This is not investment advice. Ex ante, there’s a good chance it constitutes a cautionary tale, and is the exact opposite of investment advice. It’s a story about a non-derivatives expert doing derivatives stat arb for fun. Those stories tend to end badly. Please do your own research, avoid taking dumb risks, and don’t come crying to me if a bug in my Excel or Python model is the reason you got a margin call.
In the interest of full disclosure, I am doing a version of this trade right now. YOLO.
Financial engineering is a lot like running a slaughterhouse. You have some cuts that are valuable, and some stuff you grind up and stuff into sausages, and some odds and ends end up being somewhere really weird — until the development of recombinant DNA, the main source of insulin was crushed pig pancreases.
Sometimes, this leads to interesting arbitrages. As a broke bachelor, I was delighted to discover that chicken is very cheap indeed if you’re willing to eat chicken liver. And in the futures market, there’s some very affordable chopped liver I’ve decided to take advantage of: European dividend futures. (I first heard about this trade by reading Harley “The Convexity Maven” Bassman in this post. Bassman gets 100% of the credit for noticing the anomaly; I’m just looking at the theoretical implications and the exact way to put on the trade.)
Specifically, I’m long some Euro Stoxx 50 dividend futures, which I may hedge intermittently by shorting futures for the Stoxx 50 itself. Right now, the index yields about 3.5%, with dividends of €122.66, this year, consensus of, €130.39 in 2020, and €137.98 in 2021. And yet, dividend futures are available for 122.4, 123.1, and 120.2, respectively. In other words, futures are pricing in substantially lower dividends than analysts expect.
What’s going on?
Of Dividends and Derivatives
Let’s start by thinking about the theory of dividends, equity prices, and futures.
Academic finance tells us that the value of a stock is the net present value of all future dividends, discounted back to the present at an interest rate that represents the returns investors will accept in exchange for risk.
Any student of market psychology knows that lower hurdle rates get expressed as higher rates of return. Nobody gets a bonus for being the first equity fund manager to say that he expects stocks to return 6% a year rather than 10% a year, so everyone ratchets up growth expectations to compensate for higher valuations. The game theory here is straightforward. Investors’ expectations of future equity returns are tightly correlated to returns in recent history. Few asset managers want to admit that when the market is up 20% for the year, expected future returns should be lower because investors are paying more for future cash flows, so to make their own models tie out to future expectations, they raise growth expectations.
In the 90s, some academics noticed that US equity prices implied some combination of extraordinarily high future growth and unusually low required rates of return. And in 1998, Michael Brennan at UCLA suggested that we do something about it.
Brennan’s idea was simple: dividend futures. Instead of requiring investors to buy all future S&P 500 dividends at a clip, let them pick individual years. His original paper walks through the reasoning, citing the robust market in treasury strips as an example.
This proposal was itself an elegant piece of game theory. In the aggregate, the finance industry would prefer not to interrogate the specific components of implied future growth. If dividend futures imply that expected equity returns are low, that’s bad for the people running multiple trillions of dollars in long-biased equity vehicles. On the other hand, those people aren’t the ones deciding whether a given bank will offer dividend futures. So, shortly after Brennan’s paper, dividend futures started to trade.
In the US, the dividend futures market hasn’t been especially robust. As it turns out, ideas invented by finance professors rather than derivatives desks are more appealing to finance professors than to derivatives traders. But in Europe, the market is a bit more robust, so that’s where we’ll focus.
Origins of the Mispricing
If you want to buy something, it’s good to ask why it got so cheap. We can look at three possibilities:
- The market price of the futures is perfectly accurate; Stoxx 50 dividends are going to be cut.
- There’s some elaborate tax trade going on, in which shares of dividend-producing stocks get shunted into low-tax jurisdictions to collect the dividend, and then get resold, and one leg of this trade involves hedging the risk that dividends will be cut.
- European retail investors are buying structured notes that bet on index levels, and the banks that sell these notes buy the underlying index and hedge out their dividend risk.
Let’s explore each of these in turn.
The “Dividends are Going Lower” Hypothesis
If you believe in efficient markets, there’s a very straightforward interpretation of cheap dividend futures: based on the information available to investors today, Euro Stoxx 50 dividends will decline over time.
This has not been a bad bet. Here’s a chart of sell-side consensus for Stoxx 50 dividends compared to what actually happened:
Consensus was below what they ultimately reported a mere 13% of the time. Analysts are improving — three years out, they were 60% too high for 2009, 17% too high for 2014, and just 9% too high for 2018 — there’s clearly some upside bias to the numbers. You can see two effects in this chart. First, it’s visually easy to spot the financial crisis, with 2008’s numbers actually starting out somewhat reasonable, rising as European financials absolutely printed money buying AAA-rated CDOs funded with commercial paper, and then un-printed all that money when the trade unwound. Second, though, even in comparatively normal periods, you can see that estimates tend to start out 5–15% too high and gradually come back to earth.
