Moontower #227

Friends,

I published a new resource:

The Essential Paul Graham (Moontower reading guide)

Description

Paul Graham is a software developer, entrepreneur, writer, and founder of the venerable VC/incubator Y-Combinator. His writing is legendary for its conversational, concise, witty, and incisive style that conveys the nature and promise of, above all, craft. The “what” and “why” of this document Over the past decade, I’ve read the majority of Paul’s essays. But like all great writing, it deserves reading and re-reading. I was delighted to discover that David Senra, host of one of my favorite podcasts, Founders, has reviewed many of Graham’s best essays over the course of 4 episodes.

After listening to his distillation of these essays and re-reading them myself I organized my favorite takeaways as well as my favorite takeaways from David’s favorite takeaways. Like a double distillation of whiskey, the remainder is “the essential Paul Graham”.

Personal thought

The insights in here would be useful to anybody. But because there is great emphasis on the imperative and difficulty of finding work that one is actually excited to do, these lessons have magnificent compounding potential. Make the ambitious teens, college students, and 20-somethings read these essays.

The takeaways are grouped according to topic. They are mostly direct excerpts from Graham but Senra’s reactions are mixed in as well. Senra has terrific taste in passages and is masterful at tying ideas back to common themes across many other founders.

Money Angle

Know-Nothing Sizing

We’ve been talking about how the market does follow the fundamentals you are earning a return because corporate profits are there.

See prior posts:

I also discussed my own approach to portfolio construction (see Inflation Replicator) which backs determines allocations not by expected return but by my tolerance for risk for various levels of confidence. You zero in on an asset allocation with question like “Are you willing to accept a 5% chance of losing 20% of your wealth in 1 year?” If the answer is “no” then you can’t be 100% invested in equities.

As far as equity risk goes, the recent post Index Investing: The Nature of the Proposition can prime your intuition for the risk of the SP500, a diversified equity index with a positive expected return, negative skew, and fat tails means for practical questions like “how likely is it to lose X% over some period of time?”

The key thing to notice — my personal allocation sizes relegate “expected return” to the back burner. I roll with the assumption that systematic risk is irreducible and beta returns aren’t compensation for labor/research but patience and pain tolerance. It’s a weird circular argument — there’s an equity risk premium because if there wasn’t everyone would take a riskless rate which would then lower demand for equities, once again creating an equity risk premium.

Just a thought: I don’t think the meta-game of investing is near some asymptote where we need to question the assumptions of that recursive argument. However, I can imagine temporary scenarios that would necessitate such suspicion. The scenarios would spring from some mix of incompetence to shameful incentives, but the scenarios are not stable equilibriums. One such scenario would include corporate managers en masse internalizing the logic of “meming themselves into an index” and the index committees reacting inflexibly. The long-run check on that behavior is the index committees harming their own brands in the process.

In writing this, it occurred to me that maybe one of the most underrated qualities of being a trader is to relentlessly harbor paranoia without being a doomer. If you aren’t paranoid, your imagination is lacking. But if you’re a doomer, you’re lazy. You have paranoid instincts without discipline — you mistake fuzzy thinking for critical thinking. This is the heart of the trope “do you want to be right, or do you want to make money?”. You know the type:

Ok, back to portfolio sizing. I build the portfolio from a risk-first perspective not an expected return perspective. I call this “Know Nothing Sizing”. When it comes to broad asset classes, my confidence level in the returns is smaller than my confidence level of the risk.

This is not just vibes. It’s a pillar of portfolio construction in the quant world:

Volatility is more stable than returns.

From Advanced Portfolio Management:

A large wave is composed of fewer, smaller waves riding on it, with many ripples on top of the smaller waves. The effects accumulate. Similarly, stock returns are the result of a large shock, such as the market, followed by a few smaller ones, like sectors or larger style factors, and then even fewer, smaller ones. Like waves, many of these movements have similar amplitude over time. We say that their volatility is persistent. This is a blessing because it allows us to estimate future volatilities from past ones.

From the conclusion of Matt Hollerbach’s post Convergence Time:

Stock returns have fatter tails, slowing convergence. Also investment returns, volatility and correlation seem dynamic and not static.⁴ But we have to start our study somewhere.

If investment returns are mostly random, then prior returns possess enormous amounts of error. Therefore they are always suspect. You can’t confidently learn anything about the underlying return from even moderate sample sizes. This is another reason why I don’t use trend or momentum to determine future returns.

On the other hand, small samples produce reasonable estimates for standard deviation and correlation.

