Archive for the ‘Options’ Category

A Guess at the Value of Long Inflation Tails

December 7, 2021 1 comment

In my last post, “You Have Not Missed It,” I promised the following:

“There is one final point that I will explain in more detail in another post. Breakevens also should embed some premium because the tails to inflation are to the upside. When you estimate the value of that tail, it’s actually fairly large.”

So, as promised, here is that explanation.

Viewing the forward inflation curve as a forecast of expected inflation (whether using “breakevens” or, more accurately, inflation swaps) is biased in a particular way. Or, at least, it should be. The “breakeven” inflation rate is the rate at which a long-only investor over the ensuing period would be roughly as well off with a nominal bond (which pays a real rate plus a premium for expected inflation) and an inflation-indexed bond (which pays a real rate, plus actual inflation realized over the period). Obviously the inflation-indexed bond is safer in real space, so arguably nominal bonds should also offer a risk premium to induce a buyer to take inflation risk.[1] Ordinarily, though, we ignore this risk and just consider breakeven inflation to be the difference between real and nominal yields. Inflation swaps are cleaner, in that if inflation is higher than the stated fixed rate, the fixed-rate payer on the swap ‘wins’ and receives a cash flow at the end, whereas if inflation turns out to be lower than the stated fixed rate, it is the fixed-rate receiver who wins. So from here on, I will talk in terms of inflation swaps, which also abstract from various bond-financing issues of the breakeven…but the reader should understand that the concept applies to other measures of expected inflation as well.

Now, suppose that you expect 10-year inflation to come in at 2% per annum. Suppose that in the inflation swap market, the 10-year rate is 2% ‘choice’ – that is, you may either buy inflation at 2% or sell inflation at 2%. Since you expect inflation to be 2%, are you indifferent about whether you should buy or sell?

The answer is no. In this case you should be much more eager to buy 2% than to sell 2%, given that your point estimate is 2%. The reason why is that the distribution of inflation outcomes is not symmetrical: you are much more likely to observe a miss far above your expectation than to observe a miss far below your expectation. Therefore, the expected value of that miss is in your favor if you buy the inflation swap (pay fixed and receive inflation) at 2%. There is, in other words, an embedded option here that means the swap market should trade above where most people expect inflation to be.

We can roughly quantify at least the order of magnitude of this effect. Consider the distribution below. This chart (Source: Enduring Investments) shows the difference, from 1956 until 2011, of 10-year inflation expectations[2] compared with subsequent 10-year actual inflation results. The blue line is at 0% – at that point, actual inflation turned out to be right where a priori expectations had it. The chart obviously only covers until 2011 since that is the last year from which we have a completed 10-year period. Recognize that I am not charting the levels of inflation, but the level of inflation relative to the original expectation.

Notice that the chart has a cluster of outcomes (and in fact, the most-probable outcomes) just to the left of zero, where expectations exceeded the actual outcome by a little bit, but that there are very few long tails to the left. However, misses to the right, where the actual outcome was above the beginning-of-period expectations, were sometimes quite large. The median point (where half of the misses are to the left, and half are to the right) is 0.21%. But this is not a symmetric distribution, so if we randomly sample points from this distribution, we find that the average of that sample is 0.59%.

So, if you buy the inflation swap at 2% when your expectations are at 2%, on average you’ll win by 59bps, at least historically. Of course, past results are no indication of future returns, and a Fed economist would argue that we have much better control of inflation now than we ever have in the past (Ha ha. I crack myself up.). And inflation volatility markets, when they can be found, don’t trade at such high implied volatilities. Noted, although the wild swings in growth and the deficit and the money supply, not to mention recent realized outcomes, might make more cynical observers question whether we should be so confident in that view right at the moment.

Moreover, a counterargument is that at the present time an investor also has the advantage of investing when expectations are fairly low, so the downside tails are not as likely. The worst outcome of that whole 1956-2011 period was an 8.75% undershoot of inflation versus expectations. This happened in the 10 years following September 1981, when expectations were for 10-year inflation of 12.70% and actual inflation was 3.95%. But with expectations at 2.50%, is it really feasible to get a -6.25% compounded inflation rate? That would imply a 50% fall in the price level (and, I should note, it would mean that investors in TIPS would win hugely in real space since they get back no worse than nominal par. But that doesn’t help the swap buyer).

To be a little more fair, then, the following chart considers only the periods where inflation expectations were 5% per annum or less at the beginning of the period. That truncates only 10% of the distribution, but as you might expect the vast majority of the truncation is on the left-hand side. This is fair because it’s naturally harder to miss far below your expectations when your expectations are very low to begin with.[3]

The value of the expected miss in this contingent view is 1.13%. So, in order for the market to be priced fairly if general expectations are for 2.5% average CPI inflation the 10-year inflation swap would have to be around 3.63%. Again, even allowing for the “policymakers are smarter now” argument (an argument quite lacking, I would argue, in empirical evidence) I would feel comfortable saying that 10-year inflation swaps, and breakevens, should embed at least a 50bps or so ‘option premium’ relative to expectations.

I don’t believe that they do. Indeed, consider that the buyer of 10-year TIPS (with breakevens at 2.50%) not only wins if 10-year inflation is above 2.50% but the average win historically (conditioned on breakevens being below 5% to start, and by construction only considering wins) has been about 2.07% per annum – a massive outperformance. Not only that, but any losses are essentially guaranteed to be small because the tails on the left-hand side are truncated: if inflation is negative (that is, if the loss would have been greater than 2.50%) it is limited by the fact that the Treasury guarantees the nominal principal.

As an aside, we do consider this sort of option in other contexts. In the Eurodollar futures market, for example, we recognize that the person who is short the Eurodollar contract (and therefore gets a positive mark-to-market when interest rates rise) is in a better situation than the long (who gets the positive mark-to-market when interest rates fall), because the short gets to invest wins at higher interest rates and borrow losses at lower interest rates, while the long must borrow to cover losses when interest rates are higher, and but gets to invest wins when interest rates are lower. As a result, Eurodollar futures trade lower than the forwards implied from the swap curve, since the buyer needs to be induced by a better-than-expected price. And there are other such examples. But I am pretty sure I have never seen an example of an embedded option like this that is priced so differently relative to history than the embedded options in the inflation market!

[1] However, since this risk is symmetric – the seller of the bond also has risk in real space, but in the opposite direction – it isn’t immediately obvious why one side should get an inducement over the other. So I will leave the ‘risk premium’ aside.

[2] For long-term inflation expectations back before the advent of TIPS, I used the Enduring model relating real yields to nominal yields, about which I’ve written previously. You can find a brief discussion of this and an illustration of the model at this link:

[3] The author’s wife has been known to make something like this observation from time to time.

Categories: Options, Theory, TIPS Tags: , ,

Meteorologists and Defenseless Receivers

September 15, 2014 Leave a comment

The stock market really seemed to “want” to get to 2000 on the S&P. I hope it was worth it. Now as real yields seem to be moving higher once again (see chart below, source Bloomberg) – in direct contravention, it should be noted, of the usual seasonal trend which anticipates bond rallies in September and October – and the Fed is essentially fully ‘tapered’, market valuations are again going to be a topic of conversation as we head into Q4 just a few weeks from now.


