The Real Reason Behind Berkshire's Exploding CDS Spreads
an article to
The other day CNBC's Dennis Kneale posed an interesting query of why AAA-rated Berkshire Hathway's (NYSE: BRK.A) credit default swap spreads ("CDS") were trading so wide, having risen from as little as 7bps in 2007 to an astounding 500+bps currently. After all, Berkshire's portfolio was down only 9.6% last year versus the S&P 500's 37% total return drop. Mr. Kneale logically concluded that this must be yet another "extreme situation" in the market. However, this is by no means a simple case of market misperception regarding Berkshire, as its exploding CDS spreads come as a direct result of its massive foray into equity index derivatives at the end of 2007.
click to enlarge images
One can begin to unravel this mystery by examining Berkshire's various credit spreads. As one can see in the chart above, Berkshire's corporate debt spreads moved generally in line with USD AA-rated swap spreads during the course of 2007. However, this relationship began to break down in mid 2008, as Berkshire spreads rose to more than 200bps and briefly flirted with the 300bps level. Toward the end of 2008, its debt spreads came back down to 100bps level, yet remained well above AA-rated swap spreads.
Berkshire's credit picture was even more dislocated in the CDS market. After its 5-year CDS traded as low as 6.7bps in 2007, Berkshire's CDS spreads began to expand in line with the growing concerns in the credit market owing to the sub-prime mortgage crisis yet still finished 2007 at a still moderate 32bps. Prior to the Lehman Brothers bankruptcy, Berkshire's spreads had widened to 100bps, but then quickly shot up to over 300bps before peaking at 490bps in late November. Although its CDS spreads gradually fell back to the 300bps level toward the end of 2008, over the last two weeks they have notably widened again setting a new high of 525bps on March 5th for its five-year tenor.
Although multiple theories abound as to what is driving the dislocation of Berkshire credit spreads, the simple explanation results from its sale of $37.1 billion in notional value of long-dated (15-20 year) equity index put options on the S&P 500, the FTSE-100, Euro Stoxx 50 and the Nikkei 225 equity indices. The bulk of this transaction was executed at the end of 2007 to net Berkshire a total of $4.9 billion in option premium. Owing to steep drops in the equity markets, declines in long-term interest rates and a sharp rise in equity index volatility, this position has moved drastically against Berkshire. As of December 31st, 2008, Berkshire estimated that the equity index puts were now worth a gfair valueh of $10.0 billion and hence it had incurred a paper loss of $5.1 billion on the options. Although in his annual letter to shareholders Mr. Buffett is quite sanguine about the magnitude of these losses and their eventual outcome, I can assure the reader that my former equity derivative trading colleagues on Wall Street are notably less relaxed about Berkshire's equity index put positions.
First of all, Berkshire's estimate of fair value for the options assumes long-term interest rates and dividend yields of 4.0% and an implied equity market volatility of 22%. Based on my trading experience and using current market data for these pricing inputs, I estimate a fair value closer to $14 billion for the options as of year-end and a number approaching $16 billion as of the lows in the equity markets on Friday. Though Mr. Buffett argues at length as to the shortcomings of the Black-Scholes pricing model in his annual letter, I can assure the reader that former Wall Street colleagues are using pricing assumptions much closer to mine than to Mr. Buffett's.
Second of all, because Mr. Buffett is known to extract some of the best contractual terms when it comes to trading derivatives with Wall Street (so-called "most favored client" status), Berkshire was able to enter into these transactions without having to post any collateral at the outset nor in the future (see page 19 of the Berkshire Annual Letter).
Thus, since the value of the short puts has increased threefold and Wall Street has no recourse to Berkshire for collateral to cover its liability, Wall Street has suddenly become saddled with roughly $15 billion of Berkshire exposure, which is rather significant as Berkshire has only $30 billion in public debt outstanding. As a result, credit risk managers have been forcing equity derivative traders to buy CDS to protect against this exposure. This drive to reduce counterparty credit risk to Berkshire has been the principal culprit in the sharp rise in Berkshire credit spreads. The fact that Berkshire does not have listed equity options on its stock may also be adding to the CDS hedging pressure, as Wall Street cannot buy put options on Berkshire directly.
While this claim may seem outrageous, when one examines the relationship between Berkshire CDS spreads and my estimate of the fair value of its short index put portfolio, one can see that the two move nearly in lock-step with each other with a daily correlation of 0.96.
