Making Property Taxes Apples to Apples

You will be working from home more often. Not all of you but many of you. That means browser tabs devoted to Zillow searches in Austin, Nashville, Vegas, Denver, and Miami. Geo-arbitrage won’t be as dramatic as software devs had hoped since the big companies will cut your pay when you leave, but in some of these places you could sustain a 20% pay cut and still be better off (at least if you’re leaving SF).

One of the biggest inputs into cost-of-living comparisons are so-called SALT (state and local) taxes. Since 2018, SALT deductions are limited to $10,000. They were previously uncapped. This has created even larger disparities in cost-of-living between states. CA, IL, NJ, and NY have income taxes that get a bit handsy with their residents.

Beyond state income taxes, one needs to consider property taxes for a more complete picture. Texans enjoy zero state income tax but hefty property taxes. NJ residents are assaulted from both ends — above average state income taxes and punitive property taxes. How about CA? The state income tax, gas tax and the cost of renewing a vehicle registration are nothing short of sunny weather ransoms.

But what about CA property taxes? The answer to this is sneaky and can be used to understand the impact of property taxes in general. But I’d go further and say that if you have not walked through the math the way we are about to, then you may be walking around with some very mistaken impressions about the cost of housing.

Property Taxes: Apples to Apples

The effect of property taxes depends on 2 core variables. The property tax rate and the assessed value. If you are weighing a house in CA to a house in NJ you want to make an apples-to-apples comparison. How do you do that when the rates are different and the methods of assessing value are different?

Let’s isolate each effect.

[Obviously the cost to buy a home has many factors that can mostly be tucked under the headings of supply and demand. Yet the effect of property taxes is significant so it’s worth isolating. It’s also worth noting that since a primary residence is most people’s largest asset, a property tax is a defacto, albeit incomplete, wealth tax. Economically it’s passed-thru to renters so it hits everyone]

Assessed Value Effect

Property taxes are waged on assessed value. In NJ, assessed value resets whenever a home trades. So if you buy a $1,000,000 home and the property tax rate is 1% you owe $10,000 per year in property tax. As the estimated market value of your home changes, your assessed value changes. So if your market value jumps 15% in one year you can expect a big increase in your tax bill. It may lag the full market return but the idea is the assessed value tracks the value of the home. Downturns in prices require homeowners to plead their case that the home’s value has declined if they want relief on their taxes.

Like NJ, CA assessed value resets to the purchase price after a transaction. But then CA diverges from other states. A month before I was born, in June 1978, CA passed Prop 13, a ballot proposition that has created distortions in wealth that few could have foreseen. Prop 13 froze assessed values at 1976 levels for homes which have not since traded. It also limits increases in assessed value to a cap of 2% per year.

Combined with a NIMBY attitude to permitting new construction, CA features a lopsided sight to behold — multi-million dollar homes with single-digit thousand tax bills. Nice for those owners but not socially desirable.

Consider:

  • The flipside of having seniors be able to stay in their homes is that it limits worker mobility by poorly allocating big homes to people who don’t need them. It basically keeps rooms off the market. If you are a senior citizen on a fixed income you are not going to sell the home you’ve outgrown to buy a condo with much higher property tax than the big house you leave behind. And that’s after you pay a huge cap gains bill.
  • Prop 13 starves the state of tax revenue that needs to come from somewhere. So the state income tax can be seen as a wealth transfer from young, working Californians to older, entrenched Californians.

In a state that has seen generational wealth built on a loop of buying real estate, and cash-out refis it’s easy to see how Prop 13 has contributed to the party. Let’s pretend you buy a home in CA and NJ.

Assume:

  • Each home costs $1,000,000
  • Each has a property tax of 2.5%. We are isolating the assessed value effect so need to hold the tax rate constant.
  • Each home has a real (inflation-adjusted) return of 2% per year.
  • The only difference is the CA home is assessed only when you buy it, but the NJ home is assessed each year.

The CA home’s IRR will be .14% after-tax while the NJ home’s IRR is -.52%. The CA home outperformed the NJ home by .66% per year over 30 years. On a $1mm home that’s over $275,000 simply because the NJ home is re-assessed every year.

It gets crazier. The effect actually explodes with higher appreciation rates. If we double the appreciation rate to 4% per year, the CA homes nets you $700,000 more than the NJ home. Remember that the tax rates are the same! We are just isolating the impact of fixing the assessed value at the purchase price.

The main takeaway is Prop 13 is a call option on inflation. Your home is much less of an inflation hedge than you think if its assessed value increases in-step with the market value.

[This year Prop 15 is on the CA ballot. Prop 15 would repeal Prop 13 for commercial properties only. Based on the examples above, it’s obviously something RE investors are highly concerned about.]

Rate Effect

What if you wanted to compare the price of homes in 2 places with different property tax rates? Let’s pretend CA no longer had Prop 13. Like NJ, it’s property taxes were re-assessed annually. This allows us to simply isolate the impact of differing tax rates.

Let’s assume:

  • Each home costs $1,000,000
  • CA tax rate is 1%
  • NJ tax rate is 2.5%.
  • The homes do not appreciate over 30 years (just to keep it simple)

Let’s explore 2 methods of comparison:

The Mortgage Method

If the homes do not appreciate then their assessed value remains fixed at $1mm. This makes it easy — the CA home owes $10,000/yr in taxes and the NJ home owes $25,000. On a monthly basis, the NJ come costs an extra $1,250. If mortgage rates are 3% we can find that a $300,000 30-year mortgage corresponds to a $1,250 monthly payment. So we can say that a $1mm house in CA costs the same as a $700,000 house in NJ since the $700,000 plus an additional $300,000 mortgage would equate to the cost of the CA home.

The IRR Method

The IRR on your home’s value will approximately differ by the spread in the tax rates. In the table below, we see that the CA home returns 1.44% more (close to 1.50%) over 30 years. If we use an inflation rate of 3% to keep consistent with what I chose as a mortgage rate, we find that the NJ home costs you $300,000 more over the 30 year holding period than the CA home, matching the result from the mortgage method.

Combining Effects

To compare the price of a home in CA to a home in NJ you need to account for both the difference in property taxes and how assessed values are treated. Let’s combine the results in one model with more realistic numbers:

  • A 4% annual home appreciation in both markets
  • A 2% inflation rate
  • CA tax rate is 1%
  • NJ tax rate is 2.5%
  • CA assessed values do not increase, NJ is re-assessed annually

CA, due to Prop 13 and a lower property tax rate, has an almost 2% edge in annual return (3.29% vs 1.34%). Since these are nominal returns and inflation is 2% per year we see that the NJ home end up actually losing value in real terms. The fact that the home is re-assessed every year means that even though the home’s value is growing faster than inflation the taxes are also growing very quickly.

I don’t want to have you miss the point — these CA and NJ homes were assumed to grow at the same rate of 4% per year and yet the CA home earned you an extra $900k in present value vs the NJ home. This is strictly due to lower property taxes and Prop 13.

We know that home appreciation in CA has been faster than NJ (my family considered moving to CA in late 70s, early 80s so we are very sensitive to the comparison). The difference in property tax policies has a staggering delta in terminal wealth when applied to CA real estate boom over the past 50 years.