To use an American football analogy, the stock market right now is in an extended position like a wide receiver reaching for a high pass, but with no rules in place to prevent the hitting of a defenseless receiver. This kind of stretch is what can get a player laid up for a while.

Now, it has been this way for a long time. And, like many other value investors, I have been wary of valuations for a long time. I want to make a distinction, though, between certain value investors and others. There are some who believe that the more a market gets overvalued, the more dramatic the ensuing fall must be. These folks get more and more animated and exercised the longer that the market crash doesn’t happened. I think that they have a point – a market which is 100% overvalued is in more perilous position than one which is a mere 50% overvalued. But we really must keep in mind the limits of our knowledge about the market. That is, while we can say the market is x% overvalued with respect to the Shiller PE or whatever our favorite metric is, and we can say that it is becoming more overextended than it previously was, we do not know where true fair value lies.

That is to say that it may be – I don’t think it is, but it’s possible – that when stocks are at a 20 Shiller PE (versus a long-term average of 16) they are not 25% overvalued but actually at fair value. Therefore, when they go to a 24 PE, they are more overvalued but instead of 50% overvalued they are only 25% overvalued because true fair value is, in this example, at 20. What this means is that knowing the Shiller PE went from 20 to 24 has no particular implications for the size of the eventual market break, because we don’t actually know that 16 really represents fair value. That’s an assumption, and an untestable assumption at that.

Now, we need assumptions. There is no way to keep from making assumptions in financial markets, and we do it every day. I happen to think that the notion that a 16 Shiller PE is roughly fair value is probably a good assumption. But my point is that when you’re talking about how much more overvalued a market is than it was previously, with the implication that the ensuing break ought to be larger, you need to remember that we are only guessing at fair value. Always. This is why you won’t catch me saying that I think the S&P will drop eventually to some specific figure, unless I’m eyeballing a chart or something. In my mind, my job is to talk about the probabilities of winning or losing and the expected value of those wagers. That is, harking back to the old Kelly Criterion thinking– we try to assess our edge and odds but we always have to remember we can’t know either for certain.

Bringing this back to inflation (it is, after all, CPI week): even though we can’t state with certainty what the odds of a particular outcome actually are, we can state what probability the market is placing on certain outcomes. In inflation space, we can look at the options market to infer the probability that market participants place on the odds of a certain inflation rate being realized over a certain time period (n.b. the market currently only offers options on headline inflation, which is somewhat less interesting than options on core inflation, but we can extract the latter information using other techniques. For this exercise, however, we are focusing on headline inflation.)

What the inflation options market tells us is that over the next year, market participants see only about an 18% chance that headline inflation will be above 2.25% (that is, roughly the Fed’s target, applied to CPI). This is despite the fact that headline inflation is already at 2%, and median inflation is at 2.2%. So the market is overwhelmingly of the opinion that inflation declines, or at least rises no further, from here. You can buy a one-year, 2.5% inflation cap for about 5-7bps, depending who you ask. That’s really amazing to me.

Looking out a few years (see table below, source Enduring Investments), we see that the market prices roughly a 50-50 chance of inflation being above the Fed’s target starting about three years from now (September 2016-September 2017, approximately), and for each year thereafter. But how long are the tails? The inflation caplet market says that there is no better than a 24% chance that any of the next 10 years sees inflation above 4%. We are not talking about core inflation, but headline inflation – so we are implicitly saying that there will be no spikes in gasoline, as well as no general rise in core inflation, in any year over the next decade. That strikes me as … optimistic, especially since our view is that core inflation will be well above 3% for calendar 2015.

Probability that inflation is above
in year 2.25% 3.00% 4.00% 5.00% 6.00%
1 18% 5% 3% 1% 0%
2 41% 19% 8% 3% 1%
3 46% 25% 11% 5% 3%
4 50% 31% 15% 7% 4%
5 52% 35% 18% 10% 6%
6 50% 35% 19% 11% 7%
7 50% 36% 21% 13% 8%
8 49% 37% 22% 14% 9%
9 48% 37% 23% 15% 10%
10 47% 37% 24% 16% 11%

What is especially interesting about this table is that the historical record says that high inflation is both more probable than we think, and that inflation tails tend to be much longer than we think. Over the last 100 years (since the Fed was founded, essentially), headline inflation has been above 4% fully 31% of the time. And the conditional probability that inflation was over 10%, given that it was over 4%, was 32%. In other words, once inflation exceeds 4%, there is a 1 in 3 chance, historically, that it goes above 10%.

Cautions remain the same as above: we cannot know the true probability of the event, either a priori or even in retrospect when the occurrence will be either probability=1 (it happened) or probability=0 (it didn’t). This is why it is so hard to evaluate meteorologists, and economists, after the fact! But in my view, the market is remarkably sanguine about the prospects for an inflation accident. To be fair, it has been sanguine…and correct…for a long time. But I think it is no longer a good bet for that streak to continue.

RE-BLOG: Tales of Tails

December 19, 2013 4 comments

Note: The following blog post originally appeared on June 27th, 2010 and is part of a continuing year-end ‘best of’ series, calling up old posts that some readers may have not seen before. I have removed some of the references to then-current market movements and otherwise cut the article down to the interesting bits. You can read the original post here.


…I also raised my eyebrows at an article in the UK Telegraph which declares that the Fed is considering a “fresh monetary blitz” since the recovery is faltering. I am always happy to be skeptical when an article doesn’t name names, but this seems to me to be fairly likely to be true:

“Key members of the five-man Board are quietly mulling a fresh burst of asset purchases, if necessary by pushing the Fed’s balance sheet from $2.4 trillion (£1.6 trillion) to uncharted levels of $5 trillion.”

The strategy makes sense, if you believe that the long-term effects of dramatic monetary policy movements can be evaluated over a period of a couple of quarters. I would not be surprised at all to discover that the thinking at 20th Street and Constitution Avenue is something along the lines of “hey, we did it once and didn’t cause inflation, so why not take out the paddles again? CLEAR! ZAP.” I’ve written before of the odd set of speeches we saw earlier this year describing a wondrous alchemy that the Fed seemed to believe they could accomplish: buy assets rapidly to save the economy by keeping rates low and adding liquidity. Sell the assets without completely reversing the effect by doing so slowly. Clearly, if there is real belief that the Board can pump and dump without the “dump” causing any problems, then for God’s sake why not pump?

Obviously, that’s a bunch of hooey, but I remain wary that there may be those who believe it.

The market on Friday was led (and maybe even supported) by financial stocks, because the market finally learned the form of the financial reform bill. It is bad, and will cause severe damage to bank earnings. It isn’t as bad as some people feared, but it is about as bad as was ever likely to become law. Prop trading at banks is still banned, and banks will have two years to push trading of commodities, non-investment grade bonds, and CDS that are not cleared through an exchange to separately-capitalized subsidiaries. Most derivatives will have to be cleared and traded on exchanges, which means less customization (bad for dealers, and bad for clients too). This law will be bad for turnover, bad for margins, and will cause leverage ratios to decline (probably the only reasonable part of the prescription, from my view). The Dupont model tells me those three things imply much lower ROE.

So why did bank stocks rally? This is worth a deep reflection because it explains something about markets.

