Working Liquidity Into Your VAR

VAR isn't worth much, argues Colin Lawrence, managing director and global head of market risk management at BZW in London, unless you figure liquidity and transaction costs into the equation.

Liquidity is a universal concern for anyone holding a portfolio of any type of asset. It applies to consumers holding durable assets as well as to banks holding derivatives, liabilities and assets. A homeowner may have a beautiful house, wonderfully appraised, but can't sell it. Insolvencies often occur because you can't get out of your position. Maybe it is difficult to put a value on what you're holding. For all institutions that are market-makers in financial instruments, the question posed for managing risk as well as for regulators is: What is your ability to get out of the position, or at least to hedge it effectively?

The concept of liquidity is immensely important for using VAR accurately. VAR is intended to measure the largest amount of money a position or portfolio could lose, with a given degree of confidence, over a given time horizon. This definition gives latitude in choosing both confidence level and time horizon. In practice, however, most banks choose, say, a 98 percent confidence level for their overall portfolio and a one-day time horizon. Indeed, this is the number that I report to the board of BZW.

Why 24 hours? Why not a minute, a year or 10 years? One reason is that we have ignored liquidity-the ability to convert the asset to cash at the best price. Another reason is that we have ignored the influence of transaction technology. Can the instrument be sold at the bid in the market, as VAR assumes? Let's say your position is very big in that particular instrument. If you go to the marketplace and let everyone know you have it, you can be squeezed by the people's perception that you have the position on. That is one risk you face.

The second risk is in the size of the market-when you want to sell that instrument you are limited in who you can sell it to. Of course the greater your network, the more you've invested in marketing and resources, and the greater your ability to sell it.

The third issue is the demand situation. If you have a big position, you may have to move down the demand curve and realize a lower price if you want to sell it.

By assuming a one-day horizon (or any inflexible time horizon) within VAR, what is missing is any calculation of the risks associated with liquidity-when and if a position can be sold and at what price. At BZW I have constructed a VAR model that incorporates the liquidity premium, and I test it by shadowing several large elements of the daily VAR I prepare on a bankwide basis. What we have done is work out a method by which you can unwind a position, not at some ad hoc rate a regulator imposes on you, but at the rate that market conditions tell you is optimal, so you can actually set a risk value for the liquidity. In general, that is going to raise significantly the VAR, or the amount of capital you are going to need to run that position.

It's a relatively simple concept, one that is illustrated every day in the newspapers. During a very volatile period for an asset, a bank might be forced to hold its position for a long time. Rather than phrasing the question as a regulator might (that is, by deciding that the liquidity factor is important and therefore VAR needs to be multiplied by a factor of three-a number that is pulled out of a hat), we have rephrased the question.

Given the bid/offer spread that exists in the marketplace, and given that the bid/offer spread varies with how much I can unwind, the actual risk depends on the size I've got relative to the size I am going to unwind. Then we estimate how you would liquidate that portfolio. In the end you will end up with a liquidity-adjusted number, VAR and the number of days required to get out of it.

Scenario testing and stress testing are also crucial to making VAR useful to institutions. You get one number from VAR if you look at only one confidence level, say 98 percent. That is misleading. (Simple, because management may like one number, but misleading.) The correct way to look at VAR is, first, to look at every confidence interval. You can't just look at the 98 percent level, particularly for derivatives where you could have huge convexity exposure. So we think that Greek limits, the so-called gammas and vegas which are useful for marginal hedging of books, are useless for effective risk management. If you have any big swing, these are irrelevant. What is a long gamma position could become a short gamma position quickly.

Like a snowball rolling downhill, big market movements are unstoppable. Stress testing will show what the value of the portfolio will be in any given position, and liquidity should be stress tested, because the bid/offer spread can move as well by leaps and bounds in volatile markets. Volatility goes up and liquidity dries up. Recently, during the copper crisis, we were asked, "Where is the market?" We said there isn't one. You can't unwind it. That's a case in which the transaction cost is so high, you have to stay in it. You have to hold your inventory.

Not only is it important to look at all confidence levels-what also becomes apparent when dealing in real-life situations is that the normal distribution pattern that VAR expects simply doesn't occur. Normally distributed volatilities are misleading. For a firmwide portfolio it's not so bad, because the diversification is so great that even the non-normal distributions of each position become normal in the aggregate. The normal distribution implicit in vanilla VAR is legitimate.

To take account of the limitations of VAR, BZW now uses a cascading structure to set nonlinear limits for its traders, rather than boundary limits when these can be "snowballed" through.

I publish a vast range of portfolio numbers daily for BZW traders. We look at distribution, use parametric approaches, have a cascading structure in setting limits and we don't use normality at all. Non-normality is very important. Nonlinear VAR takes account of all volatilities, convexities and nonnormalities, and we use distributions virtually up to 100 percent to show the entire range of possibilities and probabilistic outcomes.

Though it has its drawbacks, VAR is necessary to aggregate risk. It is the only tool a bank has to determine whether the value of its assets and capital means that it will be solvent tomorrow.