Wrapping Up

Having grown up in NJ and now lived in CA, I have noticed a massive divide in how people have earned their money and wealth. You cannot live here and not notice the wealth built in real estate and not think about how policy has enabled it. When you start comparing apples-to-apples, the headline prices of CA homes are not as relatively expensive as they appear. Don’t hate on Californians though. Those SALT taxes are still burying all of us who still work for a living.

In sum:

  • Prop 13 allows homes to be a call option on home appreciation/inflation
  • High property taxes on homes that are re-assessed require rapid appreciation to not render the home ‘dead money’
  • Compare homes with different property taxes by amortizing the difference in monthly payments into a mortgage

Sending a thanks to @econompic who I discussed these topics with. As another NJ to East Bay transplant he has given these ideas plenty of thought as well. And on the math side, he gave me the idea to use IRRs instead of CAGRs. CAGRs are simpler because they are compounded returns which require no more than a start value, ending value, and time period. They are commonly used when calculating a return for a stock or fund that you buy and hold.

In this case, IRRs or NPVs are preferable since there are many cashflows.

Straddles, Volatility, and Win Rates

One of my favorite follows on #voltwit is @SqueezeMetrics. The account more colloquially known as “the Lemon” has a personal crusade against using implied vol to refer to option prices. Recall, volatility is just the asset’s standard deviation of returns. It’s usually an annualized number. So if the SPX has a 15% volatility that just means you expect the SPX to return +/- 15% about 68% of the time1

“Lemon” prefers using the average expected move, more commonly known as the straddle.

Thus tweeted the Lemon:

I think the convention of turning the straddle price into an annualized standard deviation is obfuscatory. Straddle gives you the average move that’s priced in. Why complicate that?

I can see how the distinction between average move (aka the “straddle”) and standard deviation (aka the “vol”) is “obfuscatory”.

So let’s clear it up.

Expect to learn:

  • The math relationship between the straddle and the volatility
  • How the distinction relates to win rates and expectancy
  • Why the spread between the straddle and volatility can vary in turn altering win rates
  • My own humble opinion on the matter

Turning Volatility Into A Straddle and Vice Versa

A handy formula every novice trader learns is the at-the-money straddle approximation2:

Straddle = .8Sσ√T

where S = stock price
σ = implied volatility
T = time to expiry (in years)

Ok, let’s pretend the SPX is $100, there’s 1 year to expiry, and implied volatility is 15%. Plug and chug and we get a straddle value of $12 or 12%. Pretty straightforward.

Straddle/S = .8σ√T

If we want to simply speak in annualized terms then we can assume T = 1 and can simplify:

Straddle as % of Spot = .8 x σ

Which of course means if you know the annualized straddle price as a percent of spot you can go in reverse to get the volatility:

σ = Straddle as % of Spot x 1.25

When is this useful?

Let’s say based on a stock’s past earnings move you see that it usually moves 5% per day. In other words, the earnings day straddle should be 5%. Then, you can find the standard deviation:

5% x 1.25 or 6.25%

The standard deviation is a volatility which you can annualize to plug into an options model which will spit out a 5% straddle price.

6.25% x 252 = 99.2% vol

Knowing the 1-day implied volatility is useful when you are trying to estimate a term volatility for a longer period that includes the earnings day (topic for another time).

What’s the practical difference between straddles and volatility?

Volatility is a number you stick into a model to generate a price for an instrument you actually trade. In this case, a straddle. If you input 15% vol into our above example, you will find that a 1-year straddle will cost you 12% of spot.

If you buy this straddle your return is equal to:

Absolute value of SPX return – 12%

Your worst case scenario is the SPX is unchanged and you lose your entire 12% premium. You are “long volatility” in that you want the SPX to move big one way or another.

So let’s talk about what we really care about — expectancy and win rates.

Expectancy

The point of the model is to generate a price that is fair for a given volatility. 12% was the fair theoretical value for a 15% vol asset.

If you pay 12% for the straddle on a 15% vol asset you have zero expectancy.

But that’s not the whole story.

Win Rates

Expectancy and win rate are not the same. Remember that the most you can lose is 12% but since there is no upper bound on the stock, your win is theoretically infinite. So the expectancy of the straddle is balanced by the odds of it paying off. You should expect to lose more often than you win for your expectancy to be zero since your wins are larger than your losses.

So how often do you theoretically win?

A fairly priced straddle quoted as percent of spot costs 80% of the volatility. We know that a 1- standard deviation range encompasses about 68% of a distribution. How about a .8 standard deviation range?

Fire up excel. NORMDIST(.8,0,1,True) for a cumulative distribution function. You get 78.8% which means 21.2% of the time the SPX goes up more than .8 standard deviations. Double that because there are 2 tails and voila…you win about 42% of the time.

So in Black-Scholes world, if you buy a straddle for correctly priced vol your expectancy is zero, but you expect to lose 58% of the time!

Outside Of Black-Scholes World

The Black Scholes model assumes asset prices follow a lognormal distribution. This leads to compounded or logreturns that are normally distributed. This is the world in which the straddle as percentage of spot is 80% of the annualized volatility.

In that world, you lose when you buy a fairly priced straddle 58% of the time. Of course fairly priced means your expectancy is zero. What happens if we change the distribution?

I’m going to borrow an example of a binary distribution from my election straddle post:

  • 90% of the time the SPX goes up 5.55%
  • 10% of the time the SPX goes down 50%

    Expected move size = 90% x 5.55% + 10% x 50% = 10%

Expected move is the same as a straddle. The straddle is worth 10% of spot. Your expectancy from owning it is 0.

If this was Black-Scholes world, we would say the volatility is 1.25 x 10% = 12.5% (not annualized). But this is not Black Scholes world. This is a binary distribution not a lognormal one. What is the standard deviation of this binary asset?

We can compute the standard deviation just as we do it for coin tosses or dice throwing.

σ= √(.9 x .05552 + .1 x .502)

σ = 16.7% (again, not annualized so we can compare)

Note that your straddle is 10% but your volatility is 16.7%. That ratio is not the 80% we saw in the lognormal world, but instead it is 60%.

Note you cannot repeat the earlier process to find the win rate. You can’t just NORMDIST(.6,0,1,True) because the distribution of returns is not normal. Luckily, with a binary distribution our win rate is easy to see. In this example, if you pay 10% for the straddle you lose 90% of the time.

Even if you paid 6% for the straddle you still lose 90% of the time. However if you bought the straddle that ‘cheap’, your expectancy will be massively positive!

My Own Humble Opinion

When there is a short time to expiration, arbitrarily let’s say a few weeks, my mind’s intuition might latch on to a straddle price. I might think in terms of expected move as one does for earnings in getting a feel for what is the right price. But on longer time frames I prefer to think of implied vol because I am going to be dynamically hedging. Measures of realized vol can be readily compared with implied vol.

If I look at a straddle price for a long period of time, say 1 year, I might fall into a trap thinking “20%? That just sounds high.” I’d rather just compare the implied vol which would be 25% (remember 1.25 x straddle), to realized vol since I am interested in the expectancy of the trades, not the win-rate.

