Understanding Vega Risk

In a chat with an options novice, they told me they didn’t want to take vol (vega) risk so they only traded short-dated options. This post will explain why that logic doesn’t work.

Here’s the gist:

It’s true that the near-term option’s vega is not large. That is counterbalanced by the fact that near-term implied vols move faster (ie are more volatile) than longer-term vols.

The goal of this post is to:

  • demonstrate that near-term vols are more volatile both intuitively and with napkin math
  • show the practical implications for measuring risk

Near Term Vols Are More Volatile

An Intuitive Understanding

Think of the standard deviation of returns that a stock can realize over the course of a week. If there is a holiday in that week the realized volatility will likely be dampened since there are 4 days of trading instead of 5. If Independence Day falls on Friday, Thursday might see even lower volatility than a typical trading day as fund managers chopper to the Hamptons early. On the other extreme, if a stock misses earnings and drops 25%, then we have a Lenin-esque week where a year happens. The range of realized volatilities is extremely wide. This requires the range of implied volatilities to be similarly wide for a 1-week option. Those large single-day moves are diluted when they are part of a computation for 1-year realized volatility (there are 253 trading days in a year).

This concept is easily shown with a “volatility cone” (credit: OptionsUniversity)

Here we can see the standard deviation of realized volatility itself declines as the sampling period lengthens.

The Napkin Math Understanding

The intuition for why the range of short-dated volatility is wider than long-dated volatility is easy to grasp. To cement the intuition let’s look at a numerical example.

Consider:

A weekly option [5 days til expiry]

Assume the stock’s daily vol is expected to be 1% per day. The fair implied vol can be computed as follows:

IV = sqrt(.01² x 5 days x 52 weeks) = 16.1%1

Remember variances are additive not standard deviations so we must square daily vols before annualizing them. We take a square root of the expression to bring it back into vols or standard deviation terms.

Ok say 1 of those days is an earnings day and is expected to be 3% daily vol.

IV = sqrt([.01² x 4 days + .03² x 1 day] x 52 weeks) = 26%

Look what happened.

The single-day expected vol jumping from 1% to 3% means there is more variance in that single day than the remaining 4 days!

.01² x 4 days < .03²

How did this earnings day affect the fair IV of a longer-dated options?

A 2-week option [10 days til expiry]

 IV =  sqrt([.01² x 9 days + .03² x 1 day] x 26 bi-weeks) = 21.6%

A 1-month option [21 days til expiry]

IV = sqrt([.01² x 21 days + .03² x 1 day] x 12 months) = 19%

The increased vol from a single day is clearly diluted as we extend the time til expiry. When we inserted a single day of 3% vol:

  • The 1-week option vol went from 16% to 26%. 10 vol point increase.
  • The 1-month option went from 16% to 19%. 3 vol point increase.

To understand why this matters look at the effect on P/L:

Remember, the vega of the 1-month straddle is 2x the vega of the 1-week option.

    • The 1-week straddle increased by 10 vol points x the vega.
    • The 1-month straddle increased by 3 vol points x 2 x the vega of the 1-week straddle

      10x > 6x

      The 1-week straddle increased in price 10/6 (ie 66%) more than the 1-month straddle!

      (This is why event pricing is so important. The astute novice’s head will now explode as they realize how this works in reverse. You cannot know what a clean implied vol even is unless you can back out the market’s event pricing)

Practical Implications For Measuring Vega Risk

Comparing Risk

So while a 1- month ATM option has 1/2 the vega of a 4-month option2, if the 1 month IV is twice as volatile it’s the same vega risk in practice. You need to consider both the vega and the vol of vol!

In practice, if I tell you that I’m long 100k vega, that means if volatility increases [decreases] 1 point my position makes [loses] $100k. But this risk doesn’t mean much without context. A 100k vega position means something very different in a 1-week option versus a 1-year option. Looking at a vol cone, we might see that 1-week implied vol has an inter-quartile range of 30 points while 1-year vol might only have a 3 point range. You have 10x the risk if the vega is in the weekly vs the yearly!

Another way of thinking about this is how many contracts you would need to have to hold 100k vega. Since vega scales by sqrt(time) we know that a 1-year option has √52x or 7.2x as much vega. So to have the equivalent amount of vega in a 1-week option as a 1-year option you must be holding 7x as many contracts in the near-dated.

Normalizing Vegas

It’s common for traders and risk managers to normalize vega risk to a specific tenor. The assumption embedded in this summary is that volatility changes are proportional to root(time). So if 1-week volatility increased by 7 points, we expect 1-year vol to increase by 1 point.

This is an example of normalizing risk to a 6-month tenor:

Observations:

  • Your headline raw vega is long, but normalized vega is short
  • Your 2,000 vega in a weekly option is more vol risk than your 10,000 vega in the 6-month
  • You want the belly of the curve to decline faster than the long end. This is a flattening of the curve in a rising vol environment and a steepening in a declining vol environment.
  • If the entire vol curve were to parallel shift lower, you’d lose as you are net-long raw vega.
  • If we choose to normalize to a different tenor than 180 days, we would end up with a different normalized vega. The longer the tenor we choose, the shorter our normalized vega becomes (test for yourself).

Critically, we must remember that this summary of net vega while likely better than a simple sum of raw vega is embedding an assumption of sqrt(time). If you presume that vol changes across the curve move in proportion to 1/sqrt(t), the value of calendar straddle spreads stays constant. At this point, you should be able to test that for yourself using the straddle approximation in the footnotes. This would imply that as long as your total normalized vega is 0, you are truly vega neutral (your p/l is not sensitive to changes in implied vol).

As you might expect, that assumption of sqrt(time) vol changes across the curve is just a useful summary assumption, not gospel. In fact, on any given day you can expect the curve changes would deviate from that model. As we saw above, the bottoms-up approach of adding/subtracting volatility with a calendar has uneven effects that won’t match up to sqrt(time) rule. Your actual p/l attributed to changes in volatility will depend on how the curve shifts and twists. Perhaps the decay rate in a vol cone could provide a basis for a more accurate scaling factor. It does require more work plus scaling to time allows us to normalize across assets and securities more understandably rather than using some empirical or idiosyncratic functions.

Conclusion

Just because the vega of a longer-dated option is larger doesn’t necessarily mean it has more vol risk.

  • We need to consider how wide the vol range is per tenor. We looked at realized vol cones, but implied vol cones can also be used to approximate vol risk.
  • We need to recognize that a steepening or flattening of vol curves means the price of straddle spreads is changing. That means a vega-neutral position can still generate volatility profits and losses.
  • Changing straddle spreads, by definition, means that vol changes are not happening at the simple rate of sqrt(time).
  • Measuring and normalizing vols (or any parameter really) always presents trade-offs between ease, legibility/intuition, and accuracy.

Shorting In The Time Of ShitCos

HTZG, GME, now HWIN.  The more slandered or shorted or ridiculous the name is the more bullish it seems to be for the stock. Just imagine explaining this to an alien.

“I bought a deli for $100mm. It’s an investment.

A deli? Well… it’s a place where people from the surrounding neighborhood go midday for some protein stuffed into wheat…umm, no, not every person in the neighborhood. Just like some of them. Why not everyone? There are other delis I guess. And a McDonald’s. Oh, you have those too? Yea I love the fries myself. Ah, yes back to the deli. Right, so the deli actually has to buy the ingredients. Correct, it doesn’t grow them. Slaves? What? No, no, no. Those people are called “employees”. I have to pay them. And yes, that guy needs to be paid too. IRS. We call him IRS.

Did I mention it has the best dills?”

The entire shorting business model appears to broken. In a period where concentrated shorts are getting lit up, in a period where diamond hands combined with brick brains, shorting just looks like return-free risk. Or at least the style where you try to recruit support after establishing the short.

I think @Mephisto731 is correct. Probably super correct. The best time to sell insurance is after the earthquake blows out your competitors.

You’re sneering. Fine, I’ll play along.

Common Objections To Shorting

It’s common for shorting detractors to mock the strategy as negative EV for 2 reasons. I’m just going to annihilate them now so we can get to a more productive discussion.

  1. Stocks have positive drift (aka “stonks only go up”)

    I get it, you are fighting the most fundamental risk premia. The “equity risk premia”. First of all, that’s debatable. After, all most stocks go to zero. Stock indices have risen over time thanks to rebalancing. But more clinically, the negative drift, can be offset by just offsetting the beta. You can short the target and get long a basket to sterilize the drift. So, in practice, and possibly in theory, this positive drift objection can be put to rest.

