What Drives The Stock Market

My recent post, Nah…you just ain’t seein’ the ball addresses the lazy confession you hear when professional investors moan “the market doesn’t care about fundamentals”.

At the end of that post, I pointed to research that shows that in the long-run fundamentals remain the largest driver of returns.

Good businesses pay off. While the wrong price can ruin any investment that math becomes less relevant the longer the holding period (this is Buffet’s “pay a fair price for a great business” compounder philosophy).

Here’s 3 more bits that show the stock market is still governed by the force of financial gravity (profits):

1) What’s Driving Stock Market Returns (3 min read)
Ben Carlson

It’s ridiculous to assume this means the gains in the stock market are somehow rigged, fake or manipulated.

There is no man behind the curtain pulling levers to ensure stocks go up.

In fact, over the long run, fundamentals still play an important role in the stock market’s success.

There have been times when prices have gotten ahead of themselves but for the most part stock prices have been going up because earnings have been going up.

Another myth of the stock market is that all of the gains are due to multiple expansion. While it is true that valuations have been slowly rising over time as markets have gotten safer [Kris: I’m not sure about “safer” but I expect valuations levitate over time and a priori risk-adjusted returns to get worse], multiple expansion has probably played a smaller role than most people assume.

The late-John Bogle had a simple formula for expected returns in the stock market that looks like this:

Expected Stock Market Returns = Dividend Yield + Earnings Growth +/- the Change in P/E Ratio

In his book Don’t Count on It, Bogle applied his formula to each decade in the stock market going back to the turn of the 20th century to see how well fundamental expectations matched up with the actual returns.

The difference between the two is essentially human emotions.

Bogle published the data through the 2000s so I’ve been updating his work into the 2010s and 2020s. Here’s the latest data through the end of 2023:

There has been some multiple expansion in the 2010s and 2020s but nothing like the 1980s, 1990s or even the 1930s. Earnings growth has been the main driver of stock market returns since the end of the Great Financial Crisis.

 

2) Why Stocks Move (Twitter thread)
Brett Caughran

Brett is very much in the gears of fundamental pod shop investing providing extensive training to portfolio managers.

Excerpts:

  • I’m here to assert: fundamentals are all that matter (with an investment horizon longer than 3 months). Sure, not in a given day, week, month or quarter. Shorter movements in stock prices are certainly influenced by positioning, sentiment & flows.
  • But extend the horizon even a few months (let alone a few years) and one thing hasn’t changed in markets over the last two decades, and won’t change in the next two decades: fundamentals are deterministic to stock prices. The analysis I will present below is a ~3 month analysis of why stocks move.
  • There are two very common proxies for “fundamentals” when looking at a stock, 1) revisions, i.e. how consensus estimates are changing and 2) consensus expected growth…To try to make this point, I did an analysis of the top & bottom 25 stocks in the S&P 500 this year. I applied a very typical “why did the stock move” decomposition analysis of revisions, P/E and growth algorithm shift to try to isolate why these stocks move. [see the thread for the details].
  • By no means am I saying that fundamental equity investing is easy. I’m showing you an ex-post analysis. Monday morning quarterback. The hard part is using process & judgment to identify these dynamics ex-ante. What I’m telling you is fundamentals still matter. Don’t fall into the trap that fundamentals don’t matter. They have this year, and they always will.

Personal bit of color for what it’s worth: a friend of mine is one of the largest and best performing fundamental pod managers on the street. (When I hear what goes into the process I’m convinced the average professional investor looks like a bear on a bicycle compared to what’s happening at the right side of the power law performance curve). I think this friend would very much agree with Brett. Take it as you will.

 

3) A simple theory of the stock market (7 min read)
Steve Randy Waldman

This post is more of a red pill compared to the others. I’m quite sympathetic to its argument as stock returns maybe have become a load-bearing pillar of the “affluent professionals — call them the top 30%”

Excerpt:

Equity holders who have come to rely upon high equity returns regardless of the timing or valuation of their purchases. Equities fluctuate, sometimes wildly, but the most enfranchised citizens now expect an upward ratchet over a five to ten year horizon. Speculators’ own self-fulfilling behavior joins forces with tacit but determined state support to deliver on that expectation.

While sympathetic, I don’t yet subscribe to Waldman’s deeper suspicion because I haven’t seen the turn card on the flop. Like what happens to the stock market if earnings have a sustained fall without cover for major intervention (like if the last major earnings cliff wasn’t caused by a virus).

Waldman himself includes this chart of corporate profit margins in the post:

A conspiratorial mindset should should be pulled away from the derivative of the function (stock prices) and focused on the function itself — profits margins. Profits varied around 2.5% while the boomers were still hippies, bounced about 5% when I was a kid, found a new home around 10% in the age of smartphones, and then nearly doubled again since covid. The time for profit margins to double roughly halving along the way. There are so many forces that could go into a picture like this plus technicalities of how accounting and tax laws may have changed that I’m not going to embarrass myself with any guesses.

But the output is unmistakable: earnings are growing from both the top* and bottom lines. Again the chart Ben Carlson posted:

When you zoom out, the SPX time series is still tracing what it always has.

*For the top line: see S&P 500 REPORTING YEAR-OVER-YEAR REVENUE GROWTH FOR 13TH STRAIGHT QUARTER

Commitment

One of the memorable ideas from Peter Thiel’s Zero To One is the 2×2 grid with quadrants of definite/indefinite + optimism/pessimism.

Luke Burgis has a concise discussion of it in Are you a Definite or Indefinite Optimist, or Pessimist?.

Thiel laments the influence of either type of “indefinite” mindset.

Luke agrees:

This also comes down to the key question of agency. The “indefinite” doomers and optimists lack a sense that they are personally responsible for anything, and so are less likely to contribute to bringing about the future they believe will happen.

This means there is an aspect of reflexivity involved, of course. Perception creates reality. If enough people are indefinite optimists, then nothing will happen (because not enough people will take concrete action) and the future will actually become worse than the present.

“Indefinite optimism” leads to option hoarding. I’ve written about this in The Option Cage (12 min read). The popularity of that post affirms the sense that we are intrinsically repelled by optionality mindsets propagating beyond the realm of tactics and into a way of life. The seduction of such nihilism is liberating yourself from specific commitments. It’s a way of lowering the stakes for your ego. It’s a pre-excuse. You can always hide behind “I never went all-in”.

But there’s no reward without risk.

Sure, there are lucky exceptions. Probably more than ever these days if we’re being honest. You can become a rich cog in a wildly profitable business. You ride a great wave, get overpaid considering how little risk you take, and now complain that you make $500k a year and feel broke. That’s the universe reminding you that maybe your fat paycheck is downstream of the same forces that make everything feel so expensive. It’s tied together. You can’t with a straight face think that your pay is justified while the inflation in your consumption basket is not.

(Yes, you work hard. Yes, your skills might be more scarce than what it takes for a typical job. And you are very much rewarded for that. But risk is required for a truly asymmetric outcome.)

Risk requires uncomfortable levels of commitment. Risk, or even better, “accountability” (from the most popular twitter thread I’ve ever seen), is incompatible with an appetite whose primary macronutrient is optionality. That friend that always bails on their plans sees all their commitments as options not futures. The plan was just an insurance policy against “something not better coming along”.

This brings me to today’s read:

Committed: How to give a damn about your work (7 min read)
by Rick Foerster

I’ve spoken to Rick. He walks the walk. This article starts strong and gets better:

In an apathetic world, full of short-termism and an addiction to the slow drip of incentives, the treasured virtue is commitment.

We are surrounded by conditional people, who need to “be engaged” or receive the whip of stimulation to get moving. They wait, until the move is obvious and success certain.

But we unlock the best in life when we become committed, even in the face of uncertainty.

Further reading:

Moontower #225

Friends,

One of the memorable ideas from Peter Thiel’s Zero To One is the 2×2 grid with quadrants of definite/indefinite + optimism/pessimism.

Luke Burgis has a concise discussion of it in Are you a Definite or Indefinite Optimist, or Pessimist?.

Thiel laments the influence of either type of “indefinite” mindset.

Luke agrees:

This also comes down to the key question of agency. The “indefinite” doomers and optimists lack a sense that they are personally responsible for anything, and so are less likely to contribute to bringing about the future they believe will happen.

This means there is an aspect of reflexivity involved, of course. Perception creates reality. If enough people are indefinite optimists, then nothing will happen (because not enough people will take concrete action) and the future will actually become worse than the present.

“Indefinite optimism” leads to option hoarding. I’ve written about this in The Option Cage (12 min read). The popularity of that post affirms the sense that we are intrinsically repelled by optionality mindsets propagating beyond the realm of tactics and into a way of life. The seduction of such nihilism is liberating yourself from specific commitments. It’s a way of lowering the stakes for your ego. It’s a pre-excuse. You can always hide behind “I never went all-in”.