There are all kinds of house of mirrors when looking at vols and straddles and thinking about winning percentages. As Lemon says, it’s “obfuscatory”. Everyone should do what works for them.

If you tend to be long vol, be aware having more losing months than winning months might be completely normal. It’s baked into the math. And the more skewed the distribution, the worse your batting average will be.

But in the long run it’s your slugging percentage that matters.

Recap

  • Straddles as a percent of spot are 80% of the volatility (all annualized)
  • Straddles tell you the average move.
  • Fair straddles have zero expectancy.
  • You lose more often when you win when you are long a straddle.
  • Your win sizes are larger than your losses.
  • Skewed distributions change the relationship between win rates and expectancy. They also change the relationship between straddle prices and standard deviations.

The Curse of the Reserve Currency

I’m familiar with the US dollar as the world’s reserve currency through a conventional lens. As a deliberate bargain between the US and the rest of the world.

It goes something like this:

The US enjoys a stable currency effectively lowering her cost of capital. In exchange, US Naval might enforces order on maritime trade routes. The safety of shipping lanes is a global good lifting all economies through the efficiencies of comparative advantage and arbitrage. This global good would be difficult to coordinate without a single cop like the US so the world accepts this bargain as reasonably fair even if it might nitpick aspects of it.

If you are a just being introduced to this idea you can see my notes on:

I recently read a different perspective on this global arrangement. In this alternative view, the status quo was not an explicit or even implicit deal between the US and the rest of the world but an emergent phenomenon. The distinction is important because the force that maintains it is not international diplomacy shaped by national interests. Instead, it is simply the position at which the equilibrium is at rest according to economic gravity. The invisible hand working bottom-up not authority working top-down.

Yakov Feygin and Dominik Leusder explain:

The dollar system evolved not as a tool of imperial statecraft, but as the project of a transnational elite that has effectively usurped control of an international public good.

Frameworks for understanding the persistence of the dollar system tend to vary from from reductionist to outdated, often examining international politics with discrete nation states as the main unit of analysis. In this view, the dollar is a product of hegemonic US interests, wielded as a tool of statecraft. But global financialization has upended this framework: elite interests are not aggregated domestically but internationally, and are transmitted via the balance-of-payments mechanism and the financial system…Herman Mark Schwartz, one of the foremost experts on the dollar and American hegemony, offers a better way to think about the dollar—namely, as the state money of a quasi-imperial global system, in which the different economic regions are tied together by a shared reserve currency. This ‘imperial currency’ is more of a by-product, and less of an enabler of (or even an enabling constraint on) American expansionism and military adventurism, both of which preceded the reserve currency status of the dollar.

In this version of world order, the status quo is not actually to any nation’s benefit but to a political and economic class whose interests transcend sovereign borders. This leads to a counterintuitive conclusion:

to the extent that the world has prospered since Bretton Woods, it is in spite of, not due to, the USD being the reserve currency.

The full case is laid out in The Class Politics Of The Dollar System (Link)


My Selected Excerpts And Notes

The Soft Power Of Issuing The Reserve Currency

Two clear geopolitical advantages accrue to the US because of its reserve currency status:

  • Sanctions

  • Dollar liquidity swap lines

The source of the Federal Reserve’s power over the eurodollar system—and the vulnerability of emerging markets within it—is the global reliance on central bank backstopping. In the 2008-9 crisis, the Fed deployed so-called central bank liquidity swap lines to backstop the global system. These took the form of reciprocal currency arrangements between central banks: The Fed replenished the dollar reserves of other central banks in exchange for local currency. The real power of the swap lines is not who gets them but rather who doesn’t. In a recent piece for the Nation, Andres Arauz and David Adler highlight how these swap lines can be used for a form of monetary triage, in which the United States decides which countries have better prospects for weathering economic storms.

Questioning the Narrative

Despite the advantages, dollar eminence should not be a goal. The long-run cost outweighs the near-term benefit.

Dollar primacy feeds a growing American trade deficit that shifts the country’s economy toward the accumulation of rents rather than the growth of productivity. This has contributed to a falling labor and capital share of income, and to the ballooning cost of services such as education, medical care, and rental housing. With sicknesses like these, can we say for certain that the reserve currency confers substantial benefits to the country that provides liquidity and benchmark assets denominated in that currency?

How The Plumbing Works

Offshore dollar pools depend on the liquidity of treasuries and near substitutes as collateral to raise cash in the event of a margin call.

The reason for these dollar pools is twofold. First is the need to fund trade. The Eurodollar system facilitates trading relationships between countries with different currencies by giving them access to a common stable currency in which to denominate trade—the dollar. Dollar credit allows the execution of contracts without actual, US-issued currency being exchanged. Instead, the system functions as an exchange of IOUs to deliver receipts at various periods of time.

Because 80% of trade in emerging market economies is denominated in dollars, firms with receipts in a domestic currency acquire unsustainable debt in dollars if the domestic currency falls. For this reason, central banks attempt to stockpile dollar assets, most commonly US debt. To acquire them, they usually run a persistent trade surplus by repressing the real wages of their workers. (I need more clarification on this point)

This might be sustainable in the short run, but in the long run, it leads to periods of economic stagnation, or international trade and currency wars.

The second driver of these offshore dollar pools is wealth inequality and outsized corporate returns. Large corporations, pension funds, and extremely wealthy individuals cannot bank their money in the retail banking system. Instead, they hold them in pools of dollar liquid denominated assets that can be converted into dollars quickly. While this ‘shadow banking’ system has legitimate uses, it also facilitates tax evasion and kleptocratic corruption.

The dollar system thus facilitates and fuels the power of elites who have an interest in maintaining the status quo. A globalized system with a dominant key currency aids the accumulation of rents at the expense of higher consumption from workers in exporter countries and the hoarding of those rents in the legal black hole of offshore finance.

Zooming In: How It Hurts The US

  • Financial “Dutch Disease”

    Talent or ample resources have a downside. Some might even say a curse. It can make you lazy or overly reliant on your intrinsic advantage. Here’s the idea applied to USD dominance.

    Demand for high quality dollar-denominated assets saddles the United States with a financial ‘Dutch Disease’; a situation in which the reliance on exporting a single commodity raises the exchange rate and thus squeezes out the production of tradeable, value-added goods in favor of services and financial rents….Dutch diseased economies often result in a shrinking, narrow elite whose power rests on income from sales of the single commodity, or the services and management that bloom around the cash flows generated by this commodity. For the United States, this single commodity just happens to be the dollar.

  • The evidence

    The most visible cost of the disease is the steady appreciation of the dollar since the 1980s, despite a falling US share of global gross domestic product. The main domestic symptom has been the rising costs of non-tradable goods—such as medicine, real estate rents, and education—over tradable goods. This disconnect is at least in part responsible for the country’s low rate of inflation, falling wage share, and increased economic insecurity despite access to a wider range of consumer goods. While the American consumer can now purchase an ever-expanding set of appliances, electronics, and small luxuries, services that are necessary for economic mobility and household sustainability are increasingly out of reach.