  2. Stocks have unbounded upside but limited downside

    This has no bearing on the EV of shorting. Anyone familiar with options understands that individual stocks have positive skew. If a stock is $100 despite everyone knowing that it is bounded by zero and infinity then the odds of it going down are the counterbalance. And the fact that most stocks go to zero is in keeping with that understanding. So, stop citing the unbounded upside as a reason why shorting is negative EV. Remember EV is a sumproduct of terminal prices and probability.

That said, shorting is no stroll in the park. We just don’t need to fabricate objections like the ones above to show that.

The Real Reasons Why Shorting Is Difficult

  • No limit to arbitrage on the short side

    First, think of the long side. I’ll paraphrase Sam Bankman-Fried’s explanation from his recent Odd Lots interview:

If AAPL stock price went to $1 tomorrow, Warren Buffet or whoever would just buy the whole company. It makes billions of dollars in earnings and you could just buy all the earnings for less than the stock price if it got low enough. But on the short side, there is no mechanism to moor the stock to reality (although as we learned from the Archegos saga, a secondary to feed the ducks, has consequences).

This lack of limit to arbitrage doesn’t change the EV of the stock which is already balanced by probabilities, but it does change the path behavior. You need to borrow shares to be short, and any share borrowed means a future buy order. So inflows of cash can cascade into forced covering since the short-seller is effectively levered.

  • The negative gamma effect

    I’ve explained this before with respect to shorting, but I’ll re-hash it simply. When a fund sizes a short it does so as a percentage of its AUM. Say the short is 10% of its AUM. You can think of the AUM as the denominator and the dollar-weighted short as the numerator. This ratio starts at 10/100.

    What happens if the fund wins on the trade because the stock drops 50%?

    Well, now the fund has made 50% on a 10% position, so its new equity is 105. Yet, the size of the short shrank with the stock halved. So now the numerator is 5, not 10 units. So the short is now 5/105 or 4.7%. The fund needs to more than double the size of the short to maintain constant exposure as a percentage of AUM. Both the numerator and denominator moved in a way that reduced the position.

    This looks just like short gamma. You need to sell more as the stock falls!

    When the stock rallies, the size of the short (numerator) increases, while the fund’s equity (denominator) gets hammered. Both forces conspire to force short-covering. Or buying, in a rallying market. Negative gamma. And to think, you often pay to borrow stocks, so you get the indignity of paying theta to play this game.

The Options Approach

Let’s address the ways we can use options to be short.

  • Synthetic shorts

    If you want to implement the short in the most similar way to a short stock position, then you will want to structure a “synthetic short”. Just like a stock position, it has 100 delta and no Greeks except exposure to cost of carry. But you faced that risk from the prime you borrow shares from anyway.  In this case, the borrow cost is embedded in the options but the clearing rate for that cost will be inherited from the arbitrageurs with the best funding rates.

    How to implement a synthetic short

    You buy a put and short a call on the same strike in the same expiry. To prove to yourself that it is the exact same exposure as a short stock position work through this example:

    Stock is $100
    You buy the 1 year 100 put for $10 and sell the 1 year 100 call at $10.

    The stock drops to $80 by expiration. What’s your p/l?
    What if the stock ripped to $120?

The synthetic short will have the same path risks as an actual short so let’s move on to option strategies that mitigate the path risk.

  • Outright puts

    If short-selling seems like it has negative gamma, you could always substitute your trade expression with long options. At least, you get something for the theta.  So while you will be paying to borrow, it might actually be at a better rate than you can borrow from your broker. And the moment you buy the put, the funding rate is capped at the implied cost you traded at. If the borrow gets more expensive from that point forward, your put will actually appreciate in step with its rho.

    The risks of buying puts are familiar. You can be wrong on timing, vol, how far the stock actually falls.  You can get middled. Your thesis can be right but not right enough.

    The benefit is you cannot lose more than the premium (unless you dynamically hedge…but if you are using the puts directionally then you shouldn’t be doing that anyway). This simple fact turns your strong hand into a weak hand. You always reserve the right to roll your puts down as you take profits or up to chase the rising stock. But the basic position, while risky, is path-resistant. And path is why shorting is so hard.

  • Put spreads

    Buying a put vertical (buy 1 put, sell a lower strike put, same expiry) sterilizes many of the Greeks since you buy and sell an option, including some of the borrow costs.  The tighter the strikes the more the bet looks like a pure probability play. If the strikes are wide, your further OTM will not offset the Greeks of the near put as much (if you think about it, an outright put position is the same thing as a put spread where the further OTM strike is the zero strike).

    If the stock has a lot of negative sentiment around it, depending which put spreads you choose, it’s possible you are getting a bargain if the put skew is especially fat.

Options and the “Write Down Your Thoughts” Effect

I’m not shilling for options here. I’m just pointing out that in a market that is scaring vanilla short sellers away, there are trade expressions that allow you to stay in the game at the time when you probably want to the most. Even if you decide not to use options, there is a benefit from walking through the trade construction process — it will tighten up your thinking. It’s like journaling.

Before choosing an option implementation, you should write down your answers. I’d be surprised if the answers to these questions didn’t impact how you might frame a vanilla short.

Let’s walk through questions you must answer before buying a put spread.

  • Edge: if the put spread I’m looking at pays 6-1 what do I think the true odds are? 4-1? 3-1? The amount of edge AND the fact that we are talking about a bet with a sub 25% hit ratio will dictate my risk budget.
  • Risk budget: How much am I willing to lose in premium?
  • Should I spread my risk budget over several months or is there a specific catalyst or expiring lockup that favors concentrating the bet in a single month?
  • Which put spread should I buy? Would I rather buy $1,000,000 worth of the 85%-80% put spread or the 70%-65% if $1,000,000 buys me 2x as many of the further OTM spreads. Or maybe I prefer a higher delta trade, that pays off more often but pays smaller odds. This forces me to think about price targets and the market’s relative implied pricing of those targets. It directs your attention to the meatiness or winginess of your thesis.
  • Does the winginess or meatiness of my thesis correlate to any other forces in the market or is it a purely idiosyncratic idea? For example, if you were interested in owning put spreads on a portion of the ARKK basket, then you could concentrate your put spreads on the subset of the basket that offered the best implied odds. Your thesis wasn’t specific to a single stock but more of a general liquidity trade.
  • How much dry powder do you want in reserve to roll your put spread up when the stock rallies? What thresholds would trigger rollups? Likewise, if the stock sells off, will you roll spreads down? How about down and out into a further calendar month? Will you roll down on a 1-to-1 basis (taking profits) or aggro win-big-or-go-home style where you use 100% of the collected premium to buy a boatload of further OTM put spreads?

Working through these questions refines your thinking and creates a plan for different scenarios. I find that the granularity of options and layers of relative pricing force me to “write down my thoughts” in a way that delta 1 trading can easily gloss over.

Conclusion

Short-selling is hard. Not because it’s negative EV, but because limits to arbitrage and the reality of levered return math create perilous paths. Whether the bruises from the recent mania will usher in a “golden age of short-selling” remains to be seen. But removing an entire direction of returns from your arsenal seems short-sighted. It’s a surrender to the current moment just when you should be thinking hardest about profiting from names that on a long enough time frame will have prices that match their ShitCo status. Options provide a more path-hardy set of trade expressions and may become table stakes for investors (ie hedge funds) whose mandates should not allow them to ignore the short side.


Related:

The difficulty with shorting and inverse positions

Shorting Bimodal Stocks

A Thought Exercise For Outsourcing Liquidity Risk

Understanding Edge

In my indoctrination into trading, the term “edge” was equated to the bookie’s “vig” or a casino’s “house edge”. This makes sense since I started in this business as a market maker. The interview questions I faced were focused on mathematical expectation or expected value. For example, if someone offered you a game that pays you the number that comes up on a single die, what would you pay to play? The weighted average payout of the game is $3.50. So if you can pay $3 to play, you’d make $.50 in theoretical profit. Of course, you could still lose if you roll a 1 or 2, but if you could do this every day, you’d earn 14% ($.50/$3.50) in the long run.

The basic premise of the market-making business is 2-fold: capture edge and manage risk so you can survive to actually see that long run.

  1. The edge comes from identifying the fair price.
  2. The primary risk management levers are diversification and sizing.

If you can price accurately and manage risk competently, you can crystallize the edge as surely as the Wynn prints money.

In this post, I will share:

  • the nature of edge in both trading and investing contexts
  • unbehaved edge in the real world
  • intuitions you can take with you

The Nature Of Edge in Trading And Investing

First, let’s define fair value. I will decompose it into 2 concepts.

