Between 2005 and 1Q 2008 Berkshire Hathaway sold index put options totaling approximately $40bn notional amount, receiving almost $5bn in premium. These at-the-money options were written over the S&P500 and three international indices (most likely the FTSE100, EuroStoxx50 and Japan's Nikkei or Topix - these are the most liquid indices for long dated options). The initial term of the options was either 15 or 20 years.
Before taking the other side of these trades, the investment bank counterparty would have formed a view on the following risks:
(1) What is the right price for long dated index volatility? Very long dated options have significant vega (sensitivity to implied volatility). One volatility point changes the model value of a 20 year S&P500 put by approximately 0.75% of the notional amount. By contrast, a 1% move in the index changes the model value by only 0.09% (9% delta).
There are takers for the other side of this volatility risk. Well, maybe not for 20 year duration, but at least out to 10 years or so. Constant buyers of long dated vega are retail investors, usually purchasing structured protected products - the simplest protected product is a zero coupon bond plus a long dated call option.
(2) Where is the 20 year forward for the S&P500? Buying puts from Buffet means the bank is short the S&P500 forward. Unfortunately, selling calls to retail investors also leaves them short the forward. The market's demand for long dated forwards has always been so one-way that these forwards tend to trade rather high. Put another way, long dated options typically imply very low estimates of cash dividend growth. Presently, the 15 year S&P500 cash dividend growth implied from forward prices is negative 3%pa. Do we really think $30 of S&P500 dividends today (2.15% yield) will have dwindled to $16 in 2028? It's the same for international indices too.
Berkshire and Buffet think completely differently to an investment bank in relation to these risks. Roughly summarised, their thought process is "markets ain't gonna be down in 20 years, we could use the premium income wisely, we never have to post collateral so let's just hit vega bids when they look attractive." Note the market call here is perfectly in sync with Berkshire's view that long term returns on equity markets will be in the mid single digit range. Selling puts for premium in the absence of collateral covenants is a useful source of risk-adjusted long term funds.
But it is the forward quirk which leads me to question Berkshire's strategy. No, I don't agree with Mish Shedlock that "anyone short S&P puts is asking to have their heads handed to them on a platter." Berkshire's approach is simply not the same as a "hidden" put selling strategy embedded in a so called lemon hedge fund.
No, the flaw in Berkshire's put selling strategy is that it locks in negative dividend growth rates: they get less money for their puts than they deserve. If Berkshire do stand behind their long run market call, they ought to believe that cash dividends will grow, on average, over the same timeframe. Sure, financial stocks may cut dividends in the short run, but it seems inconceivable that the market grows 5%pa over 20 years and cash dividends fall 3%pa - the index dividend yield in 2028 would be less than 0.5%!
Berkshire could be paid up front for opposing this paradox. So, Warren (I know you're an avid reader), I would have overlaid a fixed for floating dividend swap to reverse your forward position. 1 year cash dividends on the S&P are around 2.15%, or say $1bn on $46bn notional. The "fixed" leg paid by Berkshire would be an annual payment of $1bn increased by a fixed 3%pa for 20 years. The floating leg received by Berkshire would be the actual dividends paid on a notional portfolio of $46bn invested in the S&P500.
This dividend swap should generate an up-front payment to Berkshire of some 13% of the notional amount, or $6bn. This is the same order of premium that Berkshire received for selling the puts in the first place. Two premia for the price of one view! Provided cash dividends grow by 3% or more on average, there is also the promise of further payments to come. If Berkshire like their put selling strategy, this one's the proverbial no-brainer.
Thursday, May 8, 2008
Warren Buffett's Vega Games
Labels: derivatives
11 Comments:
Great analysis. However, I believe you are looking at the dividend curve as of today. The dividend curve, as shown by the dividend swaps, has changed dramaticly since the credit cranch. In Q1 2007 growth for SPX dividend was 10% for the first 3 years and 5-6% for years after. SX5E dividend growth was even higher as dividends in Europe ussually float with earnings and earning predictions were going through the roof. Therefore Buffer was locking in a biggest dividend growth assumption in the last 15 years when he sold those puts. For the last 9 months your thesis is correct.
One more point - the notional of the dividend swap you proposing should be delta notional, not notional of the option...
Agreed, crazy russian....maybe Berkshire did time the bulk of their put sales to pick up decent dividend growth assumtions in the forward in 2006/early 2007....this still doesn't change the ability to now trade out of their long fixed div position at -3% or so. In fact it would be rude not to.
For your information, my SPX and 15yr forwards were calculated using c-p prices sourced as of 8 May 08.
Your point on delta notional for the div swap is well made, if Berkshire simply wanted to hedge....but again if Berkshire are happy with 46bn of notional put exposure they ought to be comfortable with a similar size dividend swap, simply as a value trade. Who wouldn't want to short forwards at -3% implied div gorwth?
Your claim seems like that current forward price is mispriced. That essentially has nothing to do with put selling by Warrent Buffet. If Buffet shares the same view about future dividends in S&P 500, then he can get into the dividend swap separately to exploit the perceived anomaly. His interest was selling the index puts and he could not miss the deal because he doesn't agree the forward price trading in the market.
Agreed with Crazyrussian... great analysis.
