2008: Beyond the 95th Percentile

Statistical thinking in financial risk management – Several years ago I traded Hartford Financial Group (HIG) profitably at prices from 80 to 100. More recently, I lost pretty good money buying at prices under 40. After the shares got down as low as 4.58, fueled in part by concerns about their exposure to losses on variable annuity guarantees with the S&P 500 at levels of 800 or lower, I started wondering, was there some way to pick up on the risks presented by these guarantees?

Looking at their 10-K, there is a fairly long section devoted to disclosure of this risk. In reading it you want to look for the phrase "95^th percentile":

Variable Annuity Equity Risk Impact on Statutory Distributable Earnings

In addition to the impact on U.S. GAAP results, Life's statutory financial results also have exposure to equity market volatility due to the issuance of variable annuity contracts with guarantees. Specifically, in scenarios where equity markets decline substantially, we would expect lower statutory net income and significant increases in the amount of statutory surplus Life would have to devote to maintain targeted rating agency, regulatory risk based capital ("RBC") ratios and other similar solvency margin ratios. Life's statutory net income for the years ended December 31, 2007, 2006 and 2005 was $729, $1.1 billion and $821, respectively. Life's statutory surplus as of December 31, 2007, 2006 and 2005 was $5.8 billion, $4.7 billion and $4.3 billion, respectively. In order to estimate the impact equity markets could have on statutory financial results, Life projected 2008 statutory net income and the amount of statutory surplus required to maintain our financial strength ratings (targeted statutory surplus) under various stochastic scenarios and assumptions consistent with other sensitivity analyses performed by Life. Each scenario included the effects of guaranteed living and death benefit reinsurance, in-force hedging assets in place at December 31, 2007 and future dynamic hedging of GMWB riders. The sum of Life's projected 2008 statutory net income and the (increase) decrease in the amount of targeted statutory surplus in each scenario is an estimate of the Life's "statutory distributable earnings". Subject to legal or regulatory constraints, statutory distributable earnings are usually available to dividend to an insurance entity's parent holding company to support debt and dividend payments to shareholders. To illustrate the effects of a tail scenario, at or near the 95th percentile, Life estimates that 2008 statutory distributable earnings generated by its variable annuity business could be $1 — $2 billion worse than the mean of the stochastic scenarios. These tail events involve U.S. equity market declines of varying degrees, including rather large equity market declines of 20—25% from December 31, 2007 levels, or a combination of more moderate equity market declines in scenarios where the Japanese yen significantly strengthens against the Euro or the U.S. Dollar and interest rates rise significantly.

The "rather large equity market declines of 20-25%" are well less than the 50% from 12/31/07 to 11/21/08. Hartford wasn't seriously considering the possibility that the tail could get out past the 95^th percentile – that the S&P could get into the 700 area.

Beyond the 95^th percentile - Large companies of this type have risk management functions, usually run along statistical lines where the distribution of possible inputs and outcomes is viewed in terms of bell-shaped curves. Anything beyond two standard deviations, approximately the 95^th percentile, or the 5^th percentile on the other tail, is frequently disregarded as remote possibilities not worth worrying about.

2008 not normally distributed - That is the distinguishing feature of the year 2008 – the whole market has gone beyond the 95^th percentile, into an alternate reality, where the tail risks (and losses) keep doubling ad infinitum.

For years up to 2008, I made money fairly reliably using an analytical system that regarded the P/B, P/S, or P/E of certain types of stocks as being log-normally distributed. The strategy was, to buy stocks at the 20^th percentile or below and sell them at the 50^th. I have an interest in options, and adapted the ideas from the options pricing models.

Applying a similar line of reasoning to the S&P 500, I could say the 95^th (or 5^th) percentile of the index was 827.3. Of course, the index went under that level and kept going.

Applying similar thinking to Hartford's stock price, based on P/B, the 5^th percentile would be 30.91, well above the current 15.xx, or the 52 week low of 4.58.

Why it doesn't work – Bell-shaped distributions don't work where you have a succession of yes/no possibilities which compound each other. Although HIG has taken steps to hedge its exposure to the S&P 500 through variable annuities, it still has some exposure along these lines:

As the S&P goes down, HIG approaches a realm where its RBC will no longer make it double A. If it is no longer double A, it may have trouble selling certain products. AIG was exposed to collateral calls in the event of downgrade. A downgrade is a yes/no proposition.

To avoid a downgrade, HIG may decide to raise raise capital, a yes/no proposition.

If the market knows HIG will have to raise capital, short selling will ensue, and the share price will decline. It's not whether the short-selling will ensure, it's whether the market gets a whiff of the capital adequacy issue, yes/no. That's why the quickie deal with Allianz (AZ) was good, even with the heavy dilution of existing shareholders.