  1. Expectation

    This can be a price that is ultimately an arbitrage. The die game from the intro or a casino game can be squeezed into this since the asset’s expectancy can be computed. With a large enough bankroll or sufficiently small bet size, it’s practically impossible to lose in the long run. Cash/futures arbitrage and creating/redeeming ETFs trading away from NAV are market examples.

  2. The liquid price

    In the market maker pasture, I was raised in, we’d call any price that was transparently and liquidly trading “fair value”. If the market for an option was “choice” or “pick’em” with deep-pocketed players on both sides then it was “fair”. We might say “fair value is $5, Goldman Sachs by JP Morgan”. In other words, a GS client was $5 bid and a JP Morgan client was offered at $5, it was trading, and there was enough size available for anyone else to basically participate. It’s a fleeting concept, but useful. We could use that price as a benchmark to compare less liquid derivatives as we looked for relative value.

With the idea of fair value established, we can begin exploring the nature of edge with a familiar toy model — the coin flip.

The Power Of Small Edges

Imagine a coin flip game. Call the toss correctly, make $1, otherwise, lose $1. Let’s pretend you could predict the coin flip with 50.5% accuracy. Sweet.

  • What’s your edge?

The expected value of playing the game is 1% because your payoff is equal to .505 * $1 – .495 *$1

  • What’s the standard deviation?

    From the binomial distribution, we know the standard dev or vol is √(.505 * .495) or 50%

  • What’s your risk/reward (Sharpe ratio)?

    I’m going to use the term “Sharpe ratio” in a specific context, as the ratio of edge to volatility. This is intuitively important since edge doesn’t mean much without a measure of variance. For this single toss, the Sharpe ratio is a measly .02 (1%/50%).

1% edge on this coin flip doesn’t seem like much. The .02 Sharpe ratio is a laughable signal to noise ratio. But as we increase N from 1 flip to many, the binomial distribution can be closely approximated by the familiar Gaussian curve [Taleb, spare my window, I’ll address reality later].

Look closely. The Sharpe ratio increases with N. Specifically, it increases at the rate of √N.

Why? Because the edge or numerator grows linearly with N while the denominator, or vol, only increases at √N. This property of edge is the foundation of trading and gambling. With enough trials, victory is nearly guaranteed. With a 1% edge on a coin flip, you are 90% certain you will be up money after 4,000 trades. So if you have 10 traders making 20 trades each business day, in one month you are more than 90% certain you are winning. In one year, you can’t lose.

Getting A Feel For Edges

Let’s look at the math in reverse. In Excel, we can use Norm.INV() to find what return corresponds to a desired probability for a given EV and vol. Let’s say we want to be 95% certain we make money. In math language, we are interested in the point where the 5th percentile return of the CDF is equal to 0.

We want to ask Excel:

How many trials do I need to have so that my Sharpe ratio sets my 5th-percentile return to zero?

To do this let’s standardize the vol to 1. The equation we need to solve is:

NORM.INV(5%, EV, 1) = 0

To solve for EV we use Excel’s goalseek function. We find EV = 1.645

Since we standardized the vol to 1, then we have discovered that at a Sharpe ratio of 1.645 (again Sharpe is EV/vol), the 5th percentile return is 0. That is the Sharpe ratio we need to be 95% certain we make money.

Remember that having 1% edge on a single coin flip only has a Sharpe of .02

But as we increase N, the Sharpe increases by √N :

SR of 1 trial x N/√N = SRN
.02 x N/√N = 1.645
N = 6,764

If we flip the coin 6,764 times, we are 95% sure we will make money even though we have a tiny edge on a volatile bet.

Let’s recap in English what we did here:

  1. Compute the risk/reward or Sharpe for a single bet
  2. Figured out the risk/reward needed to be 95% certain we will make money on a series of bets
  3. Computed how many times we need to play to achieve that risk/reward

Let’s look at the relationship between a single bet Sharpe to how many trials we need to be 95% certain we win.

  • If we have .02 Sharpe per bet, we need to do 25 trades per day for a year to be 95% certain of making money.
  • If we have .10 Sharpe per bet, then 1 trade per day will help us realize the same risk/reward over the course of a year.

This table highlights another important point: by increasing the Sharpe per bet by an order of magnitude (ie from 1% to 10%) we cut the required number of trials by 2 orders of magnitude (27,055 to 271).

Think about that. The improvement in Sharpe leads to a quadratic reduction in trials needed to maintain the same risk/reward for the series of bets.

Inverting the logic:

If the risk/reward of your bet is halved, you need to bet 4x as many times for the strategy to maintain the same overall risk/reward.

From Trading To Investing

The domain of many individual bets fits more under the umbrella of trading. For investing, we tend to think of the annual Sharpe ratios of investing styles or asset classes. Without looking this up, I’d guess that the SP500 has a long-term Sharpe ratio of about .40. I’m estimating an 8% annual return divided by 20% vol.

We can use the same math we did above to see how many years we’d need to invest to be 95% certain we did not lose money in nominal terms. Turns out the answer is 17 years. The table below finds the number of years for other combinations of expected return and volatility.

Years Required to Be 95% Sure of Profit

The Real World

Bell curves are great to build intuition but they are not reality. We can’t really be 95% sure we’ll make money by holding stocks for a generation because the historically sampled returns and volatilities are just that — sampled. We don’t know what the actual distributions are. Fat tails, skew, other moments I don’t even know about. 

We can use a highly skewed bet to demonstrate how volatility can distort our impression of risk. This renders the Sharpe ratio useless in highly skewed scenarios.

Consider 2 stocks, both are fairly priced at $100. We’ll call them Balanced Corp and Skewed Corp.

Balanced Corp is 50% to go up or down $10.

Skewed Corp has a 90% chance of going up $3.33 and a 10% chance of dropping $30.

Using the bimodal distribution we find that the stocks have the same volatility. However, they would have different straddle prices if there were options listed on them.

(It’s a good exercise for the reader to use what we know about expected value to manually compute the call and put prices).

So here we have 2 stocks with the same true volatility but different straddle prices if we compute them via expected value. Of course, we would not use B-S for a stock that was discontinuous and was going to magically open at one of 2 prices in a year. But this does show how the effect of a strong skew would suppress the value of a straddle for a given level of volatility. 

This is actually more intuitive than it appears. FX carry is a highly skewed trade that might exhibit minimal vol on a daily basis. The volatility imputed by the straddle understates the risk because it derives most of its value from the behavior of daily moves, where the risk of a jump will be better reflected in the cost of OTM options. In the above case, the Balanced Corp 90 put is worthless while the 90 put on Skewed Corp is worth $2 (10% of the time it finishes $20 in-the-money).

So if you use straddle prices to impute volatilities which are then used to calibrate Sharpe ratios, you may be understating the risk of highly skewed assets. Your risk/reward ratio is actually overstated which means it will take far more trials to realize your edge, assuming you actually have any. And remember how diabolical the math is…if your Sharpe ratio is overstated by 2x (let’s say you think it’s .8 and it’s actually .4), then you need 4x the number of trades to maintain the same assumptions about making or losing money. How would you feel if you found at the long-run for your given strategy wasn’t 10 years, but 40?

Takeaways About Edge

Self-aware investors and traders are always questioning their edge. Evaluating a track record or doing post-mortems on your own strategies requires being able to handicap the true distribution of your trades. The more Gaussian they look (for example if you play limit poker instead of no-limit) the easier it is to ascertain the strength of your edge statistically. You can tell the difference between bad run vs a change in the quality of your edge. Some runs would be almost impossible if your edge was real.

Edge is scarce. When we prospect for it, we should expect to mostly find fool’s gold. There are many reasons for this.

On skew

While both high volatility or high skew make it harder to determine if you have an edge statistically, skew is especially tricky. It is hard to see without liquid option surfaces. Here’s an intuitive way to see how skew distorts reality. Imagine finding a video poker machine that didn’t show its payoff table. Under the hood, it gives slightly worse payoffs on a pair of Jacks or better, but offered a billion to one on the Royal Flush. You could play that machine for days or even weeks and never realize you had massively positive EV.

On sample size

  • Having a small edge or number of trials makes it hard to verify an edge. Remember that when evaluating anyone trading highly volatile assets (ie crypto), engaging in highly skewed trades (carry, staking tokens for yield, option selling), or making a few concentrated bets per year (much of discretionary fundamental investors).

  • Remember the phrase “to think in N not T”. If there is a flow that shows up every day for a month do you have a sample of 30 or just 1 bit of behavior spread over 30 days? It’s the philosophical version of how auto-correlation artificially inflates N.

On luck vs skill

  • If you have negative edge, trade less. Short-term variance may turn up a friend named “Luck”. In the long run, she’s lost your number. 