However, Buffett has in the past expressed great concern about counterparties. It seems that in your dividend swap Berkshire would be exposed to default risk of the counterparty.
The sale of index puts does not contain this kind of risk. It's unlikely that the one who is long puts will fail to collect when they come due. In the mean time Berkshire has cash in hand for whatever use they deem fit.
@ Anonymous (May 12)
Yes, potentially this leaves Berkshire with credit risk, but on day 1 the mtm of the swap would be (in my hypothetical - and probably too large - example) $6bn, with the counterparty exposed to Berkshire . the mtm is this figure by definition as Berkshire received the $6bn up front payment as part of the transaction.
This is why I suggested that Berkshire agreed to pay +3%pa on the fixed leg (to create this credit exposure buffer). For Berkshire to find itself exposed to the counterparty, cash dividend growth would need to be very significant indeed, or implied dividend growth rates in the forward would have to incease materially.
Andrew -- you've gone very quiet.
Is there an address i can email you on?
Paul Murphy/Alphaville
paul.murphy@ft.com
This week the market is barely being propped up (really dropping more slowly) on the news the Buffet took a stake in Goldman.
Guess what, Warren needs the bailout and the existing fantasy accounting regime to remain intact. In one of his typical sort of braggy moves he disclosed about a year ago that his company Berkshire-Hathaway sold long dated $40billion notional of Puts on the S&P. This is very similar long dated vol writing trade that did in LTCM (though i think they did it delta neutral after writing calls), except LTCM was mark-to-market and Berkshire is an insurance company and gets to use long term actuarial (and as an actuary who has gone to the dark side-hedge fund, I know the fantasy assumptions that go into that) estimates of equity returns and volatility to value that liability.
In fact he should be getting killed on that position as a) he sold this over a period when volatility was at historical lows and has now reverted to the higher end but not unprecedented levels that it achieves over long periods of time and , and b) the move in the market has been down and it is obvious his forward projections of the S&P would be accreting at a ridiculously higher level even over the last three years than they actually did.
What does this mean? He cannot bear to have the regulatory regime changed from book value accounting to mark-to-market otherwise he would be exposed ala the Wizard of OZ. So he needs the last remaining pillar of the current regime to remain intact (hence his stake in Goldman) and to calm the markets because believe me, he must be aware of this.
Yours is a great analysis as to why he probably mispriced them in the first place, though you don't directly address the valuation reporting issue except to say he and Berkshire “think different” than an investment bank.
Don’t take anyone’s actions at face-value in this unwinding of the great credit bubble.
In fact under the obscurely titled C-3 Phase II directive of the NAIC ( National Association of Insurance Commissioners) that tells insurance companies how much capital they need and how to calculate that amount), there is an embedded assumption in the probability distribution that Equity prices grow at 8% per annum. This is so obscure that FASB says essentially whatever the actuaries say is ok by them. I had discussions with the main consultant to the group that put that together therules in 2005 as it seemed highly irresponsible to me, and he conceded that that was the case. In the attached they discuss the fitting of the distribution to be used (on page 37) and it is fit to post WW-II performance up to Dec 2003 (the market had already rallied significantly off the 2002 low) since then equity prices have been FLAT. Which means versus assumptions the market is down about 30-40%. The Orwellian term the regulation uses is “Real-World Scenarios” versus using the actual market implied levels which from their perspective is unreal (but is where things actually trade).
http://www.actuary.org/pdf/life/c3_june05.pdf
eppyramot....
Interesting theory. However, BRK *IS* using "fair value" accounting or mark to market for its derivatives. From their 10K:
"The gains/losses from such contracts are principally attributable to non-cash changes in the fair values of the related contracts and reflect changes in applicable underlying credit standing, equity index values, interest rates, foreign currency exchange rates and other factors. These contracts generally may not be settled before the expiration date (up to 20 years in the future with respect to equity index contracts) and therefore the amount of cash basis gains or losses will not be known for years. Nevertheless, the fair values on any given reporting date and the resulting gains and losses reflected in earnings will likely be volatile, reflecting the volatility of equity and credit markets."
Berkshire uses GAAP on the holding company level and insurance accounting differences only apply to their insurance subs.
Property and Casualty insurers generally carry easy to value assets -- listed stocks and bonds. The difficult part of their balance sheet are the liabilities. BRK has an excellent reputation for conservatism in their evaluation of insurance liabilities.
Note that this is the exact opposite of Banks, that have significant valuation risk in their assets, ie loans and easy to value liabilities, ie deposits.
Therefore, your hypothesis is wrong, which would have been obvious from even a casual reading of their financial statements.
Your comment that he "should have been killed on that position" is especially odd, since he has booked them at market value and had taken paper losses as well as gains on these.
Volatility is not a significant issue since Berkshire is significantly over capitalized and is designed to withstand volatility from natural catastrophes.
As mentioned above, the contracts have no counter party exposure and also have no provision for posting collateral. Since they are European options, there will be 15 to 20 years before any cash changes hands, other then the up front payment to Berkshire.
Finally, the obscure reference -- points to risk based capital calculations for LIFE insurance. Berkshire has no material life insurance operations -- it is a Property Casualty insurer and reinsurer.
as I know- for Warren its all games- he is a person to play
as I know for Warren its all games- he is a person like this
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