But there’s no reward without risk.

Sure, there are lucky exceptions. Probably more than ever these days if we’re being honest. You can become a rich cog in a wildly profitable business. You ride a great wave, get overpaid considering how little risk you take, and now complain that you make $500k a year and feel broke. That’s the universe reminding you that maybe your fat paycheck is downstream of the same forces that make everything feel so expensive. It’s tied together. You can’t with a straight face think that your pay is justified while the inflation in your consumption basket is not.

(Yes, you work hard. Yes, your skills might be more scarce than what it takes for a typical job. And you are very much rewarded for that. But risk is required for a truly asymmetric outcome.)

Risk requires uncomfortable levels of commitment. Risk, or even better, “accountability” (from the most popular twitter thread I’ve ever seen), is incompatible with an appetite whose primary macronutrient is optionality. That friend that always bails on their plans sees all their commitments as options not futures. The plan was just an insurance policy against “something not better coming along”.

This brings me to today’s read:

Committed: How to give a damn about your work (7 min read)
by Rick Foerster

I’ve spoken to Rick. He walks the walk. This article starts strong and gets better:

In an apathetic world, full of short-termism and an addiction to the slow drip of incentives, the treasured virtue is commitment.

We are surrounded by conditional people, who need to “be engaged” or receive the whip of stimulation to get moving. They wait, until the move is obvious and success certain.

But we unlock the best in life when we become committed, even in the face of uncertainty.

Further reading:

In my market-making life, I often had positions that were net short extrinsic option premium but long convexity. (A common junior option trader question would be to ask the candidate to create a structure that had that profile. A good answer is — a vega-neutral iron fly which can be roughly by shorting 1 ATM strangle and buying roughly 1.4 25d strangles. Vega-neutral butterflies were often quoted in the gold options market. They wouldn’t ask for it by name but the structure would usually be a iron fly with a strange ratio that amounted to zero vega.)

With that niche bit of trivia, I present this week’s sponsor: Helium

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Money Angle

My recent post, Nah…you just ain’t seein’ the ball addresses the lazy confession you hear when professional investors moan “the market doesn’t care about fundamentals”.

At the end of that post, I pointed to research that shows that in the long-run fundamentals remain the largest driver of returns.

Good businesses pay off. While the wrong price can ruin any investment that math becomes less relevant the longer the holding period (this is Buffet’s “pay a fair price for a great business” compounder philosophy).

Here’s 3 more bits that show the stock market is still governed by the force of financial gravity (profits):

1) What’s Driving Stock Market Returns (3 min read)
Ben Carlson

It’s ridiculous to assume this means the gains in the stock market are somehow rigged, fake or manipulated.

There is no man behind the curtain pulling levers to ensure stocks go up.

In fact, over the long run, fundamentals still play an important role in the stock market’s success.

There have been times when prices have gotten ahead of themselves but for the most part stock prices have been going up because earnings have been going up.

Another myth of the stock market is that all of the gains are due to multiple expansion. While it is true that valuations have been slowly rising over time as markets have gotten safer [Kris: I’m not sure about “safer” but I expect valuations levitate over time and a priori risk-adjusted returns to get worse], multiple expansion has probably played a smaller role than most people assume.

The late-John Bogle had a simple formula for expected returns in the stock market that looks like this:

Expected Stock Market Returns = Dividend Yield + Earnings Growth +/- the Change in P/E Ratio

In his book Don’t Count on It, Bogle applied his formula to each decade in the stock market going back to the turn of the 20th century to see how well fundamental expectations matched up with the actual returns.

The difference between the two is essentially human emotions.

Bogle published the data through the 2000s so I’ve been updating his work into the 2010s and 2020s. Here’s the latest data through the end of 2023:

There has been some multiple expansion in the 2010s and 2020s but nothing like the 1980s, 1990s or even the 1930s. Earnings growth has been the main driver of stock market returns since the end of the Great Financial Crisis.

2) Why Stocks Move (Twitter thread)
Brett Caughran

Brett is very much in the gears of fundamental pod shop investing providing extensive training to portfolio managers.

Excerpts:

  • I’m here to assert: fundamentals are all that matter (with an investment horizon longer than 3 months). Sure, not in a given day, week, month or quarter. Shorter movements in stock prices are certainly influenced by positioning, sentiment & flows.
  • But extend the horizon even a few months (let alone a few years) and one thing hasn’t changed in markets over the last two decades, and won’t change in the next two decades: fundamentals are deterministic to stock prices. The analysis I will present below is a ~3 month analysis of why stocks move.
  • There are two very common proxies for “fundamentals” when looking at a stock, 1) revisions, i.e. how consensus estimates are changing and 2) consensus expected growth…To try to make this point, I did an analysis of the top & bottom 25 stocks in the S&P 500 this year. I applied a very typical “why did the stock move” decomposition analysis of revisions, P/E and growth algorithm shift to try to isolate why these stocks move. [see the thread for the details].
  • By no means am I saying that fundamental equity investing is easy. I’m showing you an ex-post analysis. Monday morning quarterback. The hard part is using process & judgment to identify these dynamics ex-ante. What I’m telling you is fundamentals still matter. Don’t fall into the trap that fundamentals don’t matter. They have this year, and they always will.

Personal bit of color for what it’s worth: a friend of mine is one of the largest and best performing fundamental pod managers on the street. (When I hear what goes into the process I’m convinced the average professional investor looks like a bear on a bicycle compared to what’s happening at the right side of the power law performance curve). I think this friend would very much agree with Brett. Take it as you will.

3) A simple theory of the stock market (7 min read)
Steve Randy Waldman

This post is more of a red pill compared to the others. I’m quite sympathetic to its argument as stock returns maybe have become a load-bearing pillar of the “affluent professionals — call them the top 30%”

Excerpt:

Equity holders who have come to rely upon high equity returns regardless of the timing or valuation of their purchases. Equities fluctuate, sometimes wildly, but the most enfranchised citizens now expect an upward ratchet over a five to ten year horizon. Speculators’ own self-fulfilling behavior joins forces with tacit but determined state support to deliver on that expectation.

While sympathetic, I don’t yet subscribe to Waldman’s deeper suspicion because I haven’t seen the turn card on the flop. Like what happens to the stock market if earnings have a sustained fall without cover for major intervention (like if the last major earnings cliff wasn’t caused by a virus).

Waldman himself includes this chart of corporate profit margins in the post:

A conspiratorial mindset should should be pulled away from the derivative of the function (stock prices) and focused on the function itself — profits margins. Profits varied around 2.5% while the boomers were still hippies, bounced about 5% when I was a kid, found a new home around 10% in the age of smartphones, and then nearly doubled again since covid. The time for profit margins to double roughly halving along the way. There are so many forces that could go into a picture like this plus technicalities of how accounting and tax laws may have changed that I’m not going to embarrass myself with any guesses.

But the output is unmistakable: earnings are growing from both the top* and bottom lines. Again the chart Ben Carlson posted:

When you zoom out, the SPX time series is still tracing what it always has.

*For the top line: see S&P 500 REPORTING YEAR-OVER-YEAR REVENUE GROWTH FOR 13TH STRAIGHT QUARTER

From My Actual Life

Last week I mentioned our household’s new discovery — comedian Nate Bargatze. He has 2 Netflix specials his most recent special is on Amazon Prime. The following bit comes from the new one and just gets me and the 10-year-old dying every time. (Apologies but I could only find a TikTok link and it includes close-captioning which is an absolute affront to the craft of stand-up)

Tiktok failed to load.Enable 3rd party cookies or use another browser

Another skit we find re-watching too much is this one from Nate’s appearance on SNL a few months ago. The writing and delivery is perfect.

@bestandup

I’ve never seen the real internet #natebargatze #eagle #baldman #bestandup

♬ original sound – bestandup

That skit reminded me of being in 5th grade when a set of twins from South Africa transferred into my elementary school. I’ll never forget how in a proper English accent, the first thing I ever heard of one them say after raising his hand on the first day: “Will we be using the Imperial or Metric system?”

If the accent wasn’t enough I didn’t know what the words they dripped from even meant.

Mental note: put gum on their chairs. Welcome to 80’s grade school in NJ nerds. No one gets out of here well-adjusted.

☮️

Stay Groovy

Moontower Weekly Recap

Nah…you just ain’t seein’ the ball

When I hear someone mope “the market doesn’t care about fundamentals” I change the channel.

Market prices are a collection of point spreads. I don’t really understand the logic of such an argument.

If the relationship between fundamentals and returns were easy to understand in advance, then price would adjust to make the trade hard. A “cheap” company that stays cheap is implying a low future ROIC. If you buy shares and the company is able to find better opportunities to re-invest its capital than what was implied, you’ll win.

