### From WMD to Wow: Buffet's Derivative Loss Estimate

Nearly 3 years ago, I wrote about the puzzling Buffett's derivative deal at the time -- selling huge amount of "at-the-money" puts for several major indices, including SP500. I was trying to figure out what was his rationale of these deals, since they seems to be contradicting to his now famous "Weapon of Mass Destruction (WMD)" remark about OTC derivative, and these deals are hugely dangerously -- limited upside, huge downside. Though I reminded everyone that Buffett himself was no green hand at all for derivative business, and his core business -- insurance and re-insurance -- are basically put-selling business.

Now we all know what happened afterward -- especially in the later part of last years. In last quarter's earning release, the way Berkshire marking these derivatives raised some eyebrows. The market conditions at the end of last year would guarantee that no matter how he marked his derivative book, it would already incurred huge loss for him. But how huge? Doug Kass has been shorting Berkshire (and presumably making some profits) and in his recent article, he mentioned these derivative deals, along with Buffett's major stock holdings - AXP, WFC, BNI, USB, KO, COP -- all suffered hugely since last September's Berkshire quarterly earnings. Can the derivative deals, on top of these stock loss, break his back?

Now the big question is, in next few days -- 2/27/09 to be exact, Berkshire is going to report the results for the last quarter of 2008. How bad will the numbers be? For me, as a derivative trader, the most intriguing question is: is Buffett being forth-coming with his marking of the derivative book? Or more ominously, can he afford to?

In this article, I will run some numbers and scenarios to see how these derivatives should be priced and where the loss should come from. We all know there are 2 obvious sources -- 1) the "delta" loss due to the huge drop in stock market (SP500 from 1300 in mid '06 to 900 at end of '08 -- and now 770 as of last Friday); and the "vega" loss due to the index implied volatility jumping from 15 in mid '06 to now over 45. However, there is a third piece of surprise (also against him) that when I work out the number, it even shocked myself. Let's get to the details.

Here is what we roughly know about these deals (Based on the Reuters report, somewhat differ from what I discussed in my early article):

"...put options Berkshire wrote on the Standard & Poor's 500 .SPX and three foreign stock indexes. Buffett said these require payouts only if, when the options expire between 2019 and 2027, the indexes are below where they were when the options were written. Berkshire has received $4.5 billion of premiums..."

Without knowing the details, we made a conservative estimate assuming all the puts were written on SP500 (we all know last year SP500 actually performed better than most foreign markets, so we are doing Buffett a favor by putting all contracts in SP500). We assume the average length of the contracts is 15 years. Mid '06 to Early '07, SPX implied volatility was in the range of 10-19 (remember for a few days before the onslaught of subprime storm, VIX was trading below 10!) Let's assume Buffett sold those puts at 20 vol. At the time, Fed Open was at 5% (Source), and generally options are priced at the slight upward yield curve, and higher interest rate would lower the put price, so let's be more favorable to Buffett by assuming these contracts were priced BELOW spot rate, or 4.0%. Assuming the puts were done at 20 vol with 4.0% rate were extremely favorable assumption for Buffett.

With SPX at 1300 and strike at 1300, 5475 days to expire (15 years), 20 vol, 4.0% forward rate, for 4.5 billion premium, the trade would be 500 million Vega. We assume Buffett didn't hedge the 12 delta (even though the strike was at the spot, due to the far away expiration date and 4% rate, actually the delta was tiny -- would be even tinier if the rate is 5%).

Now let's move this contract forward:

- If nothing changes (no change in index and vol), just move the clock forward by 3 years, he would make $573 mil in interest from $4.5 bil, and loss of $466 mil due to forward moving close to the strike (that's a very intriguing characteristic in far-away option contract!) The deal would have a net gain of $107 mil.

- Now SPX dropped to 900 on Dec 08 (his quarterly end date): Assuming no vol change: net loss (with his interest income) is $4.25 bil.

