Black Swans?

1. 1. Whatever you do, whatever they do, whoever they are, whoever you are, economic cycles will survive. See my article of 2 April 2008. The path of economic growth and the role of central planners.
   2. People learn from their mistakes. The next mistakes they make will be fiendishly novel and clever.
   3. If it is breakable it will break. It is nearly impossible to say when this will happen. In the meantime, it all looks pretty unbreakable.
   4. Trying to make it unbreakable is like getting people to learn from their mistakes. New ways to break stuff are quickly found.
   5. After it is broken, an arbitrary number of people will tell you they told you so, and for an arbitrary number of reasons. Some of these will actually be people who did tell you so. Of these most of them have been telling you so for the last 12 centuries and so would have almost surely been right eventually. Of those who only recently told you so, before the fact, most of them just got lucky. The others are probably the ones who broke it in the first place.
   6. An arbitrary number of persons will tell you how to make it unbreakable. Some of these will be people who told you so. You can recognize them, they are the loudest.
   7. If after considering their solutions you think some of them sound reasonable, refer to 4 above.
   8. Bad things will happen, they always have and they always will. So will good things. The trick is to avoid letting the bad things completely destroy you. So that you will be around for the good things. And when bad things happen, some of the bad things will happen to you. The only way to avoid all the bad things is to avoid all the good things as well, since we never really know if something is a good thing or a bad thing until it’s too late. If you think that everything that happens is a good thing, the next bad thing that happens will be the last thing that ever happens to you. If you think that everything that happens is a bad thing, the last thing that happened to you will be the last thing that ever happened to you. And that’s no way to live.

In 2008, investors quickly became acquainted with the concept of liquidity, or the lack of it. But what do we mean by liquidity, and how do we price it?

Liquidity premia are already priced in some markets such as the treasury market where the spread between on and off the runs is the implied liquidity premium. But how about markets where you have a single asset and there is no concept of off and on the runs? I would like to look at liquidity from the point of view of option implied volatility in order to understand the relationship between volatility and liquidity in more detail. There are two effects at play which are somewhat inter-related which complicates how we think of the dynamics between volatility and liquidity. I would also like to think of these relationships in a non-mathematical way to avoid the complexities that mathematical rigor would introduce. Let’s just get the picture right before we go further.

Volatility tends to rise in liquidity crises. There are two possibilities here. The first is that volatility increases with decreasing liquidity. The second is that the unobserved continuous time volatility is unchanged but that decreased liquidity results in prices being observable with lower frequency (and thus at increasing intervals of time.)

Let us deal with the latter case within an option pricing context. But lets also do it simply. Well, lets at least try.

An option buyer has a right but not an obligation. An option seller or writer has the obligation but not the right. The option writer therefore has to hedge themselves for the possibility that they may have to perform under the obligation. The Black Scholes formula prescribes a hedging strategy, suggesting at any given point in time, the amount of cash (a negative amount, thus borrowing) and underlying instrument in the correct proportions, so that the option obligation is hedged. Since these proportions vary with the cost of borrowing and the underlying price level, there is significant trading involved in maintaining a hedging position. With trading comes trading costs. Even assuming away transaction costs, there will be a profit or loss generated from the trading activity. Hedging an option always generates a trading loss since one is continuously buying high and selling low. Crudely, the more volatile is the underlying, the larger the trading loss. The higher the interest rate, the more costly it is to hold the static hedging position. If one regards the option premium as the cost of hedging it and thus the trading cost plus carrying cost, the higher the interest rate, and the higher the volatility, the higher the price of the option.

Let’s concentrate on the volatility aspect. Volatility is by far the most important factor in pricing an option. So much so that options are often quoted in terms of implied volatility. We know that option prices are an increasing function of the underlying volatility. This is true under all established option pricing models continuous time processes to those which admit discontinuities.

Recall that we assume that the underlying volatility is unchanged but that we now vary the liquidity of the underlying market. This is modeled by varying the interval between transactions and thus price observation. The less liquid is the market, the longer the interval between observations.

The longer the trade interval, the more costly will be the trading cost of hedging since one cannot execute at the prices one wishes to. The cost will vary as an increasing function of the maximum possible gap or jump in the price of the underlying across intervals. It is not dependent on the actual size of the jump or on some probability adjusted size of jump. For the hedger, they must have some idea of the maximum possible jump. Now for a given volatility, the maximum possible jump size is a function of the length of the interval. Luck may result in a price mean reverting within the interval but as one cannot observe it, and one cannot rely on luck, the maximum jump size is an increasing function of the size of the interval.