But it’s going to take time to find out. You can’t make a statement like the “market doesn’t care about fundamentals today”.

Moaning that NVDA is unmoored to fundamentals, besides being underperforming-the-index cope, is comparing something you can see (a price) to what you can’t (what happens later). The price itself is mostly driven by the future. You can’t evaluate if the price did a good job until the later happens.

And even then you can be fooled.

In my early SIG days I remember Jeff gave a talk arguing that the dot com boom then bust wasn’t irrational. You only needed to look at the options market to see why.

A price is just an expected value — if the underlying distribution is highly uncertain, exactly as you might expect the distribution to be in 1999 when the internet and fiber promised to change the world. The price of dot coms are bounded by zero so they have no choice but to go through the roof based on such world-changing mathematical expectation.

But option surfaces make higher resolution statements than the 2-D nature of a share price. [See the Market Innovation section]

AMZN used to be a 250 vol name. Stick 250 vol into a 1-year option price and look at the difference between the mean and median expected stock prices (median = geometric mean)

The options market said the stock was probably worth zero.

[Relevant reading: this post about the windowmaker is a lesson in what option butterflies mean]

And the options market was right for many of the dot-coms.

In fact the AMZN we are familiar with today is a delightful justification of the prevailing pricing back then — some company is going to reach breathtaking proportion if this tech is as important as we think. We just couldn’t predict which one. And in fact, owning the basket and following a index rebalance algorithm that sheds the losers (aka the Nasdaq index) worked out just fine because AMZN made up for Pets.com.

[Fun fact: iirc, AMZN did end up trading down to the implied mode, ie the most expensive butterfly, in the early 2000s washout.]

You can disagree with share prices. Your portfolio is how you disagree. And when the “later” happens you’ll find out if the future fundamentals were well anticipated by the today price.

I’ll be blunt. When I hear investors bitch about prices vs fundamentals I just hear a confession. “I can’t see the ball clearly anymore.”

Which is exactly what you should expect to happen in a competitive red queen domain unless your learning rate increases faster than the market’s lesson-internalization script runs.

Competing for provable alpha, the type that sits on many reps lending itself to statistical summary, means playing the trading game. Finding mispriced coins that will be flipped in the short term. Similar to arbitrage-inspired trading where futures and options expirations are a catalyst for convergence between prices and reality.

The competition for provable alpha is fierce. However the focus does open the door to alphas from having a long horizon. Long-term investors call this “time arbitrage”. That’s more of a clever marketing term than an investing phylum but it does hint at the reality of investing. (The fact that there is alpha in having a long-term horizon is also convenient cover to say “ignore our short term results”.)

You are unlikely to find the kind of provable alphas that are easy to raise money for. In fact, most investors who have such alphas don’t need or want your money. The “time arbitrage” people will happily take your money though. And you won’t be able to prove if they have alpha (otherwise you’d never hear from them), but this also means it’s the only chance you have of investing with someone who has an edge.

You just won’t know until later.

And even then you might still not know.

[Unless they boot you as an LP. Then you definitely know.

“Wait so if I pick the best horse my reward is being asked to redeem?”

Sorry, there’s no luxury more protected than a sure-fire compounding machine. You can buy your way into almost anything else from sex to a trip through space — but if you try to buy your way into a money copier the price adjusts until the ink runs out.

(Actually, as “strategic” investors know, you can buy your way in with other ways to add value. But nobody’s money is greener than another’s.)]

A couple pieces I’ve read recently suggest market prices are doing their job. And also enlightened me on a significant (and not what I expected!) reason for “value” underperforming.

[Emphasis in the excerpts is mine]

Total Shareholder Return Linking The Drivers of Total Returns to Fundamentals
Michael Mauboussin

A terrific paper by one of my favorite researchers.

From the conclusion:

Total shareholder return (TSR) is the capital accumulation rate for investors who reinvest dividends at no cost. TSR is a popular return measure despite the fact that few investors earn it for the stocks of companies that pay a dividend. Investors fail to earn the TSR because they do not reinvest the dividend or cannot reinvest the full amount due to taxes or other costs. Price appreciation and the capital accumulation rate are the same for the stocks of companies that do not pay a dividend, which includes about 65 percent of U.S. public companies.

We can break down TSR into drivers, including net income growth, change in shares outstanding, P/E multiple change, and the benefit of reinvesting dividends. We examine each of these drivers and link them to underlying economic principles.

It is useful to think about the value of a business in two parts: a steady-state value and the prospects for future value creation. The steady-state value assumes that the company can sustain its current earnings forever. Future value creation reflects the ability to earn a return on invested capital in excess of the cost of capital, the amount of investment the company can make while maintaining a positive spread, and the length of time a company can create value with its investments. Historically, about two-thirds of the value of the S&P 500 has derived from the steady-state value.

The market determines the appropriate P/E to apply to current earnings through an estimate of the cost of equity capital. The cost of equity is the opportunity cost of equity investors and is commonly estimated by adding an equity risk premium to the risk-free rate. Over the past 60 years, the steady-state P/E has gone from a low of 5.1 in 1981 to a high of 17.7 in 2020.

The multiples of companies with high P/Es tend to regress toward the steady-state P/E over time because the relative contribution of future value creation shrinks. This reflects market saturation and competition. Some companies can defy this downward drift by either sustaining a high return or by investing in new businesses.

Investors often consider dividends to be part of total returns. But for investors using TSR, price appreciation is the only source of investment return that contributes to accumulated capital. Indeed, dividends and share buybacks have the same result in a TSR calculation because they both increase the percentage ownership in a company. In the case of dividends, the investor uses the proceeds to buy more shares at the ex-dividend price. In the case of buybacks, the investor does not sell and hence winds up with a higher percentage of the company. These are equivalent, save for the reality that dividend reinvestment generally has a cost (see appendix A).

Value traps exist when a company appears statistically inexpensive, often based on the P/E as compared to the stock’s past or to the market overall, but the future drivers of TSR perform poorly. The two main culprits in the bad results are growth below the average and P/E multiple contraction that captures fleeting or elusive prospects for value creation.

We explain TSR through drivers including EPS growth and changes in the P/E multiple. We have noted the severe limitations of EPS and multiples to explain value. To compensate, we seek to link these concepts to underlying fundamental drivers. Doing so gives investors and executives a framework to understand the past and to anticipate the future.

We decompose the returns for value and growth stocks in recent years.

Excerpts of note:

  • Autocorrelation in net income growth is -0.10 for 1 year, -0.20 for 3 years, and -0.28 for 5 years. This is consistent with the academic literature that shows low persistence in net income growth. These results show that extrapolating past net income growth into the future is rarely a good idea.
  • The presumption that buybacks always increase EPS is incorrect. The common portrayal is that net income is divided by fewer shares, which automatically leads to a boost in EPS. This simplistic analysis neglects the fact that the company has to fund the buyback, either with excess cash or additional debt. Excess cash generates interest income, and debt comes with interest expense. As a result, buybacks affect net income as well as shares outstanding.
  • Appendix A: Dividend and Buyback Equivalence—Think Percentage Ownership
    • Dividends and buybacks have the same impact on corporate value. But executives think of them very differently. They consider dividends to be a commitment tantamount to capital expenditures and buybacks as a way to return excess cash after they have paid all of their bills and made of all of their investments.
    • In practice, dividends and buybacks are different because of tax consequences and the impact of gaps between stock price and value. But to understand TSR, the central distinction is between actively or passively increasing the percentage ownership in a company.
  • Decomposing TSR for Value and Growth Over the past 15 years or so, “value” stocks have provided substantially lower Total Shareholder Returns (TSRs) than “growth” stocks. Value stocks are those with low multiples of price to sales, earnings, and book value. Growth stocks are characterized by above-average sales growth, high Price-to-Earnings (P/E) ratios, and positive stock price momentum.
    The S&P 500 Value Index tracks the investment return of large-capitalization value stocks in the S&P 500. The index includes about 400 stocks that have an average market capitalization of $60 billion as of September 29, 2023. The S&P 500 Growth Index draws about 235 stocks from the S&P 500 that qualify as large-capitalization growth. The average market capitalization was $110 billion at the end of the third quarter of 2023. The stocks of numerous companies are in both indexes.

    Exhibit 16 shows that the annualized TSR from 2007 to 2021 was 7.6 percent for the Value Index and 13.3 percent for the Growth Index. We end in 2021 in order to use forward P/Es, but the value index still underperforms the growth index by 330 basis points annualized if we include the returns from 2022.

    We can compare the drivers to see why the results varied. Companies in the value index grew their net income at a 5.2 percent rate during the period, a little slower than the 5.9 percent rate for the members of the growth index. But the translation from net income to Earnings Per Share (EPS) was impeded by net equity issuance among the value index constituents and aided by equity retirement for the companies in the growth index. As a result, EPS rose 3.3 percent per year for the value index and 8.0 percent for the growth index.