Bank stocks rallied because as bad as the legislation is, the fact that we now know the form of the legislation removes the most onerous tail risks.

Bob Merton, many years ago, observed that the equity of a company can be thought of as a call option on the value of a firm: the value can only go to zero, if the firm is insolvent, but can be worth a great deal. So what do we know about options? One of the things we know is that a great deal of the value of an option comes from the expected value of unlikely, extreme outcomes. If you remove the chance at the home run, an option gets much cheaper.

This is one big reason that bear markets often end with a sharp rally off the lows (although please note that it does not follow that every sharp rally implies an end to the bear market!) – once the disaster case, the chance of an outright crash or broad economic or financial calamity, recedes in probability, the value of equities rise appreciably. A company which avoids bankruptcy by a hair will see its stock rise dramatically when the chance of losing everything goes away. Observe the behavior of many of the financials during the crisis. When TARP and other bank-supportive mechanisms began to have traction the sector leaped, not because earnings were about to be multiplied 10 times but because the fear of zeros greatly receded.

(Aside #1: Most analysts, of course, look at equity values as related linearly to earnings, and in normal circumstances they are. …a PE of 25x is rich, 15x is cheap, for example. But this is likely because behavioral biases prevent analysts from considering the value of the disaster which they think is very unlikely. In any case, a 15x multiple might be quite expensive indeed compared to a 25x multiple, if the former company is about to receive a legal judgement that could potentially destroy the firm. Indeed, one real problem with conventional investment analysis is that the 15x multiple stock might be cheap, or the multiple may in fact be a sign that tail risks are higher for this equity than for the 25x one. Buying enormous dividend yields is often unproductive because the high yield implies a market belief, often correct, that the dividend is not likely to be paid or paid in that amount.)

(Aside #2: Because so much of the value in an option comes from the tail, evaluating options using simple Black-Scholes when the underlying risk isn’t lognormal can be extremely dangerous, especially with exotic options that have path-dependent valuations and with options on underlying instruments that are known to have a high likelihood of non-linear performance – near-bankrupt equities, for example. Black-Scholes implied vols are nearly useless in such a case).

So, owning a stock or stocks generally when the tail risks are about to recede is a good recipe for making sparkling returns. But we have another name for this sort of investing strategy: “catching a knife.” You can own an AIG-like bounce, but also get run over by Lehman. On the flip side, because as an equity investor you own these negative tail events naturally, you can add a lot of value by avoiding the blow-up.

Rising volatility, then, tells you two things: first, it tells you that the market’s sense of the risk of a possible calamity is growing; second, it tells you that once these fears recede you might earn a solid return. You already knew this; it’s why the VIX is considered a contrary indicator by some.

Does it make sense to be investing more, then, when a blowup might happen, or investing less? As it turns out, the answer to this question is not entirely clear but thanks to the Kelly Criterion we can make some observations. The Kelly Criterion describes the optimal bet size, as a proportion of the bankroll, for a series of uncorrelated bets with a given edge and payoff. The simple observation (which becomes a lot less simple after they start involving the math) is that you want to bet more of your payroll if you are (a) getting good odds and (b) are very confident of the outcome. That is, your bet size should increase if you are getting good odds, and have a good edge. Kelly worked out the math to determine what the optimal bet size should be under certain conditions.

The relevance here is as follows: when a crisis hits, two things are happening to you as an equity investor. First, you are becoming more confident that the market will reward you for buying when everyone else is selling, because (as noted above) unless the world actually does end you are likely to be getting a good price. Second, though, you need to recognize that the increasing chance of debacle implies a worse payoff. In April of 2008, the chances of losing everything the next day were pretty slim. In mid-September 2008, the chances were appreciable that a bunch of your portfolio might be in trouble. So your edge (confidence in winning, if the bet was repeated a bunch of times) was growing, but your odds (payoff if you win, relative to your loss if you don’t) were worsening.

The schematic below shouldn’t be taken literally, but is meant to illustrate the basic relationships.

These lines are the pure results from the Kelly formula for the indicated inputs. Perhaps an investor might consider his/her “bankroll” in this case to be the maximum portfolio concentration in equities. Obviously, if you are extremely confident that you are going to win, then no matter what the payoff you should be making a pretty reasonable bet; therefore, the lines converge on the right. But as we move left, we get a sense of the tradeoff between the edge and the odds. When volatility is rising, the investor is moving to the left, implying a lower confidence of a payoff; if the market is trading to lower prices, it improves your odds but you can see that you would need vastly better odds to counteract the effect of increased uncertainty. I would suggest that in the range of normal investor confidence, rising volatility implies that you should tend to be taking chips off the table, even though it means you may miss a minor pop if the world doesn’t end.

We are not currently in a crisis quite like what we saw in 2008. But the elevated levels of implied volatility suggest that crisis is not so far off as we would like to see it. I think this means that we should be avoiding the possibility of the long negative tail, and taking chips off the table.


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Brace for Data Impact

October 17, 2013 19 comments

Not a bad trick!

The government shuts down, and the Administration threatens default; the stock market drops a few percent, and then rallies to new highs. Then the shutdown ends, and the stock market rallies again because the shutdown ended.

I lose track of the mental gymnastics required to reconcile prices rising perpetually no matter what the news – or, what is worse, rising regardless of whether the news is “A” or “not A.”

I saw an analyst report recently in which the writer argued that stocks were not overvalued per se; they were only one standard deviation above fair value. I don’t disagree very much, quantitatively, with that view…it sounds about right. But the way it is expressed is somewhat misleading. We know that roughly two-thirds of a normal distribution is contained between +1 standard deviation and -1 standard deviation from the mean. This implies that only about one-third is outside of one standard deviation, and only half of that on the upside. In other words, a market which is “only one standard deviation above fair value” is in the 84th percentile or so of richness. Or, if we were to throw darts randomly at the distribution, about five of those darts would represent “down” and one would represent “up” from that level.

Now, whether or not we call that “expensive” or a “bubble” (I don’t think it qualifies as a bubble) is mostly a linguistic argument rather than a financial argument. The financial/investing argument is whether it is smart to be invested in an 84th percentile market or not.

The answer isn’t quite as clear as it seems because it depends on how rich the market is when you sell it. If you buy at the 84th percentile and later sell at the 84th percentile, then you’ve gained the growth in earnings and any dividends over that period. So it’s not an automatic loser. Similarly, if you are holding a bad poker hand but push all your chips into the middle, you might win against someone else’s hand in the event that theirs is even worse. But that doesn’t mean it’s a good move. In investing, as in poker, you win by making your biggest bets when odds are favorable, and avoiding bets when odds are adverse. And sometimes, that means you have to sit at the table for a long time waiting for good odds! So, whether stocks are “expensive” or not at the 84th percentile is to an important degree irrelevant to me. What is relevant is sizing my bet to reflect my chances of winning, which aren’t very good right now.

