It is possible that the evidence exists, however, they have not referred to in the formal complaint at this time. For the time being what they have in the complaint seems to indicate that ACA assumed that Paulson would be long the equity, and GS simply failed to correct them. If so, it was a costly assumption for ACA and their parent.

Why might ACA assume that Paulson was long equity? The Paulson trade resembles a more common and widely executed trade which attempted to profit regardless of the direction of credit spreads in the reference portfolio. The Magnetar trades were of this nature. The trade involves being long the equity or junior tranche of the cap structure while being short the mezz or senior tranche of the cap structure on a delta neutral basis. This trade generates profits if spreads widen or tighten. How? The equity tranche is convex to spread widening. The more senior tranches are relative concave to spread widening. By delta hedging a long equity (convex) position with a short mezz (concave or negatively convex) position, the convexity of the bundle can be very pronounced leading to a long spread volatility position. As this was a common trade at the time, ACA might reasonably assume that the Paulson was attempting the same trade. It appears not, and that Paulson did not have a long equity position against the short mezz. It was in fact an unhedged and highly speculative trade for Paulson and one which could have gone wrong with serious results. ACA had probably assumed more sophistication on the part of Paulson than was the case. Paulson was no expert in structured credit. His background was in risk arb, a very specific hedge fund strategy. Betting on mortgages was a macro call. Using structured credit instruments to leverage this bet was arguably reckless. Fortune shone on Paulson and his bet paid off.

Guilty or innocent, GS has already been condemned by the public. Investor forums are replete with condemnations of Goldman the Vampire Squid. That much is clear. Whether this is justified or not is another matter which is not so clear.

The constructive fraud issue I think is unfounded and in any case will be very hard to prove. The related misrepresentation issue will imply fraud and boils down to the evidence, which has yet to be presented definitively by the SEC.

The lesson in all this is clear. Caveat emptor. What kind of investor are you? In the context of Poker, if you play the hand, then all you are concerned with are the details of the deal. If you play the player then it is your job to find out all about who you are playing against. And do your own homework. Quite how some of the CDO liabilities got rated AAA is a mystery to me. The speed at which the underlying collateral and the tranches were downgraded certainly calls into question the quality and value of credit ratings agencies judgment.

If the SEC is successful in its complaint, it will certainly open a can of worms. Lets just look in one narrow area, retail structured products. See all those retail structured products which are offered by private banks? Some of them are constructed with the needs of the investor in mind, but some of them are constructed because someone wanted to make a bet, and the other side of the deal needed to be found. Look at the disclosure in a structured product. Are you told who designed it? Who had a hand in designing it? Who is on the other side of the trade? Was it initiated by the structurer or their client? How many private investors would even dream of asking these questions?

There is a more interesting although less likely scenario.

Say that the SEC wanted to prosecute Paulson. Why is not important. Say the SEC has no proof. A formal complaint would go nowhere and there would be a risk of a libel countersuit, or a frivolous litigation countersuit.

The SEC might decide that it has a case against GS in a related capacity, that of a conflicted agent. The case is thin but it would allow the SEC to bring allegations against Paulson, that it cannot substantiate, with immunity from libel prosection in the course of prosecuting its case against Goldman.

This is of course mere speculation.

• I want to bet that Club X will lose their next match, he says.
• Sure, says his bookie, let me see if I can find someone to take that bet.
• The bookie makes a few calls and finds little interest.
• We need someone to scrutinize the team, says the agent. It will help in finding the other side of the bet.

Enter Mr R whom the agent has found to scrub down the team. At some stage, with the involvement of Mr R as an independent party in scrutinizing the team, the agent finds Mr Q who is willing to bet that Club X will win their next match.

Club X promptly loses their next match.