    Both indexes enjoyed P/E multiple expansion, although the contribution was 1.6 percentage points for the value index and a larger 3.6 percentage points for the growth index. Interest rates dropped over this period and growth companies have longer implied durations, a measure of the weighted average time investors have to wait before they receive cash flows. Assets with long durations are more sensitive to changes in real interest rates than those with short durations. The growth index likely benefited more than the value index when rates dropped during this time.

    The sum of EPS growth and P/E multiple expansion led to price appreciation of 4.8 percent for the value index and 11.6 percent for the growth index. Those drivers explain most of the TSR difference between the indexes.

  • When governments tax dividends and capital gains at the same rate, as is the case in the U.S. in 2023, the decline in the stock price is roughly equivalent to the dividend. If taxes on dividends are higher than those on capital gains, the decline in stock price will be less than the dividend.

Pods, Passive Flows, and Punters
Drew Dickson

Excerpt:

I am as convinced as ever that, eventually, it is the fundamentals that matter. Eventually, the market is a weighing machine. If you want some evidence – even from some of the most iconic, well-followed, index-heavy, retail-engaged, pod-owned, successful companies, it is still, eventually, about the fundies.

Let’s take some of the winners as an example. And by winners, I mean game-changing, world-dominating winners.

You’ve surely noticed what has happen to Nvidia lately. We used to just call these winners FANGs, and then FAANGs and then FAMANGs, but Nvidia has insisted on joining the league table. It now has a $1.7 trillion market cap. And in the last five years, the stock is up about 1,700%. Guess what else is up about 1,700%?

Nvidia’s earnings estimates.

How about Facebook, aka Meta, which goes through periods of hatred and love with equal vigor? Well, over the past seven years it has bounced around a lot but still has generated nearly 260% returns. And forward earnings projections? They’re up 280%.

We can stretch things further back, and look at Google over the past 14 years (earnings up 885%, stock up 980%); or Amazon during the same period (earnings up nearly 2,500%, stock up about 2,800%).

Or we can go waaay back and analyze Microsoft over the past 22 years. Forward earnings projections have increased from $0.93 in February of 2002 to $11.57 today. That’s nearly 1,150%. The stock is up just over 1,200%.

And finally, from one of my favorite former-CEOs Reed Hastings, we have good old Netflix. About 18 years ago, analysts were forecasting that Netflix would generate 11 cents of earnings in the coming 2006 year. Here in 2024, they are forecasting a whopping $17 of earnings in the coming year. That is a whopping EPS increase of 14,889%.

And how about the stock? We’ll it is up a whopping 14,882%.

Fundamentals matter, sports fans. Fundamentals matter.

Admittedly, some of these examples above are very long-term, but even when we self-select with some of the biggest, most exciting, long-term winners out there, and ignore the losers (of which there are many), it is still clearly apparent that it is the fundamentals that matter most.

So basically, it probably isn’t terrible advice to ignore the rest of it. Ignore the noise. Ignore the talking heads on CNBC. Ignore prognostications of meme-stock sith lords. Ignore the volatility. Embrace it, actually. And just focus on the fundamentals. Get those right, and you will likely win.

Can you take advantage of it? Can you take advantage of the noise?

There’s Always Something Going On

“Two centuries ago, it took a year to send a message around the globe. Now it takes a fraction of a second. We have no idea what this means or what the consequences may be. Man’s knowledge and ability have dangerously exceeded his capacity to understand either.”

— Dee Hock, founder of Visa, writing in his journal at an advanced age sometime in the 1980s or 90s.

This is from the opening chapter of Neil Postman’s eerily prescient Amusing Ourselves To Death:

The information, the content, or, if you will, the “stuff” that makes up what is called “the news of the day” did not exist-could not exist-in a world that lacked the media to give it expression. I do not mean that things like fires, wars, murders, and love affairs did not ever and always happen in places all over the world. I mean that lacking technology to advertise them, people could not attend to them, could not include them in their daily business. Such information simply could not exist as part of the content of culture. This idea – that there is a content called “the news of the day” – was entirely created by the telegraph (and since amplified by newer media), which made it possible to move decontextualized information over vast spaces at incredible speed. The news of the day is a figment of our technological imagination. It is, quite precisely, a media event. We attend to fragments of events from all over the world because we have multiple media whose forms are well suited to fragmented conversation. Cultures without speed-of-light media – let us say, cultures in which smoke signals are the most efficient space-conquering tool available – do not have news of the day. Without a medium to create its form, the news of the day does not exist.

Postman’s book, a long essay really, is one of the most profound I’ve ever read. It’s lessons serve as user notes for the world we see around us today. Like close-captioning for our eyeballs. (my book notes)

It took me awhile to find that quote because the compressed version I had in my mind is stored as a prescription for myself not a transcription. You can trace my version back to Postman’s sentiment but its is optimized for usefulness not fidelity. It goes:

“Kris, there’s always something going on somewhere — you must choose what to focus on”

I conjured the Postman bit and the Dee Hock quote because a paradoxical byproduct of hyper-connectivity is isolation. It’s not just having your nose buried in your phone as you wait to order a matcha latte. It’s far more insidious.

Which brings us to this illuminating post:

Is Modern Mass Media A Mind Prison? (9 min read)
by jasonpargin

This is one of the those essays that puts a finger on the sense that we are all being played but struggle to point out the perpetrator. Of course if it were as easy as pointing out a single source of the strife, then it might also be solvable. The source unfortunately seems to be something like [waves hand in big circle] “incentives”. That’s my attempt to fill in what Jason doesn’t focus on. He skips right to diagnosis and cure which is the right approach anyway.

[My opinion: the cause is the most speculative part of the malaise around us and has so many facets we’d be playing a hopeless game of top-down whack-a-mole whereas addressing our individual responses is plausible.]

Excerpt from the end:

I actually believe this to be the single most successful technique for social control in the 21st Century, convincing those most eager for change that it can only come through thrilling and glorious action, a battle of pure good versus pure evil. “Why bother voting on this boring bond issue? I’m not leaving the house for anything less than a war to overthrow capitalism! And don’t ask me to hang out unless you agree, I don’t befriend class traitors.”

The truth that the system is so afraid of us learning—and that we’re happy to let them keep from us—is that actually changing the world requires a stunning amount of tedious, quiet work, of dry reading and learning and organizing and slowly changing obstinate minds. Mathematically, this includes engaging at least some minds you previously considered ignorant or hateful. And this persuasion occurs, not through flashy performative acts, but by slowly earning trust until your opponents want to agree with you.

The system wants you to equate tedious work with neutered slavery and to equate liberation with sexy drama because it knows the opposite is true, that if you restrict yourself to flashy and dramatic solutions, you will be exactly as useful to the status quo as any other sedentary daydreamer. There is a reason the system has no problem feeding you a steady stream of fantasies about violently overthrowing it. 

The reality is that the amount of focus and desire required to blow up the occasional building or pipeline is nothing compared to the lifetime of quiet labor required to understand the system well enough to actually build a better one. And that better world, if it arrives, will require the cooperation of some truly unpleasant people, because all of civilization is nothing but truly unpleasant people learning to peacefully cooperate. 

From My Actual Life

I taught my 5th grader’s math class on Thursday (lesson plan). I did a dry-run with a group of 3rd-5th graders the night before.

Yinh was like “baby Boiler Room” vibes. I promise I didn’t throw my car keys on the table. My favorite comment: Illegal SF Algebra Speakeasy

The following morning: I survived!

Look, today’s letter was admittedly dystopian. Guilty as charged. But that’s no way to start a week. And I heard there’s a void in lifehacking advice this week what with the no-alcohol guy putting out fires with the ladies and all. So I’ll step in with an antidote to the exhaustion —> [try new morning routine] —> end up where you always do cycle:

Cold plunges, manifesting, sound baths, chakras. Meh. The original chicken soup for the soul is just share with your neighbors. Remember you can “just do stuff”. You have gifts. Activate them. It’s nice for others. It’s great for you.

Don’t forget the gist of what Postman said — there’s always something going on. It’s news because they made it news and put it in in front of your face. And what they put is not random. You can find any fact on any day to feel aggrieved. If you aren’t going to do something about “the news” anyway, close the tab. Don’t let the algos choose how you spend the next minute. Outrage is a choice. You can pick literally anything else.

Maybe it’s that freedom that scares you.

Moontower #224

Friends,

We’ll cut straight to the links today.

The Serendipity Machine (7 min read)
by

Nabeel S. Qureshi

I started lurking on Twitter about 8 years ago. I didn’t start tweeting until 2-3 years into lurking. I started as a reply guy as one must if they aren’t already a somebody. I joined Twitter with the specific goal of learning how to invest which is different than trading. After getting the hang of it (Twitter not investing) I published my recipe for using Twitter. It’s still valid except I don’t use Tweetdeck anymore.