  • MMT as full blown financial Dutch disease

    Justin Czyzsczewski writes:

    In the MMT view, there is no recourse against a government going off the rails. Some developing countries are said to suffer from a “resource curse“, when an abundance of natural resources means the government doesn’t rely on taxes, and so becomes unresponsive to the wants and needs of the populace. In the past, kings with powerful armies ruled in the same way. There is a very real risk of the same phenomenon when government spending becomes untethered from taxation.

Zooming In: How It Hurts Developing Nations

  • The need to hoard dollars crowds out productive domestic investment

    For the rest of the world, the ills are clear enough. In developing countries, the need to insure their economies against currency crises and debt deflation has meant the accumulation of dollars at the expense of necessary domestic investment. These policies are usually accompanied by a suppression of consumption and incomes to establish a permanent trade surplus vis-à-vis the dollar system.

  • Dollar liquidity lowers the cost of corruption

    The dollar system allows corrupt elites to safely transport their ill-gotten earnings to global banking centers located in jurisdictions with opaque ownership laws.

While the dollar system has undoubtedly had a disproportionately negative effect on developing countries, the main fault lines that emerge from the dollar system are along class, rather than national lines.

In other words, a rich Chinese national has more in common with the US elite than their fellow citizens.

Obstacles and Remedy

  • Elites’ preference for status quo

    Developed world exporters like Japan and Germany also maintain a growth model based on cost competitiveness and wage suppression. An increased role for the Euro or the Yen would undercut these models. For resource exporters, it facilitates corruption and tax evasion through simple capital flows. In the United States, it benefits financial industry elites, who can reap the rewards from intermediating capital inflows into US markets, while the cost of non-tradable services like tuition, healthcare and real estate rises for everyone else. Across all countries, elites win.
  • Reducing Inequality

    Too great a share of the national income is in the hands of high-saving entities with dollar liquidity preferences, such as high net worth individuals and large corporations. To reverse this imbalance, income would have to be transferred from these powerful interests to China’s workers—a dynamic described by Albert Hirschman as early as 1958.

The fact that the dollar system is primarily based on social, rather than geopolitical conflict means that the best solutions suggest at a reform of the system in a manner that empowers people at the bottom of the global social hierarchy.

Binary Straddle Example Based On The 2016 Election

This is a dramatization loosely based on the 2016 election.

It may be hard to remember, but leading up to the election the market would sell-off when Trump’s odds increased and vice versa. So let’s make some assumptions.

  • It’s the morning of the election, the SPX index is trading for $100 and the election day straddle is trading for $10.
  • If Donald Trump wins the SPX goes down. If he loses the SPX goes up.
  • The SPX price is completely binary. It will go to either an “up price” or a “down price”.
  • Trump is liquidly trading at 10 cents on the dollar to win the electoral college in betting markets.

If Trump wins the election where does the SPX go?

[This section is blank for your algebra]

If you felt lazy here’s my work:

  • The expected value of the 1 day change in SPX is 0. It’s fairly priced at $100.
  • The probability of the SPX going down is 10% since that’s Trump’s implied probability of winning.

    For both of these statements to be true in a binary situation we know the expected down move which occurs 10% of the time is 9x the expected up move when Trump loses.

    P(up) Stock_up + [1-P(up)] x Stock_down = 0
    .9 x Stock_up + .10 x Stock_down = 0
    .9 x Stock_up = – .10 x Stock_down
    Stock_down / Stock_up = -9 / 1

  • Now let’s bring in the straddle.

    The straddle is trading $10 or 10% of spot. The straddle is the expected absolute value of the change in the SPX.

    P(up) x Size_up + [1-P(up)] x Size_down = Straddle
    .90 x Size_up + .10 x Size_down = 10

    Using the substitution that Size_down = 9 x Size_up:
    .9 x Size_up + .1 (9 x Size_up) = 10
    1.8(Size_up) = 10

    Size_up = $5.55
    So Size_down which is 9x Size _up must be $50

If Trump has a 10% chance to win the election tanking the market AND the straddle is worth $10 then the market was expected to rally 5.55% if he lost. If he won the implied sell-off was 50%!

If that didn’t sound reasonable to you (but you were certain the event was a true binary) then there are relative bets to be made between vertical spreads, outright straddles and election odds depending on what you disagreed with.

To recap:

The exercise here was to turn a binary event with

a) an implied probability

and

b) a straddle

into an implied up and implied down price after the election.

Formulas you can remember based on the above algebra:
Up Move Magnitude = straddle / (2 x P(up))
Down Move Magnitude = Up Move x P(up)/P(down)


A little post-script based on my memory of 2016. At the beginning of the year, there were giant buyers of gold and upside call verticals in gold. Whispers were that it was Drunkenmiller and perhaps a few other macro whales. Well, whoever was buying these call spreads was spot on. Gold had a sharp rally in Q1 of 2016 before settling in somewhere like up 20% in the first half of 2016. A big move for a sub-15% vol asset.

Fast forward to election night. The futures markets were unhinged. In the peak of panic over Trump winning, the SPX was down nearly 10% while gold spiked higher. By the light of the following morning, the market had whipsawed from those points and Drunkenmiller or whoever was leaving footprints in gold had allegedly used the election night headfake to rebalance the long gold position on the highs into an SPX position on the lows.

The 10% straddle seemed to be well-priced, but somehow the GOAT macro trader realized the sign of the Trump move was exactly backward!


Some broker chatter I loosely recall after the election:

Banks that were long Nikkei variance hedged with short US variance allegedly crushed it that night as the Nikkei observation for the variance calc was down over 5% while the US point-to-point return was little changed despite the hellacious path. The Japanese markets closed in the middle of the US night when SPX was at its lows.

There are a number of exotics and bank traders who read this so maybe one of them will fill me in on the color or veracity of that 🙂

Marketing Yourself

Financial careerists will find useful ideas in this Shawn Wang post which likely had developers and designers in mind:

How To Market Yourself Without Being A Celebrity (Link)

In fact, if the thought of “marketing yourself” offends you then you are exactly the person who needs to read it. Some of you reading this are crushing it and don’t think you need to self-market. But consider another perspective. A public-facing body of work is an invitation for others to engage. This is an obvious benefit to ladder-climbers. But even if you are satisfied with your career arc, building this outward invitation will be rewarding. It can lead to collaborating on passion projects or causes, it can reduce your cost to hire, and it leads to more credible introductions into domains you are interested in. Domains where you are just a beginner. You are transmuting your prior track record into more general mana.

The entire essay is filled with useful strategies and specific tips down to the tradeoffs of platforms.

Some sections I especially liked:

  1. Personal branding strategies

    Anything but average: I identify as a “Basic Bro” – I have my PS4, and Nintendo Switch, I like Marvel movies and watch the same Netflix shows you watch. Just like the million other Basic Bros like me. Totally basic. Totally boring. NOT a personal brand. In fact anything not “average” is a good candidate for inclusion…

    Identity + Opinions: [Shawn gives examples] I really want to give you more hints on this, but I’m afraid if I gave more examples I might limit your imagination.

  2. Marketing Yourself In Public

    Don’t Lie: Stephen Covey calls this the Speed of Trust. Once you lose trust, everything you say gets run against a suspicion check, and you have to put up more proof points to be taken seriously.