To some extent, the realization of mark to market investment losses is yes/no. As long as regulatory and/or rating agency capital models show a company can absorb additional mark to market losses without requiring additional capital, the answer is easy – hold to maturity. But if the company can't absorb further mark to market losses without additional capital, there is a tipping point, where it makes sense to incur losses in order to prevent the risk of further market deterioration.

A series of tipping points like this can reduce a company's stock price to a fraction of previous levels, rapidly and sometime permanently. A normal distribution has nothing to do with it.

Bubbles and parabolic curves fatal to normal distribution – With the wisdom of hindsight, any phenomenon that is driven by a causal factor that is in a bubble will not be normally distributed. For example, house price appreciation was a bubble: continuously increasing prices were necessary to maintain the "normal" distribution of default rates. The entire Structured Finance system was dependent on default rates staying within the bounds of a normal distribution.

Oil prices are an important driver of our economic results and oil prices have been in a bubble, which has now burst. So, do not look for our economy to stay within its normal range.

CDS prices are in a bubble which soon will burst. CDS spreads drive credit which drives our economy. Again, not a good sign for normal economic activity.

Destabilizing the Financial System - Regulatory and rating agency capital models work along these statistical lines. AIG's collateral calls came from banks who were relying on the CDO insurance for regulatory capital. The whole system became unstable as market prices of the collateral underlying the CDOs went outside of its "normal" distribution.

Stress case models in use when MBIA (MBI) and Ambac (ABK) wrote the RMBS and CDO insurance that got them in trouble worked along similar lines, based on the concept that the migration of ratings on bonds was subject to some sort of normal distribution. One of MBIA's earlier investor presentations featured a learned discussion of stress testing at the 99.5 percentile, rigorous, you can't get there, never gonna happen...The way the migration worked out, half the triple A ratings went into exile.

What drove ratings migration was the greed and incompetence of Moody's and S&P in originally rating so much toxic waste as triple A. A normal distribution has no descriptive power for such a phenomenon.

Implications for Investors – In this type of environment, outsize returns and losses are possible. Reversion to the norm stops working. Smaller than normal position sizes will mitigate this risk, while diminishing rewards on winners. Businesses that rely heavily on variable expenses will perform better, because they can respond to extreme revenue decreases by reducing costs. That is one strength of the homebuilders, they use independent contractors for much of their work, so expenses are matched to income. A manufacturer, particularly one with a large debt load or heavy legacy expenses, cannot reduce expenses proportionate to revenue.

A number of businesses and industries seem to have experienced a 20 to 30% decline in future revenues, a sudden drop off. GDP may decline 5%, almost inconceivable until recently. GDP is supposed to kind of go up 3% or so a year, pretty boring and not much variation.

Businesses that can generate cash in the face of decreasing revenues will be more resilient. EMS firm Jabil Circuits (JBL), for example, orders inventory sufficient to fulfill current orders, so if orders decrease, inventories decrease, generating cash. Manufacturers or retailers run the risk of excess inventory, tying up cash and pressuring margins by closeouts and fire sales.

Yes/no points will increase. There will be the question, can a company roll over its debt as it matures during 2009? At what cost? Will they breach covenants and lose their financing or pay fees and higher rates to secure waivers?

Carrying over into 2009? - Most of this was written a month ago, and before many pundits started on the 2009 prognostications. 2008 was a year of extremes: many phenomena went beyond the 95^th percentile. The question is, will 2009 be similar, or will more business and economic indicators return to their former behavior, where they seemed to be securely confined within the bounds of a normal distribution? Will reversion to the norm start to work again?

Disclosure: Long HIG, ABK, MBI and JBL.

Comments

[SEF:]

Your comments are all spot on with respect to the industry. The one aspect that you article did not touch upon is that the losses from 2008 will impact the life insurance industry in 2009. This is so as Q4 of 2008 earnings will not be announced until early 2009. Considering the bulk of the losses in the S&P 500 did not occur until Q4 of 2008, this will have a major impact on DAC write-downs and additional reserves needed to guarantee life-time GMWB's in the future.

On another note, the life insurance industry has not even started to write down the value of the commercial real estate holding and bonds associated with these vehicles. A prudent investor should keep this in mind when they consider the overall health of the industry.

Jan 01 09:44 AM

[Beenaroundlong:]

The Hartford's risk managment analysis (originally developed within P&C in the 1990's) does not use bell shaped, normal distributions as its underlying liabilities are notably skewed with fat tails. Unfortunately, the life company's models are much primitive and, while now being refined, may not have adequately represented the risk in the tail.

Jan 01 02:53 PM