# Quantifying the Nightmare Scenarios

Dartmouth’s Eric Zitzewitz is one of my favorite co-authors, and a whiz at tracking financial markets. And when he mentioned to me last week that a close look at the options markets told an interesting tale of fear, I asked him to share his observations. Here goes.

Quantifying the Nightmare Scenarios
By Eric Zitzewitz
A Guest Post

There’s no shortage of fear about the economy. But just how fearful should we be? Perhaps financial markets can provide some guidance.

There’s a neat mathematical trick, by which we can use option prices to quantify the probability of the stock market falling by various amounts. Breeden and Litzenberger (1978) show that by comparing the prices of options at adjacent strike prices, you can calculate the approximate value of securities that would pay \$1 if the underlying stock traded in a certain range on expiry day.

“Option prices suggest that there is a very real chance of, dare I write it, another Great Depression.”

(Economists know these as Arrow-Debreu securities; they approximate what option traders call “butterfly spreads” when strike prices are close together.)

For example, using last Friday’s options prices, we can calculate that it would cost 10 cents to buy a portfolio of options that pays \$1 if the S&P 500 falls below 250 on December 18, 2010. If markets were risk-neutral (I’ll come back to this), we could infer that the market thought there was a 10 percent probability that the value of U.S. stocks could fall to one-third their current value by the end of next year. Such a drop would leave the index down to one-sixth of its peak level in late 2007. By way of comparison, in the Great Depression the value of stocks fell to between one-sixth and one-seventh of their earlier values.

In other words, option prices suggest that there is a very real chance of, dare I write it, another Great Depression.

Here is a graph of the probability distribution for the value of the S&P 500 in December 2010 — as implied by the options markets. The red line uses option prices from the end of September 2008 (after Lehman’s collapse); the blue line uses prices from Friday. As you can see, the probability of a substantial drop in the value of stocks has moved from relatively remote to quite substantial. Not only has the distribution shifted to the left, but the left tail has gotten thicker, suggesting there’s much more concern about extremely bad outcomes. (The dashed line indicates where I have used the pricing of the last two options to infer prices of options that are further out of the money.)

This graph yields a pretty interesting story. The most likely scenario is the S&P 500 ends in 2010 between 800 and 1,000, which is up 5 percent to 30 percent from today. But today’s market is being held down by the prospect of a Depression-like decline in stocks.

What do these bad-news scenarios look like? Surely the value of financial firms would be zero, but as these are only around 10 percent of today’s index, the dismal outcomes must be more widespread. Profits would have to fall significantly, with little hope of medium-term recovery. Such a decline in profits would go hand in hand with a sustained decline in incomes across all sectors.

There’s an important caveat to all this. Even when the market price of a bundle of options paying \$1 if “the S&P 500 is below 250 in December 2010” costs 10 cents, we cannot infer that there’s a 10 percent chance of this happening. Since this security would help hedge against extreme wealth losses, investors should be willing to pay an insurance premium. Furthermore, the investors buying these securities could be panicking and overpaying for them, and the more sanguine may be unable to offset this fear if their money is tied up elsewhere.

Regardless of whether it reflects risk aversion, panic, or a true probability, the 10 cent price being paid for a dollar of Depression insurance highlights the fears that are holding stocks down. Policymakers have been trying to reassure investors that they understand the risks of depression and will do what is needed to avoid them. These graphs provide a measure of how far they have to go in convincing us.

#### frankenduf

i am not convinced the Obama administration will do what is needed- their refusal to nationalize the 'too big to fail' banks, and their agreement to cut the original stumulus plan will both keep us on course to repeat history- even if they instantiated more aggressive policies, the further problem is that the european financiers are also recapitalizing peace-meal, with rhetoric that deflation isn't likely!?- history will not judge kindly those that know the danger, but are too cowardly to act

Looking at the distribution it looks like chances of having S&P index at 1500 are about the same as having the index at 300. Besides the most likely scenario isn't that bad. Worst case scenario is quite scary. But best case scenario is pretty good too. Am I interpreting it right? Can someone please correct me if I am wrong. This looks very interesting.

#### M.B.

The way that the blue line has shifted so far from the red line indicates the imprecise nature of predicting the future.
I'm of the view that increases in the S&P during the late 80s and early 90s were without any foundation. What we have seen so far is just normalization after an over-shoot on the way up. The gloom and doom speculation is something else.

#### Brandon

frankenduf:

Huh, all we need to do is embrace socialism and throw trillions of dollars at the problem and we're saved? And it's the clear-cut? I wish I'd know this sooner.

#### Eric M. Jones

So where was this information February 2008 when I should have moved aggressively into hardtack and navy beans? I am constantly amazed that all these geniuses appear after the horse has left the barn.

Stay tuned until a year from now when a boat-load of sothsayer economists tell us why---whatever is going to happen---happened.

Mad Jim Cramer called the Dow bottom as 8300.... Would that it were so.

I sure hope President Obama is as smart as I think he is.

#### Nylund

Comments 1 and 4 get to the heart of how hard it is to reassure the market.

You have person 1 basically saying, "I don't trust the markets to correct this on their own, and I believe we need a lot of intervention to make things better."

and you have comment 4 which seems to suggest, "I believe the market left alone will fair better than any attempts at government intervention."

Its impossible to reassure both types of people with the same plan, and the best you can do is reassure one group or the other. If I read the polls right, more people are of the first type (but really, it matters not which group has more people, but which group has a larger control of the market).

One thing is for certain. Nothing Geithner has said has made either type feel any better.