I included several outstanding guides to getting the most out of Twitter in that post. This new post by Nabeel Qureshi is a tremendous addition packed with smart advice on both what to do and what not to do.

Plentiful, high-paying jobs in the age of AI (18 min read)
by

Noah Smith

I really like this essay because it grips you with a clickable headline that speaks to common fears but proceeds to not just speculate but teach.

The best part of this post is hinted at in its subtitle:

Comparative advantage is very subtle, but incredibly powerful.

I make the same mistake Noah addresses in the post that most people make: we confuse the concepts of comparative advantage with competitive advantage. The difference is crucial and the engine’s of Noah’s argument.

It’s a great learning post and personally I find the marriage of comparative advantage to opportunity cost the best way to remember its meaning.

The concept of comparative advantage is really just the same as the concept of opportunity cost. If you Google the definition of “comparative advantage”, you might find it defined as “a situation in which an individual, business or country can produce a good or service at a lower opportunity cost than another producer.” This is a good definition.

Money Angle

I follow economist Steve Hou on Twitter. This is a good podcast episode and still relevant despite being over a year old:

🎙️Market Huddle interviews Steve Hou (3 hours)

The theme:

This week we welcome Steve Hou from Bloomberg. Steve recently did a presentation at the Bloomberg Portfolio Conference where he spoke about investing in a new inflationary regime, and it’s our great pleasure to talk about his research.

The interview is long because they step through Steve’s presentation (link to slide deck). Steve believes we have entered a period of structural inflation as many of the forces that came together to create disinflationary growth over the past 40 years have unwound and in even reversed.

He labels:

The “Four Ds” of inflationary undercurrents:

  1. De-carbonization and commodity underinvestment
  2. Demographic ageing of working age population
  3. De-globalization and supply chain re-shoring
  4. Dominance of fiscal policy over monetary policy

He then shows how various asset classes have responded under the regimes of the 4 quadrant model (inflationary growth, deflationary recession, and the cross-regimes of disinflationary growth and stagflation). But rather than just show us the average returns Steve shows us the distributions of those returns which creates various smiles and surfaces.

The slides are easy to read and worth your time. You can grasp broad, useful heuristics quickly about how asset returns relate to macro drivers. A few ideas that stuck out to me:

  • There is a trade-off between assets that have high inflation beta and their Sharpe ratio.

    In other words, assets that protect you from inflation are expensive. No free lunch. But his framework does lend itself to a frontier where you can choose your tradeoffs based on how eagerly you want to hedge inflation. I have seen this idea before in research that shows commodities are crappy stand-alone investments but can still improve portfolios by zigging when you need them to. See Diversification Imperative.

  • Steve expands on the point I alluded to on Thursday: TIPs are often unsatisfying inflation hedges.

    The reason is that TIPs are still bonds. So when inflation is anticipated they should appreciate, but rising inflation often coincides with rising rates which hurt bond prices. If you hold TIPs until maturity then the returns should compensate you for realized inflation but if you’re not sticking around for the long-run then you’ll find the underwhelming as the 2 drivers that set mark its prices can partially offset each other and mute returns.

  • Bloomberg created a “pricing power index” to identify equities that should perform well during periods of high inflation.

    Contrary to what you expect, it’s not companies that have high-profit margins that comprise the index — it’s companies whose margins are stable. In other words, profit margin volatility is a better proxy for pricing power.

  • Bloomberg also applies the bond concept of duration to equities to compute a “low duration index”. That slide points specifically at the FOVL ETF by iShares.

 

Money Angle For Masochists

There was a confident fellow on twitter a couple weeks ago that ventured into the options section and became a main character (for the healthy readers who need translation — “he stepped in doo doo”.)

He mansplained “I don’t think you know how options work” to a few long-time derivs traders including our dear friend Tina. He argued that by selling deep ITM calls on DJT (the Trump stock) you could short the stock without paying the steep borrow rate. This can be easily disproved by options 101 put-call parity but alas he dug in deeper. The thread is performance art plus an education in why options are the real underlying market.

I didn’t pile on so much as try to point out some of the subtleties that were not part of the main discussion but easy to overlook:

Link to thread

I try to be nice on the internet but Tina and several of the attacked are friends so the need to subtweet the clown got the better of me. I chose the GI Joe “learning is half the battle” PSA format which ties back to using Twitter to improve without the side effects:

From My Actual Life

Recently discovered the comedian Nate Bargatze. This humor leaves me crying. It’s very reminiscent of Sheng Weng — observational humor wrapped in deadpan story-telling. Domestic life as a middle-aged dad and husband, being raised in the 80s…straight in my veins. Nate is totally clean and the jokes are free of politics. Even the 10-year-old was laughing aloud.

Speaking of the 10-year-old…as a 5th grader, he’s camping with his school for the next week. I never did anything like that with my school but apparently this is a thing in CA. In my town, there are 4 public elementary schools that feed into 1 big middle school so it’s a cool way for him to hang out with 5th graders from the other schools as a preview (we moved intra-town during COVID so he transferred elementary schools…between that and sports he seems to know much of the town’s 5th graders anyway).

He’s beyond excited for this trip…meanwhile I need to bring tissues for his mom at drop-off.

I said for his mom. I’m not crying, you’re crying.

 

☮️

Stay Groovy

Inflation Replicator

Apparently yesterday was weird.

The stock market like went down or something. Bad stock market [rubbing my portfolio’s nose in red paint] you go up!

This is being attributed to “hot” inflation data which lowers the odds of a rate cut plus a weak treasury auction that saw 10-year yields pop 20 bps. Probably doesn’t help mortgage rates either.

Anyway, it’s a nice backdrop to riff on some personal asset allocation stuff.

I think in broad strokes and prefer simplicity.

Stocks

VTI, IWM, international Vanguard funds, and a handful of private managers. Very rarely invest in a single stocks.

Fixed income

This is mostly T-bills. I prefer short duration because the rates are best there and I’m uneasy about locking in nominal yields at these levels. A minority of fixed income slice is some medium duration TIPs in a tax-advantaged account. We’ll talk about inflation further below.

[The only long duration fixed income comes from some life insurance products and that is also a small position. My friend Rajiv is a quant on the insurance side (he was at a fund that bought lapsed policies — strange little corner of finance) and is my sherpa on thinking through these complicated products. I have a term policy but one of our family members got an insurance license to set all our families up whole life policies commission-free (there’s still an embedded management fee from the issuer). I have one in-depth article on insurance if you’re interested that was born out of research on IDF feeders and PPLI, topics that were of professional and personal interest. The short of it — insurance is a surgical tool not a cornerstone.]

Miscellaneous

The above part of our portfolio is weighted conservatively (about half and half). We have a small exposure to RE PE that’s we’ve had a stake in for over a decade but no longer own home. If we buy a house the funds will be drawn from out T-bill allocation so on balance our portfolio risk will increase.

Finally, about 10% of our portfolio is the weird barbell stuff that we are comfortable with going to zero. It’s comprised of SAFE notes and actively managed crypto VC stuff. 100% of this sleeve has come from reverse inquiry — either my wife or I asked if we could invest in a friend’s project or business.

I prefer the asymmetry of asking and sometimes not getting filled vs getting propositioned and knowing I’ll be filled. You will make mistakes sometimes of course, but despite a market-maker background, in real life I prefer to lift not be a resting bid or bet and not call if you like poker analogies.

Managing the portfolio

When I say “broad strokes”, I mean keeping the portfolio weights within a band that in a typical year doesn’t require rebalancing more than once. This allows some leeway to be a market timer around the edges or not look at your portfolio for long stretches.

It’s a system that accommodates the rhythm of your life. Sometimes I’m interested in markets and other times I’m just head down on other things. [My wife describes my superpowers as being patient and FOMO-immune. The funny thing is I grew into both of these traits which tells me they aren’t “fixed” sliders. In my 20s, I looked over the fence a lot. It’s a recipe for anxiety. Anxiety can be productive so I’m not recommending anything, just calling it as I see it.]

One of the things I do around the edge of the portfolio is mess with the energy weight. Some of this is old habits — most of my option trading career was being active in oil and gas. But I also see energy as fundamental to the concept of inflation and inflation is the largest tax on investment returns. I actually see the core of our portfolio not as means of getting rich — it’s just preserve purchasing power as best we can without incurring major drawdowns so we can sleep well at night. Because sleeping well = health. And so long as we are healthy, I’m confident our human abilities will provide prosperity. I’m trying to sterilize the impact of the random number generator and rely on idio — in life terms.

[Aside: If you were to plot how much of one’s net worth come from their income vs investment returns I suspect you’d get some measure of fragility — at least in the first half of their careers when you would expect human capital compounding to vastly outpace financial compounding. A 30- year-old with $500k in the bank who makes $90k a year has an unhinged Robinhood account.]