- Now assuming he marked the vol at 35 (As reference, at the end of Dec 08, VIX was between 45 to 50, LEAPS SPX options were trading at 40 vol). His loss is now $12.07 bil.

- Now here is the biggest surprise: What did the Fed do in last 1 year when the financial turmoil broke out? Fed dropped rate all the way from 5% to almost 0 (spot Fed Open is now at 25 bps). Far term rate dropped substantially accordingly. Long term Treasury yield is at 2.75% to 3.5%. What happen if we drop the rate used in the marking of these contracts, by merely 1% (while we all know that the Fed Open drop 5% during the period)? With rate at 3%, Buffett's derivative portfolio now loss $15.7 bil (still assuming he can collect $0.5 bil interests from his original 4.5 bil premium)!

How about 2.5%? The loss is $18 billion!

Let's do a little stress test: if the original deal was done at a somewhat worse but more realistic level: sold the put at 18 vol (rather than 20) with 5% rate (rather than 4%); now we mark the current book at 35 vol with 3% rate at 900 SPX level. The loss is $38 bil.

People have been focused on how Berkshire would mark the vol level at this quarter. Now I have shown it's equally critical how it would mark the rate level. With the term so far away, the loss due to rate is much more ominous.

Three Strikes. Last year, 3 major macro-events all moved against Buffett's massive short puts: the world market crashed, the corresponding implied volatility shot sky high and remained in the high vol regime; but lastly and most surprisingly (and massively damaging to Buffett), is the rate drops.

Berkshire may argue that these are OTC contracts that are so far away that he really does not care how it is marked as long as he does not need to trade out at this time. But will he mark honestly and fairly, not to fall into the same pitfalls he once strongly criticized? And what happen to the counterparty of these deals?

Only a few days away to find the answer.

Selling Out-of-Money Puts. The interesting character of far term put options is: the forward price (which determines what is "at-the-money") is very sensitive to interest rate, and can be very far from the spot. So even Buffett sold those puts with the strike at the spot, he actually sold tons of way out-of-money puts (notice the small delta I indicate above)! We all know derivative history is filled with story of traders blown into pieces selling out-of-money puts. The question is: did Buffett realize he sold tons of out-of-money puts when he did that deal?

By the way, with such small delta, it would be little help to the huge loss even when he would hedge.

(The author can be contacted at huangxinw@gmail.com.)

Now we all know what happened afterward -- especially in the later part of last years. In last quarter's earning release, the way Berkshire marking these derivatives raised some eyebrows. The market conditions at the end of last year would guarantee that no matter how he marked his derivative book, it would already incurred huge loss for him. But how huge? Doug Kass has been shorting Berkshire (and presumably making some profits) and in his recent article, he mentioned these derivative deals, along with Buffett's major stock holdings - AXP, WFC, BNI, USB, KO, COP -- all suffered hugely since last September's Berkshire quarterly earnings. Can the derivative deals, on top of these stock loss, break his back?

Now the big question is, in next few days -- 2/27/09 to be exact, Berkshire is going to report the results for the last quarter of 2008. How bad will the numbers be? For me, as a derivative trader, the most intriguing question is: is Buffett being forth-coming with his marking of the derivative book? Or more ominously, can he afford to?

In this article, I will run some numbers and scenarios to see how these derivatives should be priced and where the loss should come from. We all know there are 2 obvious sources -- 1) the "delta" loss due to the huge drop in stock market (SP500 from 1300 in mid '06 to 900 at end of '08 -- and now 770 as of last Friday); and the "vega" loss due to the index implied volatility jumping from 15 in mid '06 to now over 45. However, there is a third piece of surprise (also against him) that when I work out the number, it even shocked myself. Let's get to the details.

Here is what we roughly know about these deals (Based on the Reuters report, somewhat differ from what I discussed in my early article):

"...put options Berkshire wrote on the Standard & Poor's 500 .SPX and three foreign stock indexes. Buffett said these require payouts only if, when the options expire between 2019 and 2027, the indexes are below where they were when the options were written. Berkshire has received $4.5 billion of premiums..."

