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Lots Of Options

Oh, year-end illiquidity is lots of fun, isn’t it?

After yesterday’s fairly high-volume selloff (the 1.5bln shares was the highest non-witching volume since July 1st), the market launched higher overnight on essentially nothing. The rally was attributed to oblique comments by ECB President Trichet that we should not underestimate Europe’s determination to resolve the current crisis, in an article in the Financial Times entitled “Trichet hints at bond purchase rethink.” The thought is that the ECB might buy more sovereign bonds.

So what? Supposedly, the ECB is sterilizing the purchases, draining the money they use to buy bonds with. So all that they’re doing is elevating sovereign bond prices above market-clearing levels. I can see how that helps the politicians who want to spend more money and not pay higher interest rates (one of the funniest things I have read in the last few days is that the 5.8% aggregate interest rate on Ireland’s package was “punitive.” Really? The market wasn’t willing to fund you at anything close to that level. How is 300bps below market rates “punitive”?), but I don’t see how it helps equity markets. Especially, U.S. equity markets.

But the 2.2% rally in stocks, to the highest level in weeks and above the 1200 level on the S&P, occurred on slightly more than $1bln shares in volume. That’s not horrible, but it’s not exactly a sign that everyone is piling into the boat before it leaves the pier. The VIX fell, but not enough to make you think risk is switched off; the dollar declined, but not so much that it looks like investors are rushing back to the continent. I expect the T-1000 isn’t done yet merely because Trichet murmurs soothing bromides to the newspapers.

The economic picture is improving on this side of the pond, no doubt, but before attributing the rally to that one should be aware that the S&P was essentially over 1200 before ADP even printed. The ADP report was in fact slightly better-than-expected, at 93k (as I noted yesterday, the risks to ADP were to the upside, and the risks to Payrolls are on the downside although less so now). The ISM report was as-expected. Car sales were a bit stronger than expected, but 9.27mm domestic car sales is not going to get anyone thinking that happy days are here again (especially since the Big Three are all still making cars). In general, these are cheerful numbers but not exactly explosive.

Bond yields, though, were explosive! The 10y note yield jumped 17bps to 2.97%, and inflation swaps widened 5-6bps. That 10y yield is the highest since late July, and with the strong autumnal seasonal pattern fully past the bond market looks on fragile ground. Before the ECB ramps up their own purchase program, they should reflect on the fact that the Fed’s unsterilized program has failed to keep yields from rising. The purposes of the two central banks are different, but their chosen weapons – purchases of sovereign bonds, in an effort to keep interest rates from rising or to push them lower – are the same.

If yields continue to rise, eventually duration extension of mortgage portfolios begins to become an issue. Although the mortgage securities market is slightly smaller now than it used to be, and although many mortgage securities are now held by an entity that seems to care little about its duration (the Fed), the hedging needs of mortgage portfolios may still be problematic if they occur in December. Liquidity isn’t very good in December. Moreover, the fact that the Fed doesn’t care about hedging changes in its portfolio duration doesn’t mean that changes in the behavior of its portfolio will not matter. Higher mortgage rates imply smaller prepayments, and smaller prepayments means the Fed’s need to reinvest those prepayments is also smaller. I am not a mortgage quant, so I don’t know exactly where the inflection points are that we have to worry about. But as a former rates trader, I know we should be worrying about them.

While I am mentioning delta-hedging (since that is what a mortgage hedger is doing by buying when the market is rallying and selling when the market is declining: delta-hedging the options embedded in the mortgage security), it is perhaps an opportune time to mention another concern that has been troubling me recently.

Let me first digress for just a moment to introduce quickly a couple of options-related concepts. Those of you who are intimately familiar or at least very comfortable with options concepts can skip this next section.


Quick Option Primer

The delta of an option is the sensitivity of the option’s price to a change in the price of the underlying instrument. For example, if I own a call option with a delta of 0.3 and the underlying bond rises one point, then I expect the option price to rise 0.3 points (all else being equal).

The delta of an option is intimately related to the strike price of the option (that is, the price at which the option owner can elect to buy, if it is a call option, or sell, if it is a put option). If the current price of the underlying security is below the strike price, then a call option’s delta will be less than 0.5. If the current price of the underlying security is above the strike price, then a call option’s delta will generally be above 0.5.[1] So, as the price of the underlying security goes from very far below the call option’s strike (“out of the money”) to very far above the strike (“in the money”), the delta goes from something near zero – it isn’t very sensitive at all to movements in the underlying price – to something near one – it moves in lock-step with the security it is about to become, once the option is exercised.

The way that the delta changes with respect to movements of the underlying security’s price around the strike price is called the gamma of the option. For an option with high gamma, the delta of the option changes very rapidly. The option, in other words, may go from being very insensitive to movements in the underlying security, to extremely sensitive to those movements, all in a short period of time. A crucial point is that the gamma of any vanilla option is at a maximum when the underlying instrument is at the strike price.