Finally, it has even been rumored that Mr. Buffett used a particularly toxic form of equity index derivative known as a "worse-of-option". In this case, one bets on the performance of the worst performing index among a basket of indices. Such an option can be worth significantly more than an option struck on the performance of the overall basket itself. So, let us assume for the moment that Mr. Buffett is correct and the US equity market regains its current 56% loss by the time the Berkshire options expire between 2019-2028, yet somehow Japan or European does not.
Berkshire could then, in theory, still end up owing money to Wall Street on the part of the $37.1 billion, which was linked to these "worse-of-options".
Not to pick on Japan, but 19 years later the Nikkei 225 Average is still trading at less than 20% of its all-time high set in December 1989 and is off over another 50% from the time of the Berkshire put option sales. And not to be overly depressing on the US front, one must all also bear in mind that the S&P 500 Index took 25 years to recover its 1929 highs.
So, Mr. Kneale, there is no mystery behind Berkshire's bloated credit spreads, which come as a result of Mr. Buffett's massive sale of equity index puts, the market's ensuing drop and Wall Street agreeing to waive its ability to demand collateral from Berkshire. The good news is that if the equity markets begin to recover, then the price of the Berkshire equity index puts will plummet and equity derivative dealers will shed their Berkshire CDS holdings, thereby driving down Berkshire credit spreads. However, the bad news is that if the equity markets continue to deteriorate, then Berkshire credit spreads may wider even further, as Wall Street will be forced to continue to reduce its Berkshire credit exposure related to equity derivatives.
So, bonne chance to Mr. Buffett and his short equity index put option positions, but I am afraid that Wall Street equity derivative traders and the CDS market will continue to fret over their Berkshire exposure for a considerable time to come.
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Nice - this is the first time I’ve seen an explanation of this phenomenon that I buy. I think it requires connecting another dot (or perhaps connecting it with a darker pen). Market put holders' buying of CDS is part of a larger risk reduction strategy. The protection they’re buying is not, at this point, based on the duration of the market put at all, but rather on its value at any given time. As markets climb, they hold less, as they fall, more is demanded. As we reach the five-year window where a repayment-caused default would be covered by CDS, time will become a factor.
Something else: if the risk managers use Black-Scholes to value their puts, and if Buffett’s right in his critique (that it breaks down in valuing long-dated options), the CDS buyers are willing to pay too much for protection, resulting in an even higher price. So selling CDS on BRK is a way to piggyback on the market inefficiency that forms the basis for BRK's equity put investments.
"Berkshire's estimate of fair value for the options assumes long-term interest rates and dividend yields of 4.0% and an implied equity market volatility of 22%. Based on my trading experience and using current market data for these pricing inputs..."
What values did you use for the variables? How can I compare your valuation and BRK's without knowing your assumptions as well as Buffett’s?
“The bulk of this transaction was executed at the end of 2007...”
I don’t think so, so I’d like you to source this. According to the 08AR, BRK wrote the market puts between September 2004 and January 2008. Though it’s not clear that all of BRK’s equity options were index-based until 2006, I think in 2005 substantially all of them were. BRK’s fair value liabilities for these contracts held at year end:
millions
2005: $ 1,592
2006: $ 2,463
2007: $ 4,610 ($4,500M in premiums collected to date)
2008: $10,022 ($4,900M in premiums collected to date)
Just as the 2008 liability increased dramatically due to the dramatic market decline, liabilities for contracts held through previous years would have decreased gradually as markets gradually climbed. So it appears they sold rather briskly in 2005, perhaps clearing pent-up demand for such instruments, then slower in 2006, then faster in 2007 as more market participants sought insurance at historically high market valuations.
What this means is that the average “strike price” of the options, the price below which BRK would have to pay, may be lower than you think, if you used the end of 2007 as the basis for the bulk of the portfolio.
"...it has even been rumored that Mr. Buffett used a particularly toxic form of equity index derivative known as a ‘worse-of-option.’”
I find the chances of this to be insignificant, and have seen nothing in anything Buffett or BRK has said to support it. Buffett’s a good risk manager, and this scheme would increase risk dramatically. Also, market put sellers would rarely need insurance against more than one index.
"Our put contracts total $37.1 billion (at current exchange rates) and are SPREAD among four major indices: the S&P 500 in the U.S., the FTSE 100 in the U.K., the Euro Stoxx 50 in Europe, and the Nikkei 225 in Japan."[2008AR, emphasis added]
I find it far more believable that CDS sellers would generate such a rumor to increase their profits.
