Bill Gross Wasn't Short Enough German Bonds
This is fun:
Bill Gross should have listened to Bill Gross.
Just before the selloff in German government bonds, the manager of the Janus Global Unconstrained Bond Fund said the debt was the “short of a lifetime.” Yet instead of betting all-out against German bunds, Gross wagered they would trade in a narrow range for the time being, fund holdings posted on the website of Denver-based Janus Capital Group Inc. show.
Gross had been employing a strategy known as a strangle on Treasury and bund futures, selling both puts and calls that would be profitable if the bonds stayed range-bound, but which would cost him if they moved a lot in either direction. I thought it might be fun (for me) to try to deconstruct the transactions. Here's the Janus holdings disclosure as of March 31. Of particular interest are 10 short-term options on government bond futures:
- Four options on "TYM5," the 10-year U.S. Treasury future maturing in June, 1 one of which was Gross's largest long holding at 9.14 percent of assets.
- Six options on "RXM5," the 10-year German bund future maturing in June, one of which was Gross's largest short holding at 15.81 percent of assets.
I've pulled them out here:
A first question is: How big were those trades? Janus's disclosure says:
Derivative holdings include options contracts, forward currency contracts, swap contracts, and futures contracts. The allocations shown reflect delta-adjusted notional exposure for options (which accounts for sensitivity to the underlying asset price), notional exposure for other derivatives and market value for all other securities.
So we can try to figure out the notional exposure of those contracts. Gross's fund had net assets of $1.46 billion as of March 31, so negative 15.81 percent of the fund would mean a short position of about $231 million. But those option numbers "reflect delta-adjusted notional exposure for options." In other words, selling a call option on 100 euros' worth of bunds doesn't create 100 euros of bund exposure, because the call option might not end up in the money. Janus, sensibly, adjusts the reported size of its position based on delta, which measures the option's sensitivity to the underlying assets. If an option goes up by 25 cents for every 1 euro move in the underlying bund future, then its delta is 25 percent, and Janus (apparently) counts only 25 percent of the total underlying amount in its holdings disclosure.
Using Bloomberg delta numbers as of March 31 -- probably not identical to Gross's calculations, but close enough 2 -- we can calculate out total notionals, and get something like this:
So Gross seems to have sold call options on about 1 billion euros' worth of bunds -- in a fund with just $1.46 billion in net assets -- and sold put options on about a third of that amount. On the other hand, he sold put options on about $800 million worth of Treasuries, and sold call options on about one-fifth of that amount. 3 That sounds pretty bearish on bunds -- he's selling many more calls (which go up when bund prices go up) than puts (which go down when bunds go down), so it fits, very loosely, with Gross's claim that bunds were the "short of a lifetime." His Treasury bet, on the other hand, looked relatively more bullish.
Now, $2 billion worth of trades in a $1.46 billion fund seems ... large ... but remember that Treasury prices -- and even bund prices -- don't move around that much. Options are worth more -- and selling options is riskier -- when the underlying asset is very volatile, and at least as of March 31 these bonds weren't particularly. Despite the large notional amount of these trades, they seem to have had a pretty small market value: They were out-of-the-money options on relatively stable bonds, and you'd have expected -- as Gross seems to have expected -- that they'd expire out of the money. Just using historical prices for those options 4 we get something like this:
So these options on $2 billion worth of government bonds were worth about $8 million as of March 31. 5 So depending how you count, these options represented more than all of the size of his fund, or less than 1 percent of it.
Remember, Gross had sold all of these options, so that $8 million represented a liability of his fund. But he'd collected premium for selling the options; assuming (falsely) that he sold them on March 31, then the premium would have been about $8 million (the fair value of the options), or about 0.54 percent of the value of the fund. If you can sell options like that a few times a year, and they all expire worthless, then that's a good way to juice returns in a low-interest-rate world. That was explicitly Gross's fund's strategy: selling insurance, as it were, on moves in bond prices. His portfolio commentary said that "Volatility sales were a major driver of positive returns" in the quarter ended March 31.
On the other hand! Those options expire worthless only if bund and Treasury prices don't move much. If they do, then Gross needs to pay up. Here's the payout profile at expiration -- later this month -- for his bund option positions 6 :
Again, that looks sort of bearish: Gross loses more if bund future prices go up, and less if they go down. But he does lose money if bund future prices go down enough. They went down: The German 10-year yield went from 0.18 percent on March 31, down to 0.1 percent on April 21 (when Gross called the 10-year bund the "short of a lifetime"), up to 0.589 percent today, corresponding to a move in the futures price from 158.76 up to 160 and back down to 154.29. When Gross advised shorting the bund, the futures were at 160, and this trade looked very bearish: He was short the bund all the way down to 158, with just a couple of months until the trade expired and he took his profits. And he was right; the bund went down to 158. But then it kept going. Now futures are at around 154, and in hindsight he -- or, at least, his trading as of March -- seems to have been unduly optimistic on the bund.
Here's a rough cut at the historical value of his March 31 bund options position, versus bund yields:
Don't take the scale at all seriously here. 7 The point is that from roughly the start of April until roughly the time that Gross told everyone to short bunds, he looked to be short bunds: His position went up in value when bund yields went up (prices went down), and it went down when yields went down (prices went up). And then in late April, when the bund rapidly fell below his floor price, things reversed, and his position that had seemed to be short bunds turned out to be long.
