Buffett derivatives, just ignore the volatility

Buffett derivatives, just ignore the volatility

Dan McCrum | Apr 14 16:44 | Comment | Share

Part of the BUFFETT DERIVATIVES SERIES

There’s an old Russian proverb, popularised by Ronald Reagan, which comes up among due diligence types: trust, but verify.

It seems appropriate to keep it in mind when thinking about Berkshire Hathaway, which is a sprawling insurance company and conglomerate indulged by the market largely on the understanding that its charismatic, cunning and greedy-in-a-good-way leader will do the right thing.

Hence our interest in a series of very large derivative contracts written by Warren Buffett between 2004 and 2008, which reveal a willingness to at least work creatively within the confines of fair accounting disclosure.

So far, with much help from Pablo Triana, professor at the Esade school of business, and our readers, we have considered one reason why Berkshire Hathaway took the bets – for the float, because it is at heart an insurer.

We’ve also looked at how Berkshire probably got away with reporting lower mark-to-market losses than it might have, and the strange way in which the conglomerate could factor its own ability to pay into the estimate.

Which brings us to the final piece of the disclosure puzzle: volatility.

Regular readers will recall that Berkshire sold $50bn worth of notional put options in return for $4.9bn in premium. Long dated European style options on broad stock indices in the US, Europe and Japan, they can be exercised only at expiry between 2017 and 2028.

A lack of collateral requirements are one reason why Buffett wrote the options, so he only faces cash payments in the distant future when they expire. (Some of the other reasons, to do with their pricing and what it says about finance generally, we’ll look at in the final part of this series to come).

Still, Berkshire does have to mark-to-market the liability created by those contracts even if the great sage thinks the whole process renders the accounting earnings for his company meaningless.

The odd thing about that valuation process is that it only spat out a liability of $10bn at the height of the financial crisis, just twice what Berkshire had received in premium as markets lost their mind.

As we have explained before, the company treats these as level 3 obligations for accounting purposes – that is they are highly illiquid and so can only be marked to model.

The model is based on the Black-Scholes formula, which uses a series of inputs: the strike price, the price of the underlying (in this case equity indices), time to expiry, the risk free interest rate, and volatility.

That last one poses a well known problem. Historic volatility can be observed, but future volatility can only be guessed at.

Professor Triana, in his latest paper on the puts, describes how Buffett approached that problem for the purpose of the accounts:

Berkshire has opted for a peculiar way of dealing with volatility. The firm is using the Black-Scholes volatility parameter as a static forecast and has stoically stuck by such prediction even in the face of some of the most wildly swinging markets ever contemplated.

Indeed, here are the volatility assumptions disclosed by Berkshire:

Berkshire does describe how it got there (our emphasis).

The weighted average volatilities are based on the volatility input for each equity index put option contract weighted by the notional value of each equity index put option contract as compared to the aggregate notional value of all equity index put option contracts. The volatility input for each equity index put option contract is based upon the implied volatility at the inception of each equity index put option contract.

So it is the average of the volatility numbers which Berkshire used at the time it wrote each contract, weighted by the notional size of each contract. And those volatility numbers were anyway Berkshire’s own estimates of long term volatility, by the way.

What the company is doing here is neglecting the “smile”.

Options on the same underlying asset but with different strike prices typically register different implied volatility numbers. As Prof Triana writes:

The smile (or the less symmetrical skew, more typical in the case of equities) reflects traders’ desires to bump up the values of options that are further from at-the-money strikes, in particular those with deep out-of-the-money or in-the- money strikes. Given the real-world chance that those extremes will be reached and given Black-Scholes’ underpricing of such contingencies given its assumption of a normal probability distribution, traders feel that such options need to be worth more if they are to be sold at all.

So common trading practice is to adjust volatility assumptions according to how far an option is in or out of the money, were it to be exercised at that moment.

By sticking with a constant figure throughout, Berkshire appears to be ignoring or neglecting this reality, the same option portfolio being endowed with essentially an identical volatility input whether at-the-money or deep in-the-money or deep out-of-the-money.

Observed volatility also changed quite considerably after the options were written. For instance on the S&P 500 (tabulated at the end of last year):

Berkshire does provide the numbers in some quarters to make some adjustments, to see if those volatility assumptions really matter.

Prof Triana collates the fair value for the put contracts given an increase in volatility assumption by two percentage points and four percentage points, everything else being equal. Nebraskan vega:

In the fourth quarter of 2008, choosing 26 per cent instead of 22 per cent as the volatility figure would have put the liability at $10.9bn, a 9 per cent increase.

Now, Berkshire more than any other large US company is built on the principle of taking the long view. The company is allowed to hoard capital on the basis that when an opportunity to put it work arises Warren can do so better than anyone.

So maybe it is okay to give Berkshire a pass when it comes to disclosure that fits with that philosophy. What do you expect, this is Buffett and he has every confidence in the future of the world.

Yet Berkshire is also unusual in that its plain financial disclosure is the main way it communicates with shareholders. Mr Buffett writes one letter a year, and then he submits to questions at an annual meeting in a stadium where the crowd starts to get restless if questions and answers veer into the overly detailed or financial.

At the same time, the point of mark to market accounting is that it is a snapshot based on what is happening at that moment in time. More banks would have survived the crisis without government assistance if they could have just put some helpful long term assumptions into their models. Even if you think that makes little sense, it is the system we have.

So what might have happened if Berkshire had used a volatility number reflective of market conditions?

Falling into the temptation of interpolation, one may venture to conclude that marking a 32% (42%) volatility would have led to around $12bn ($14bn) in liabilities, a decidedly larger accounting setback for the firm.

Big deal? Well, for starters Q4 2008 would have registered a large quarterly loss rather than the small gain that was reported (at 22% vol), and annual profits could have decreased by 25% to 50%.

Mr Buffett professes not to care about the movements in earnings caused by the derivative contracts. But if he didn’t care, why leave a finger on the scale?