Without knowing the details, we made a conservative estimate assuming all the puts were written on SP500 (we all know last year SP500 actually performed better than most foreign markets, so we are doing Buffett a favor by putting all contracts in SP500). We assume the average length of the contracts is 15 years. Mid '06 to Early '07, SPX implied volatility was in the range of 10-19 (remember for a few days before the onslaught of subprime storm, VIX was trading below 10!) Let's assume Buffett sold those puts at 20 vol. At the time, Fed Open was at 5% (Source), and generally options are priced at the slight upward yield curve, and higher interest rate would lower the put price, so let's be more favorable to Buffett by assuming these contracts were priced BELOW spot rate, or 4.0%. Assuming the puts were done at 20 vol with 4.0% rate were extremely favorable assumption for Buffett.

With SPX at 1300 and strike at 1300, 5475 days to expire (15 years), 20 vol, 4.0% forward rate, for 4.5 billion premium, the trade would be 500 million Vega. We assume Buffett didn't hedge the 12 delta (even though the strike was at the spot, due to the far away expiration date and 4% rate, actually the delta was tiny -- would be even tinier if the rate is 5%).

Now let's move this contract forward:

- If nothing changes (no change in index and vol), just move the clock forward by 3 years, he would make $573 mil in interest from $4.5 bil, and loss of $466 mil due to forward moving close to the strike (that's a very intriguing characteristic in far-away option contract!) The deal would have a net gain of $107 mil.

- Now SPX dropped to 900 on Dec 08 (his quarterly end date): Assuming no vol change: net loss (with his interest income) is $4.25 bil.

- Now assuming he marked the vol at 35 (As reference, at the end of Dec 08, VIX was between 45 to 50, LEAPS SPX options were trading at 40 vol). His loss is now $12.07 bil.

- Now here is the biggest surprise: What did the Fed do in last 1 year when the financial turmoil broke out? Fed dropped rate all the way from 5% to almost 0 (spot Fed Open is now at 25 bps). Far term rate dropped substantially accordingly. Long term Treasury yield is at 2.75% to 3.5%. What happen if we drop the rate used in the marking of these contracts, by merely 1% (while we all know that the Fed Open drop 5% during the period)? With rate at 3%, Buffett's derivative portfolio now loss $15.7 bil (still assuming he can collect $0.5 bil interests from his original 4.5 bil premium)!

How about 2.5%? The loss is $18 billion!

Let's do a little stress test: if the original deal was done at a somewhat worse but more realistic level: sold the put at 18 vol (rather than 20) with 5% rate (rather than 4%); now we mark the current book at 35 vol with 3% rate at 900 SPX level. The loss is $38 bil.

People have been focused on how Berkshire would mark the vol level at this quarter. Now I have shown it's equally critical how it would mark the rate level. With the term so far away, the loss due to rate is much more ominous.

Three Strikes. Last year, 3 major macro-events all moved against Buffett's massive short puts: the world market crashed, the corresponding implied volatility shot sky high and remained in the high vol regime; but lastly and most surprisingly (and massively damaging to Buffett), is the rate drops.

Berkshire may argue that these are OTC contracts that are so far away that he really does not care how it is marked as long as he does not need to trade out at this time. But will he mark honestly and fairly, not to fall into the same pitfalls he once strongly criticized? And what happen to the counterparty of these deals?

Only a few days away to find the answer.

Selling Out-of-Money Puts. The interesting character of far term put options is: the forward price (which determines what is "at-the-money") is very sensitive to interest rate, and can be very far from the spot. So even Buffett sold those puts with the strike at the spot, he actually sold tons of way out-of-money puts (notice the small delta I indicate above)! We all know derivative history is filled with story of traders blown into pieces selling out-of-money puts. The question is: did Buffett realize he sold tons of out-of-money puts when he did that deal?

By the way, with such small delta, it would be little help to the huge loss even when he would hedge.

(The author can be contacted at huangxinw@gmail.com.)