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."

Sunday, February 15, 2009

How to recapitalize the banks with no money down!

Many people have come up with proposals to recapitalize the banks with distressed assets. Since the latest plan from Treasury Secretary Geithner still leaves a lot of room for extrapolation, let me propose my ideas for how this might be done without expending government funds up front.
This idea is based loosely on Ashby's Law: using Variety to absorb Variety. In other words, since the cost of a government guarantee is uncertain, the government can charge an uncertain but correlated back-loaded amount for it.

Context

Banks have distressed loans or securities backed by loans with high and uncertain delinquency rates. Market assigns a high risk premium to this valuation uncertainty, thus bid/ask spread is too big and no trading takes place. Without trading, there is no generally accepted market value for these assets and no confidence in any valuation models. Thus, these assets count for very little in terms of bank capital.

Problem statement:

How can government provide certainty to these distress assets so that they will count substantively toward bank capital?

My idea is as follows:
1. As per original TARP idea, hold reverse auction for pools of such distressed securities or loans.

2. Offer term is as follows, government will sell a 5y Put on this pool at $X in exchange for a 5y Call on this pool at $Y. Bank will propose the strike prices: X and Y.

3. Government will value these calls and puts using internal models and accept an exchange when the Call is valued at Z % or more of the value of the Put.

4. The Call is detachable and sellable on the market to private investors, but the Put is nontransferable.

5. Repeat above steps.

Now why should this work without the bad side effect of triggering more writedown of similar securities on other banks' books?

1. Most importantly, the Put sold by the government put a floor on the value on the pool of assets and changes the psychology of investor toward these assets: i.e. the uncertainty in the value of this pool+Put is greatly reduced. Thus, the uncertainty premium drops and the standard option models for this pool+Put combination become a better approximation to reality. In contrast, the standard option models would not describe well similar pools held by other banks without the floor guarantee.

2. The danger of model error is mitigated due to the well-known Put/Call Parity relation:

For any underlying, the value of the Put = value of the Call + strike price with riskless return - fair value of the pool, assuming the Call and Put strike prices and maturities are the same.

A VERY important property of this relation is that it does NOT depend on modeling assumptions at all. Thus, with Call and Put strike prices that are not too far apart and riskless rate driven to near zero. A reasonably fair exchange offer can then be constructed. Coming up with workable Cut and Put strike prices should be much easier than coming up with a fair value for the Put option alone.

3. Since the government already control several banks via capital infusion or conservatorship, the government can mandate these banks to submit exchange offers with reasonable strike prices to jump start the auction process. As the number of bidders, information availability, and market conditions changes, the hurdle rate of Z can be adjusted in subsequent auctions.

4. There is NO cash outlay by the government initially. There may be a cost when the Put is excercised at maturity, but there is also opportunity to sell the Call before or at maturity at a profit.

5. Valuation is done on a pool level, not individual securities. So if banks submit pool with varied loans and securities, there may be some diversification benefit and it would be difficult to impute prices to individual positions.

An Example in Numbers

A numerical example should make this even more clear.
Say the pool is booked at $60, but the best market offer is $20. The bid/ask spread is at $60-$20=$40. With no trading, the pool may contribute nothing to the bank capital. Let's say the bank offered a Call at $65 in exchange for a Put at $45 and the exchange is accepted. Bank will write down $15 for this pool. Now the bid/ask spread is $60-$45=$15 and the pool can be counted at $45 as part of the bank's capital. This lower uncertainty actually is input into the valuation of the Put and Call on this pool.

At th end of 5 years, if the pool has market price of $35, the government loses $10 and the bank loses $10. If the price would be $55, the bank would make $10 and the government might have made money by selling the call sometime before the end of the 5 years. If the price would be $65 or above, the bank would make $15 max, and the government would make $5 or above on the call.

Market professionals will readingly recognize this as selling a Collar on the pool to the bank. Though I think this scheme is straight-forward enough to explain to the public and the US Congress. In simplest terms, the government is offering to give a floor guarantee for these assets in exchange for a piece of the upside profit. And by providing the floor guarantee, the government is increasing the chance that it will profit on the upside along with the bank.

I would be most interested to hear of weaknesses or problems with this approach. Please feel free to add your criticism or suggestions for improvement.

Friday, January 9, 2009

Rules and Betrayals in the New Year

The major conundrum for investors these days is that many "Rules of Thumbs" that've worked for years and years no longer worked this past year. After witnessing the collapse of major firms: AIG, BSC, Lehman and then seeing Citigroup go begging for funds, the investors' set of comfortable believes were devastated.
Collapse of basic markets such as CP, money market, Repo, which almost all companies rely on for daily operations destroyed the faith Main Street once had for Wall Street. Thus, all assumptions are called into questions.

Investors feels betrayed and either do nothing or want to review every contingencies. This is rational. Yet Rules of Thumbs are really useful. They hid complexity and speed transactions. The more deeply one looks into a business, the more uncertainties one will find. For example, Reliance on Authority is a useful Rule of Thumb. It usually works quite well and is still the dominant decision making mode for individuals when it comes to complex subject such as medicine. It works by reducing complexity to a level that we're comfortable with in handling on a casual basis.

Rating agencies were set up to be Authorities who boiled down the complexities to a simple set of rankings. Yet this year, ratings no longer worked to predict credit risk. Consider the Seasonal Pattern, a common assumption in various retail business. Just because we sold 2000 coffees the same time last year, how do we know we'll sell 2000 today? May be there'll be a medical studies showing linkage to some serious illness? Are such fear probable? Very likely not. However, by using this Rule of Thumb, we got used to assessing these probabilities at zero. Now that we don't trust the rule of thumb, we'll give them a substantive probability, which is likely to be higher than a realistic estimate.

Alternatively, we might freeze in indecision. If we considered all the possible events that could go wrong, would we ever drive on a freeway? For new drivers, they have to muster up a large measure of courage and trust to go up that first on-ramp. It is no different for investor wading into an environment without rules of thumb that they trust. Until new rules of thumbs are developed and trusted, the investment process itself will be slow.

What might the new rules be like?

OLD RULE - US government will never nationalize banks, that's for third world socialist countries.
NEW RULE - US government has a constructive and active role to play in the economic system.

This mean we need to become more like "Kremlinologist", who read the subtle signs and portents to interpret future policy trends of the various US government bodies: regulators, executive branch, the conress, as well as the Federal Reserve. More specifically we need to look at President-Elect Obama's choices and priorities:

- energy
- global warming
- education
- health care
- infrastructure stimulus

By Obama's choices of appointments, we can see how these priorities will be funded. Biofuels industry, in particular, could get a lot of government assistance. At the same time, we need to consider the bailout's boundary effect: that is, the US government is selecting specific key companies to support and letting the rest find their own ways. A long queue of industries has formed to tap government assistance, but many of them will be turned away. Weak hands become take-over targets. Correct bets on where this boundary of support will be extended or withdrawn could be handsomely rewarded.

Many Rules are evolving and being redefined. Understanding these changes are essential to understanding where an active investor base can form. Let us explore how they are changing and what they may look like in the future in this and other forums.
 
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