  • In chess, a difference in ELO can be used to handicap a match between 2 players. Chess has no element of randomness. The signal is extremely strong. Backgammon has randomness, so the predictive strength of the ELO spread increases with match length. This comment in a chess forum cements this:

    While Magnus Carlsen would stand virtually no chance against the top chess programs, the Elo rating difference between Extreme Gammon, (the best bot) and the top humans is more like 75 points, so XG would be something like a 2-1 favorite in a 25-point match against the top human player.

The importance of edge

  • When I was a market-maker we were always on the lookout for a new source of edge (perhaps a new name to trade or spotting a new flow to trade against). Edge is pure gold. Its scaling properties are amazing if it’s genuine. We were encouraged to not worry about risk if we could find a legit edge. The firm would find a way to hedge some portion of the risk if the edge was worthwhile, and you could always use sizing to manage the risk. Finding edges was top priority. It’s what you build businesses around.
  • A 1% edge in a stock or ETF is enormous. Imagine buying a stock that was trading “fair” for $50 for $49.50. This is an order of magnitude more edge than HFTs earn. Hold my beer now as we do options. If the fair price for a call or put is $.50 and the bid/ask is $.49-.$51, you are giving up 2% edge every time you hit or lift. Before fees! Option prices themselves are more volatile than the underlying stock so from the market-maker’s perspective the Sharpe of the trade might be pretty small (getting 2% edge on a security that might have a 100% vol for example). But think of the second-order effect…the optical tightness of the market and high volatility of option prices means it can take many trades before the option tourist realizes just how much the deck is stacked against them. For independent market-makers, like I was 10 years ago, the tight markets made our business worse because our risk and capital limits did not allow us to keep pace with the volume scaling required to make up for the smaller edge per trade. But the large market-makers welcomed the increased transparency and liquidity because they could leverage their infrastructure effectively. 

  • If you make a 50/50 bet with a bookie but need to pay them 105 to 100 you are giving up 2.5% per bet (imagine you win one and lose one…you are down 5% after 2 bets). Now think of a vertical spread or risk reversal in the options market. Pay up a nickel on a $2 spread? Might as well have a bookie on speed dial.

Edge in the real world is nebulous

Firms with provable edges don’t try to raise money. If it’s provable it does not need more eyeballs on it. The epistemological status of edges that are trying to raise money is unknown. Many will never get the sample size to prove it. Asset management is the vitamin industry. It sells noise as signal. It sells placebos.  There will always be one edge that never goes out of style — marketing.

True mathematical edge is hard to find.


Related:

  • Nick Maggiulli’s Why You Shouldn’t Pick Individual Stocks: On The Existential Dilemma Of Stock Picking (Link)

  • Moontower Money Wiki: Time And Human Capital (Link)

Interview Questions A Market Maker Gave Me in 1999

SIG is well known for asking probability questions to filter trainees. This is not surprising. They view option theory as a pillar of decision-making in general. Thinking in probabilities takes practice which is why they like to look for talent amongst gamers who make many probabilistic decisions and need to interpret feedback in the context of uncertainty. They require many hours of poker during  “class”. In this 3 month period, junior traders live and breathe options in lovely suburban Philly after apprenticing (“clerking”) on a trading desk for about a year.

Here’s some of the questions I remember from my interviews in 1999.

  1. You flip a single die and will paid $1 times the number that comes up. How much would you pay to play?
    • Suppose I let you take a mulligan on the roll. Now how much would you pay (you are pricing an option now btw)?
  2. My batting avg is higher than yours for the first half of the season. It’s also higher than your for the second half of the season.

    Is it possible your avg for the full season is higher than mine?

    (Hint: Simpsons paradox)

  3. You are mid game that you have a wager on. Opponent offers to double the stakes or you automatically lose. (Like the doubling cube in backgammon)

    What’s the min probability of winning you need to continue playing?

  4. You’re down by 2 with seconds left in regulation basketball game and have a 50/50 chance of winning a game if it goes to overtime. You have a 50% 2-pt shooter and a 33% 3-pt shooter.

    Who do you give the ball to?

    (simple EV question)

  5. You are given $1,000,000 for free but there’s a catch. You must put all of it into play on roulette.

    What do you do?

  6. There’s a 30% chance of raining Saturday. 30% chance of raining Sunday.

    What’s the probability it rains at least one day?

To encourage you to try before looking up the answers, I’ll make it annoying…the answers are somewhere in this thread.

I wrapped that thread with a short post on Trading And Aptitude (Link)

Option Theory As A Pillar Of Decision-Making

  • Understanding Options and Decision-Making (Thread)
    @HideNotSlide

    In an old Barron’s Roundtable, Jeff Yass, the founder of SIG had strong words about how fundamental option theory is to decision making.

    Of course this sounds self-serving, from a guy who understood options as a young teen. But it reminds me of a more famous investor. Warren Buffet. I’ll rely on readers to find it but I remember Munger saying that Buffet was already thinking of options at a precocious age. While Buffet calls derivatives “weapons of mass destruction” his own investing history shows an explicit use of options (his put-selling maneuvers are well-documented…and critically path-resistant since they are not marked-to-market). I’m not a Buffet expert, but his use of “insurance float” sure looks like something that came out of the mind of a derivatives trader.

    • The Moontower Volatility Wiki is growing every week due to submissions from the online vol community. It also includes every post I’ve written on options, many of which try to use options theory to understand markets and think about probabilities.
    • Decision-making is a practice.
      • A pillar of sound decision-making is thinking in probabilities or as Annie Duke’s book is titled, Thinking In Bets. Here’s the notes I took on an interview with her which captures the essence.
      • This weekend I came across a great post by in the same vein by Jonathan Bales The Time I Sold Furbies For Money. I especially liked the bits about Belichick’s non-punt, and poker pro Phil Laak about learning what “5% feels like”. [Phil is a good friend of some friends I made in the options game so it was especially cool to see his thinking turn up in that post].

        I’ve previously commented on the neat analysis Bales himself did on the question of when you should “work for free”. You should follow @BalesFootball if you want to sharpen your “thinking like a gambler” sword.

  • A Personal Take

    I added thoughts on my days at SIG in response to the Yass thread. Here’s the text:

    When I was a Susq I heard Jeff speak a few times. It was always engaging.

    They were savage in my days there but the doubling down on tech and brains thru the years probably makes Jeff the richest dude in the world you never heard of (unless you look at pol donations, then you know). One of the talks was on the primacy of markets (Yass is an extreme libertarian, free-marketer, no fool should be allowed to keep their money type. Appealing views to many traders, esp when they are young). This post was one of his market lessons: Dinosaur Markets.

    One of my interactions with Jeff was a mystery to me:

    I remember when I was a 1st year mm on the Amex and I reported a giant trade that got crossed in AIG on the internal chat. I got a dm. “Pls call”. It was from Jeff. I was never so scared. Was I supposed to break that cross up? I called Jeff from an Amex phone and he just asked me for the trade details. Implied vols, who the broker was, what bank crossed it. I told him and he abruptly hung up. That was it. Still don’t know why of all the trades I’ve ever on reported why that warranted a call.

    Other times I’ve heard Jeff speak was on why the dot com bubble was not an example of market inefficiency and it goes back to understanding option theory and the relationship of volatility to positive skew and what drives volatility. I’ll write about that one sometime.

    He also speaks to every trading class for an hour that goes thru the 3 months of theory and mock trading in Bala Cynwyd. In my class he talked about career risk with NFL coaches affecting decisions (he defended an oft- mocked Barry Switzer decision to not punt)

    I will always be thankful for having worked and learned at SIG. I really didn’t have any business being hired there (2000 was the largest cohort bc $ was raining from the sky. They needed warm bodies to pick it up) and I think I’m proof that traders can be shaped and aren’t born. [By the way, this is very much why I try to teach what I’ve learned. Hopefully people smarter than me can build on it and let me invest in them 🙂 ]

    Incidentally, the head of HR who hired me gave important advice I always remember. When I explained I had a few higher offers she said:

    “You’ll be rich whatever you choose. Decide who you want to work with.”

    She knew SIG held the nuts.

Structuring Directional Option Trades

This post is a response to Twitter buddy @demonetizedblog

Let me take a stab at a “process” answer.

Introduction

For directional trading 90% of the work happens upstream of the option expression.

The option trade construction is the most trivial part of the process. Your fundamental work should inform your opinion of the distribution. This can be compared with the implied distribution from the vol surface.

This mental process is entirely different from vol trading. Remember, you aren’t dynamically hedging. Directional trading and vol trading have totally different starting points.