    Don’t share secrets: I always think about Christopher Lee, who fought in the British Special Forces in World War 2 before his legendary acting career. When pried for information about what he did in the War, he would say: “Can you keep a secret? Well, so can I.”

    Inbound vs Outbound Personal Marketing: Borrowing from Hubspot’s Inbound marketing and Seth Godin’s Permission marketing. Outbound Personal Marketing is what most people do what they look for jobs – only when they need it, and trawling through reams of job listings and putting their CV in the pile with everyone else. Inbound Personal Marketing is what you’ll end up doing if you do everything here right – people (prospective bosses and coworkers, not recruiters) knowing your work and your interests, and hitting you up on exactly the things you love to do.

    Market Like Nobody’s Watching: Because normal comfort zones are not set up to market yourself, you should try to do a little more than you’re comfortable with. An aggressive form of this advice? If you’re not getting complaints about how you’re showing up everywhere, you’re not doing it enough. This makes sense to some people, and is way too upfront and annoying for others. We all have to find our balance – it’s your name on the line after all.

    Market Like One Person’s Watching: Marketing is more effective when it is targeted at a specific someone instead of just everyone…

    Market for the Job You Want: This is a variant of “Careful what you wish for… You just might get it.”

DCF As A Lower Bound

Sunblock stock (SUN) makes 10% in a sunny year. Loses 2% in a rainy year.

Umbrella stock (RAIN) loses 2% in a sunny year. Makes 2% in a rainy year.

Assume:

  • The year is 50% to be sunny.
  • The risk-free rate is 0%

A few things to think about

  1. SUN has a higher expected return and Sharpe than RAIN
  2. We can see the stocks have -1 correlation
  3. There is an arbitrage. You can put 50% into each stock and earn 4% in sunny years and 0% in rainy years for an EV of +2% on the portfolio

What can we expect?

The market prices of these stocks will adjust.

Let’s keep it simple and presume:

  1.  SUN’s price stays constant. Its returns characteristics are unchanged.
  2. RAIN’s price is to be bid up so it returns only 1% in a rainy year and loses 3% in a sunny year. Note that RAIN’s expected value is now -1% per year instead of zero.

Why would the market bid that much?

This is the subject of my latest post, You Don’t See The Whole Picture. (Link)

Expect to find:

  • A simple math example to show how the diversification benefits of an asset can benefit a portfolio EVEN if the asset has a negative expected return
  • Examples from the market-making and option trading worlds which describe the “supply chain of edge”. When you see prices that don’t make sense it’s possible you don’t see the info embedded in a higher link in the chain. Whether that’s due to analytical or structural limitations, incentives, or something else is a question you need to consider.

Some Musings I Left Out 

If I felt comfortable larping as an actual businessperson I might have included a few more thoughts in the post:

ComplementsFB can pay up for WhatsApp because they are the most efficient buyer. So the price to a bystander, who can’t see Zuckerburg’s dashboard, looks insane. And in fact, in isolation, the price might be insane. But to the party where its value is highest, it can be a bargain.

Disney paid $4b to buy Star Wars rights. It was a win/win for Lucas and Mickey. The synergies lower the effective price.

Substitutes

Sometimes tech giants scoop up small firms as acqui-hires or to leap-frog R&D time/cost. But I imagine sometimes it’s just defense. Kill Simba before he grows up to inherit the Sahara. Once again, the price looks high in isolation but this “strategic buying” is informed by a wider context.

A Lower Bound

The stand-alone value of a business is the intrinsic value of a call option. But, there is a non-zero chance that some combination makes the asset worth even more. An excessive price is a mix of intrinsic and extrinsic. Going further, is it possible the extrinsic premium increases in proportion to connectivity?

Louis Pasteur wasn’t doing R&D at chocolate chip cookie company, but he would have been paid more at a Nabisco than at his local French universities. But they need to find each other.

In a connected world, awash in capital, the DCF of any business in isolation might be just where the bidding starts.


The most practical implication of these ideas is that you are not paid for diversifiable risks, so you incinerate theoretical money when you don’t diversify. This is true regardless of your actual investment performance.

The Diversification Imperative is a reminder of the only free lunch in investing. (Link)

You Don’t See The Whole Picture

Overpriced Or Just Overpriced In Isolation

☀️Sunblock stock (SUN) makes 10% in sunny year. Loses 2% in rainy year.

☂️Umbrella stock (RAIN) loses 2% in sunny year. Makes 2% in rainy year.

Assume:

  • The year is 50% to be sunny.
  • The risk free rate is 0

A few things to think about:

  1. SUN has a higher expected return and Sharpe than RAIN
  2. We can see the stocks have -1 correlation
  3. There is an arbitrage. You can put 50% into each stock and earn 4% in sunny years and 0% in rainy years for an EV of +2% on the portfolio

What can we expect?

The market prices of these stocks will adjust to there is no arb.

Let’s keep it simple and presume:

  1.  SUN’s price stays constant so its returns characteristics are unchanged.
  2. RAIN’s price is to be bid up so it returns only 1% in a rainy year and loses 3% in a sunny year. Note that RAIN’s expected value is now -1% per year instead of zero.
Why would the market bid that much?

Because there’s still an arb.

You could put 30% of the portfolio into SUN and 70% in RAIN and still earn 50 bps per year with NO risk (remember RFR is 0%)!

What can we generalize?
  • A low or neg correlated asset, even one with a negative expected return, can improve a portfolio.
  • Assets can look appear overpriced in isolation, yet their price is more than justifiable.

When You Don’t Understand The Price You Don’t Understand The Picture

Price is set by the buyer best equipped to underwrite the risk.

If you weren’t willing to bid RAIN up you can bet SUN would have.

This leads to 2 important warnings.

1. You must diversify

Financial theory dictates that you do not get paid for diversifiable risks. To be blunt, you are incinerating money if you don’t diversify. The SUN/RAIN example can show how you would expect to lose money in RAIN in isolation because the market is priced assuming you could buy SUN. I cover this idea more in The Diversification Imperative.

2. You might be a tourist

It’s worth asking yourself, does X look overpriced because I have the wrong perspective? You are looking at RAIN but don’t see what the SUN investor sees.

A Market-Maker Example

If X is willing to pay me a high looking price for a stock or option, what’s the probability they are selling something else to someone else such that they are happy to pay me the “high” price?

Let’s say a call overwriter sees a modest surge in implied vol and is happy to collect some extra premium. Except he’s selling calls to a Citadel market-maker who’s happy to pay the “high” price because her desk is selling index vol. In fact, they are selling index implied correlation at 110%. You might be happy selling the calls for 2% when they are usually worth 1%, but if the person buying them from you knows they are worth 3% at the time you sold them then make no mistake, you are playing a losing game.

However, if your professional edge is in deeply understanding the stock you are selling calls on, then you might be the one capturing the edge in the expensive calls. You are capturing it ultimately from the fact that index volatility is ripping higher and market makers are simply capturing the margin between the weighted option prices of the single stock in proportion to the index volatility. So you, the informed single stock manager, is making edge against the index volatility buyer who set off the chain of events.