These days I have a small overweight to oil. This is something I’m in and out on with horizons of about 1 year. It’s purely on vibes. I bought XLE in late 2020 after the oil crash and when Tina told me that you couldn’t even touch the Brent call skew in the early part of the Ukraine invasion I sold the position (and in a “old degen habits die hard” moment told her to buy wheat calls if the skew was still stale — iirc that was timestamped on a whatsapp screenshot on twitter).

I bought oil again after it sold off and Biden showed his bid. I would check in with Tina and ask when there was a bunch of producer hedging in the back months and bout 18 month WTI futures (Z23 at the time). I rolled my Z23’s back to Z24 in the recent rally. Nice roll-up yield in those bad boys.

yahoo

[A good buddy who runs a commodity fund once described the “does a deferred future roll to the spot or predict the spot” as the particle/wave debate in commodities which I love. I believe the empirical answer leans more towards rolling but in theory there should be limits to how poor the prediction aspect can actually get.]

The backwardated market had me opting for oil futures instead of oil stocks.

It’s worth whoring the fact that moontower.ai has neat tools for comparing 2 names. This is a scatter plot of 60 day implied volatility between USO (which holds the prompt future) vs XLE. It’s a fuzzy choice because oil stocks are more correlated to longer dated futures but USO has better option markets than say USL (12 month etf).

Quick observations:

  • Median vol ratio is USO is 125% of the XLE vol
  • Vols are at the lower end of their ranges
  • Extremes have seen XLE be 50% more volatile than USO, and USO be 200% more volatile than XLE
via moontower.ai
via moontower.ai

We recently added the ability to zoom in:

via moontower.ai

Back to the reason for oil. It’s an overweight because I’m just trying to provide some extra insulation against inflation in the portfolio. The choice of futures was simply tactical.

We are going to see that the relationship between oil and commodities vs inflation is quite interesting and has trading ramifications.

Bond yields popped yesterday due to inflation concerns. Since TIPs are still bonds, their yields also rose.

10 year TIPs yield

But the nominal 10-year treasury yields rose faster than the TIPs yields which means implied inflation breakevens expanded further!

See What I Learned About TIPs to understand the mechanics

TIPs are admittedly a weird product and since their pricing anticipates inflation their returns don’t correlate well with inflation. Especially if you buy the ETF since that’s basically a constant maturity exposure that rests on implied more than realized inflation (it’s more complicated than that but that’s the point — it’s poorly understood. I urge you to be careful learning finance from influencers — I’ve noticed so much bad reasoning on TIPs on YouTube.)

But even pros who understand TIPs find them to be annoying and unsatisfying. Conceptually they are a great idea, but the product-market fit leaves something to be desired. Which is a funny way to introduce the following idea — you can replicate the TIPs return without TIPs. But even if you’re like “why would I want to replicate a bizarre return stream”, I can offer a reason at the end to consider it.

First, the replication.

You can simply buy a commodity index + a nominal bond to mimic the performance of the inflation-protected bond.

Corey Hoffstein demonstrates this beautifully in TIPs versus Commodities: Just Return Stacking?

This is pretty cool because TIPs are a smaller less liquid market than the legs of the replication so you gain flexibility.

It gets better.

A PM friend of mine at a pod who started in fixed income told me that TIPs traders literally hedge their books with nominal bonds + oil futures (as opposed to a commodity index which Corey uses).

The Bloomberg commodity index (BCOM for those who partake) has a 22% weight in 2024 to oil-related products and 30% to energy if we include nat gas.

source

With a minority weight in the commodity index I was curious how the simpler bond + oil replication performed.

I used Composer to compare the TIP ETF vs a portfolio of:

  • USL (12-month oil ETF)
  • TLH (~20 year bond)

Composer makes it easy to construct and track “symphonies” (portfolios with recipes for weights and automatic rebalancing intervals).

I used inverse vol weighting using 6 month realized volatility, rebalanced quarterly.

[Inverse vol weighting means you hold assets so that they contribute equally to risk in the portfolio. So you will hold more TLH than USL]

Link to symphony for oil + bonds TIPs replication

Voila, the pink line (our portfolio) very closely matches the TIP performance for the past 5 years.

Out of curiosity, I re-ran the portfolio adding GLD to the mix. Again, inverse vol weighting.

Link to symphony for oil + gold + bonds TIPs replication

Here’s the performance metrics:

There’s also a display for historical weights by day:

Anyway, if you have ever been interested in direct inflation hedges but find TIPs uninvigorating, this is food for thought.

I’ll add an additional reason why replication might be worth the seemingly small basis risk — commodity futures and nominal bonds are protected from the small but non-zero risk of the BLS tampering with the CPI index.

Note

I am not paid or affiliated with Composer, just a fan. In fact, I’ve reached out to them in the past and even wrote a post for them:

On Having An Edge

I like how Composer lets you follow custom strategies the same way you might have a ticker watchlist.

Many people are already familiar with it, but if not, you can also check out Portfolio Visualizer’s easy-to-use fund backtester:

https://www.portfoliovisualizer.com/backtest-asset-class-allocation

If you annualize volatility with 252 days can you use that number in a 365-day option model?

A Moontower reader asked a question that gets into one of the most confusing topics for option traders:

If I’m pricing options using calendar days(365), then I should even annualize realised volatility by multiplying 18.8(√256) instead of 16 (√256, approx trading days). In order to compare the VRP ratio on same scale, am I right?

I know firsthand from watching people wrestle with option models that this topic has put many brains in a blender. It’s worth a blog-post sized answer. My hope is that you will not only walk away clear-headed but bursting with ideas to explore.

A typical starting point

You compute close-to-close realized daily volatility for the past 252 trading days. Those days comprise the past year. You get an average daily vol of 1.875%. You annualize it by multiplying 16 to get 30% volatility.

observations:

  • Before the addition of Juneteenth, a non-leap-year had 252 trading days.
  • After Juneteenth was added to the holiday calendar, there are 251 trading days.
  • A leap year will typically have 1 more trading day than a non-leap year.
  • 2024 is a leap year that has 366 days and 252 trading days which is what we expect for a leap year.
  • If the daily standard deviation is 1.875% you should annualize by multiplying by √252 but traders will typically just estimate by multiplying by 16 (ie √256). If you are building a model, don’t use the estimate, but a lot of trader workflow involves quick assessments so it’s worth noting where the mental math shortcuts are.

The central question is:

Can you put 30% annual volatility into a typical 365-day option model or should you have annualized by √365?

The answer is a satisfying mix of reasoning and arithmetic.

What’s even better is you will be able to appreciate a range of answers across a spectrum of complexity and be relieved that for 99% of you, the additional complexity is not worth the brain damage. But the insights can still lead to a flood of additional inspiration for anyone interested in volatility!

The key to the question: the meaning of 252 trading days

Straight to the heart of it:

Recognize that when you sampled 252 days of trading data you did in fact sample the volatility that transpired over a 365 day year.

Why?

Because the daily volatility that transpires from close-to-close is not just the volatility from the open to the close!

Close-to-close volatility = close-to-open volatility + open-to-close volatility

[Note: I’m using the word “volatility” in place of the technically correct term “variance”. Variance is volatility squared. Variance is additive across time so it’s the units you use to do the underlying math but the more colloquial “volatility” is  reader-friendly. You probably encounter the word “volatility” an order of magnitude or more than the term “variance” (does Zipf’s law apply to financial glossaries?) so why raise the cognitive load for the typical reader when the advanced reader’s burden of translation is quite low by virtue of them being, well, advanced.]

When you computed the realized vol from 252 days you included the volatility that occurs overnight and over the weekends/holidays. Although you only have 252 samples, it includes information about 365 days.

The core of the issue isn’t that you are missing information, it’s that you haven’t allocated it to the correct containers (ie time periods). You bluntly assigned it to trading days creating the illusion that the information only applies to 252 intervals whose boundaries are restricted to 6.5 market hours.

This is more clear if you compute your own ratios of close-to-open volatility divided by close-to-close volatility. You can start to answer questions like:

  • What percentage of an asset’s volatility accumulates overnight?
  • Do you think it would be higher for global assets like oil and gold or GME?
  • How about weekends…how much of Friday close to Monday close volatility is captured from Friday close to Monday’s open?

All of this reduces to a comforting answer:

If you put your 252-day annualized realized volatility in a 365-day model it will generate a well-priced option assuming next year’s realized volatility is similar.

[Similarly had you annualized by √365 or ~ 19 you will overestimate the volatility and therefore the option price].

Where the brain damage begins: interpreting implied vols

The harder problem is interpreting what an IV means in the first place.