[At the end of the post you’ll see when the two approaches come to the same conclusion and when they don’t. This can lead to directional traders to trade with vol traders and everyone is happy. It’s still zero-sum. It’s just that the losses can be incurred by whoever provided the liquidity to the dynamic hedger. That entity was not part of the original trade]

Ok, so when it comes to directional trading vs vol trading, you must be clear what game you are playing.

This post is about structuring directional trades.

What’s the distribution?

First, you do a bunch of fundamental voodoo and come up with a distribution of possible stock returns.

[I’ll wait]

Good. We are going to discuss options now. Relax. Take a breath. Don’t worry about fancy words like “moments of a distribution” or kurtosis. You are a fundamental investor. It’s fine to think in prices, percentages, and bets.

Now what?

Let’s establish a focusing principle.

You want the short leg of an options spread to correspond the most likely landing spot of the stock based on your analysis. If those options are the cheapest on the board you might want to consider that the option surface is not presenting you an opportunity. It agrees with you. Don’t rush over that. This is not intuitive. Many fundamental managers buy the strike of where they think the stock is going. Don’t do that. Instead let’s review some basics about distributions. Without real math.

  1. A biotech stock worth $100 might be trading for that price because it’s 90% to be 0 and 10% to be $1000. True bimodal.

    Code-switching this idea into options:

    • The 100 call is worth $90.
    • All the OTM 100 point wide call spreads are worth $10.
    • All the butterflies are zero.

      What are some courses of action here?

      Let’s say you can afford 1 100 strike call. You could have also chosen 9 900/1000 call spreads. Or 3 of the 700 calls. In this case, all the propositions are the same because the options are correctly priced.

      [Prove this to yourself. I’ll wait.]

      Cool. Now you can imagine how if some of the options were priced differently you might be able to find an alluring proposition.

  1. New stock to consider. An insurance company also trading $100. This is not a bimodal stock. Perhaps it looks more like a bell curve with a high peak shifted to the right of the forward price because a pumped up put skew is signaling strongly negative skew.

    Wait. Why does that push the peak to the right?

    Think about it. For that stock to be $100 with a long left tail, it must have a greater than 50% probability of going up. The verticals will show you that. It’s the opposite case of the biotech stock and with much less volatility.

    • If you were super bullish you might want to load up on the depressed slightly OTM calls.
    • If you were bearish but thought the left tail was not as long you might want to buy the .50d/.25 put spread to express the view by exploiting the excess skew you think the market is embedding in the OTM puts.

Just remember, options give a shape to the distribution. Not every $100 stock has the same distribution. Think about where the $100 comes from? What upside force is counterbalancing the downside? The biotech stock has a very long right tail 900% away counterbalancing a large mass of probability that’s only 100% away. The $100 stock price is nothing like the insurance company. Options allow you to express the bet you want to express. The stock price alone is too blunt.

Once you let that simmer you can start to ask yourself useful questions:

  • Would you rather own 1 atm call or more calls for a total of the same premium at a higher strike?
  • Now compare that to call spread candidates. How many call spreads can you buy and at what moneyness?

The nice thing about vertical spreads is they cancel out many of the “greeks” effectively taming your vega and gamma exposures. The bets can be thought of as binaries allowing you to make simple over/under bets. To calibrate your impression of the possible magnitude of a stock move, you consider the moneyness or how far away from stock price the chosen strikes are. The moneyness will depend on your intuition for the volatility of the stock. You will have a sense for which spreads are “close” or “far”. These are technical terms.

And since I mentioned volatility, let’s say a few words on that to help you avoid some landmines.

Is the vol cheap or expensive?

If you are a directional trader you don’t care if the right volatility for an option is 55% or 56%. You aren’t dynamically hedging. But you don’t want to go to the used-car lot without at least checking Carmax online. You can compare the implied vol to the distribution of historical realized to make yourself feel like you did diligence.

Here’s a simple way:

Compare the IV to the stock’s historical vol of a comparable tenor. So if you are considering a 6 month option look at the distribution of 6 month historical vols to see if you are on the high or low side of the range. How? Looking at a vol cone will get you a quick optical answer.

Here’s Colin Bennett’s example (with my highlight) from his book Trading Volatility:

If the recent realized volatility is elevated and you wanted to buy long-dated options it might be a poor time to buy options. You can either wait, trade structures like verticals that have little vega exposure, or even create a directional trade by selling options.

Here’s a few extras to consider when selecting an expiry:

    • The nearer the option tenor, the more event pricing matters. The event’s variance is a larger proportion of the total variance until expiration.
    • Longer dated options have takeover risk. (Cash takeovers mean your LEAP extrinsic goes to zero. Sorry.)
    • Do you plan to roll the exposure to maintain it or is there an expiration to your thesis? The more often you roll the less rebalance timing risk. This has to be weighed against trading costs.

The Real Work Is Not In The Options

When you throw a proper punch the fist is just the delivery method. The point of contact. That’s the option expression. The real work happens from the torque in your hips. That’s the fundamental analysis behind the punch. An advantage of directional trading is you can think in discrete bets once you’ve done your fundamental homework.

Discrete trades let you:

  • Think in terms of how many bets you get paid back vs how much premium you layout and compare that to the probability your fundamental work suggests.
  • You’d like to get to a statement that looks like “I’m willing to risk 1 bet to make 3 because I think the proposition is a 50/50 shot.”
  • This establishes your expectancy and shape of the p/l.
  • Combine that info with your bankroll and now you can size the trade.

Bonus Section: Volatility Traders

I said that directional trading and volatility trading are different games. I’ll briefly talk about that.

First of all, even vol managers sometimes make discrete bets. They will “risk budget” a trade. I’m willing to spend $1mm on 150% calls for winter gas. Or whatever, you get the idea. They might even set up a separate account for tracking and attribution for this.

But really this risk budgeting or discrete framework is different from managing a relative value volatility or market making portfolio. In that environment, you are often responding to values moving around some cross-sectional trading model. You see edge, you pick it up, throw it on the pile and manage the blob. With a decent size book holding thousands of line items you are going to need 3-D goggles to slice and dice the positioning and the risk. You might not even know what you are rooting for sometimes. If you are short SPX correlation and long 200 of the 500 names then you are massively overweight vol in the 200 and you are “synthetically short” vol via the index in the other 300. Hundreds of names x hundreds of strike x hundreds of expiry and you need to bucket and compute quickly and accurately. Totally different animal from directional perspectives.

This does not mean that vol traders and directional traders don’t land on the same conclusions occasionally. A vol manager who finds a name that “screens cheap” might be looking at the same thing a fundamental manager is seeing. The fundamental manager is coming from a different vantage point, but might feel that a stock is hiding some serious upside and the nominal price of the calls are a bargain. In this case, the fundamental manager is going to struggle to find liquidity as the call options might be cheap for a few contracts but once they start calling around the street find that no market maker is willing to join the resting retail offers.

You may be wondering why the screens are so low in the first place? Why are they stale? The market maker’s dashboards are flashing green too. They know those options are cheap. But remember this is a game. They aren’t going to bother lifting the offers for a few contracts. They would rather freeroll on the possibility that some donkey overwriter who systematically sells calls without price sensitivity dangles a mid market offer. Then they’ll lift. (gratuitous “Do You Even Lift Bro?” clip)

So when do vol managers and directional traders trade with each other? All the time. Here’s 2 examples.

  1. Imagine a fundamental trader who is directionally smart but not vol savvy. They might buy calls, and the market makers who have been keeping tabs on this pattern of flow realize its predictive of a price move but has not historically beaten them to implied vol (perhaps it’s one of these dumb accounts that buys the strike of where they think the stock is going. They should probably hire a vol trader, if for nothing else to show them how to do p/l attribution). So the market makers sell the calls and overhedge the delta. Trading 101.
  2. A very common case where directional traders and vol traders are happy to trade is on vertical spreads or ratio spreads. Say a directional hedger buys put spreads. Vol traders can be happy to sell them so they can buy that tail option that the hedger gave them as the lower leg of the spread. A similar example would be a 1 x 2 ratio put spread. Say the stock is $100 and the directional trader buys the 80/75 1 x 2 put spread for a cheap or even zero premium. In their mind, they make make money all the way down to $70. They don’t start to lose money until the stock has dropped more than 30%. The vol trader has a different view. The vol trader cares about path and they know if the stock trades down to $80 quickly and vol explodes, they are going to be long vega and have ammunition to sell into the panicky vol buying. That 1 x 2 put spread is going to mark ruthlessly in the directional traders face. The directional trader didn’t respect path. Option traders are extra wary of path because they are highly leveraged businesses warehousing complex portfolios with non-linearities. There’s no better training for visualizing risk up, down, through time, across correlations, and at different speeds. The trader who honors path will often be the reason that “option that will never hit” is priced so high.