Post-crisis, the cadence has gotten steadier, and hasn’t changed direction. On average, consensus is 15% too high two three years out, 7% too high two years out, and 2% too high at the start of the year. Hope does not spring eternal, but it’s close — two months before the last dividend of the year, consensus for full-year dividends is still about 40 basis points too high.
This gives us some good rules of thumb for assessing realistic dividend estimates. Based on recent history, 2020 dividend estimates are about 4.5% too high, and 2021 estimates are around 9.7% too high. That gets us to a current expected dividend of 124.78 for 2020 and 125.80 for 2021. In other words, we’re eliminating most of the 2020 discount right off the bat — 2020 futures are about 1.4% too cheap by this math. But 2021 is still surprisingly affordable, trading about 4.5% below the recent-history-adjusted estimate, and the further out you go, the bigger the discount gets. At today’s prices, 2028 dividend futures are pricing in dividends 32% lower than what a prudent model would suggest, and 24% below current expected dividends.
The direction of this discount makes sense; a lot more can go wrong in Europe by year-end 2021 than year-end 2020. But the magnitude is still suspicious. It’s almost as if European dividend futures are priced based on the last ten years of dividend estimate revisions, rather than the last five. (Using dividend revisions data for 2008’s dividends onward, we’d expect current consensus to be 23% too high, implying that the real 2021 dividend will be more like 112.
If you’re going down your checklist of things that can go wrong with historical data, one concern you might have is survivorship bias. What if European companies are actually even worse at paying their dividends than the data imply, but they get booted from the index? Good news: survivorship bias works out in your favor here. When a company gets removed from the index, it gets replaced with another, hopefully healthier, company.
The Tax Trade Theory
In a certain kind of writeup, this section would be the meat of the analysis. European investors have, off and on, engaged in complicated tax trades involving dividends. The Cum-Ex scheme, for example, involved multiple investors getting tax credits for dividend taxes paid on the same stock. This was a story in 1992, the subject of a major investigative journalism effort in mid-2018, and still the subject of law-enforcement actions later that year.
Tax trades like this tend to produce otherwise un-economic behavior, because the whole purpose of the trade is to mitigate economic risk and net out everything except the tax angle. If tax traders are structurally long dividends, they might hedge that exposure by shorting dividends through futures.
Unfortunately, this trade is hard to analyze from the outside. Practitioners are not exactly publishing whitepapers on how to minimize tax burdens, and on the other side prosecutors and journalists have every incentive to exaggerate the scope of the trades. So, hedging dubious tax strategies remains a possible explanation, but not one amenable to much further analysis.
It is worth noting, though, that taking the other side of a transaction from a price-insensitive seller is a pretty decent way to make money.
The Structured Products Theory
The best explanation for the Stoxx dividend futures tax anomaly is exactly that phenomenon: a seller who is not motivated to seek a good price, because the real economics of the transaction are elsewhere.
For example: European investors like to buy structured products. These products have a return pegged to the index, but offer limited downside. For example, an investor might buy a note that returns either a) half the appreciation of the Euro Stoxx 50, or b) the principal, whichever is higher. This is easy to replicate with options, but that’s not something your typical retail investor will do, so structured products tend to have large markups.
These notes are usually structured to have returns based on index levels, not index returns, so anyone who sells a structured note and buys the index to hedge is net long the dividends. And European banks don’t like to keep equity-like risk on their books, so they sell the dividend futures to get to flat.
Structured products are a large and growing force in European markets, with €272.9bn outstanding at the end of Q2 ’19. That’s up 9% Y/Y; the amount outstanding has grown around 2.3% compounded over the last six years.
New structured note issuance is the metric to focus on, though: if banks hedge when they issue new notes, the new notes are the marginal price-setter for dividend futures. The relationship between realized market volatility and note issuance isn’t as clean as I’d like to see, but in general sudden increases in volatility are associated with increases in note issuance.
The structured note data I’m using is issued on a long lag; we won’t get Q3 data until the quarter’s nearly over. However, there’s a rough proxy: the largest market for these products is Germany, and Google searches for “Zertifikate” correlate (albeit weakly) with growth in structured note issuance. Based on that indicator, Q3 should show healthy growth.
This hypothesis works if a) the underlying trade is profitable even if the dividend leg is a bad deal, and b) banks would rather make a suboptimal trade than keep risk. Anecdotally, structured products are sold at a ~2% markup to the cost of replicating them through options, and also-anecdotally, European banks are terrified of net exposure to volatile assets.