Rob Carver distills it nicely in Is maths in portfolio construction bad?:

Classic portfolio optimisation is very sensitive to small changes in inputs; in particular it’s very sensitive to small differences in Sharpe Ratio, and correlations – when those correlations are high. It’s relatively insensitive to small changes in standard deviation, or to correlations when correlations are low.

It’s extremely difficult to predict Sharpe Ratios, and their historic uncertainty (sampling variance) is high. It’s relatively easy to predict standard deviations, and their historic uncertainty is low. Correlations fall somewhere in the middle.

If we assume we can’t predict Sharpe Ratios, then some kind of minimum variance (if we have a low risk target or can use leverage) or maximum diversification portfolio will make theoretical sense

If we assume we can’t predict Sharpe Ratios or correlations, then an inverse volatility portfolio makes the most sense

Outside of the universe of large cap stock indices it makes a lot of sense to use the relatively predictable components of asset returns – volatility and correlation.

Using volatility as an input makes a lot of sense – it’s highly predictable, and will help reduce your exposure to potentially problematic assets.

If we assume we can’t predict anything, then an equal weight portfolio makes the most sense.

I’ll add a few comments and then a practical thought for you to consider as you ponder your portfolio.

1) A reminder that volatility understates risk in the presence of extremely strong skew.

See:

2) The equal-weight or 1/N sizing rule is a better candidate for the name “Know Nothing” since that’s what you’d do if you didn’t even have an estimate for the volatility. Equal-weight makes more sense for sub-portfolios like a collection of start-ups or angel investments but it’s rare for someone to have their entire net worth in such an illiquid basket.

3) Finally, a thought to consider.

There is a 100% chance that at some point in the future you are going to look at a statement and find a single security, private fund, or magic coin in a 50%+ drawdown assuming no leverage.

(I’m much less certain if you use stop-losses or momentum rules.)

And if we want to measure real instead of nominal returns, I’d make that statement about any asset classes like “equities” or “bonds”. It’s not only happened before, but here’s an uncomfortable truth — the worst is always in the future.

This fact is reminiscent of one of these strange dorm-room kind of conversations that option traders have about what shape a platonic volatility term structure should have. They generally conform to a power law, y = axᵏ, but I’ve been around traders must smarter than me debating what the bleak truth might mean for that specification. As far as I know nobody trades on such debates but hey the portals are there for inquisitive minds. Since it’s not 2am I’m gonna stay focused on more present matters.

Even though it sounds bleak, it’s not a doomer comment in any practical sense.

Even if that happened in Amazon today and you had been invested in Amazon for 20 years, you’re still way ahead.

No matter what, you’re going to invest because there is no alternative. But understanding that reality is important to make an honest decision about how concentrated you want to be.

The conditional probability of a drawdown of 50% while the world doesn’t end is still tiny. Said otherwise…most of the ways we drawdown 50% do not coincide with the world ending. The lowest bar of risk management means avoiding that happening to your portfolio independently of it happening to everyone else.

Money Angle For Masochists

A reader sent me this amazing note (lightly edited). Eliciting a response like this is always the lofty goal.

I was going through your earlier posts today. (this and this)

I got the general idea that you’re replicating the payoff by buying some amount of shares by shorting some amount of t-bills for a while, but for some reason, the terms never truly sank in:

C = S * N(d1) – X * N(d2) [assume rfr=0, etc.]

I didn’t quite follow why

S * N(d1) represented the “expected value of the shares going in the money”, and
why we specifically have to short X * N(d2) worth of t-bills to self finance, and why X * P(ITM) < S * delta in your post initially

Today I was playing with MoontowerGPT and it really sunk in using this example.

I asked it to give me a discrete distribution for a $100 stock such that the expected values summed to $100.

So like:

I wanted to price the 102 call intuitively, and then the terms all made sense.

S * N(d1) represents the portion of the $100 expected value that comes from all prices above 102. (i.e. 105 * 0.25 + 110 * 0.25 = 53.75) and
the amount of t-bills to short is (102 * 0.5 = 51)

so the call per BS would be worth $2.75 (53.75 – 51)

…but also I realized:

C = [(110 * 0.25) + (105 * 25)] - [(102 * 0.25) + (102 * 0.25)]

re-arranging the terms, that’s

C = (110 - 102) * 0.25 + (105 - 102) * 0.25

which is really the weighted average of the payoffs of the call option in different scenarios above.

Like woah, everything just came down to weighted averages!

Anyways, nothing too revelatory here, but using MoontowerGPT for example has been amazing, and I felt that moment where everything came together (similar to when I watch a 3Blue1Brown video), thought I’d share! 🙂

Stay Groovy

☮️