Monday, April 20, 2009

The Myth of the One Price

In recent newspaper columns and letters, I see many people lamenting that financial engineeers created products which 'they don't know the value of'. This sentiment is understandable in that much of financial communications are geared to assuring the public that the money manager and banks knows 'precisely' what they are doing.

I thinks it's time we come clean: we don't know THE price of the CLO, CDO, or CMO tranches.
For that matter, we do not know THE price of your stock investment or municipal bond investment either. The most liquid investment you can think of, say US treasury bond, still does not have THE price. What's going on? Is this whole finance thing a sham?

The real culprit here is that we're posing a bad question.

If you want to know how much your 300 shares of IBM is worth, you'd look it up in the newspaper or quoting service, right? The problem is that that price is the last trade from the prior day or the current day. It does not guarantee that you will be able to sell your shares at that price. In fact, for liquid stocks, there will be bids at varying prices for varying size of trades. So you would be able to sell into those bids if your size fits into their requirement. This means, that you don't really know how much your shares are worth until AFTER you've sold them. Furthermore, selling your shares may move the market, such that right AFTER you've sold the shares. Another lot with exactly the same # of shares may sell at a different price.

If I don't wish to sell the shares, then I cannot know EXCATLY what they would bring on the market. That is why we do NOT know THE price of even the most liquid asset. However, the ranges of bids and offers do give me a range of maximum and minumum prices which should bracket the execution price if the trade was done. The more liquid an asset is, the tighter this range will be. We can think of this range as a measure of the uncertainty in the pricing of the stock.

For the very illiquid assets, such as low rated ABS backed by subprime loans, there are very few or no bids and offers and no transactions! Thus, the possible range of price is large indeed. By the user of models, one can narrow the estimate of the price much more and this is typically what is used for the asset's Fair Value a la FAS 157. However, as many have noted, the model depends on historical data and sometimes unobserved assumptions which add more undertainty to their output. We can certainly say that the pricing for these assets are very uncertain.

In other words, when people say that we don't know the price of an asset, they really mean that the uncertainty in the asset pricing is very large.

Risk Accounting Explored

This change in perspective dovetails nicely with the Risk Accounting proposal by Andrew W. Lo and David E. Runkle in their FT article, "Insights: Crisis fuelled by accounting" on 4/1/09: "It takes the GAAP accounting framework as the starting point, but uses the language of probability and statistics to describe the future realisations of any accounting variable."
This is an excellent proposal which I support strongly with several caveats.

1) I would focus on the income statement first rather than the balance sheet. Since some of the equity component are primarily plugs, there is no meaningful independent measurement of their uncertainty. By analyzing the uncertainties in the Asset incomes and Liability expenses, one would derive the uncertainty in Net Income. Also, one must take into consideration the impact of off-balance sheet items. Assuming that we capture the non-NI charges/adjustments, the Net Income uncertainty would generate a better estimate of the equity market value than using the balance sheet components, I believe.

2) Treating the asset incomes and liability expenses as random variables still could subject us to the inference-from-history criticism. This applies if the asset/liability random variables are calculated as distributions based on parameters estimated from historical data or as historical distributions.

3) Correlations betwen Assets and Libilities must be taken into consideration. For example, an Asset portfolio and Liability portfolio with the same variances would be a perfect match if they are perfectly correlated, i.e. the Net Income (which equals "asset income" - "liability expenses") uncertainty would be reduced to zero. However, they might be a bad match if they are negatively correlated, i.e. the variation in Net Income would be maginified instead of cancelled.

4) We are still unlikely to be able to quantify uncertainty due to tail risk/black swan events since there is rarely enough data to explicitly model them. However, this is an area where human judements might be usefully applied.

In view of these caveats, I would propose that we consider other methods to incorporate more subjective views and nonparametric models. One possibility is to apply Bayesian based inference methods such as the Dempster-Shafer theory of evidence. I shall endeavor to create an example of such a risk qualified income statement in a future blog entry.

Benefits of Risk Accountings

To the public:

The biggest accomplishment of using this method of financial reporting is to convey to the public that accounting is NOT an exact science, but rather a principled and methodical best estimate of the conditions of a company.

To the investment professional:

Let's quote Lo and Runkle again, "By viewing future values of accounting concepts as random variables, the well-developed framework of probability and statistics can be used to quantify the impact of events such as credit crunches, flight-to-quality, and volatility spikes on corporate balance sheets and income statements. Without filling this gap in GAAP, the relationship between financial crisis and a company’s prospects cannot even be articulated in an operationally meaningful way."
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