So, the structured products theory is probably the best argument, which means the trade is fundamentally a liquidity-providing one: traders who don’t care about short-term mark-to-market losses can buy dividend exposure on the cheap from banks with regulatory reasons to sell it. This makes the dividend futures trade the mutant evil twin of what was going on in 2006, when European banks could arbitrarily lever up as long as the assets they bought were rated AAA, which encouraged American banks to manufacture AAA-rated CDOs for them.
Fortunately for us, this trade sounds like it will end with a whimper, not a bang, as non-European investors optimistic about European equities buy the cheap dividend-futures beta instead of the more expensive full-index variety.
If dividend futures are cheap, which ones are cheapest? The magnitude of the divergence between futures and expected earnings grows over time, but at a steady pace. In a naive model, we can take consensus as gospel truth, and extrapolate future growth based on recent growth rates:
Cells in yellow are based on extrapolated growth rates.
And for visual learners:
Note that these are returns on the notional value of the derivatives. You can lever up quite a bit — the margin requirement for these futures is in the 35–40% range, so the 8.8% implied return on the 2023 contract turns into 24% with leverage.
But, as discussed above, dividend expectations tend to be too optimistic. So let’s consider a saner model, where we adjust the next few years down by the usual decline in consensus expectations, and assume a slower future growth rate:
The general cadence seems to be that the curve is steep for the first few years. You get paid a lot more for taking 2021 risk than 2020, etc. Further out, things flatten. Using the realistic model, 2028’s dividend pays about 56bps more per year (unlevered) than 2023’s.
These term structures might look familiar: they look a lot like yield curves. It’s not a coincidence. You can think of a dividend as extremely junior debt. It’s not an obligation, the way debt is, but investors have strong expectations that dividends will be maintained. The dividend is junior to all actual creditors, but given the Stoxx 50’s over-50% payout rate, and given that dividends are less volatile than earnings, you can think of expected dividends as senior to a company’s capital expenditure plans.
All this makes the dividend future a very special asset indeed: it’s a fixed sum paid at a future date, so it has theoretical duration equivalent to a zero-coupon bond with the same maturity. But it’s also a payout based on corporate profit growth; in a world where interest rates rise (and the duration exposure hurts), profits are probably up, too. Even better, it’s inflation-hedged: while companies can’t pass on all inflation costs to consumers, they can pass on some of them, and over a longer period things should equalize.
This makes the medium-term dividend future an extraordinary financial chimera, a theoretical bet on equity, fixed-income, and inflation.
There’s one more thing to add. In my return calculations, I implicitly assume a buy-and-hold strategy. But since we’re moving along a yield curve, we can also benefit from roll-down yield. If the 2022 contract trades at a 9.9% discount to expected dividends, and the 2021 contract trades at a 4.5% discount, then in a year, holding that yield curve fixed, we’d expect the 2022 contract to appreciate 6.1%. This is adding an assumption to the model, but it’s a reasonable one: dividend futures less volatile, and closer to fair value, as the dividend year approaches.
In this model, interestingly enough, returns are not linear: while distant futures trade at a wider discount, the flattening curve means that the expected change in discount is smaller. The sweet spot of the curve is, as it turns out, 2022:
If you want a short-duration bet without a lot of excitement, the 2020 and 2021 futures get better returns than short-term debt, and shouldn’t be especially volatile. Looking further out, 2022 has the best implied returns from our dividend “yield curve” — which, as a reminder, is an entirely theoretical construct based on reasonable hypotheticals, not a real yield curve. Past that point, overall returns continue to improve, but expected one-year returns are worse.
There are two reasons you might look further out the curve:
- If you want to bet on economic stasis in the Eurozone, you want to be long duration, so you’d own the longer-dated futures. There are other ways to get long duration, but they involve buying negative-yielding debt.
- If you think futures are underpriced, and that this underpricing will resolve itself quickly, that also suggests the long-duration futures. If futures prices perfectly matched the conservative dividend model, 2028’s contract would appreciate from 90.8 to 138.7, an absolute return of 48% and a levered return of 131%. Not bad for a bet on blue chips in a mature economy!
I’m staying away from the longer-duration futures because I don’t believe in the stagnation thesis (stagnation is an unstable state). But it wouldn’t be crazy to put on a “barbell” trade, with the 2022 contract as a bet on the mispricing status quo and a smaller 2028 bet on the possibility that the gap between futures pricing and expected dividends suddenly collapses.
Controlling Risk: The Why and How of Hedging
Now that we have a mechanism to explain the mispricing, and a sense of which contracts are most mispriced, we should think about the implications. Retail investors tend to buy structured products as an alternative to equities, and they look for alternatives when equities do badly. The net result of this is that a long dividend futures trade is also a short-gamma trade: when the index drops, a) the expected value of future dividends is probably lower, and b) the demand to sell index futures rises as retail investors sell out of equities and buy structured products instead, and banks offload the dividend strips on the futures market.