If you liked this post, consider checking out the Moontower Volatility Wiki.

The Moontower Volatility Wiki

Many beginners to options ask me and other professionals what they should read to learn options. I’ve seen this question asked enough times that I built a wiki that I can reference instead of needing to come up with an answer every time.

Voila…The Options Starter Pack (Link)

In the process of curating that I figured why not go the extra step…Introducing the Moontower Volatility Resources wiki (Link)

In addition to Moontower trading content, you will find select options content from the rest of the online vol community.

To maximize how useful this wiki there are a 2 important points.

  1. I will be keeping this wiki updated, but it is not open source. At this time, I think readers are best served knowing I’ve pre-screened submissions.
  2.  If you find a blog, book, video, interview, etc that you feel deserves to be here please submit it. I won’t guarantee I’ll include it but the benefit is we can keep this resource high quality and free of spam.

So there’s a tension involved…one side is that in order for this to be useful it can’t be a free-for-all. If you want a free-for-all there’s Reddit and Twitter and upvoting and ‘like’ buttons. This is not that. This is intended to be a reference with evergreen content subject to my standards. Like any manner of gatekeeping, I will miss things and I might let subpar stuff slide in. Sorry in advance. I’m always open to hearing suggestions/complaints. You’ll need to trust that I’m competent and care.

The other half of this tension is it requires engagement even though it’s not open-source. If you come across a source, a tool, a course or anything that fits neatly with this wiki then please share it.

Finally, here’s the excerpt from About This Wiki:
Option strategies range from directional hedging/speculation to the complexity of index dispersion portfolios and exotic structured product books. You cannot learn to trade options from reading. It is a craft and your understanding of it comes much faster when you have a position. When the feedback of the position comes in the form of mark-to-market p/l you learn what the position is sensitive to. Greeks like delta, gamma, and vega are immediately less abstract.

The good news is I believe any numerate, motivated person can learn options.

The bad news is two-fold:

  1. Experience is expensive.
  2. It is a craft best learned as an apprentice.

#1 is unavoidable. Straight talk — you will lose money learning. Guaranteed. Act accordingly. Don’t sell naked options and make sure worst-case scenarios are tolerable. Bid/asks are expensive. Sure, they might only be a few pennies, but 1 cent on a $1 option is 1% slippage. That’s 10-100x the slippage you pay to trade stock. Vast fortunes have been built on that 1% slippage. It will grind you as surely as a blackjack dealer if you play long enough without an edge.

#2 has better news. The internet in the form of blogs, podcasts, electronic brokerage and social media (esp Twitter) has never made it easier for a voracious learner to educate themselves, find mentors, and have meaningful discussions that would have been impossible even as recently as 2000 when I got into options trading.

I was fortunate to discover options trading right as I graduated college. I joined Susquehanna (SIG) and learned how to think about options, risk, and trading from Jedis. Their curriculum and methods for teaching were so comprehensive, tested, and systematized that it was a massive source of competitive advantage. The cared deeply about cultivating talent. They did not care if you knew what an option or interest rate was when they hired you. They looked for drive and aptitude only since they were secure in their ability to teach everything you needed to start managing a portfolio in as few as 18 months out of college.

I am not a math whiz. I was one of the <5% of hires who got a higher score on verbal than math SAT. Options intimidate many people simply because of the Greek letters and the math behind the models. I get it. I’m intimidated by math whizzes too. I have no more than HS Calc BC math education and a single stats course in undergrad. But the truth is, you don’t need to be able to derive Black-Scholes any more than billiards champ needs to know physics. Don’t get me wrong — the intuition behind the models is critical but the bar to acquire that is much lower than a math degree.

Much of my writing is an attempt to bring the reader to an intuition of the math in the same way that I was taught. I hope it’s even more accessible since my own weakness in math makes it easy to imagine being in the average reader’s shoes.

This wiki sits in that sparse space in-between the basics you might learn from the Series 7 and the nerdom that is derivatives structuring at a French bank. This is that mushy practical area in-between sophisticated retail and professional vanilla options user. It is an area, that will become more popular thanks to the boom in retail option activity and r/WSB. The vig and risk of options is going to weed out many of the new tourists but the few who persevere and have a deeper thirst to learn should find this wiki helpful.

And for the finance professionals who use options directionally but do not “trade volatility”, the resources found here might be just the bridge you need to understand volatility surfaces a bit better. This can improve your trade expressions, risk management, timing and ultimately executions.

If you have feedback, my door is always open.

-Kris

A Former Market Maker’s Perception of PFOF

It feels like payment for order flow controversies flare up every few years. When I see some of the takes I know how marine biologists felt after Jaws hit the cinemas in 1975.

Except they didn’t have Twitter to scream into.


I’m going to assume you already know what payment for order flow is.

If you need the basics, A16’s Alex Rampell and Scott Kupor have you covered. (Link)
If you want the GOAT of high finance’s version, here is the Matt Levine post I shared last week. (Link)

Now if you stop at Levine’s post I’d forgive you. There’s really no following that guy. But now that I’ve said that, you own the downside of reading further and if I say anything useful here I’m in-the-money.

I think my experience qualifies me to hopefully add some perspective to the discussion. I have been trading options for 21 years with the first half of those years on the floor. Even though I’ve been trading prop for the past decade I’m a dyed-in-the-wool market-maker. You can take the dog off the floor, but you can’t take the floor out of the dog. (Full disclosure: I used to work for SIG who was an early payer for order flow, but I had no insight into that side of their business).

An Image Problem

Payment for order flow sounds terrible. It sounds like payola. Greasing the radio DJ to get your record played on-air. That’s a bribe to the regional gatekeeper. There’s widespread misconception that when Citadel pays for flow it’s attempting to use the info to front-run the order. This is a dizzying misconception.

No trader thinks front-running random retail flow makes any sense.

Write that on a chalkboard 50x please.

The Nature of Adverse Selection

Drive it home: no trader thinks front-running random retail flow makes any sense.

In fact, the opposite is true. The entire basis of trading against retail flow is that it is a random mix of buys and sells and not autocorrelated. You want to trade against your drunk uncle Sal who has a good feeling about the Jets this Sunday. We call this “dumb” flow. Sorry, but that’s what it’s called.

On the other hand, we refer to institutional flow as “smart flow”. Not because it knows which direction the stock is going to go, although this can be the case as anyone who has been contra to SAC flow back in the day can attest. The reason we don’t want to trade against the flow is that it’s autocorrelated. 1,000 shares is the tip of an iceberg. Nobody eats just one chip just as nobody buys just 1,000 shares.

The options equivalent is putting someone up on a trade, only to have them reload 5 minutes later. This past fall, Softbank string-raised tech calls every day for a couple weeks. Masa-son is not smart paper, but he has a big stack. Truthfully, the threshold to be an undesirable counterparty is surprisingly low. I remember hearing a SIG trader at a conference a few years after I left. He mentioned that their studies had shown that the adverse selection of an options trade went up dramatically once it was greater than 16 lots.

Let’s understand this. Consider a pro-rata exchange where your limit bid is on equal standing with other limit bids but your fill is proportional to your size. So let’s say you are bidding $1.25 for 100 option contracts and the total bid quantity is 1000. If a retail sized order sells the bid for 10 contracts, you get filled on 1 because your size was 10% of the total displayed size. The pro-rata system (vs maker-taker which is a queue based on speed) incentivizes traders to show far more liquidity than they really want to. They don’t want to get their whole bid hit but they need to show size to be entitled to any reasonable percentage of the incoming orders. When an order sweeps the book, banging out the displayed size on the bid, the market makers are instantly sad. They know they are on the wrong side of a “smart” order.

The possibility that the flow you trade against is adverse, smart, institutional – whatever you want to call it – has a deep implication. You make a wider market than you would have if you could just tell the difference between the adverse flow and the random retail flow.

THIS IS THE EUREKA MOMENT WHEN INSIGHT RUSHES IN…

The brokers have realized they can segment the market between orders that can be facilitated on tighter spreads and those that require wider quotes. Liquidity has a price. Without PFOF, spreads need to be cushioned by the probability that an order is institutional. Instead, PFOF creates a tiered market where the cost of liquidity is proportionally aligned with the risk on a per trade basis. Retail traders get better fills. There’s less deadweight loss.

Institutional traders might complain, but its an illusion that they should have gotten the price that a retail trader should get. The risk business is not the widget business. You don’t get volume discounts.
Analogies 

“The opportunity to trade against random flow” as a source of revenue is a bit abstract. You are already familiar with price discrimination in other domains.