Thus, the less liquid is a market, the larger the trading intervals, the larger the maximum possible jump and the larger the trading cost in hedging an option on the underlying. The larger the trading cost implies the larger the premium or the price of the option.

We now make a leap in transitioning from the option to underlying by noting that the underlying is a zero strike option on itself, assuming prices can never be negative. Even without this leap we can make our next observation.

Liquidity can be priced in implied volatility spreads. While an absolute level may be hard to obtain, we can obtain some notion of price for an instrument trading under liquid versus illiquid conditions. The details I leave to the mathematicians among us.

One can imagine using this methodology to price the value of having monthly versus quarterly liquidity in hedge funds for example. Already volatility is a factor for sorting and ranking hedge funds in a mean variance framework. This is the Sharpe Ratio. One can think of a Liquidity Adjusted Volatility leading to a Liquidity Risk Ratio which measures Return over Risk free divided by Liquidity Adjusted Volatility.

One simple application of this methodology is in pricing liquidity in different liquidity classes of the same fund. Since returns and volatility are the same, one would like to decide whether to invest in the less liquid class in return for a discount in fees. Now you can quantify it.

During the Asian Crisis of 1997, the Malaysian equity market fell initially by over 60% in from early to late 1997. It then rebounded by nearly 50% in early 2008 before falling another 60% for a total drawdown of some 76%. In Jakarta, the initial loss was 57%, the bounce 73% the subsequent fall 53% for a cumulative loss of 65%. In Hong Kong stocks fell 46% then rallied 34% before falling 40% for a total drawdown of 58%. In Singapore the initial loss was 39%, the bounce 36%, the subsequent loss 42% for a cumulative return of -52%.

Since then those markets have recovered and the economies rehabilitated themselves. 

Since their highs in 2007, the FTSE lost 46% in the initial fall, rebounded 28% from Sep 2008 lows to Dec 2008 before falling to a new low in March, the Eurostoxx fell 45% to Sep 2008, rose 30% to Dec 2008 then fell 27% to March 2009, the S&P500 fell 36%, rose 30%, fell 27% before rising 23%.

The psychology of crashes and recoveries is that initially, investors take leave of their senses and the market rises to some highly overvalued level unsupported by fundamentals. Something happens to burst the bubble and once again investors take leave of their senses in an avalanche of panic selling. Markets fall precipitously to levels unreflective of fundamentals. That is not to say that fundamentals themselves are not rapidly evolving. Governments and regulators get involved in an effort to avoid systemic failure. Investors are at first skeptical and there is no market recovery. After a while, the new measures take hold but only slightly. Investors take leave of their senses in a wave of buying fueling a relief rally. The market surges beyond the paltry improvements in fundamentals. Repeat with less volatility until investors come to their senses and market prices come to reflect fundamentals a bit more closely.

The question is which one was the big relief rally? Was it the November, December 2008 rally or the March 2009 rally? If it was November 2008, then the market low of March 2009 may have been bottom or close to bottom and the current rally is the start of a proper recovery. If the current March 2009 rally is the big relief rally, then it is likely to run out of steam soon, and the market will likely test the lows of March later this year. If it survives the test then we have the beginnings of recovery. If it barrels through to a new low, then the bear market is alive and well and new levels of support will need to be formed and tested.

The reality of the fundamentals is that things will not improve for some time yet. The first quarter 2009 results are not going to be positive, how can they be? The market has either discounted them or not. That is a matter of psychology. As for the medium term fundamentals, unemployment is on a trend with considerable momentum, trade is also on a downtrend, the various rescue plans of the US government are not very detailed and at best fail to address a number of important issues, are a supply side solution without addressing demand side problems and the outlook for economic growth is at best highly uncertain. Things could improve quickly with the volume of stimulus that has been applied, or they could simply muddle along. The point is that with volatile fundamentals, it is impossible for the market to price them.

The market is therefore likely to be a trading market driven by sentiment more than fundamentals. Direction is therefore dependent on the weather.

Later in the year, I expect we will have more clarity either way. It could be worse or it could be better. I hold with the optimists. Nothing lasts forever, not bull markets and not bear markets.