• Wait a minute, who arranged this bet? The football association says?
• We did, says the agent.
• You didn’t tell Mr Q that the bet was initiated by Mr P. This is fraud. See you in court. Says the regulator.
• Wait a minute. Mr Q knew what the bet was about. He has been betting for years. We didn’t force him to take the bet. And since when did it matter who was on the other side of a bet? Says the agent.
• Don’t be ridiculous. We all know that Mr P is one of the best punters in the game. It is not wise to bet against him. Says the regulator.
• Not before this bet no you didn’t know that. So, you’re saying you would bet that Club X would win as long as Mr P was not betting that Club X would lose. Says the agent.
• That’s right, says the football regulator. You have to identify both punters. If you did, Mr Q would not have taken the bet. Says the regulator.
• But what you are then saying by implication is that Mr P can influence the outcome of the match. Are you investigating Mr P?
• Well, no, says the regulator.

• Are you saying that Mr P can either:

1. Choose the players in the team?

2. Coerce the players to throw the match?

You need both conditions to be true to be able to influence the outcome. You see, choosing the players is one thing, but Mr Q is fully aware of the line up before the bet is made. So on the second point, are you saying that Mr P can influence how the players play? Says the bookie.

• Mr P could choose the players, says the regulator. This is clearly a conflict. The players were terrible.
• But Mr R had the final say in who plays. And by the way, Mr R knows full well that Mr P was proposing the players. Mr R still had the final say. Says the agent.
• But not that Mr P was betting against the team, says the regulator. You said that Mr P would be betting that Club X would win. That’s misrepresentation. Says the regulator.
• How is this relevant? Asks the agent.
• If Mr P was betting on Club X to win, he would hardly also bet on Club X to lose would he?
• No, of course not.
• So what is Mr P doing in all this? Asks the regulator.
• You tell me. Mr R never asked. How is this relevant? Says the agent. Mr R had ultimate say over the team. In fact, Mr R placed a bet on Club X to win.
• Because they thought that Mr P was also betting on Club X to win. You knew that Mr P was betting they would lose. Says the regulator.
• But the team might have won. Mr P might have been wrong. Would you be suing us then? Heck, we placed a small bet on Club X to win ourselves.

Is investing a zero or constant sum game? In derivative markets, FX, commodities, the game is trivially constant sum. In equities there is some debate.

Some claim that ownership of equity is a claim on future cash flows and is therefore not a zero sum game. The value of equity is therefore sensitive to growth rates and discount rates extending far into an uncertain future.

The sensitivity of valuations to this uncertain future is too high so that valuations are too uncertain to be of much value. If the valuations were as stable as some proponents of equity investing purport, their models would not be able to explain the volatility in equity prices.

As far as I am concerned, investing is very close to a constant sum game. The pie is growing but at rate close to GDP growth in order of magnitude. It does not come close to the volatility observed in the markets. This volatility must therefore represent the winners and losers around the long term trend growth rate. This trend growth rate is so small relative to the volatility that one may as well regard the game as a constant sum game. So, where there are winners, there are losers, and its all a mighty big game.

Fundamentals are only of value in their impact on investors expectations and behavior.

A minority non-control investor in a public company can talk all day about their claim on assets and cash flow and still be no more closer to being an owner or operator of the business.

A minority non control investor in a private company beyond receiving dividends owns little more than a concept of charity.

Investment can sometimes seem like just one big casino, and for many it is. For the house and the card counters, the size of the markets makes it fertile hunting ground indeed. One overriding principle in all games of strategy, even where chance plays a hand, is that you always play the players, not the cards. Games of pure chance are for mugs, and the house. The house always wins.

Its a jungle out there and the majority of the players are sheep. There are professional traditional investors who may be more sophisticated, although many of them believe that fundamentals drive prices and analyse companies to that end. The more sophisticated investor realizes that fundamentals drive prices through mass psychology and thus take a more trading oriented approach, reacting to the reactions of others.

At the top of the food chain are the lions, wolves, hyenas and cheetahs. They realize that fundamentals are meaningless beyond the impact it has on the sheep, the cattle, the intermediate predators, the scavengers and the top of the food chain, themselves.