Bonds are back in rally mode for now. The traditional seasonal pattern, which calls for a peak in yields on September 4th, has been strikingly useful this year (the high closing yield for the 10-year note was actually September 5th). But the main portion of that seasonal pattern is coming to an end. Yes, the Fed is continuing to buy bonds, but core inflation is now heading higher rather than lower as it was prior to last month, and we all realize that the can has only been kicked for a couple of months. Still, the VIX plunged on Wednesday and Thursday, so investors clearly don’t anticipate any near-term volatility in markets. That seems really odd to me, since we are about to see the densest economic release calendar we have seen in many years. When I was an options trader, we scaled volatility by the density of economic releases (weighted by the importance of the release). I can’t imagine wanting to sell volatility when we have the Retail Sales and Existing Home Sales reports on Monday, Employment Report and Chicago Fed on Tuesday, New Home Sales on Thursday, Durable Goods on Friday, and lots of corporate earnings besides; and the following week has PPI and CPI and the Chicago PM and ADP and ISM.

And meanwhile, in somewhat astonishing fashion today the dollar got clocked, falling to the lowest level since February. There are certainly some people in Washington scratching their heads on that one. All in all, I am not convinced by the VIX’s brave face that it is the right time to sell such insurance. I would be a better buyer of volatility at these levels.

Option-Like Payoffs

It seems we have a lot of option-like payoffs looming in the next few months.

By that I mean that we have a number of events that are likely to result in either-or (binary) outcomes. Think of them as options that are going to either finish in the money or out of the money. For example, either President Obama will win re-election, or he won’t. Either the Bush tax rates will be extended, or they won’t.

Those two are truly option-like, in that they also have a fixed maturity. We will know in 33 days who the President for the next four years will be. While the Bush tax rates could always be extended retroactively to cover 2013 even if it takes until February to hammer out an agreement so that can happen, the deadline to make transactions that put income or capital gains into 2012 rather than 2013 is December 31st.

Now, what we know about options is that as you get closer to expiry and are “near the money,” your gamma increases. Gamma is a measure of how quickly the option’s delta changes – how quickly you go from feeling like a likely winner to a sure loser. An example will help. If you own $660 call options on AAPL (closing price today $666.80), and they expire in a year, then it’s probably roughly a coin flip whether those calls will end up in the money or not.[1] We would say the delta is about 0.5. If AAPL sells off to $650, then looking one year out it’s still probably pretty close to a coin flip – obviously slightly less likely, but not a bunch. Maybe 0.49 is your delta, meaning that you have something like a 1% worse chance of ending up in-the-money.

But if, on the other hand, the options are expiring at 4pm today, then your $660 call is looking pretty good when the stock is trading at $666.80 at 2pm. Your delta might be 0.95. But when, by 3pm, the stock drops to $650, your chances of winning have declined dramatically. Your delta is perhaps 0.02. Because these odds move much more dramatically, we say this option has more gamma. This is a function of both the time to maturity and the nearness of the strike to the current price.

Option traders, who try to manage their risk by delta-hedging an option, like gamma a lot if they’re long options, and dislike it immensely if they’re short options.[2] That’s because if they’re short, the hedge involves them buying into strength (aka “buy high”) and selling into weakness (aka “sell low”), and often leads to frenetic trading and on occasion, serious moves on expiry day.

Where am I going with this? An observation: as we get closer to these “option events,” if they are still not resolved one way or the other the markets will likely grow more volatile. Consider what happens to an equity investor thinking about the ‘fiscal cliff’ as year-end approaches and no deal has been struck on taxes. The investor is going to be increasingly concerned about selling stocks in which he has gains, to book those gains in 2012 in case the tax rates go up a lot. If it appears that Congress is starting to resolve some issues, then this selling pressure may relent and the markets rebound. This could go back and forth as often as the headlines change, and I will tell you that those headlines will get more frequent as the deadline draws nearer. This implies to me that market volatility will probably increase as we get closer to the election, and as we move into year-end, because of these option-like events.

There are other option-like events, although less certain in timing (Israel attacks Iran, or not. Spain asks for aid and gets it, or not. Greece defaults, or not). These will have less obvious “gamma effects,” although as long as in each case they have at least two plausible outcomes that could well happen, it will tend to contribute to volatility.

In other words, with the VIX is near the lows for the year options seem inexpensive to me.

I’m having these thoughts today because I’m watching the wild gyrations in gasoline, which was -12 cents at Wednesday’s lows (finishing -7 cents) and +14 cents today. November gas covered nearly the entire 2-month range in 2 days’ trading. More near to my heart, inflation breakevens have spiked for the last few days (+8bps today) after spending half of September retracing from a spike to touch all-time wides (see chart, source Bloomberg).

Note that this is the ten year breakeven, so it isn’t reacting here just to gasoline. And I am not aware that the outlook for growth has changed dramatically this week, nor any major money metric. What is going on? My only guess at the moment is: gamma. Small things, like a win for the Republican challenger in last night’s debate, can cause big changes in expectations, and this will become even more true as long as the race stays tight.

If we look at just that market, we could also mull the technical issues. A market that spikes to all-time highs is one thing. A market that spikes, retraces, and then rallies back to a new high would be quite another thing altogether, and might signal a new range for inflation expectations is being formed. And oh, my, would that be significant?

The equity market remains elevated, and rising inflation expectations will eventually take a toll on multiples. It always does. I don’t want to bet against equities while inflation is currently low and the Fed is trying to push the market higher, but I believe we have some volatility ahead. With implied volatilities so low on options right now, it may be worth buying puts.

[1] I am ignoring the important nuance that in this case, the forward price will be different than the spot price – it’s not important for my illustration, but you really want to compare the strike price to the forward price of AAPL, not the spot price. I make this footnote just so that readers familiar with option theory won’t think I don’t know what I’m talking about.

[2] Again, this isn’t quite true. An option trader knows that an option with a lot of gamma also has a lot of time decay, and vice versa. As a former options trader, I can tell you there is no more helpless feeling than being long gamma on expiration day and watching the market sit in a 2-tick range, knowing you’re going to lose all your time value with no delta-hedging gains, and nothing you can do about it.

Let the (Political) Games Begin

August 13, 2012 3 comments

The Olympics are over, so the political games begin in earnest. Over the weekend, presumptive Republican Presidential nominee Mitt Romney made his first revealing executive decision when he tapped Wisconsin Congressman Paul Ryan to be his running mate.

The selection changes the contours of the U.S. political race, as veep selections often do. It probably does not create any near-term consequences for the markets, but as and if the Romney/Ryan ticket gains in the polling (as they surely will; for starters, announcing a VP pick almost always produces a bounce but also this tends to energize the base that Romney absolutely needs good turnout from to win) it is likely to be beneficial to equity markets at the margin. The improvement, if it happens, will not be uniform. Some industries, such as autos, which benefit from direct government largesse will probably do worse; but the notion that smaller government may be in train with somewhat greater probability is likely to have positive impact on perceived long-term values. And any possibility that a fiscal conservative (that is, Ryan, not Romney) might be a senior member of the executive branch is likely to have salutatory effects, all else equal, on U.S. Treasury credit as well.

More than likely, these effects will be mere ripples in a much more turbulent pond. In an ordinary Presidential election cycle, markets and market sectors can ebb and flow with the fortunes of the incumbent and challenger; this cycle though is anything but ordinary. European events can, and most likely will, dominate the macroeconomic picture as well as global risk appetites and foreign exchange swings. Which is to say: you can cheer for whoever you want in this election, without worrying whether it will help your investments!