#### Dober

As I understand history, the government was hyper-active during the depression, as was doing everything it could that it thought would help. Sound familiar? We now know that they actually made things much worse, particularly with protectionist and socialist policies. Buy American clause in the stimulus? Indications seem to be that we may avoid protectionism as that clause was eventually watered down, and enough people know that protectionism will destroy our economies, but the danger exists, and I think that is what the options are showing us.

#### Tim

Having just finished The Black Swan, I am reminded of Taleb's complete disdain for Gaussian curves such as these. That said, I disagree with many of the extensions of his premise: the fact is that history very often does occur in repeatable patterns.

I really wonder how much his book- or the concepts popularized by it- has further darkened investors thinking about the likelihood of a normal cyclical recovery!

#### real economic minded

again the question of what to do comes up- quanitifying is not enough- needs qualifying as well- what do I mean- I called a family members broker today- am watching over investments- was ready to "just say no" -- but was told- there was a gain-- the bail out to one group has prompted increased buying- and change- still the question of manufacturing needs to be addressed- cheap labor- smaller electric cars-- healty transportation..... am almost --convinced if countries like mexico and china became real competitive - and there was global cooperation re the enivronment, reducing pollution--using wind--- etc. -- everyone benefits- perhaps not equally- but more so--

I have one more question if Professor Eric can answer. How did the curve look liked 2 or 3 years ago?

#### Brandon

More accurately, Nylund, I take the stance that the market is too complicated for any of us to so simplistically describe an effective solution to this problem.

Anyone who is 100% convinced either way is wrong, IMO.

#### Eric M. Jones

My dad once commented that if a guy can make more money recommending financial strategies than actually following his own advice and keeping his mouth shut--he will....

#### Terry

This is interesting, but I'm not sure it helps much to inform a decision about the direction of the economy through next year. I think Eric and Imad make some key points and ask some key questions.

Following up on Imad, has anyone taken a historical look at how these options have fared in predicting the markets 18-24 mos. ahead of time? If they tend to be accurate, I'd be a little more concerned, but I suspect the accuracy of a mean prediction is pretty random.

Maybe most interestingly in the graph is the broadening spread of views since last September. It reaffirms what we all feel: Greater uncertainty.

#### S.K.Eptic

The only way to understand a situation (the economy) is by understanding what is shaping it and how long the influences will be felt. The credit portion of the economy has collapsed due to mistrust caused by bad bonds (AAA turns out to be BAD) credit default swaps, and other dubious instruments that have allowed the magnification of distress through over leveraging, this has all but destroyed the credit markets and much of the assets of some very large banks. Underlying this collapse were 2 factors, demographics of an aging American population, and the multiple bubbles that the baby boomer population anomaly managed to create. I am not blaming boomers per se, but the amplification of so many individual choices by so many - buying homes created a 1st housing bubble in the late 70's, 401k investment created a bubble in the stock market several times. Bad economic planning including spending the Social Security Trust Fund, rather than investing it, dismantling of Depression Era regulation (why do we need this, we haven't had a depression in years? - dangerous thinking by those in power) and total lack of regulatory oversight while the banking & housing markets were rife with fraud.

The economy did not just fall over on its own, it had help from many sectors, the Federal Reserve was using fake numbers to create a false economy, the corporations lost all sense of civic morality and stole everything that wasn't nailed down and sold it overseas. These deeds had many names Leverage Buyouts, in which the victim company paid for its own death at the hands of banksters and other agents of fraud. Ponzi schemes like Madoff, Outsourcing jobs and importing poverty were yet more traits of those whacking away at the piers supporting this once diverse and robust economy. Allowing Banks to merge into mega monsters was a supreme act of stupidity as we find the government with its hand in our pocket bailing out the crooks with our tax dollars, helping them fund idyllic retreats on private jets and bonuses that would make a pig gag.

To allow all this to happen under the supposition that "free markets" will know best and those who manage corporations will do whats best to make sure their company succeeds is balderdash. The capitalist system is like a fire, a fire stops only when it has burned through all the fuel available, greedy CEOs stop only when they have burned through all the capital available to them. A fire can be contained through regulation, hence our mastery of the flame to make it our servant. It works in our engines and our planes, our homes and our powerplants, fire can serve man. Capitalism must be regulated to serve mankind, not enrich the greedy and stupid who would drive it to extinction and then feign innocence.

To plot this complicated and distressing situation in a single chart with 2 meager data points is a disservice to all who look to your knowledge and experience for enlightenment. I hope you can spend some time and give this topic the thorough going over it needs.

#### Nono Lazlo

In spite of all the hot air, accounting and securities fraud, guilt and fear, world wide capitalism is on sale. It doesn't matter what the wise guys or saps are putting on the Pass/Don't pass line.

Van Morrison can play and extract cash from Moscow and Hong Kong as easily as he can play the Beacon Theater in New York. The same goes for Crest, Pepsi, Boeing and everything J & J sells.

Take the massive amount of cash on the planet-- \$70 trillion dollars, subtract the fraudulent mortgages and crap paper worth 20 cents on the dollar; add back the trillions the international Fed will print to make up for it, and ask yourself if people will still need to brush their teeth, using diapers, drinking beer, flying Dreamliners, etc.

If 2012 brings and extinction event as the History Channel would have you believe, all bets are off, and the Options Clearing Corp won't clear your trades anyway. So unless you're planning to build a bunker or ack, harden up and act like there will be a tomorrow, with rising rents and insurance premiums.

#### Middle America

Well written SKeptic and Nono! Nod to Eric as well.

Life goes on.

Value is still valuable.

Although I'm still on board with the Chicago school, its going to be an interesting ride.

#### brian

I couldn't agree more with S.K.Eptic and Nono. Nice words - I agree with both of your summaries.

#### MikeM

Yes, because we all know the math did a great job of calculating risk last year.