Their job is to figure out how all the other herds, packs and prides behave. Their objective is to pick out the weaklings from the herd. Occasionally there will be the opportunity to take down an entire herd, or better, a pack or even better, another pride. The sharp investor or trader is not only aware of fundamentals but who owns the stock, who trades the stock, what are their instincts and trading habits, how do they react to good news and bad, how quickly they act and who runs and who fights. Market impact is all that counts, so one has to know all the players and their firepower and thus marginal impact.

There are examples of successful retail punters. Sheep are after all not extinct. There are enough sheep to feed the wolves and still propagate the species.

Hyenas prey on the weak, foxes prey on the stupid, cheetahs on the slow. Each predator has qualities and strategies suited to their prey.

Betting on a deal closing or breaking. If you know the water is poisoned, all you have to do is take lots of antidote and wait by the water. Eventually there are lots of carcasses that are energetically free to devour.

Front running volatility. Watching structured products issuance in the retail investment market gives clues as to chronic demand supply imbalances in the vol market. A professional vol trader may look at vol surfaces and technicals to trade. The predator watches the root source of demand and supply and trades ahead of even the professional vol trader.

Knowing who is in play, what do they need, what are their instincts, what they will likely do next, what is their impact, is ultimately more important than knowing companies. The only time knowing companies is important is when you have control, or if not control then significant influence, or if you have the staying power to match the maturities in the fixed term securities issued by the company. If you have neither, knowing the company may be intellectually satisfying, but of little value otherwise.

In a constant sum game the number and nature of the players is very important. You can’t have more wolves than sheep. When convertible arbitrage suffered in 2005 it was preceded by a period when over 90% of new issuance went to hedge funds and only the scraps fell to non-arbitrageurs. When equity quant strategies hit a speed bump in 2007 they had all crowded into a small cap value overweight position. When trades get crowded, the traders get burnt. Not enouigh sheep. Diversifying among managers doesn’t help in zero sum games. You only pick up the transaction costs. When a strategy gets crowded there are only two things to do, get out of the strategy, or concentrate your bet to one manager who will be top dog. You can recognize this manager, he is the contrarian in a crowded strategy. The contrarian in an uncrowded strategy is a difficult bet. You just don’t know.

Favour environments where there are lots of sheep and a few wolves. Just make sure you are betting on the wolf, or are yourself one. If you are unsure, you are the sheep. Its a theorem. Part time investors are excellent prey.

Strategies are cyclical, even absolute return ones. The cyclicality arises often from the balance of sheep to wolves. As the wolves gorge they deplete the sheep and end up crowding each other out. Some sheep learn and become wolves. At the height of the feeding frenzy the wolves are eating each other. Get out of the way. But cycles are precisely that. The sheep never learn, they only need time to regenerate. There is always another generation of sheep for the slaughter.

Darling’s budget is not only a mistake from an economic point of view, it is a strategic mistake politically.

1. Cut taxes. Sounds crazy but consider that labour and capital mobility has increased since the mid 80’s. A country is producing a product called Domicile, the price of which is Taxation. Today, demand for Domicile is elastic. Raising marginal tax rates is likely to reduce total tax revenue.

2. Cut the top rate. Drastically. The top rate is the most elastic bracket. Raising the top marginal tax rate will result in reduced tax revenue.

3. The inelastic bracket is the middle bracket. Unfortunately these represent the swing vote and wold be political suicide. Strategically, this bracket should be left alone or cut. I favor cutting.

4. Cut corporate taxes as well. Cut inheritance taxes. Attract foreign tax arbitrage capital.

5. Strategically, cutting taxes is rational but risky. It is almost certain that the immediate  is to drive the budget deficit higher. It is likely that the longer term impact is very positive as elasticity of domicile is likely to increase with time and the duration of the recovery in global growth. With an impending election loss, it makes sense to take a risky radical approach. It is short term populist and likely to win votes. If not, the fiscal problem will be inherited by the Conservatives. By the time the benefits accrue, the Conservatives would be blamed for an impairment in the UK sovereign rating. If Labour wins, there is time to claim success in time for the next election as things improve in 4 to 5 years time. Thus, doing the rational thing is also the right political strategy.