While most of Europe remains on holiday (and more and more Americans seem to want to emulate that behavior), market action remains excruciatingly slow. At 3:15 ET today, New York exchange volume was only 275 million shares and even the usual surge into the close only brought the total to 450 million. In a year of slow days, this was slower than slow. In fact, I was only able to find one session (other than half-sessions around Christmas or Thanksgiving) in the last ten years or so that had a lower volume number: the Monday after Christmas in 2010!

This lack of liquidity, with the stock market so near to setting new (nominal) highs for the year, creates instability even as it appears to suggest stability. As I argued last week, when liquidity is low there is a larger cost to initiating any move – but any move that happens is likely to be bigger.

Add to that the fact that many investors have turned to covered-call writing to earn “extra income.” Admittedly, I only have this anecdotally, as I was approached at a backyard party recently by someone who was writing naked puts (actually, they were writing covered calls, but because of put-call parity we know that that is exactly the same as writing naked puts with the same strike) and seemed to not understand my question about whether implied volatility was high enough to make that worth the risk.[1] Which, since the VIX is at its lowest level since early 2007, it’s probably not (see Chart, source Bloomberg).

If this anecdote generalizes, and there is widespread selling of options, then it takes a dangerously-illiquid situation and makes it even less stable. With lots of gamma outstanding, what tends to happen is that small moves become microscopic moves since long-gamma hedgers try to recapture their time decay (selling rallies and buying selloffs), but large moves become really large moves because short-gamma investors try to save themselves from blowing up (buying into a market rally that they’re missing, or selling stocks that are abruptly plunging, overwhelming their small ‘income’ advantage). I would be a much better buyer of options here, even in the middle of boring August.

Now, although markets are currently quiet, and government committees and the like are less-active as well (and in the U.S., elected officials are heading out to politick for the next few months), it doesn’t mean that there’s a complete lack of action. Indeed, with Dodd-Frank now steamrolling towards implementation, there are pockets of frenzied activity! One story that I saw today (which has nothing to do with Dodd-Frank) is interesting to investors since it lowers the hurdle for eliminating the payment of Interest of Excess Reserves (IOER). The title of the P&I Online story was “Money fund firms prepping in case SEC breaks the buck,” and it described how the SEC plans to vote on August 29th on whether to issue a formal proposal requiring the sponsors of money market funds to either create a ‘capital buffer’ (perhaps similar to what the NY Fed recently proposed, and I mentioned here) or adopt a floating NAV policy rather than guaranteeing a $1 price.

We’ve discussed both of these proposals before in this space, but for today the significance is that if the floating NAV policy is generally adopted by money funds, the argument that a zero IOER could destroy money funds goes away. Since this is very likely to happen soon, either alone or as part of a parcel of monetary policy maneuvers, it is not insignificant that the SEC is pressing this issue.


Tomorrow the scheduled economic data includes Retail Sales (Consensus: +0.3%/+0.4% ex-auto). Core retail sales have been negative for the past three months in succession, something we hadn’t seen since mid-2010. Four in a row would make the streak the longest since 2008, and I think it would be taken quite negatively by the markets. A positive print by Retail Sales isn’t terribly significant by itself, since the series is quite volatile, but may be enough – even though expected – to continue to push the bond market lower.

[1] Note: if you do not understand and/or are not intimately comfortable with the definitional equivalence between a covered call and a naked put, then I will put my “friendly advice” hat on and beseech you, for your own good, not to sell options until you do!

Categories: Liquidity, Options, Politics Tags: ,

Long-Term Portfolio Projections Update

December 26, 2011 7 comments

Let me first point out what this article is not: I will make no effort to predict the 3-month, 6-month, or 12-month returns of any market. Indeed, although I will later present long-term risk and return outlooks, and they are presented as point estimates, I want to make it very clear that these are not predictions but rather statements of relative risk and return possibilities. For many types of instruments, the error bars around the average annual performance are so large as to make point estimates (in my view) nearly useless. The numbers come from models of how markets behave when they are priced “like they are now” in terms of several important metrics. They are not prescient. However, that is what investing is really all about: not making the “right” bet in terms of whether you can call the next card off the deck, but making the “right” bet with respect to the odds offered by the game, and betting the right amount given the odds and the edge.

I also will not make portfolio allocation recommendations here. The optimal portfolio allocation for you depends on more variables than I have at my disposal: your age, your career opportunities, your lifestyle, your goals, any insurance portfolio and your risk tolerance, to name just a few.

What I will do here, though, is to give top-down estimates of the long-run returns and risks of some broad asset classes, and make some general observations.

Compared to last year, 10-year projected real yields are lower. For all relatively low-risk investments, expected real yields are negative. This is not terribly surprising given the current landscape: risk-aversive behavior is expensive behavior at the moment. This exercise helps to remind us of the fact that in avoiding short-term risks, we are sacrificing considerable long-term returns.

However, with that said it must be also observed that the preceding statement only is strictly true if a fire-and-forget investor makes a single portfolio decision at the beginning of the 10-year period. For an investor who may exit safe securities and enter risky securities once the compensation for taking risk is adequate, it could well be prudent behavior to eschew short-term investments in relatively risky securities. While I do not make 1-year forecasts explicitly, as investors we must always take into account the fact that we have to pay to wait for a better entry point, but at times this waiting is justified.

I don’t analyze every possible asset class. For this exercise, I limit the universe to stocks, TIPS, nominal bonds (both long Treasury and corporate bonds), commodity indices and (since many of us already own it) residential real estate. My estimates and some notations about the calculations are in the table below.

Inflation 2.40% Current 10y CPI Swaps
TIPS -0.10% Current 10y TIPS. This is not at equilibrium, but it is what we can lock in today.
Treasuries -0.38% Nominal bonds and inflation-linked bonds ought to have the same a priori expectation, but Treasuries trade rich to TIPS because of their value as repo collateral. Current 10y nominal rate is 2.03%, implying -0.38% real.
T-Bills -0.50% Is less than for longer Treasuries because of liquidity preference.
Corp Bonds -1.52% Corporate bonds earn a spread that should compensate for expected credit losses. Chart 1 below suggests that Moody’s “A”-Rated Corporate yield is about 40bps rich to where it should be for this level of Treasury yields. And these yields, remember, are being artificially held down at the moment. If Treasuries were at 3%, Corp AA fair values would be another 75bps higher. I think corps are very rich although I admittedly don’t use an actual default model.
Stocks 2.57% 2.25% long-term real growth + 1.98% dividend yield – 1.66% per annum valuation convergence 2/3 of the way from current 20.8 Shiller P/E to the long-run mean. Note that I am using long-run growth at equilibrium, not what TIPS are implying. See here for more on this method.
Commodity Index 4.78% Various researchers have found that commodity futures indices have a long-run diversification return of about 3.5%. To this we add 1-month LIBOR to represent the return on the collateral behind the futures, and a ‘relative value’ factor to reflect the performance (relative to the expected model) of hard assets relative to currency.
Real Estate (Residential) 1.38% The long-run real return of residential real estate is around +0.50%. Current metrics (see Chart 2) have Existing Home Sales median prices at 3.25x median income, versus a long-term average of 3.55x. Converging to the mean over 10 years would imply aan 0.88% per annum boost to the real return.