The decomposition of the edge between you and the market maker is unclear. But the lesson is you must know where you stand in the pecking order. When a market maker is asked why they are buying Stock A for $100 they respond “because I can sell Stock Z at $110”. There’s always a relative value reason. The more you internalize the SUN/RAIN example and how correlation relates to diversification the more natural this reasoning becomes.

Another example

Let’s consider another option relative value trade.  If volatility surges in A but not in B and they are tightly correlated let’s look at how 2 different market participants might react.

Naive

The naive investor isn’t aware of what is not monitoring the universe of names. They do not think cross-sectionally. They see a surge in A and decide to sell it. It may or may not work out. It’s a risky trade with commensurate reward potential.

Sophisticated

The sophisticated trader recognizes they can sell A and buy B whose option prices are still stale (perhaps there has been a systematic seller in B who has been price insensitive. Maybe from the same class of investor our friend “naive” came from. They don’t look at the market broadly and realize the thing they are selling is starting to “stick out” as cheap to all the sharps).

Here’s the key: the sophisticated trader will do the same trade as the naive one but by hedging the vol with B, they can do the whole package bigger than if they simply sold A naked.

The sophisticated traders are the ones who see lots of flow. They “know where everything is”. While in this example, sophisticated and naive both sold A there will be times when sophisticated is lifting naive’s offer. Sophisticated has sorted the entire market and is optimizing buys and sells cross-sectionally.

Are you the fish at the table?

Flow traders and market makers are always wondering if their counterparty is legging a portfolio that they’d like to leg themselves if they saw the whole picture.

Sometimes it’s not possible because of structural reasons. For example, the risk that banks exhaust from structured product issuance or facilitating commodity hedges for corporations originates from a relationship nobody else can access.

A bank charter means some captive audiences. But that exhaust risk is recycled through the market much like a good flows through a vertical supply chain from wholesaler to retailer, with a markup being tacked on incrementally until its sold to a Robinhood client.

The markups are not explicitly in dollars but in the currency that lubricates financial markets — risk/reward. Mathematical expectancy, like a house’s edge, is priced by its most efficient holder.

If prices are always being set by the party who most efficiently underwrites/hedges/prices the risk and you know you are not one of those parties then you should wonder…

am I being arbed?

Lessons From The Layup – Corner 3 Spread

During an interview with Ted Seides, investor Andrew Tsai recounts an internship at the well-known trading firm Susquehanna in the mid-90s (disclosure: I worked there for 8 years after college). In particular, he remembers a company outing to a dog track that summer:

I’m sitting next to one of the partners and I’m looking at the sheet of all the races, and he’s like “How are you gonna bet?” I respond, “Well, I’ve never really done this before but this dog looks like he’s got a good track record and he’s been running strong lately.”

The guy looked at me like I was a complete idiot.

He’s like, “What are you talking about, ‘How is this dog doing?'”

Andrew is perplexed. Well, isn’t that kind of what we’re talking about.

The partner starts to explain, Look at the relative value of this dog and that dog.

The lightbulb went on for Andrew.

“We started talking about spread trading and trying to capture that basis and I’m like ‘These are my guys’. It was really this culture of dissection that I loved.”

Relative Value Goggles

One of my favorite Twitter follows is the anonymous account @econompic. He’s in my top 5 and you should follow him too (only about 15% of my followers follow him which is basically as stupid as a butterfly trading for a credit). Go for the finance stuff and stay for takes on breakfast cereal, Weezer, and the NBA. Oh and the polls. You see, Jake’s polls act like the Susquehanna partner while Andrew is the rest of #fintwit. They are cleverly designed to surface mispricings in how people think about risk or relative value.

His relative value instincts are well-tuned. It’s like he has goggles that allow him to filter the world through prices. It’s a lens that’s critical for trading. One of his recent tweets is a great example of this. I’ll withhold the full tweet for now since it has spoilers. Let’s start with this screenshot:

So which shot do you take?

(take note of your answer and reasoning before continuing)

Spread Perception

The first thing that should leap off the screen is the gap between the free throw and the top-of-the-key 3. Using NBA dimensions, that’s a 15′ shot vs a 23’9″ shot. And you are rewarded 5X for it from the benevolent genie offering this bet. The reflex you need to hone is that:

Prices imply probabilities

Why?

Because of expected value. Expected value is the probability of payoff times its magnitude. Would you pay Best Buy $50/yr to insure a $1,000 TV? If there’s more than a 5% chance that it fails you might. If there was a $500 deductible then the benefit is cut by half and you need to think there’s at least a 10% chance the TV fails. And if you think you get more TV per buck every year thanks to innovation then purchasing insurance implies an even greater defect rate.

So when you weigh the cost of different choices (insure vs not insure, fix vs replace, cheaper product vs more durable product) you are implicitly weighing probabilities. Making that explicit can expose mispricings.

Let’s go back to basketball.
Dissecting the basketball shot.

Just to get a hang for the reasoning let’s start with a simplifying assumption. You are 100% to make the layup.

  • Free Throws
    How confident do you need to be from the free-throw line to forgo the certain $50,000 you’d make from a layup? At least 50% confident. If you can shoot a free throw with a better percentage than a coin flip the free throw “has more equity”. If you are a 60% free throw shooter than that option is worth $60,000.
  • Top-of-the-key 3
    $500k to make this shot. You only need to be 10% confident to justify forgoing the layup for a chance at some big money.

    Ok, here is where the probabilities should really get your senses tingling. The free throw implies a 50% probability and the top-of-the-key 3 implies 10%. Are you 5x more likely to make a free throw than this 3-pointer?

    Unless you are 7 and literally can’t heave a ball from the 3-point line, it’s hard to imagine your chance of making these shots to be so far apart. In fact, if the 7-year-old can’t reach the rim at all from long range, I have my doubts they can shoot consistently shoot 50% from the stripe in the first place. But I’m willing to concede that possibility. For an adult, that spread is too wide. You either can’t hit free throws with a .500 percentage or your chance of making a top-of-the-key 3 is greater than 10%.

    To take an outside view, consider NBA players. Guys who shoot about 40% in games, can shoot between 65-75% in practice. HS coaches can tell you that a 30% 3-pt shooter can make about half their shots in practice. Since free throw percentages are bounded by 100% you are talking about no more than a spread of 2x between free throw and 3-pt percentage. Your margin of error on the spread could be 100% and you’d still only have a spread of 4x. These shots are priced at 5x!

    An exactly 50% free throw shooter be a 12.5% 3-point-shooter using the most conservative estimates and this top-of-the key 3 is still “too cheap”. And remember, there is a conditional probability aspect to this since we are dealing in relative pricing. If you are certain you need a miracle to hit an uncontested 3-pointer there is almost no chance you are truly a 50% free throw shooter.

  • The rest of the table

To amateurs the corner-3, without a view of the backboard or the chance for a lucky bank shot, is daunting. But are you really half as likely to hit a corner-3 vs the key-3? As we get into the low probability shots it’s reasonable for a person who really knows their habits to potentially parse these odds but it takes quite a bit of experience to know that you are really 100% better at top-of-the-key 3s then corner 3s. Without that conviction, I’d take the better implied odds in the corner-3.