On the other hand, Gross's Treasury strangle seems ... fine? Fine-ish? Depends how you count. Bloomberg News reported in April that "To profit, Gross needs the 10-year yield to stay between 2.1 percent and 1.7 percent"; it's currently a bit above that, at 2.19 percent. But the Treasury future underlying Gross's options is still a bit above 127, the strike price on the puts he sold, so by my math his liability hasn't really increased since the start of the quarter. His strangle looked pretty good for a while as Treasuries remained range-bound, then started looking less good, but still not disastrous:
Again, don't take the scale too seriously, 8 but the Treasury strangle looked like it was having a good month for most of April, then had a bad last couple of weeks. But that more or less gets it back where it started from.
A few important caveats here:
- I have no idea what Bill Gross's fund actually owns! All I know is what it owned on March 31. 9 These are short-dated options and he seems to trade actively, so for all I know the position might have turned over entirely. That said, he does seem to have been caught out somehow by the bund move; Bloomberg News reports that "Janus Global Unconstrained has fallen 2.6 percent since Gross advised shorting the 10-year German bund on April 21," though the Wall Street Journal blames this mostly on Treasuries and notes that his bund short may have helped. My own math suggests sort of the opposite, but my own math is mostly guesswork.
- In particular, if you thought bunds were "the short of a lifetime," this strangle probably wouldn't cut it for you: You'd want to be more directly short bunds, and perhaps by sometime in April Gross was.
- The numbers here just aren't that big. By my math, with lots and lots of guesses and approximations, Gross's bund short seems to be about a 9 million-euro liability now. That's more than twice what it was on March 31, and almost twice what it was on April 21 when he advised shorting the bund, but it's still ... I mean, he seems to have lost a few million euros on the trade. He's not running a $293 billion fund anymore, and losing a few million euros hurts now, but this is more of a curiosity than a crisis.
Still it's a curiosity. One thing to consider is that it's hard to know what you're betting on. Here Gross thought that the 10-year bund was "the short of a lifetime," and he seemed to have positioned his fund to bet against the bund, but as events worked out his bet against the bund seems to have been swamped by an offsetting bet on the bund. It's a little reminiscent of the London Whale, who tried so hard to bet against corporate credit that he ended up betting massively on corporate credit. Things aren't always as linear as they seem; they can circle around, and circumstances might turn a smart but hedged bet on prices to go down into a bad (but hedged!) bet on prices to go up. Even very smart people can call the right trade, but then make the wrong one.
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- options expiring May 22, 2015, on
- futures contracts expiring in June 2015, on
- Treasuries with a maturity of 6.5 to 10 years (or bunds with a maturity of 8.5 to 10.5 years, respectively).
Lot of maturities to unpack.
I compute "delta-adjusted notional" by just multiplying the "percent of fund" by the fund's $1.46 billion reported size; I then compute "actual notional" by just dividing the delta-adjusted notional by the Bloomberg delta. I also convert dollar notionals into euro notionals for the bund contracts, at 1.0731 dollars to the euro based on the rate as of March 31.
My source for the deltas is the Bloomberg option calculator, Bloomberg page RXM5P 157 Comdty OV, etc. In the OV calculator I've changed the Trade Date to 3/31/2015, otherwise left everything as a default.
The delta-adjusted numbers are broadly similar: about 4 to 1 calls to puts for the bunds, 3 to 1 puts to calls for Treasuries.
Source: Bloomberg, RXM5P 157 Comdty HP, etc. So for instance on March 31, the price of the 157 bund futures put was 0.38, meaning 0.38 cents per 100 euros of notional, or 380 euros per 100,000 notional. And the price of the 127 Treasury futures put was 25/64ths, meaning, charmingly, $390.625 per $100,000 notional. (Here is the fact sheet for Treasury futures and options; options are measured in units of 1/64 of a point, or $15.625 per $100,000 notional.)
Like $7.9 million, converting euros at $1.0731.
Just assuming my notional sizes calculated above, and looking at the strike prices of the options.
The data is:
- 10-year bund yields from Bloomberg (CTDEM10Y Govt HP).
- Gross's position value is computed by multiplying (1) my estimated notionals as of March 31 times (2) historical prices of options on bund futures from Bloomberg (RXM5P 157 Comdty HP, etc.).
- Then I just normalize both to the March 31 level and look at percentage moves.
- For the position, I normalize to the negative of the March 31 level, so like if the position was worth negative 4.26 million euros on March 31 and gained 426,000 euros in value (to 3.83 million euros), I count that as a positive 10 percent move, since Gross's fund made money on it.
There's nothing particularly legitimate about comparing percentage moves in a bond yield against percentage moves in an option portfolio, but the graph looks OK.
Similar caveats to the bund one. The 10-year yield is T 2 02/15/25 Govt, the option values are my estimated notionals times the prices from TYM5P 127 Comdty HP, etc.
Also I'm just looking at these specific trades on bond futures options; he's got a bunch of rates and currency trades that might have mitigated or exacerbated these moves.
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Matt Levine at firstname.lastname@example.org
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