Chart 1: Corporate AA yields are low compared to Treasury yields. (Source: Bloomberg)

Chart 2: Existing Home prices may still fall, but they are no longer virtually guaranteed to fall!

The results, using historical volatilities calculated over the last 11 years (and put in terms of ‘real annuitized income,’ a term that means essentially the variance compared to a fixed 10-year real annuity, which in this analysis would be the risk-free instrument), are plotted below. Return as a function of risk is, as one would expect, positive. For each 0.30% additional real return, an investor must accept a 1% higher standard deviation of annuitized real income.

10-year real returns and risks (Source: Michael Ashton and Enduring Investments).

There are some surprises here (indeed, some surprises for me since I don’t do this calculation every day). The biggest of them is that the way I do the analysis, home prices are actually slightly cheap to other available assets. Please remember, this isn’t a forecast of 2012’s return, but after a long round-trip it appears to me as if we no longer need to regard our homes in general as albatross assets!

Treasuries, not surprisingly, are extremely rich and should probably be avoided by most investors who are not hedging fixed nominal liabilities. Fixed-income allocations are better in TIPS and T-Bills, although neither offers very exciting real returns. Corporate bonds look quite rich, with yields that are even lower than they should be given the level of Treasury yields, and the latter are (as I’ve just pointed out) themselves rich. Yield-seeking investors are extending credit to issuers on terms that seem not to adequately reflect the very risky business environment that currently exists.

Stocks are rich, but not as rich as they have been in the past. Last year, my 10-year projection was 2.58% annualized real return, so equities have held steady while many other asset classes (TIPS, Treasuries, Corporate bonds) have gotten richer. Be careful about whether you read that statement as “stocks have cheapened,” or “stocks are cheap.” The former, a relative statement, is true, the latter, a (more) absolute statement, is false. As investors, we clearly would prefer to make the latter statement. As a long-only investor, you should care about the value of equities relative to equilibrium, not relative to other overvalued markets, anyway. Right now, if you compare in the chart above Stocks (which are overvalued) to Treasuries (which are more overvalued), stocks look ‘cheap.’ But making such a statement is analogous to someone in Holland a few hundred years ago remarking ‘This tulip is less-overvalued than that tulip, so it’s a good investment!’ Of course, no tulips were good investments, even the ‘cheap’ ones.

As I have been saying, Commodity Indices are the most-attractive investment in my little universe. While they are historically as risky as stocks, they offer much greater value given their performance over the last year (-11.8%, basis the DJ-UBS index) compared to both equities (S&P +0.61% as of this writing) and the money supply (M2 +9.5%). The “best” portfolio depends on a lot of characteristics of the investor as well as of the portfolio, but one could do worse with a portfolio consisting of TIPS, T-Bills, and Commodity Indices as the liquid assets balancing the illiquid investment in one’s home. If you are afraid of missing the next bull market in equities and not being able to look people in the eye at the next cocktail party, then buy out-of-the-money calls on stocks. Implied volatilities have fallen sharply over the last week or two (based on the VIX), and so protecting the ‘downside’ from a regret standpoint is much more affordable than it has been.

Finally, one caveat to all of this: I have not mentioned the economic backdrop, nor incorporated my view of that backdrop into these forecasts (with the exception of choosing to value corporate bonds off of a higher Treasury yield than is actually extant, recognizing that the Fed has artificially depressed long Treasury yields). The “risk” spoken of above is based on the historical standard deviation of the various asset classes, and is independent from the macroeconomic risk we all face at the moment. From a strategic perspective, abstracting from the tumult of the time makes sense; however, every investor must also be cognizant of tactical considerations. I hope that this column helps raise some useful questions about those tactical considerations, even if it doesn’t often provide the right answers to those questions.

That’s all for 2011. Thanks to all followers and one-off readers of this column! Have a happy new year!

Same Song, Second Verse…A Little Bit Louder And…

August 4, 2011 3 comments

Well, needless to say there is a lot to cover today.

The overnight session held a lot of intrigue. Japan intervened in its currency markets to push down the yen. It seems like everyone wants their currency lower! Trichet even said (at his press conference, of which more in a minute) that a strong dollar is in the world’s best interest. Well, perhaps it is in the interest of the world-ex-US, since it helps all those other countries export to the U.S., but it doesn’t make sense to say that having any single currency strong is in the world’s collective best interest. Currencies are just a way of trading real goods, and they are zero sum. If the supplier wins, then the buyer loses, and vice-versa.

One way to have a weak currency is to flood the world with that currency. That’s what the Swiss National Bank started to try to do the other day, after all. Of course, if everyone starts trying to do it, then there’s no telling what will happen to relative currency values. That will depend on who “wins” the currency war. What we do know is that consumers worldwide will lose, as will lenders at the expense of debtors, when the increased stock of money is worth less in terms of real goods.

The Bank of England and the ECB both kept rates unchanged at their policy meetings today, which was no surprise. But ECB über-banker Trichet said that the ECB will conduct liquidity-providing LTROs (“Longer-Term Refinancing Operations”) for 6 month terms and MROs (“Main Refinancing Operations”) “as long as needed.” In a nutshell: they’re adding more liquidity. They’re easing. According to Trichet, they are going to keep monitoring inflation “very closely” since the risks to the inflation outlook “remain on the upside.” Well, that’s very prudent, Jean-Claude. Oh, and in the meantime the ECB said they’d be buying bonds, and immediately started buying Irish and Portuguese bonds.

U.S. stocks rallied on that news, which turned out to be one of the worst trading decisions, for those buyers, of the year. And it didn’t make sense, either: flushing cash into the system, causing inflation to solve otherwise-catastrophic problems, isn’t inherently bullish! Nor is buying the bonds of already-bailed-out countries when there are others at risk!

Trichet also continued his recent crazy-man routine by saying that “banks with limited market access must boost capital.” Uh, what? How do you boost capital if you can’t get to the market? Steal it?

Irish bonds did great, rallying 23bps on the day. Portuguese bonds were unchanged. Italian bonds fell, pushing 10-year yields to new highs. Spanish bonds fell too, despite the fact that Italian and Spanish central bankers were buying their own bonds. However, these markets are too big for the ECB to do much with at the moment, so Irish and Portuguese bonds will just have to do!

Speaking of bond purchases, the Wall Street Journal had a story quoting “former top Fed officials” (Kohn, Reinhart, and Madigan) as suggesting the Fed ought to consider QE3. But the headline didn’t quite get the spirit of the story, which in any case was citing former Fed officials. Here is Kohn, from the article:

Mr. Kohn, who rose to become Fed Board vice chairman before retiring from the central bank in September 2010, said its options to support the economy are “kind of limited.” But if inflation comes down and the economy doesn’t pick up, he said he would give “very serious consideration” to a new round of bond purchases.