Calendar day (ie 365 day) option models

If we believe every calendar day is an equal contributor to that 30% vol then we are saying that volatility accumulates uniformly across every day, weekend or weekday. This will overstate weekend volatility and understate weekday volatility. In terms of options pricing, the straddle would experience the full theta for every hour from Friday’s close to Monday’s open. But I assure you it doesn’t (and if it looked like it did then IV actually fell — this will be more clear soon).

Business day (ie 252 day) option models

If we use a business day model we are saying no volatility transpires over the weekend. If that were true then the straddle wouldn’t decay at all over weekend.

The reality is somewhere in between. Volatility time doesn’t pass linearly. It passes slower over the weekend (so we experience some decay but not what the full theta predicts) and faster during the week. In other words that 30% vol gets a different weight depending on the day.

The difficulty in interpreting what an implied volatility in an option model is the flipside of the time vs volatility coin — different models disagree on how much time remains in the life of an option where the time remaining is measured as fraction of a model year.

To demonstrate this, imagine it’s the night of December 31st and you are looking at an option that expires on the evening of the following December 31. An option with 365-calendar days until expiry. At this moment both models agree that a full year remains until expiration.

  • The 365-day model says there is 100% or 365 out of 365 days remaining.
  • The 252-day model says there is 100% or 252 out of 252 days remaining.

Ok, January 1st comes and goes. It’s a holiday.

  • The 365-day model says there is 99.7% or 364 out of 365 days remaining.
  • The 252-day model says there is 100% or 252 out of 252 days remaining.

Let’s say the price of the option is unchanged.

[For some reason you can see the option price but the market’s closed. The fantasy actually doesn’t screw up the point. Also, if you have traded cotton you know the options market can be open while the underlying futures market is closed — this itself is a conclusive thought exercise on the Schrodinger’s question of does volatility time transpire when a market is closed.

What if Elon dropped dead on a Saturday, do you think TSLA’s share price is unchanged on Monday — if not then you have also answered the question does volatility transpire when a market is closed.  The fact that you can only measure its impact on Monday doesn’t mean it hasn’t transpired. Don’t confuse accounting challenges with reality.]

Both models are looking at the same option price, but the 365-day model thinks there is less time til expiry — it will therefore mechanically imply a higher volatility.

January 2nd is a business day. It comes and goes.

  • The 365-day model says there is 99.45% or 363 out of 365 days remaining.
  • The 252-day model says there is 99.60% or 251 out of 252 days remaining.

The gap in time remaining between the 2 models has narrowed .15% apart versus .30% apart but the 365-day model must still imply a slightly higher vol to account for “less time to expiry” relative to the 252-day model.

Let’s skip ahead a couple business days to the end of January 6th.

  • The 365-day model says there is 98.36% or 359 out of 365 days remaining.
  • The 252-day model says there is 98.02% or 247 out of 252 days remaining.

Now the 252-day model has less time until expiration. Again both models are fed the same option price but now the business day model implies a higher volatility!

Visual aids

Let’s pretend we are looking at a $100 stock and a call option struck at $100 (an at-the-money option) that expires in 365 days.

Assume the stock price never changes and the option price every day is the price that makes the IV 30% in a 365-day model (these models are the most common and usually the default when you find an online calculator or in your brokerage software).

I populated a table including the 2024 NYSE holiday schedule.

Earlier when we stepped through the first week of the year, you could sense a sawtooth tug-of-war between “DTE % remaining” between the 2 models.

  • A business day rolling off impacts 1/252 of the second model but only 1/365 of the default model.
  • A holiday or weekend day impacts 0/252 of the second model but still 1/365 of the default model.

Therefore, as the week progresses, more time comes off the business day model and pushes up the IV relative to the default 365-day model. Then on Monday, the business day IV falls because the option prices will have experienced some weekend erosion, but the business day model thinks no time has passed. The opposite happens with the calendar day model — the volatility falls throughout the week, but then pops up on Monday because the weekend doesn’t experience a full dose of decay.

If we use the time remaining in the default 365-day model as a baseline, we can compute the difference from the 252-day model. Likewise we can display the spread of the IVs between the 2 models. As the fraction of year remaining in the 252-day model falls relative to the 365-day model, the IV implied by the 252-day model increases relatively.

This is a plot of the option’s life where the time spread means the difference in time remaining from the 252-day model vs the 365-day model:

Note that the IV difference (orange line) for the first 10 months is less than 1/4 of a vol point. It’s not until you get into the last 60 days, that the IV differences get more significant and themselves volatile. This makes sense…when you have just a few weeks until expiration a business day rolling off has a larger impact on the “business-to-calendar days remaining ratio” (the self-loathing astute reader will have noticed that this ratio is exactly what drives the volatility difference. Technically, it’s the square root of that ratio — again the volatility vs variance thing).

Let’s zoom in on the IVs. Remember, we chose an option price that makes the 365-day model always imply 30%. We are seeing how the 252-day model IV bounces around relatively based on that very same option price. (You could have fixed the 252-day model as the default and saw how 365-day IV moves around).

This is the first 9 months. The IVs are fairly close.

The last 3 months:

The same option price is creating a 5 vol point difference in IVs between the 2 models.

[It makes sense. On the last day the default model says there is 1/365 days remaining and the business day model says there is 1/252 remaining. The square root of (252/365) is 83%. The business day model thinks there is much more time remaining than the calendar day model and therefore to generate the same option price it implies 83% of the 30% IV or ~ 25% IV]

Observations

  1. When an option has 1 year until expiration, no matter what model you use you will see the same implied volatility.
  2. The moment, the clock starts ticking, the way the day is categorized will change DTE when measured as a percentage of a year (which is how the t in an option model works — fraction of a year.)A different t yields a different IV for the same option price.

    This is a big reason why all IVs are “wrong”. There is no right IV. They always depend on the ruler we use to measure. When I was on the floor most traders used a 365-day model. When it got to Friday, traders might start “running Sunday’s sheets”…what that means is they push the days ahead in the model to fit the Friday option prices. This is a kluge so they don’t have to lower their model vols only to have to raise them again on Monday when the straddle doesn’t experience its full model theta. The sawtooth incarnate.

  3. Bonus observation: It gets better. Vol time doesn’t even pass linearly intra-day either. The fist 30 minutes of the trading day is 1/13 of the business day but far more of the vol time has elapsed. Your “fraction of the year remaining” has passed faster than what the clock says.Intraday volatility decay schedules will look similar to the percentages prescribed by a VWAP algo — the first hour of the day might be 25% of the traded volume and 25% of the accumulated variance. Just like we decompose close-to-close volatility into close-to-open plus open-to-close we can decompose the open-to-close period into hours, 15-minute intervals, or even finer.

The endpoint of all this volatility accounting is a granular calendar which specifies weights to various periods. This framework can flex to accomodate earnings, economic releases, corporate events/conferences, rebalance dates, or whatever your creativity can imagine. The goal is minimize noisy changes in IV that are simply artifacts of lumpy, discrete decay schedules.

The practical takeaways

I have good news.

Unless you are in the business of trading for a fraction of a vol point, almost none of this matters. I was implementing volatility cleaning functions to trade cross asset >15 years ago. I used discrete methods like you see in the table above. Today, option firms are doing the same thing continuously. They imply IVs by integrating under the curve of a smooth, “event aware” voltime function.

For some it’s cute to know about this stuff if you want to explore further or add new friends to your idea sex orgy. But more importantly, there’s enough scaffolding here to walk away with actionable heuristics.

1) Your annualized realized volatilities (252 annualization factors) are acceptable to use in option models.

  • Implied vols from option models apply that average volatility uniformly to a set of days. This can make them difficult to interpret without grounding it in assumptions of how the volatility is allocated to business days, overnights, and weekends/holidays. But if you are comparing options to one another much of that fog cancels out.
  • And if you are hedging or speculating with options that are more than a few weeks out, the minor IV discrepancies between models are irrelevant.

2) Here’s the one that applies to most:

Don’t worry about small differences in absolute IV measures!!

Why?

  • Again: the variation in IV between models is negligible with months until expiry!
  • The difference in IV is probably swamped by the width of the spread in your long/short rates.
  • If you trade 0dtes or weeklies you are probably better served to think in terms of straddles rather than IV anyway. This renders the IV noise due to “how much time does the model think remains” moot.[Although the topic of “how much volatility should be ascribed to the overnight” is definitely an area worth exploring if you trade short-dated options since those overnights are significant percentages of the variance time.]
  • The typical option user is not doing vol arb for a few cents across asset classes (if you trade oil options that expire at 1pm on Wed vs USO options that expire at 4pm because they are relatively mispriced than you need to care about this stuff). Again, for must cases, the IV noise cancels out if you are trading listed options of the same asset type against one another.

Learn more:

⏳Understanding Variance Time (Moontower tutorial)

If you use options to hedge or invest, check out the moontower.ai option trading analytics platform

“Free” Markets Wet Dream

Just gonna speak freely here.