  • Casino’s attracting whales.

    Casinos don’t like card counters, they want customers that have positive LTV in the long run. They like whales and the type of people who buy books titled “The Fool-Proof System To Beating Roulette”. Casinos are paying for order flow when they offer complimentary suites and blacked out SUVs to and from McCarran.

  • Ad tech

    What is the internet but reams of data on customers being sold to the highest bidder so platforms (the brokers in our analogy) and in turn vendors (the Citadels) more can more efficiently convert sales (trades)?

  • Financial products

    Good driver discounts on auto policies. Life insurance physicals. Credit checks for loans. Price discrimination based on risk is the norm not the exception.

  • Retail

    As a broke 20 year old I used to frequently buy and return products at GNC. Yes, you can return a half-used tub of creatine. GNC started keeping tabs as a policy. I get it. The Ponderosa wishes it could turn away Joey Chestnut.

Competition

The discourse around PFOF has an air of monopoly sentiment. Maybe not in the Standard Oil sense of the world. There’s more firms than Citadel. You have Virtu, G1 (SIG), Two Sigma, Wolverine. It looks more like OPEC.

But there’s a big difference. These are not natural monopolies or crony handouts. Contrast the dynamic with payola. Payola was a scam that worked because the value of the bribe to the briber (the record label) was very low compared to the payoff of getting radio exposure. Meanwhile the value of the bribe was substantial to the receiving DJ who was paid a conventional salary despite being the caretaker of a government monopoly — airwaves.

I don’t think it’s surprising that high fixed cost industries settle into oligopoly-type hierarchies. The competitive forces are so strong that they double as high barriers to entry. The HFT-firms here are not defending natural monopolies. They are the survivors of the trading game who invested heavily in technology early. @hidenotslide explains in his recent post about another storied traded firm, DRW:

This brings me to my first point – firms who embraced HFT early in its evolution are today’s kings. Of the 10-20 firms that make up the bulk of high frequency trading profits, a large majority were launched before the 2008 financial crisis and many even prior to 2000. Because superior technology leads to direct competitive advantages in HFT, barriers to entry have become insurmountable over the last decade as companies have invested in ever faster exchange connections & market data feeds. A 2017 paper from researchers at Cornell & Penn argues this exact point – newer, smaller entrants that engage in HFT can survive, but they don’t get anywhere near the share of profits that larger, more established firms enjoy.

What’s absent from the narrative is how tall the pile of bodies these firms stand atop. I should know. I used to be able to work five hours a day (NYMEX alum holla) and make a lawyer’s wage. And in some years, a law partner’s carry too. Well, if you were smart you saved your money and realized it wasn’t going to last. The days of “locals” (ie wildcat market-makers) is long gone.

Many of the small firms, who saw the writing on wall and had an appetite for the long game, plowed money back into massive technology capex. Most of them just earned the right to say they lost to the best. In some cases they found small, profitable niches where they play the role of suckerfish. Respect to them, even this was not easy.

How about the remaining firms? The private giants the media likes to call “shadowy”. They were the ones who were most adept at assembling teams of software and hardware engineers working with game-theory geniuses to devise algos in a cat-and-mouse battle with competitors. The ones who stayed step-for-step with the exchanges who themselves were experimenting with matching engine rules, data, product listings and connectivity in their own battles for market share.

The truth is progress is cutthroat.

I remember the days before decimalization where you could make $5 wide verticals 3/8 wide. Today that same vertical is a choice market and the market maker gets paid the equivalent of an inter-dealer broker commission or about 25 cents. On a 3/8 wide market the market maker used to earn nearly $18.75 (or 50% of 3/8)! My business partner and I always marvel at the innovation and how little vig a trader is willing to accept to flip million dollar coins. It’s such a flex for capitalism. So much so that how good these firms are is chalked up to monopoly and not that fact that they are the survivors of the capitalism’s most brutal tournament.

How Survivorship Bias Makes Firms Look Like Monopolies

Perhaps I should not be surprised at the monopoly sentiment. Some of you will nod. “How can they make money every day?” First, I’m not sure they do, but even if they did that’s hardly a red flag. Casinos might make money every day so long as they can open. They’re not monopolies. Worrying that financial firms make money everyday is conflating market makers with investment managers because they traffic in the same products. But one of them is a customer and the other is a supermarket. With tiny supermarket margins per trade. And high fixed costs. If volumes dried up, the losses would show up even if the margins stayed flat.

A stronger, but still naïve argument, that they were monopolies would come from noticing that these shops came of age at the same time as the giant tech firms. This is a hint of how much they have in common. The difference is the size of the relative opportunities, but the tactics are similiar.

It started with skill and luck. The early big bets on talent and technology meant they were bringing guns to a knife fight. SIG wasn’t know as the “evil empire” on the Amex just because of the black jackets we wore. They understood the risk-reward was completely outsized to what it should be 25 years ago. They were amongst the first to tighten markets to steal market share. They accepted slightly worse risk-reward per trade but for way more absolute dollars. They then used the cash to scale more broadly. This allowed them to “get a look on everything”. Which means you can price and hedge even tighter. Which means you can re-invest at a yet faster rate. Now you are blowing away less coordinated competitors who were quite content to earn their hundreds of percent a year and retire early once the markets got too tight for them to compete.

SIG was playing the long game. The parallels to big tech write themselves. A few firms who bet big on the right markets start printing cash. This kicks off the flywheel:

Provide better product –> increase market share –> harvest proprietary data. Circle back to start.

The lead over your competitors compounds. Competitors die off. They call you a monopoly.

Equilibriums

Thus far I’ve only pushed back against the idea that PFOF is somehow nefarious. It is a form of price discrimination. The price discrimination is economically sensible when we price liquidity. There is a cost to having someone trade with you at the exact moment you want to trade. If you are a retail trader, that cost is tiny and we can thank technology and the competitive drive of very smart people to undercut one another so they can be the best bid for your business.

If you are an institutional trader that cost is higher. And it should be. Your cost to trade should be compared to your historical cost to trade. Not against what a retail trader’s costs are. I’d be shocked if an apples-to-apples TCA showed that this cost has increased over time. My null is the cost to trade for everyone has collapsed but probably more for retail.

I don’t have any strong opinions as to whether PFOF is the best equilibrium. One could argue we should have a single central order book, but then the exchange would have a monopoly. Plus it’s not obvious to me that the centralization of liquidity serves the heterogenous interests of all economic stakeholders across countries, regulatory regimes, strategies, time zones, and instruments.

We could entertain more incremental tweaks to the current architecture. For example an auction every minute or shorter trading hours to centralize liquidity in time but not venue. There’s probably some efficient frontier of tradeoffs. Nothing about PFOF looks villainous from my understanding of markets so if it lies along that frontier I would not be surprised.

And perhaps now you won’t be either.

How Options Confuse Directional Traders

2017 was a historically low-vol year, rewarding options sellers despite selling lower option premiums as the year progressed. Like they found a broken slot machine at the Cosmo. It wasn’t until the Feb 2018 “volmageddon” in exchange-traded VIX products, that retail discovered the dangers of selling options.

In the past year, retail, led by r/WSB, is back in the deep end of the options pool. This time they brought swimmies — they are only buying options. This limits their losses to the premiums.

As opposed to professional vol traders, most people use options as a way to bet on direction. You buy a put to bet on a stock going down and you buy a call to bet on a rally (or an “up” — a term coined by my doctor friend who always used to make fun of us finbros who talked about “puts and ups” all the time when we were in training). I tend to dissuade people for messing with options unless they have a very specific risk to hedge or if their speculative thesis is well-defined. Since options expire you need to be right not just on direction but timing as well. There’s a lot of ways to lose, get lured into trading more, and generally chop yourself up.

I’m going to demonstrate how you can lose money despite being very “right”. For good measure, we’ll extend the conversation to how hedging can actually increase your risk. Let’s jump in.

An Option Lesson

The recent action in GME justified the cigarette warning label I put on options. If the option user doesn’t appreciate the role implied volatility plays in an option price, then Benn’s tweet is mystifying:

Put options increased in value as the stock went up.

Then, with the stock on the way down @mark_dow tweets:

Put options lost value as the stock collapsed.

My kids would chalk this up to “opposite day” (apparently a modern holiday where kids wear pajamas to school). Alas, there is a more boring explanation:

Implied volatility increased as the stock price increased and fell as the stock price fell.

Pro Version

If you are eager, we can drill down a bit.