The entire payoff schedule suggests that you should either take a layup or a corner 3 as you are being offered very cheap relative pricing on those options. You can check out the rest of the tweet for the comments and replies. (Link)

What If You’re Broke?

If you read the thread there’s mention about how being broke can push you towards the layup even if the expected value of another choice is higher. This is a great opportunity to bring ideas like “risk aversion” or “diminishing marginal utility of wealth” into practical consideration.

The expected value framework above is an optimal case. It assumes every dollar has equivalent value to the player. The fancy term for this is “risk neutral”. If you have $5,000 and making another $5,000 has a “happiness value” that is equal and opposite to the “sadness value” that you experience if you lose $5,000 then you are risk-neutral. Since you are not a robot and need to eat, you are not risk-neutral. You would not bet all your money on a 50/50 coin flip. And you probably wouldn’t do it if you had a 60% of winning the flip. You are “risk-averse”.

A related concept is the diminishing value of additional wealth. This is pretty obvious. Jeff Bezos’ first million probably felt good. Today, it would be an imperceptible amount on his Mint dashboard.

Without knowing the lingo we all understand the intuition. If you are a broke college kid you might always opt for the layup. A sure $50k might mean getting out from under that 15% credit card APR, while $100k is ‘nice to have’, not ‘need to have’. That first $50k can be life-changing by getting you off the wrong path.

Likewise, the rich gal with a vacation house in Malibu is not so constrained. She can rely on the optimal pure expected value prescription. Just as a trading firm with a huge bankroll is willing to bet large sums on small edges. They will optimize for EV when the bet sizes are small relative to capital.

Our intuition moves us in the right direction. It tells us that the college student will be more conservative in choosing which shot to take. By mixing in a simple concept like “utility of wealth”, we can actually re-price all the probabilities implied by the shot payoffs.

Adjusting Probabilities For Risk Aversion

Linear vs Concave Utility

  • Risk-neutral utility curves are linear.
    If you are the risk-neutral robot every dollar you make is worth exactly the same to you. Your second million is as sweet as the first. That’s a linear utility function. Those are the curves embedded in any expected value proposition which simply spits out “pick the highest one”. I presumed such a framework in the prior table that said: “Min Probability To Accept Shot”.
  • Risk-averse utility curves are concave
    If you are risk-averse, every additional dollar is not worth quite as much as the one before it. And every extra dollar you lose hurts just a tad more than the one before it. Losing your rent money hurts more than losing your Ferrari money. So instead of a linear function, we need a function that:

    1. Is always increasing to reflect that more money is always better than less money (‘Mo Problems and other first-world complaints notwithstanding).

    2. Slope starts out faster than the linear model then flattens as we make more money.

    Luckily, there is a simple function that does exactly that. The log or natural log function. People who study “risk-aversion” and diminishing marginal utility of wealth don’t think about it linearly. They don’t presume $5,000,000 is twice as “useful” as $2,500,000. They might say it’s only 1.75 as “useful” ( ln 5 / ln 2.5 = 1.75).

    Visually,

Re-computing Minimum Probabilities As A Function Of Starting Wealth

  • 25 year old with $10,000 to his name.
    The guaranteed layup increases his wealth by 6x and log wealth by 2.8x.
    The free throw increases his wealth by 11x but his log wealth by only 3.4x!

    Look how much it raises the minimum probabilities for him to accept various shots if he has a log wealth utility preference. He needs to shoot 3s as well as a good [contested] NBA shooter to gamble on the big money instead of the layup!

  • Give that guy a $10,000,000 bank account, and he’ll choose according to Spock-like expected value prescriptions.
  • Finally, check out the implied minimum shot probabilities for various levels of wealth. The larger your bankroll the more you can rely on probabilities imputed simply by expected value. If you are fabulously rich, you aren’t paying up for life insurance, home insurance, and so forth. You’ll deal with those bills as they come. For most of us, calamities mean financial ruin.
    How we decide depends not just on the expected value but on our own situations. The more secure we are (on the flatter section of the log wealth curve) the more we can afford to act optimally.

    (There is quite a bit of fuel for liberal policymakers here. They will realize that this is another example of Matthew effect or accumulated advantage. Richer people can avoid negative EV trades like insurance. Another thought. The inflection point on the so-called Laffer curve is probably much further to the right if we re-scale the axis in terms of log wealth suggesting we may tolerate much steeper graduated tax brackets. I’m not making a political opinion so don’t @ me. I’m just observing things that I’m sure have been discussed elsewhere.)

Conclusion

Prices impute probabilities. By taking the extra effort to make this explicit we can de-fog our relative value goggles. This improves our decision making in trading and life.

Since we are not “risk-neutral” robots the correct decisions are often theoretical. Translating the prescription to your own situation is an extra step that we typically leave to our intuition. This is quite reasonable. At the end of the day, we aren’t going to define our own wealth functions in Excel (log wealth is just one example of a non-linear function that seems to accommodate our intuition but the actual slopes and smoothness can vary quite a bit from person to person).

I recommend following Jake. His polls will help you tune your intuition.

Thinking Like A Trader

Robin Hogarth would call investing a “wicked” learning environment. Information is hidden in such a way that we struggle to identify causality. I contrast investing a bit with trading and games which are fertile ground for reasoning, probability, and logic. With large enough samples, you get tighter feedback loops, a critical input to learning. I don’t know much about digital marketing or Google AdSense but my guess is market-making has more in common with SEO than it has with buy-and-hold investing.

Because of my interest in topics like learning, reasoning, and money matters, I sometimes have younger readers ask me how to “think like a trader”. I’ve pointed to some places in the past.

  • A few months ago I shared the books I’ve crowdsourced from traders: The Investing Pros Library (Link)
  • I’ve narrowed a list to target beginners in particular. (Link)
  • A collection of resources to teach kids business. (Link)

While these are all useful, the single best way to adopt a trader mindset is to do what Annie Duke recommends:

Think in bets.

Betting is really about decision-making.

Every decision you make is actually a bet that the chosen action is better than all the alternative options. Annie’s recent book Thinking In Bets is about making better decisions when you don’t have complete information. Making better decisions is so obviously important living a happy life it feels silly to even state that. Naval Ravikant says that good judgment is the most important attribute of anyone with a high leverage position like a CEO. Or the director of NIAID. If the impact of a decision is levered 10x, then a 1% better decision is an order of magnitude more valuable than the inferior one.

We spend years learning formal grammar or cherry-picked history yet most of our decision-making skills come from trial-and-error. In a complicated world where causality is opaque and noise is abundant, it’s simply too easy to learn the wrong lessons. Look around. The post-hoc fallacy is everywhere. “Since event Y followed event X, event Y must have been caused by event X.” You took an herb and your cold went away. Must have been the herb. You played video games when you were a kid, and now you have a good job. I guess Halo was good job training. There are many outcomes that people say are attributable to X when it could be even more likely that the outcome was in spite of X. Your reason for something could be the exact opposite and you don’t even realize it.

Michael Mauboussin, during a 2019 talk, said:

The best probabilistic decision-makers have more in common with each other than with the average decision-maker in their profession…Warren Buffett has more in common with Annie Duke than he has with the average investor. (Link)

Betting As ‘Decision’ Practice

A strong trading education will include an explicit education in decision-making. Markets become the proving ground for that education.