This time we have people believing there's an (anonymous, of course) party who can make up the default of billions of dollars, even of a country. Think about it for a second: these liabilities will only become due if almost all debt holders default. So let's see: a few trillion dollars' debt goes into default. As these things go, everything happens together, within six months. But… abracadabra, at that moment of global depression, out of the closet will pop these anonymous counterparties, waving their trillions to pay the debts on behalf of those going under. To quote Al Borland, "I don't think so, Tim!" What they're doing is playing musical chairs (aka trading). Every player in this markets thinks he will be able to sell the security before he is caught on the hook, secretly hoping the one on the hook is (ta-da) too big to fail.
My take is Mr. Buffett is the Fool on the Hill, taking $5 billion from these folks on the following notion: peak to peak, trough to trough, the economy and stock market cycle roughly every ten years, give or take a year or two. Therefore, odds are in the middle of the cycle (5 years after trough) the markets will be in middling to fair shape and he pockets his $5 billion (with a Fool on the Hill smile).
Remember, Mr. Buffett has two strengths, not one. Everyone talks about his investment acumen. They forget his other strength is risk assessment - insurance, after all, is his main business. His puts are nothing but a high-risk insurance policy by another name, for which he cashed a $5b premium and, like an insurer, he figures his odds of paying are pretty slim.
Yes, he's made wrong calls (COP being the most recent) but (a) he's kept his calls affordable and (b) he's batting average is still way better than .500 - so I'd be inclined to be careful about beating up on him too much.
Back to the article. What I understand it to say is: Wall Streeters are the ones assigning these crazy CDS values and, by golly, they know how to assess risk. Hmmm... aren't these the very people who said collateralized subprime mortgages had low risk? What does that tell you about their risk assessment skills?
More important, who you gonna believe: them or WEB?
Several good points were raised by BS Detector:
1. Yes, I erred on the the trades being done largely in December 2007.
Buffett didn't refer to these trades until his 2007 letter.
However, I went back through the full annual reports and he states a $14 billion exposure in 2005, $21 billion in 2006, $35 billion in 2007 and $37.1 billion in 2008 with respect to long-dated equity index options on four indices.
2. I went back and calculated the average prices on the four indices over those four years and applied the executed amount to estimate an average strike price. This came out at 90.8% of the December 2007 close of 1468 in the S&P 500, which I was using for my analysis. My bad.
3. Although this changes my strike price assumption a bit, the exposure was still recorded at $4.6Bn versus $4.5bn of premium written in 2008. So, the underlying analysis holds and the conclusions are the same.
4. In terms of the assumptions for pricing the hypothetical option as of year-end 2008, Buffetts states a 13.5 year maturity and 4% for interest rates and dividend yields and a 22% weighted implied volatility (p85). Using a price of 903 for the SPX close and my guestimate of a 1383.93 strike price, Black Scholes will yield a year-end 2008 price of 375.8 per put option.
My real world assumptions are the following:
Interest Rate: 2.68% (10-year libor of 2.56% and 15-year libor o 2.73%)
Dividend YIeld: 3.14% (28.38 spx pts paid in 2008 divided by 903)
Implied Volatility: 27.57% (VIX closed at 40% and 10-year volatility swaps were trading at 32% and then you adjust the vol down b/c the option its itm - can provide more detail if you like).
Making the following change will do the following to the option price:
IntRate down from 4% to 2.68% 375.8 -> 509.8
Dividend down from 4% to 3.14% 509.8 -> 470.6
Vol up from 22% to 27.57% 470.6 -> 518.6
Thus, the increase of 37.9% (518.6/375.8) is where I derive my estimate of a $13.79bn year-end exposure versus the $10 billion stated by Berkshire.
No time at the moment, I'll be back to this tomorrow, but:
1. I don't recall the yearly exposure numbers, but that's a good data point for determining the average purchase point each year. I think we need to make an assumption as well about the blend of the four indexes involved, but I haven't done any work to make a logical suggestion for that.
2. Your 90.8% of the December 2007 S&P close of 1468 puts it at 1333 (not 1384 - please verify your number), which is if I remember correctly rather close to the number he used in an example in this year's letter. I think the odds are good that this number was not a random choice, but was chosen to make his example reasonably close to the real situation.