Fortunately, we can hedge some of this out.
The most efficient way to hedge a long position in a dividend derivative contract is with a short position in the asset paying the dividend. This is true in both a ploddingly literal sense — a single year’s dividend is a piece of the net present value of the index, since the index is the sum of the present values of all future dividends. It’s also true in the more stylized sense that the two data points that best predict all future dividends are 1) current dividends, and 2) how fast they’re growing.
It’s entirely possible to overthink this, but here’s a simple approach:
- Choose the contract with the highest implied one-year return.
- Calculate its beta.
- Short the index to get a beta-zero return.
I don’t have full historical data, but Quandl has a time series going back to late 2013, so it’s possible to calculate the best roll yield trade and best beta hedge for 2014 onward, then to look at the results of making an unhedged trade and a hedged trade.
Overall, the results are… less promising. The unhedged bet has done better than the hedged bet in almost every time period, although the hedged version does better when you adjust for its lower risk:
So where does this leave us?
The hedging question leaves us about where we started: dividend futures do appear to be mispriced, and there’s a correlation between estimated mispricing and expected return, although that correlation gets weaker as the dividend futures go further in the future.
I had previously assumed that hedging a dividend futures position through index futures would be trivial, that it was the sort of thing a European equity derivatives trader might have invented in the 36th hour of the workweek. But no, it turns out that hedging is hard, for the intuitive reason that you’re hedging exposure to one year’s dividend by betting on a) all future dividends, and b) the risk premium ascribed to them, which is not the same risk premium ascribed to the dividend futures themselves.
Suppose you’re long dividend futures and short equities such that you’re hedged against market movements. What can still go wrong? A couple things:
- Tax changes might encourage companies to retain more earnings or buy back stock — these would be disastrous for both legs of the trade, since they’d push equities higher and dividends lower. This is not likely, given the political backlash against buybacks in the US.
- A change in tax law might encourage companies to shift dividends from one year to another, although this is even less likely.
- Companies might decide to reinvest, or return capital via buybacks, instead of paying dividends. This, too, doesn’t seem materially likely. There just aren’t a lot of investment opportunities for mature European companies, and investor preferences for dividends over buybacks changed very slowly in the US.
- The Stoxx 50 index might swap out a high-dividend stock for a low-dividend stock. There are two ways to mitigate this: one is to short shares of high-dividend companies in the index (and shrink your index hedge by a corresponding amount). You could even go really crazy: short the stocks, but buy the single-stock dividend future. Another option is to track their construction criteria to see if there are any prospective shifts that could reduce the dividend.
- If you’re levered: there is no reason a big mispricing can’t get bigger. Since dividend futures are illiquid, and the sellers are price-insensitive, and the retail demand ultimately comes from people panicking about the market, their prices are prone to dislocation.
The question to ask is not whether or not these risks can be hedged, but whether or not the returns from dividend futures compensate for them. A trade is a personal thing. Once you’ve done the work, your ultimate bet is on whether you’re overconfident or not. That’s why risk premia are above zero: sometimes you got paid to sell insurance against a disaster you didn’t consider.
- The paper that started it all: Stripping the S&P 500 Index.
- The other paper that started it all: Harley Bassman on dividend future mispricings. Consider my post an elaborate footnote to his.
- CFTC on the size and history of the market: Dividend Swaps and Futures: State of Play.
- The Pricing of Dividend Futures in the European Market: A First Empirical Analysis: Pricing has been weird for a long, long time.
- It’s also been weird in many different places: here’s a piece on cheap Japanese dividend futures from 2012.
 This gives us a useful way to think about the fact that growth stocks outperform at market peaks. If a company is growing its earnings at 2% per year, it’s very hard to justify a claim that they’ll somehow triple their growth rate to 6%. But if a company is growing at 30% per year, it’s comparatively easy to argue that they’ll maintain that growth rate a year or two longer, or decelerate a tiny bit slower. High valuations introduce uncertainty, but the uncertainty goes in both directions. If the S&P trades at 40x earnings, it’s a lot easier to explain why a company at a P/E of 100 deserves a P/E of 150 than to explain why a slow-growth company at 20x earnings deserves to trade at 30x.
This FOMO framework also helps to explain why low mutual fund cash balances and frequent IPOs are both decent counter-cyclical indicators. If you’re an investor and your peers are other investors, you express FOMO by making more bets; in your social circle, the people getting richer than you are the ones who bought more stock. But if you run a private company, you express FOMO by getting involved in the market through selling stock.