Marc Andreesen in a recent (and rare) interview:

One of the things you find about professional gamblers – they may play poker at night but what they do during the day is they hang out together and they make side bets for large amounts of money. And it’s literally a side bet of sitting in a diner and betting on whether there are going to be more red cars than blue cars passing by. What they’re doing is ‘steeling’ their own psychology to be able to pull the trigger on bets like that with a purely mathematical lens and with no emotion whatsoever. They’re trying to steel themselves to be able to be completely clinical. And so as contrast, what they then hope for that night when they sit across the table from someone is to hope they’re dealing with somebody who’s super emotional. Because the clinical person is going to just slaughter the emotional person. (Link)

I’d respectfully edit this line: “They’re trying to steel themselves to be able to be completely clinical.”

Actually, they just think they have an edge. The byproduct of that betting process is the “steeling”. This loops until they are quite clinical about the risk. This was the nature of trader training. There were many hours of poker hands and mock-trading deconstructed. Bets are hypothesis tests. The constant feedback calibrates how you map future hypotheses to future situations. Betting is a practice that tightens that loop.

In contrast, big decisions in life are hard because we don’t get much practice at them. You don’t get a lot of reps when it comes to picking a spouse (Elizabeth Taylor notwithstanding).

Ways to Learn More About Decisions

I recommend Annie’s interview with Ted Seides on his pod. I thought it stood out in the sea of “behavioral” content. I jotted some notes to jog your memory on key points. (Link)

If you agree that decision-making is a discipline that should be explicitly taught you’ll be pleased to hear there’s an organization called the Alliance for Decision Education. Its board and advisors include many notable backers including Mauboussin, Annie Duke, Prof. Daniel Kahneman, author Brian Portnoy, and several former Susquehanna execs including a founding partner. Learn more about their mission to spread decision best practices. (Link)


Caveats

  • I didn’t read Duke’s book despite really enjoying the pod.

    The content was the air I breathed in training. The principles would be a refresher for sure but hard to prioritize when I struggle to make it through my existing book queue.

  • There are diminishing returns to studying decision-making explicitly vs just practicing.

    Kahneman himself doesn’t think the awareness of bias inoculates you from it. I don’t fully agree. Naming the biases provides you with the red challenge flags to throw in the moment. I’ve had enough discussion about trades to see the value in surfacing the subliminal. To the extent that we still make mistakes and always will, Kahneman’s point is well-taken.

  • There are many schools of thought.

    Naturalistic decision making is championed by Gary Klein. The ergodicity crowd led by Ole Peters thinks many of the so-called behavioral biases like ‘risk aversion’ are an artifact of the assumptions baked into studying how people decide in contrived lab settings. There’s a lot of brain damage to be had if you dig. This doesn’t even get into more common sense questions: the limits of transferability. Are poker players actually good decision-makers away from the table?

  • A final point (and partial confession).

    There is nothing more insufferable than a trading trainee. They are so eager to tell you what decision bias you are falling for. It’s like people who just learned about nutrition or exercise commenting on your form or what you are eating for lunch. You want to chase a Pop Tart with a glass of Fruit Loops milk in front of their bulging eyes just to spite them.

    We don’t need people leaning into crappy decisions because you come off like a pedantic hack.


I mentioned that trader training included playing games and mock-trading. If you want a glimpse of what mock trading options was like, check out my recent post:

Mock Trading Options With Market Makers (Link)

If you’d like to try your hand at mock-trading futures or options with your friends or family here’s a game we used to play in either group interview settings or with brand new trainees.

You Can Mock Trade With A Deck Of Cards (Link)

You Can Mock Trade With A Deck Of Cards

Here’s a mock trading game I learned as a trainee to simulate futures and options market making. This game was commonly used as a day 1 exercise in trading class or when interviewing cohorts of college grads during recruiting “combines”.


The Futures Game

What you need:

  1. A deck of cards
  2. Nerdy friends (the more the better)
  3. A paper and pen per person to use as a tradelog

Setup:

You want to deal out enough cards to players (these are the market makers) so that there is about 25 remaining in the deck. There’s some leeway here.

Example:

  • You have 6 players. So deal them each 4 cards leaving 28 cards undealt.
  • Market makers may look at their hands but don’t share info.
  • The undealt cards are known as the “public pile”. They should be evenly divided into 4 or 5 sub-piles ideally (again there’s leeway depending on how many cards there are).
  • The sub-piles are going to represent “trading days”.
  • The cards themselves are news flow which will move the futures prices.

Description of futures prices:

  • The futures are the 4 suits. There’s a club’s market, a spades market, etc.
  • The final settlement price of the futures will be the sum of the ranks of cards in the public pile. (Ace =1 thru King = 13). So the maximum any future can be worth is 911

    It’s best to define the tradeable universe to keep the liquidity centralized.

    So you could have a diamond market, a spades market, and a “reds” market (which would be an index settling to the sum of diamonds and hearts).


    How To Play


    The first trading day

    • Reveal the cards in the first public sub-pile.
    • Market makers make bids and offers for the various markets. Tight 2 sided markets should be encouraged/required. For example:John: “I’m 65 bid for Hearts and offered at 68”

      Jen: “I’ll pay 67 for 5 Hearts contracts” (perhaps Jen is holding no Hearts in her hand)

      John: “Sold you 5 at 67” (John is holding 16 points of Hearts in his hand)

    • Record all your trades on your own pad or paper:1. Which contract you bought/sold
      2. Quantity of contracts
      3. Price of contracts
      4. Counterparty

    So for example, if I paid 51 for 4 “clubs contracts” from Mary I would record that information on my paper. Mary would record her sale of the 4 contracts at 51 on her card with me as the counterparty.

    • The trading is open outcry. There are no turns.

    Settling the trading day

    1. When the trading peters out for that “day” everyone should check their trades against their counterparties to make sure there are no so-called breaks or “outtrades”.
    2. On a central eraseboard or paper the “closing price” of each market can be recorded. So if the King of clubs and 3 of clubs were revealed from the sub-pile, then clubs “settled at 15”. Clubs might have traded 53 last in the expectation that more clubs will be revealed on subsequent days.
    3. Repeat this process for all remaining tradings days

    The last settlement

    • Compute “P/L” for all trades.

    If I bought 4 clubs contracts for $51 and clubs final settlement was $63 then I made a profit of $12 x 4 or $48. Mary’s loss would match that amount for that trade.

    The total P/L of all traders should sum to zero at the end of the game.

    Options Variant

    • Either the same group or a different group of people could choose to trade calls and puts on the final settlement price of the futures.

    So if I paid 3 for Clubs 55 calls and the final settlement was $63 then I profit the difference between the $63 and the strike ($55) minus the premium I outlayed:

    $63-$55 – $3 = $5

    • You could even get fancy and trade “vol”. You could sell say 10 clubs calls and buy 5 clubs futures to hedge the delta.
    • This game is played the same way the futures game is played or in conjunction. Repeat the process for all trading days then compute P/Ls at the end. Again if there are no errors the game should be zero-sum.