Ideal Hedge Fund Terms:

For a host of reasons, hedge funds have not offered the most investor friendly terms. The cynical view is that hedge fund managers will get away with as much as they can. The fees are high, the performance fees are charged and cannot be reclaimed if there is a subsequent loss, the manager is drifting into markets and strategies managers are unused to, liquidity is unilaterally suspended just when investors need to exit… the list is endless.

The more charitable view is that hedge fund managers have little idea how a fund should be structured; they are traders and portfolio managers and have little time or attention to spend on fund structure and terms. To be sure this is a major failing since any business needs management of liabilities as much as assets. It is telling that we refer to them as asset managers because liability management often faces neglect. And so, here is my attempt at constructing a set of fund terms and principles which are hopefully fair to manager and to investor.

Overriding Principle:

The money is yours. It is my privilege to manage your money. It is not your privilege to invest with me. Your interests come first. If that was ever violated then I am out of business. I will treat your money better than my own.

Side Pockets:

You may opt out of my side pocket class. If you choose to opt in, I will not charge you management fees on the side pocket assets under management. I will only charge performance fees on side pockets and then only when cash is realized. I will let you know when I side pocket an investment and I will provide details of each investment. If I retroactively side pocket an investment, I will charge you no performance fees. Performance fees are charged only if the investment is designated to a side pocket at inception of the position.

Gates and Suspensions:

Depending on the strategy there may be gates or not. If I run a liquid strategy, I will exclude gating in the PPM. I will restrict the right of the directors or the manager to suspend NAV and redemptions except in specific instances which will be set out in the PPM.

If I suspend redemptions, I will cease to charge management fees. I will exclude performance fees for the duration of suspension as well. That is, any NAV appreciation during the period of suspension will not be subject to performance fees.

During suspension, you are de facto a senior creditor. I will provide you with total transparency subject to non disclosure agreements.

It is ridiculous and utterly criminal and sinful for me to hold on to money against your will and then charge you management fees for the privilege.

Strategies:

I will specify my strategy with as much specificity as I can while retaining flexibility to act. This will not be easy to do, but I will to the best of my ability, specify in the PPM, what I can or cannot do. If I want to add a strategy, I will inform you and you will have the opportunity to redeem costlessly before I implement a new strategy. This restricts my ability to act quickly, or to be nimble in taking advantage of any new opportunities, but you know what you get. Alternatively, I may run the new strategy in a side pocket which you can opt into immediately or at a later date. (I am going to have difficulties finding an Administrator who can do this cheaply for all of you.)

Reporting and Transparency:

I will provide you with timely reporting. Depending on the systems I can afford, I will report to you in real time, otherwise daily, otherwise weekly, otherwise monthly. I will provide you risk and exposure reports. I will provide you position level reports only where it does not endanger the fund. I will provide high level exposure reporting and I will arrange for the fund Administrator to provide independent confirmation to you so that you can perform your own reconciliation.

I will speak to you all once a month in a scheduled investor briefing. I will take questions at the end of the call. The call will be recorded for replay. Beyond this, my head of investor relations will be happy to schedule ad hoc calls, bearing in mind that you want me to dedicate substantially all my time managing your money.

Fees:

I will charge management fees on a reducing sliding scale just like some mutual funds. I tell you that my management fees are to cover the running costs of my business, well, my costs do not rise as a proportion to my assets under management. As for performance fees, I will reserve half of my performance fees in each period into a subordination reserve. This reserve will vest (be payable to me) on a rolling basis equal to any lock up I may have but in any case no earlier than 2 years. That is, if I lose money for you, 20% of the loss will be taken away from the reserve to repay you.

Alignment of interest:

I will invest X USD of my money in the fund. I will pay full fees, and be subject to the worst liquidity terms I offer any investor. Capacity in my fund will be some fixed multiple of my investment. If I redeem from my own fund, I will disclose this and force redeem investors to maintain this fixed multiple. I am not forced to invest any fees I receive into the fund but to the extent that I do, it increases the capacity of the fund. I will be the last man standing. My capital will be the last to leave the fund.

Despite the events of 2008, many managers still violate the overriding principle: that they are looking after other people’s money. Fortunately, most managers are not like that. For too long, investor have tolerated asymmetric terms in their contracts with the fund and the fund manager. Its time to change that.