If you’re still with me, congratulations! Now for one more concept, and then I’ll explain my concern. An important concept in options theory (and trading) is the notion of a replicating portfolio. That sounds fancy, but all it really means is this: if I have sold you a call option, then when it expires I know that (a) if the option is in-the-money, I will have to deliver to you the underlying instrument because you will exercise the option. So I’d better have the bonds or stocks or whatever on-hand to deliver. And (b) if the option is out-of-the-money, I know you won’t exercise, so I don’t need to have any of the underlying on hand to deliver to you. In the period of time between when I sold you the option, and when you exercise that option, the “replicating portfolio” is (basically) a delta-weighted amount of the underlying instrument. In the example above, of the call with an 0.3 delta, if I sold you contracts on $1,000 worth of bonds then I need to have on hand $300 worth of bonds. If the bonds go up 1 point (1%), then I will have made $300 on my holdings of bonds, and the value of the option will also have gone up by 0.3 * $1,000 * 1% = $300. I am hedged. Under the conditions assumed in Black-Scholes, if price changes are continuous, rebalancing is costless, borrowing costs are the same as lending costs, volatility is constant and equal to the volatility priced into the option…then the fair price of the option is the cost of that hedging strategy. An option is nothing more than a pre-packaged hedging strategy.

And that hedging strategy has a cost, as you can see. If the market rises, then the delta of the option will increase as the option goes in-the-money. That means that to maintain the replicating portfolio, I need to buy more bonds as the market goes up. In reverse, as prices fall then the delta falls and I need to sell more bonds as the market falls. Even if there is no bid/offer spread, this is going to cost money because I am systematically buying high and selling low!


Back To The Story

You can also see implications for markets in this dynamic. While both option-owners and option-sellers can delta-hedge, if the hedging is done mostly by people who are short options then markets will tend to be more volatile since there will be lots of people buying into rallies and selling into selloffs. This is why the mortgage market can have such a big impact on the bond market in illiquid times. Owners of mortgage-backed securities are implicitly short options because the mortgagee (that’s you and me) tend to pay more slowly when rates are going up and pre-pay when rates are falling. Therefore, when rates are falling fairly rapidly and especially when the market is illiquid, sophisticated firms that have a lot of MBS (such as, say, the GSEs) will need to keep buying, and buying, and buying, pushing rates down faster and faster and faster. And the opposite effect occurs when rates are rising.

We haven’t had to worry much in the past about inflation options, because until the last year or so there haven’t been enough outstanding – relative to market liquidity – to worry about. And anyway, if they are randomly spread about then any effects from one hedger’s activities are diluted. But this is no longer the case. Dealers of inflation options are almost always two things: they tend to be short very low-strike options like -2% and -1% floors, which are generated when corporate treasurers issue CPI+2% or CPI+1% notes and then swap them. The corporate ILB market in the US is pretty small, so this isn’t a very large problem, but in 2008 it contributed to the complete collapse of the inflation swap quotes to deeply negative readings for the first several years (see Chart below, source Enduring Investments).

1y US CPI in the aftermath of the oil crash and gamma effects

The other, more dangerous case is that dealers are also almost always short high-strike options like 4%, 5%, and 6% caps on inflation. This is because customers in large majorities tend to be buyers of inflation protection rather than sellers (and you can tell this by the very high prices charged for inflation caps). The demand for this protection is nearly bottomless.

Now, we have never had a situation where inflation expectations rose suddenly, in the same way that they fell so abruptly when oil prices (and Lehman) crashed in late 2008. But if we were to have such an event – and it is certainly not out of the question – I wonder whether there are enough TIPS in the world, or people willing to sell inflation swaps into an obvious dynamic like this, to keep inflation measures from completely coming unglued. And what are the policy implications of this? If the Fed sees forward inflation expectations go from 2% to 3%, 4%, then 5% and 6% in rapid succession, what are they to do?

While I believe the teeth of this dynamic are far away – after all, core inflation is 0.6% – it may not be so far away as we think. Forward inflation between 5y and 10y is already well up and over 3% (see Chart below, source Enduring Investments), and when it comes to an inflation cap you care about each forward “caplet.”

CPI swaps curve

It isn’t something to worry about tomorrow, but it is something to worry about…unless you own caps and want to see forward inflation quotes fly!

Indeed, there is not much to worry about tomorrow…save your worrying for Friday’s Employment Report. On Thursday, the main releases are Initial Claims (Consensus: 424k from 407k), which are expected to show a significant bounce – watch bonds get smacked if they don’t! – and Pending Home Sales (Consensus: -1.0% vs -1.8% last month). I doubt this latter release has any traction the day before Employment. There are also several Fed speakers scheduled.

I expect that today’s prodigious leap higher in equities is not going to be sustained, but hope for solid Payrolls gains and a widening of the ECB bond-buying program might keep prices elevated for a day or two. I would be surprised at further extension, however, and think gravity will probably take over fairly soon.

[1] This is generally the case because the call delta minus the put delta will not sum to 1 but to the present value of 1. So if an option is only slightly in the money, with a long time to maturity, it will actually have a delta slightly less than 0.5. But this is a technical point not critical to the discussion here.


  1. Lee
    December 2, 2010 at 11:32 am

    Thank you very much for the inner look at inflation.

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