3. Premium was I believe $4.9B as of YE08. It think it was $4.5B at YE07.
4. I'll need to bone up on option pricing a bit before I can have anything close to a considered opinion on the rest, though one thing jumps at me - the interest rate. First is a nit, as I recall U.S. Treasuries are generally used as the proxy for a risk-free investment rather than LIBOR. Secondly though, I think it's reasonable to think that the recent flight-to-quality has driven yields on Treasuries artificially and unsustainably low; at YE the 10-year was at something like 2.25%, while in the years leading up to October is was rarely below 3.5%. Does B-S specify a selection methodology here? Does it even differentiate based on the time period, that longer-dated options should use a different rate than shorter-dated options? I think I know where you got your number, and I'd guess that Buffett got his by looking at a longer-term, less panic-driven sample. Are both methods legit according to B-S?
Can you reverse-engineer his other assumptions?
Also, I'd like to see your numbers again based on current levels (S&P at 750, 10-year T at ~3%).
BTW, I'm one who likes data, so more detail is always better for me personally. But to save my many detractors from having to look at ever more words, links for the details are are fine with me.
2. Yes, I massaged the strike up a bit to get the numbers to sync from 2007 to 2008.
3. Correct - for the amount sold.
4. Derivative dealers use LIBOR to price options, as that's where a AA-rated bank can fund and hedge exposures.
For BS one should use the appropriate term interest rate, dividend yield and volatility. All three have observable terms structures in the market, though can take a bit of work backing out all of the numbers.
Technically, one derives the zero-coupon curve to price options at each date in the future. I didn't bother doing this, as the curve is fairly flat past 10 years and hence is about the same at the coupon curve.
The swap rate now is around 3.3%, which drops the price of the put, but index yields have gone up a lot - but who knows what the final dividend yield will be owing to all of the cuts.
With SPX at 750, 3.29% for rates, and 3.73% for div, the price would be 591.
All the best.
Nick
On Mar 14 05:01 PM BS Detector wrote:
> Mr. Waltner:
>
> No time at the moment, I'll be back to this tomorrow, but:
>
> 1. I don't recall the yearly exposure numbers, but that's a good
> data point for determining the average purchase point each year.
> I think we need to make an assumption as well about the blend of
> the four indexes involved, but I haven't done any work to make a
> logical suggestion for that.
>
> 2. Your 90.8% of the December 2007 S&P close of 1468 puts it
> at 1333 (not 1384 - please verify your number), which is if I remember
> correctly rather close to the number he used in an example in this
> year's letter. I think the odds are good that this number was not
> a random choice, but was chosen to make his example reasonably close
> to the real situation.
>
> 3. Premium was I believe $4.9B as of YE08. It think it was $4.5B
> at YE07.
>
> 4. I'll need to bone up on option pricing a bit before I can have
> anything close to a considered opinion on the rest, though one thing
> jumps at me - the interest rate. First is a nit, as I recall U.S.
> Treasuries are generally used as the proxy for a risk-free investment
> rather than LIBOR. Secondly though, I think it's reasonable to think
> that the recent flight-to-quality has driven yields on Treasuries
> artificially and unsustainably low; at YE the 10-year was at something
> like 2.25%, while in the years leading up to October is was rarely
> below 3.5%. Does B-S specify a selection methodology here? Does
> it even differentiate based on the time period, that longer-dated
> options should use a different rate than shorter-dated options?
> I think I know where you got your number, and I'd guess that Buffett
> got his by looking at a longer-term, less panic-driven sample. Are
> both methods legit according to B-S?
>
> Can you reverse-engineer his other assumptions?
>
> Also, I'd like to see your numbers again based on current levels
> (S&P at 750, 10-year T at ~3%).
>
> BTW, I'm one who likes data, so more detail is always better for
> me personally. But to save my many detractors from having to look
> at ever more words, links for the details are are fine with me.
> Technically, one derives the zero-coupon curve to price options at
> each date in the future. I didn't bother doing this, as the curve
> is fairly flat past 10 years and hence is about the same at the coupon
> curve.
It seems to me that the risk-free rate has to be a short-term rate, that rates include risk based on duration. Unless risk-free doesn't necessarily mean risk-free.
> but index yields have gone up a lot - but who knows what the final
> dividend yield will be owing to all of the cuts.
It has to be lower. S&P dividend rates haven't been anything close to this high in 20 years.
> @BS Detector: The idea of reverse-engineering the Berkshire index
> puts intrigues me. Have you made any progress, or would you mind
> if I put an article together on it?
I haven't done anything with it. Have at it.
Deriviatives are the mother of all default, doom, and disaster and perpetrated by greedy bloated delinquint pigs.
Deriviative trading in any form should be denied and declared dead as a doornail immediately.