So a couple of guys said that if inflation comes down and the economy doesn’t pick up, the Fed should consider QE3. I suppose I can’t disagree with the proposition that the Fed should consider alternatives. Of course, inflation is not going to come down; rising core inflation is baked in the cake for quite a while ahead now. And considering QE3 (in light of the fact that QE2 didn’t work) shouldn’t take long. The only reasons to pursue QE3 are political: that is, the Fed needs to be seen to be doing something even if there’s nothing useful to do. Now, if I were around the table and wanted to help, the first thing I would do before adding another trillion in reserves that has no impact on anything would be to lower IOER and get the existing reserves into M2! I understand why they don’t want to do that, but it’s madness to buy more bonds when the money you injected the first time is still sitting in bank vaults because you’re paying banks to keep them there. Madness, I say.

The reason the Fed doesn’t want to lower the interest they pay on excess reserves (IOER) is that they believe (and have said so publicly) that it would seriously hurt the money fund industry. But I can’t figure out why the government should subsidize higher real rates for savers when in fact you want deeply negative real rates for the economy (in theory, anyway). If the government will support a +0.25% rate when -0.75% is the appropriate rate for the economy, for example, then why wouldn’t they in an analogous situation try to hold money market yields at 5% when the market wants them at 4%? It’s the same difference. It isn’t like the money fund industry would vanish if IOER went to zero. They’d adapt. I can easily think of a couple of alternative money fund structures that would work even if there wasn’t a ~25bps floor on rates. Trust markets. Look, some banks are starting to pay negative interest rates on savings, as this story about BNY-Mellon illustrates. IOER is too high.

So the market hung on after trading a little bit up overnight, then a little bit down, then up on the ECB press conference and the as-expected Initial Claims data. Then it went down, and kept going down, even when some investors made sloppy purchases in size to try and scare the shorts a couple of times during the day. But it didn’t work, because the selling wasn’t coming from new shorts but rather from old longs.

Volume on the day was huge – the biggest non-expiration day since the flash crash, I think. The S&P ended the day down -4.8%, closing at 1200.07. The Dow lost 513 points. Where is the guy who was on my case for being bearish and wrong on the S&P since 1100 last year? I hope he got out a couple weeks ago. This is what I have been saying the whole time – it isn’t that the market must go down; it’s just that the risks of this sort of event made being long a dangerous gamble. The odds were against you, if you were long at high valuations in a rickety global economy; that didn’t mean the market couldn’t keep rallying but it meant there was always a chance that you’d roll snake-eyes.

Bonds rallied, hard. The 10y yield plunged 20bps to 2.42%, only a few basis points shy of last October’s low yield. TIPS were offered early, but recovered and actually did quite well. The 10-year TIPS yield fell 14bps to 0.21%, another all-time low. If you want to think about how bad the current situation is, don’t look at nominal bond yields. They got lower during the financial crisis of 2008 (as distinct from the financial crisis of 2011), but that was when inflation was in the process of coming down and there was reason to expect it to do so. Inflation now is going up, so longer-term real yields– which represent the cost of money – are much lower now. The chart below shows that 10-year real rates (abstracting from the absolute teeth of the crisis when TIPS were treated like corporate structured notes instead of US Treasuries) are much lower now than they were back then.

Real yields are much lower than they were in the first crisis. This shows increasing fear about the future growth rate.

So investors see the long-term outlook as dim for the economy, and in fact are more morose than they were at the equity market’s bottom in 2009. In that context, equities today are still pricing in much more robust long-term growth than the bond market is seeing. Both of these markets are probably too high.

Because TIPS mostly kept pace with nominal bonds, measures of long-term inflation expectations fell only a little bit. And that makes perfect sense, when the world’s central banks are now all printing in unison. TIPS are too expensive, but relative to nominal bonds? They’re actually probably a better deal!

The short end of the TIPS curve, on the other hand, was savaged. For some while, the 1-year inflation swap has been under pressure. When it was pricing nearly 3% and energy markets were forecasting very little energy inflation, it was plainly too high. As of today, 1-year inflation swaps are marked at 0.88% (plus or minus…it was a dicey close), and since energy markets are pricing in mild declines in prices over the next year, that equates to a core CPI rate over the next year of about 1% (see Chart). But core CPI is currently 1.6% and rising – so 1-year CPI swaps are too low (or forward gasoline prices, too high).

The sharp drop in implied inflation at the front of the curve is overdone, or at least ahead of the energy markets.

Personally, I am thinking swaps are low rather than gasoline prices too high. Although commodities fell today (about 2.8% overall, energies much worse), and the headline read “Commodities erase gain for 2011 as faltering economy may curb consumption,” there are two points I would make. (1) A declining stock market is not a faltering economy. Yes, the economy is faltering but it’s not plunging. Some amount of what we’re seeing in stocks is just them coming back to more-rational valuations especially considering the economic landscape as it already is. (2) Regular readers of this column know that the supply/demand argument takes a back seat if the world is awash in cash. In that case, the exchange rate between stuff and money is far more important than the equilibrium supply and demand for a particular good. Why did commodities rally in the second part of last year? Was it because the economy was booming? Well, no…the economy wasn’t booming, and we knew that. Commodities rallied last year because the amount of money in circulation was rising and was expected to continue to do so for a while.

What are the prospects for that happening again? Well, M2 was released today and showed another hefty gain. The 52-week rise is now +8.1%; the pace is +11% annualized over the last 26 weeks. If deltaM+deltaV≡deltaP+deltaQ (the first-difference form of the crude quantity of money equation), and deltaM is +8% while deltaQ is +2% (to be generous), then we had better hope velocity is declining or…prices are going up.


While I thought (and still think) that stocks were (and are) overvalued relative to historical earnings as well as considering the economic prospects, the move today is clearly a (market) liquidity event. The fact that commodities declined even though the actions of central banks would argue for a movement in the other direction is one clue. The fact that it is August is another clue. The VIX rose to a post-flash-crash high, but is not near the flash-crash highs nor anywhere near the 2008 highs, so it is hard to say we have reached a crescendo of selling as gut-wrenching as today’s action was. There may, in fact, not ever be a crescendo. But with liquidity poor the possibility is there, and the question is whether you want to allocate your liquidity – the cash balances you have been holding in reserve for so long – to equities or commodities or whatever investment you love – at these levels or wait for a true panicky wash-out. Buying those assets now is catching a falling knife and it’s a much better strategy to wait until the knife hits and then pick it up off the floor. It would show great courage to buy stocks here. Leave the courage to the other guy. The first guy through the door is the one who is most likely to get shot.

With vols rising so dramatically and the price action so extreme, I covered all but 20% of my equity puts in the last 20 minutes of trading today. The prices hadn’t quite made it to my target but the uncertainty is too great and the implied vols are now high enough that it is no longer an efficient way to take that position. I am not sure what will come tomorrow, but if stocks decline just a little bit, or certainly if they rally, volatilities may drop quickly and so I have too many ways to lose. I should have covered the entire position, for while I am still bearish the odds are obviously no longer as much in my favor now. That was an error that fortunately can no longer cost me too much.


Tomorrow is actually Employment Friday, the most volatile day of the month (ha!). The consensus estimates have Payrolls at +85k versus only +18k last month, and the unemployment rate steady at 9.2%. I think there is room for upside on the Unemployment Rate, but the Payrolls guesses seem conservative enough especially since the +18k last month was likely an aberration that I expect to see revised a little higher. The markets could use an upbeat surprise on Employment, although I think it wouldn’t have a lasting impact since there are plenty of trapped longs who will probably sell into a rally. I suspect they may get a mild surprise in that way. But the risk is still skewed to lower equity prices and probably still-higher bond prices until the Fed bats down the notion of QE3. However if, Heaven forbid, a negative Payrolls number prints, this “second verse” could get a little louder and, as the old song goes, a whole lot worse.