This cycle of memecoins pumping feels different than the post-covid mania.

The masks are totally off. There is no pretense of value. No attempt to justify the price of anything.

It’s not a ZIRP thing, there’s positive real rates out there. And frankly, you could crank positive real rates up a few percent — the meme coins shouldn’t care. If your taking coin-flip type risks, an extra 2% on your savings still leaves you flaccid. Blue meth and viagra or bust.

All of this feels inevitable.

On gambling culture

LeBron James and Roger Goodell are in bed with Phillip Morris Draft Kings. The biggest baseball star in the world made his bookie famous (the bookie is a former commodities trader because sometimes life makes sense).

Gambling culture is corralling Americans into a holding pen in preparation for the ultimate neoliberal wet dream — put a price on everything. Abstract everything into numbers in an order book.

Here, I’ll glimpse you one of my cards — this is a bummer. They’ll beat you down for saying that because FREEDOM you commie. But it’s not actually freedom. It’s a monopolistic rigged game. But the devil is in the nuanced details. I’m not the messenger for that — instead browse Voulgaris’ recent timeline:

 
https://x.com/haralabob/status/1771188734081298809?s=20

Voulgaris is the NBA sharp (now retired and cruising the Mediterranean on his yacht) featured in Nate Silver’s book and a legend in the gambling world. He’s got lots of haters to be sure (he was quite up front about his dog living a better life than 99.99% of humans in the world), but this podcast interview is a down-in-the-dirt look at his career and the betting world. You’ll also pickup colorful lingo (“beards” “getting down”), insightful discussion of discretionary vs systematic betting, and lessons in niche sources of edge.

As gambling and financial nihilism spread, it becomes risky to sell. I sold my house in November of 2020 — I’m scared to sell anything ever again (not without immediately buying something else). Who knows when the pump is coming to something you own?!

And the more ridiculous the thing you own, the fewer justifications you need to make up for it “mooning”. Worthlessness is now an alibi.

But it’s not just the gambling culture. This feels like a natural albeit non-obvious step in progression of efficient markets. This is where I sound crazy (and if I’m wrong hopefully it’s in a way that doesn’t make you feel dumber for having heard it).

The efficient markets angle

I’m no EMH maxi. I’m more in the “efficiently inefficient” camp is you had to place me in a traditional bucket. But I haven’t studied the academic arguments deeply anyway. My street version — “the no easy trades principle”.

A major difference in mine compared to EMH, is today’s weirdness is actually an expression of efficiency because it goes back to something my closest trading homie says “the leg that makes money is the hard one”.

The sign that the market is efficient is anything that you can pencil out is not an opportunity because everyone else can too do that too. All that’s left is, well, whatever the heck this is.

The Jacked Quant asked:

Why is the noise to signal ratio is exponentially higher in quant finance compared to other realms (AI Twit, Math twit, etc)?

I answered:

Because prices are adversarial. Endless predator/prey dynamic that competes signal away with a half-life that’s a function of transparency and scalability.

Daryl Morey said when finance quants see the signal strength in sports analytics their mouths water but he talks about the flip side of the coin as being “we don’t win by beating the SP500 — we have to be the best of 30 teams.”

We’re not there yet, but you might as well choose now:

  1. Have fun, all this machinery that allocates resources is but a game now. If you like the game and do what’s required to be good at it seems like a sweet time to be puzzle solving and making loot.
  2. Get out of the abstraction of it all and ground yourself in tangible links between inputs and outputs. This is the antidote to nihilism. Look at the people you serve in the eye.

If you use options to hedge or invest, check out the moontower.ai option trading analytics platform

There’s Always Something Going On

Friends,

Two centuries ago, it took a year to send a message around the globe. Now it takes a fraction of a second. We have no idea what this means or what the consequences may be. Man’s knowledge and ability have dangerously exceeded his capacity to understand either.

— Dee Hock, founder of Visa, writing in his journal at an advanced age sometime in the 1980s or 90s.

This is from the opening chapter of Neil Postman’s eerily prescient Amusing Ourselves To Death:

The information, the content, or, if you will, the “stuff” that makes up what is called “the news of the day” did not exist-could not exist-in a world that lacked the media to give it expression. I do not mean that things like fires, wars, murders, and love affairs did not ever and always happen in places all over the world. I mean that lacking technology to advertise them, people could not attend to them, could not include them in their daily business. Such information simply could not exist as part of the content of culture. This idea – that there is a content called “the news of the day” – was entirely created by the telegraph (and since amplified by newer media), which made it possible to move decontextualized information over vast spaces at incredible speed. The news of the day is a figment of our technological imagination. It is, quite precisely, a media event. We attend to fragments of events from all over the world because we have multiple media whose forms are well suited to fragmented conversation. Cultures without speed-of-light media – let us say, cultures in which smoke signals are the most efficient space-conquering tool available – do not have news of the day. Without a medium to create its form, the news of the day does not exist.

Postman’s book, a long essay really, is one of the most profound I’ve ever read. It’s lessons serve as user notes for the world we see around us today. Like close-captioning for our eyeballs. (my book notes)

It took me awhile to find that quote because the compressed version I had in my mind is stored as a prescription for myself not a transcription. You can trace my version back to Postman’s sentiment but its is optimized for usefulness not fidelity. It goes:

“Kris, there’s always something going on somewhere — you must choose what to focus on”

I conjured the Postman bit and the Dee Hock quote because a paradoxical byproduct of hyper-connectivity is isolation. It’s not just having your nose buried in your phone as you wait to order a matcha latte. It’s far more insidious.

Which brings us to this illuminating post:

Is Modern Mass Media A Mind Prison? (9 min read)
by jasonpargin

This is one of the those essays that puts a finger on the sense that we are all being played but struggle to point out the perpetrator. Of course if it were as easy as pointing out a single source of the strife, then it might also be solvable. The source unfortunately seems to be something like [waves hand in big circle] “incentives”. That’s my attempt to fill in what Jason doesn’t focus on. He skips right to diagnosis and cure which is the right approach anyway.

[My opinion: the cause is the most speculative part of the malaise around us and has so many facets we’d be playing a hopeless game of top-down whack-a-mole whereas addressing our individual responses is plausible.]

Excerpt from the end:

I actually believe this to be the single most successful technique for social control in the 21st Century, convincing those most eager for change that it can only come through thrilling and glorious action, a battle of pure good versus pure evil. “Why bother voting on this boring bond issue? I’m not leaving the house for anything less than a war to overthrow capitalism! And don’t ask me to hang out unless you agree, I don’t befriend class traitors.”

The truth that the system is so afraid of us learning—and that we’re happy to let them keep from us—is that actually changing the world requires a stunning amount of tedious, quiet work, of dry reading and learning and organizing and slowly changing obstinate minds. Mathematically, this includes engaging at least some minds you previously considered ignorant or hateful. And this persuasion occurs, not through flashy performative acts, but by slowly earning trust until your opponents want to agree with you.

The system wants you to equate tedious work with neutered slavery and to equate liberation with sexy drama because it knows the opposite is true, that if you restrict yourself to flashy and dramatic solutions, you will be exactly as useful to the status quo as any other sedentary daydreamer. There is a reason the system has no problem feeding you a steady stream of fantasies about violently overthrowing it. 

The reality is that the amount of focus and desire required to blow up the occasional building or pipeline is nothing compared to the lifetime of quiet labor required to understand the system well enough to actually build a better one. And that better world, if it arrives, will require the cooperation of some truly unpleasant people, because all of civilization is nothing but truly unpleasant people learning to peacefully cooperate. 

From My Actual Life

I taught my 5th grader’s math class on Thursday (lesson plan). I did a dry-run with a group of 3rd-5th graders the night before.

Yinh was like “baby Boiler Room” vibes. I promise I didn’t throw my car keys on the table. My favorite comment: Illegal SF Algebra Speakeasy

The following morning: I survived!

Look, today’s letter was admittedly dystopian. Guilty as charged. But that’s no way to start a week. And I heard there’s a void in lifehacking advice this week what with the no-alcohol guy putting out fires with the ladies and all. So I’ll step in with an antidote to the exhaustion —> [try new morning routine] —> end up where you always do cycle:

Cold plunges, manifesting, sound baths, chakras. Meh. The original chicken soup for the soul is just share with your neighbors. Remember you can “just do stuff”. You have gifts. Activate them. It’s nice for others. It’s great for you.

Don’t forget the gist of what Postman said — there’s always something going on. It’s news because they made it news and put it in in front of your face. And what they put is not random. You can find any fact on any day to feel aggrieved. If you aren’t going to do something about “the news” anyway, close the tab. Don’t let the algos choose how you spend the next minute. Outrage is a choice. You can pick literally anything else.

Maybe it’s that freedom that scares you.