  • The option’s “vega” dominated its delta in both cases. The vega tells us how much the option’s price will change as the volatility rises or falls.
  • “Vanna” represents the sensitivity of the option’s delta to volatility — a second order effect. As the vol increased, the OTM option deltas increased. This is notable because it is a positive feedback loop. As the stock and vol both increase on the way up, market makers have to buy more stock to hedge. On the way down, it is stabilizing as the vol decreasing means the option delta decreases and market makers need to be “less short” to hedge the puts…it’s stabilizing because this offsets the negative gamma effect from being short puts in the first place. This one is tricky because the vanna effect is dampening the vanilla gamma effect.
  • Then there’s “volga” which is how the option’s vega changes with respect to vol. This is yet another second order effect of vol (I’ve written about that here). It feeds right back into vanna and acts as a reinforcer on the way up and a stabilizer on the way down (since spot and vol are positively correlated. We’ll get to this correlation later).
  • There are higher order Greeks than “vanna” and “volga”. Ironically, they are only known by the French. Don’t ask.

Vol traders care about these cross-currents because of how they accelerate or dampen the price of options. These effects alter hedging flows which change buying and selling pressures. Outputs become inputs so each sub-cycle in the process looks like a foreshock to something bigger, or the aftershock to something dissipating.

This might sound theoretical or academic but it’s the nuts and bolts of managing volatility portfolios. An option book with many names, maturities, and strikes looks like an amorphous blob until you use these concepts to give it shape. Once it has shape you can recognize what kind of animal it is. You can predict how it might respond to different scenarios. The measurable risk is how it will react to the market’s movements. The stock is going to do stuff. That’s a given. You are not allowed to be surprised by that fact.

The real concern is if the portfolio, this animal under your care, acts outside your range of expected behavior.

Normie Version

Rest easy. That was utter overkill for investors or even casual option punters. To understand why puts got cheaper on a selloff, you just need this picture:

It is a beautiful and simple visual intuition constructed by @therobotjames.

  • The purple bell curve is the distribution of GME stock when it’s trading for 600% vol and $200.
  • The green bell curve is the distribution of GME stock when it’s trading for 400% vol and $90.

Explanation

Despite the higher stock price, the purple curve imputes a higher probability of the stock going below $20 because the distribution is much wider at 600% vol than at 400% vol. The impact of the vol totally dominates the moneyness, or distance, the stock is away from the strike. Another way to say this is “the $20 strike is closer to $200 than it is to $90” if the volatility is that much higher when the stock is $200. This is easier to understand if we simply make the volatility disparity wider. Imagine a govt bond that trades for $100 par and a stock that trades for $200. Nobody would be shocked if the 50 strike put for the stock was worth more than the 50 strike put for the bond.

Self-contradiction?

I can see you scratching your head. In GME, we are talking about the same exact asset at 2 points in time with a contradicting proposition: namely that the probability of the stock dropping below $20 when the stock is $200 is higher than when the stock is $90!

This paradox is an illusion that happens whenever you have the benefit of hindsight. You don’t know which of these prices is the true odds. You can only trade with the information you had at the time. You cannot arbitrage the relative pricing between the 2 states of the world that we have the luxury of seeing in the rearview. Looking back you can say that the stock’s chance of going below $20 was underpriced when it was trading $90 or that it was overpriced when it was trading $400 but you couldn’t make those claims at the time. They only seem paradoxical when compared to each other.

At this point, I suspect retail traders, curious as to why they won to buying puts on the rally and lost to buying puts on the selloff, developed some understanding of vol dynamics.

Hopefully the tuition wasn’t too steep. Not all lessons are as cheap as a defined option premium.

The Expensive Option Lesson Pros Learn

Professional option traders adjust option greeks for spot-vol correlation. In the GME-case the correlation is positive just as it is in agricultural commodities. As the price increases, the vol increases. Most markets have a negative spot-vol correlation. The VIX falls when the SPX rallies. This is also true in the oil market. A supply of options hits the market during rallies as large hedgers overwrite calls.

To adjust for this, option traders will model a negative spot-vol correlation or “vol beta”. For example, suppose your ATM call option typically has a 55% Black-Scholes delta. you might model a 50% delta only, knowing that if the future goes up $1, your call option probably won’t increase by $.55 since implied vol will fall. (In fact, one of the ways to know if the counterparty you are quoting was a bank or not was by the delta the broker wanted to use on delta-neutral structures. Banks often quoted with Black-Scholes deltas while prop shops used deltas which incorporated vol betas, effectively lowering all call deltas).

When you model vol beta you are usually making a trade-off between hedging local behavior of common moves versus more unusual sized moves which will break the spot-vol correlation, in turn upending calibrated deltas. If a skirmish broke out in the Strait of Hormuz and oil ripped 10% higher I would not expect volatility to fall. Therefore, you also need to consider a matrix of outcomes.

(This is a hypothetical picture which tells us if oil rallied 10% and vol increased 50% we would lose money. Note that if vol fell in accordance with a vol beta we would have made money).

Even with respect for local and jump spot-vol correlations, you can still be caught off-guard. In nat gas, I’ve underestimated just how GME-like its vol surface can change. I’ve seen put prices not budge despite a 20% selloff in an underlying. If you are running a hedged book and have any long futures against the puts you enjoyed the full drawdown in futures without any offset from the puts. Enough to make a burly man cry.

The idea that “you only risk your premium” when you buy options is only true if you do not hedge. It’s diabolical to get crushed on a supposedly neutral position. Why? Because, you thought you were hedged. This tricked you into buying more puts than you would have if you didn’t hedge.

(All basis trades have this dangerous property. The illusion of being hedged induces you trade bigger or use leverage to push a small edge.)

Qualitative Appreciation For Spot-Vol Correlation

The GME put holder who lost money on a sell-off now understands how the change in implied volatility explains the loss. Regrettably, this is like being told you missed a flight because you were late. It’s just a mechanical explanation. What you really want to know is why did volatility come in as much as it did? In option trader terms, “why did the vol beta outperform or underperform in the first place?”

The beta itself will have quite a bit of variance since a price can follow many paths to a destination. Those paths will each be a sample of unique realized volatility. Did the price grind to X or did it gap to X? The realized beta will vary from your projected one depending on the path and the market’s interpretation of that path. If the stock gaps down due to a specific bit of news (for example news that a big short is done covering or the company issuing more shares) the gap can actually be vol-reducing as the market interprets the news as “stabilizing”. If the gap comes with no explanation, then the market might interpret this data point as another mystery piled on an already burning heap of confusion. The market will presume that the crazy stock might just rip back up again. In this case, the vol might hold up better on a sell-off that occurs without a reason in contrast to the the prior case where the reason had the narrative effect of curtailing the upside.

So in the GME case, most of the reasons the price can go down are stabilizing. We expect options to be sold in response to a sell-off, and for the vol to decline. But “most of the reasons” does not mean 100% of the reasons so there is a probabilistic distribution to what the realized spot-vol correlation could be. And that’s why we still have surprises.

The Beauty Of Options

Ultimately, options help to “complete” a market. A simple stock price is just the expected value of a stock (equity risk premia and arbitrage pricing theorists are welcome to have a cage match over that statement. I’ll be out back selling beer). By imputing more information than a one-dimensional expected value, option surfaces give us a richer picture of expectations. What’s considered stabilizing, and what’s considered unthinkable are encoded in options markets.

There’s a silver lining to the WSB obsession with options. Some of these people who showed up for a thrill will stick around to learn how to listen to how a vol surface whispers.

Prices Are More Than Expectations

Prices Are More Than Expectations

This week I came across this tweet by @NewRiverInvest:

Breakevens are not inflation expectations (thread)

It explains how implied breakevens from TIPs are not the same as inflation expectations. One of the reasons is because it’s a small market that is easily distorted.

The second reason is more technical. TIPs are actually implicit options. The face value increases with inflation but is floored at par. So if we experienced deflation you’d get your now-even-more valuable USD back. We should presume the TIPs price reflects not just inflation expectations but a premium for the option value.

This is a familiar lesson. Think about volatility risk premiums. Since convexity improves portfolio CAGRs the expected value of owning an option should actually be negative in arithmetic terms. This is why quants will fancily say “implied vol is a biased estimator of realized vol.” It’s overpriced on average but it’s correlation and convexity attributes suggest it is not overpriced in a repeated, compounding framework.

Another demonstration of “price does not equal expectation” is found in correlation itself. Correlation swaps trade at cheaper levels than implied correlation because being short correlation is a concave (ie negatively convex) position. A correlation seller will require an additional risk premia to be short it. A further explanation can be found in my notes.

So whenever you imply an expectation from a price you need to strip out any additional risk premia or preference that is embedded in the price.

Related:

This ties in well with Why You Don’t Get Paid For Diversifiable Risks (MoontowerMeta)