Let’s hope not. As a young-middle-aged investor, I want lower prices during my accumulation years and higher prices later, when I am divesting – but I don’t want them lower all at once!

Dicey (And Slicey!) Markets

May 11, 2011 6 comments

If you like trading, as opposed to investing, then these are markets for you. Commodities markets dropped sharply last week, recovered, and then a number of them dropped again today. NYMEX Crude, which had been flirting with $105 yesterday, pierced through $98 today before closing at $99. NYMEX Unleaded had recovered almost all of its loss from last week before plunging nearly 25 cents today.

Attempts to explain these moves as the natural product of any rational process are bound to be frustrated. Of course, we try. Bloomberg tried by stating (early in the day) that “Commodities fell for the first time in three days, led by gasoline and silver…as reports on inflation from London to Beijing boosted expectations for higher interest rates.” While there was definitely discussion of the i-word in both of those capitols, it is a bit of a leap to suggest that commodities markets are starting to price hawkish central bank policy when the very interest rate markets are not. I guess you gotta write something! After the weekly inventory numbers came out, showing a higher-than-expected build for Crude and Gasoline (but a draw for Distillates), the stories changed to attribute the plunge to the “surprising rise in supplies.”

A 7% move in Gasoline doesn’t happen because of a surprising weekly build. It’s a weekly number and it bounces around some, like Initial Claims. More importantly, this hypothesis doesn’t explain why Silver dropped 8.4% again today, or why Sugar was off 4.25%. And it doesn’t explain why stocks dropped 1.1%, or 10y notes rallied 5-6bps (to 3.16%).

Blame it, if you wish, on a sudden “risk-off” trade. At least that is consistent with the movement in the markets (although I always wonder why TIPS are considered “risky” instruments since they are considerably safer than Treasuries if held to maturity). But now we have just pushed the explanation back one layer. What has triggered the “risk-off” trade? Bombing in Libya? The fact that Greece is in trouble? The rising temperature of unrest in Syria? Hey, I can agree that all of these things make me nervous, but none of them is particularly new. Besides, as of this morning the Wall Street Journal was running a piece saying that a new deal for Greece is expected…by Greece…by June.

The dollar rallied today, to its highest level in a month. It isn’t clear to me if this is effect (another ‘risk-off’ reaction) or cause. You can make a plausible argument that it is the latter. Perhaps traders are covering short-dollar bets because the Fed is nearing an end of QE2 and, whether they now start selling out the portfolio or not, the transition to at least not buyingis effectively a tightening of policy and arguably could strengthen the dollar. This would tend to weaken commodities, and to the extent that monies are coming back into dollars it would tend to support fixed-income. If this is really the root cause, then it’s probably mostly out of gas…unless the buck breaks above big resistance at 76 on the dollar index (see Chart below).

Nice dollar bounce, but the going is about to get tough.

If that happens, then there may be more near-term downside to commodities and stocks and upside to bonds. I don’t expect it, but the recent volatility sure makes it seem a dicier proposition than I thought it was a couple of days ago. Several commodities are at supports, the 10y Treasury note is back testing its recent highs, and stocks are re-testing the February and April highs, which they pierced through late last month. The proximity of so many critical points makes the situation inherently less stable. And yet…the VIX is still way down at 17. The MOVE is still near multi-year lows (see Chart below). Protection is quite cheap.

MOVE index of fixed-income volatility is near multi-year lows as well.

But inflation protection is still not cheap. While 10y TIPS sold off to 0.72% today, that remains a very expensive level. How then does one protect against inflation in this environment?

I continue to be a fan of commodity indices, but institutional investors should consider high-strike payer swaptions here. Some readers will remark that this is not a fresh idea, since that has been the default strategy for many institutions for a while. So let me be clear: while that has been a default strategy for a while, it hasn’t been the right strategy for a while. Here’s why. When you buy an interest rate option (for the uninitiated, a ‘payer’ swaption gives you the right to pay a fixed rate on a swap at some point in the future, so it is analogous to a bond put), you’re paying for protection against increases in both real rates and in inflation. Remember, Fisher told us that

Nominal rates ≈ Real rates + expected inflation (+ risk premium)

So when you buy an option that pays off if nominal rates rise, you win if real rates rise, if inflation compensation rises, or if they both rise. And you’re paying for all of those possibilities.

But when this strategy was first being proposed, in mid-2009, real rates were much higher (especially on a forward basis). So nominal rates were not very likely to rise because real rates were rising; they were going to rise, if at all, because expected inflation rose. But you were paying for both pieces of that option. In the event, expected inflation rose and real rates plunged, so you’re further out-of-the-money now than you were then. Moreover, implied volatilities were very high.

Now, by contrast, implied volatilities are very low and so are real yields. It is unlikely that, if inflation starts to rise, real yields will fall much further than the 0.72% where they already sit. So you’re paying less, and getting more. Now, even if what you want is protection from inflation and not from nominal rates, at least you’re more likely to have the moving pieces going in your favor, rather than against you.

The same reasoning applies if you are a retail investor, except that there are not many options for the retail investor who wants to buy a long-term option on inflation, or nominal rates, or almost anything for that matter.


On Thursday, we get another volatile weekly supply number. This one is the supply of new jobless, also known as Initial Claims (Consensus: 430k). Recall that last week saw a spike to 474k, which even though it had some reasonable explanations attached to it was still shocking for many observers. If that figure doesn’t drop substantially, bonds are going to go straight up and stocks and commodities straight down.

Retail Sales (Consensus: +0.6%/+0.6% ex-autos) is also an 8:30ET number. Be careful here as well. Anecdotal reports seem to suggest a chance of weakness to what has been a consistently strong number for almost a year now. Unusually, this is probably less important than Claims in the mind of the investor right now, but weakness here and in Claims is where to look for market risk tomorrow.

Also out is PPI (Consensus: +0.6%/+0.2% ex-food-and-energy). Core PPI is expected to rise to 2.1% year/year and the headline to 6.5%. PPI doesn’t matter, and especially since it is sharing the 8:30ET time slot with Claims and Retail Sales it will be mostly ignored.


Two administrative notes:

1)      If you missed my column the other day on the kurtosis and skewness of commodity indices and the importance of that fact to traders in these things – it was mis-posted in one place you may have ordinarily seen it – please have a read.

2)      I finally finished an inflation-related paper that I had been working on for a long time. A few years ago I submitted it through a couple of rounds to a journal and never got it cleaned up enough to be published, but it’s cleaned up enough to put on SSRN. The paper is called TIPS, the Triple Duration, and the OPEB Liability: Hedging Medical Care Inflation in OPEB Plans. If you have a role in hedging medical care exposures in post-retirement liabilities, take a look and remember that Enduring Investments can be hired as a consultant.

Categories: Options, Trading

Lots Of Options

December 1, 2010 1 comment

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.


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