Observations After 40 Weekly Letters

As the year closes, I thought to indulge some observations about writing these weekly Moontower emails.

On Process

  • Started in March. 40 weeks in a row
  • Between the weekly email and my website I’ve written 100k words or the equivalent of a 400-page book (there’s an iceberg of notes under that)
  • The email takes about 7 to 8 hours per week 2 of them have taken upwards of 12.
  • About 1/3rd of that time would have been spent doing it anyway as I have been taking lots of notes over the years. The extra step of making it public, while intensive was still incremental, which is why I thought it would be a fun idea in the first place.
  • I started with about 20 weeks worth of ideas in the queue. After writing 40 of these, I now have about 50 in the queue. There’s a lesson about feedback loops in there somewhere. I often don’t consult the queue and just tackle something that I noticed that week.  Usually, the topic occurs to me in a way that unifies some subset of my notes.
  • The time to do this has come away from watching TV and movies, some Friday night activities, some workouts and strolls, and some sleep. Everything has a cost.

On Benefits

  • The coolest benefit has been what one friend emailed me to say he’s enjoyed the “friendship renaissance”. We have many phases in life. A number of people from my days in NYC who I have fell out of touch with now regularly email with me. Sometimes sparked by a Moontower topic. But there’s another effect that I can relate to since I get a lot of letters myself. Reading somebody every week breeds familiarity as well as an implied (or in Moontower’s case, an explicit) invitation to chat. We all know great, thoughtful people who we just fall out of touch with. The letter was a beacon to invite them back into my life even if I didn’t realize that fully when I started this.
  • I have gotten to meet many people both digitally and IRL. There’s a lot of cross-pollination with Twitter conversations so it’s hard to directly attribute, but this year has to, on average, I’ve met 1 in-person per week. And there are more connections online that I have regular chats with. I think the thought of that idea would have exhausted me in the past. Not that I’m shy, just not a social butterfly. But the meetings have been invigorating since they are rooted in a spirit of mutual open-mindedness and helpfulness. I suspect this might not even seem like something remarkable to many of you but for the few to which that may resonate, it’s worth mentioning.
  • It has been a forcing function to get me to write. Something that I have been wanting to do for a long time but required a form of accountability to get started. Your attention is so so appreciated. I’d be privileged if I could help one of you as much you’ve collectively helped me.

On Growth

  • I sent a welcome email to about 110 friends and family when I started in March. 40 people signed up for the first letter. Today, 375 people receive the email. This is an objectively tiny number but it punches so far above its weight. You are a smart, curious group of readers.
  • The growth is partially from word of mouth but mostly from something I’ve written that gets boosted by a highly-followed person. The most popular letters have been the ones in which I explain something technical from my own non-academic point of view.
  • On average, 2 people sign up per day even though it’s super spikey (about a month ago the readership grew by over 30% in a week).

On the Future

  • You can expect more of the same. I see myself as a curator and gatherer who basically takes you with me on my own learning journey. If Moontower had a theme it’s that the world is messy and by sharpening our thinking we can not only get better but be more empathetic. I’d say my pet peeve is the rampant discourse which acts otherwise. Discourse that at its best is flat and stupid, but more often, willfully manipulative.
  • You probably noticed I added the Money Angle section. This was natural since investment topics overlap with my professional domain and I thought it was useful to separate it a) for the benefit of those who find this via #fintwit and b) to spare those of you who might find those topics “too much”.
  • I’ll continue to look to you for input as how I can be helpful or more lucid. I don’t have any proper training or qualification. And while my very first letter addressed pushing past “imposter syndrome”, my opinions about how I present material is pretty loosely held. So don’t feel like you can offend me with criticism.

Music Appreciation Channels

My favorite YouTube channels are about music appreciation

1. Ryan and George are Lost in Vegas. (Link)

These 2 guys are R&B and hip-hop enthusiasts who have discovered rock and metal. Their followers submit songs for them to do reaction videos and they have amassed a million followers who tune in to see their commentary. It’s like a play-by-play for songs you know. Despite not being musicians themselves, you only need to see a few videos to realize they have innate musicality and perceptive ears. But the best part of these videos is how enthusiastic and endearing they are. It’s easy to see why they have become popular enough to quit their day jobs. I’ve been watching them for a couple of years and it’s cool to watch their palette widen and see what songs they will give their highest honor…”playlist!”

While I dig so many of their videos, including their breakdowns of Rush, Rage Against the Machine, Van Halen, and Metallica songs their’s nothing like watching them lose their minds over a song that you also love. They do plenty of hip-hop and even country songs.

Here are some of my favorites:

  • Alice in Chains: Rooster (Link)
  • Chris Stapleton: Tennessee Whiskey (Link)
  • Black Sabbath: War Pigs (Link)

And here’s a more recent one with their higher production backdrop…and is a great way to wade into the brilliance of Tool’s recent album which I’ve raved about before.:

  • Tool: Pneuma (Link)

2. Rick Beato’s Everything Music channel (Link)

Rick is a producer and multi-instrumentalist who represents the opposite end of Ryan and George’s amateur appreciation. Rick will dive into music theory and teach you what makes certain songs great. Everything from ear training to detailed top 20 lists. If you are a big music fan, music nerd, or musician this channel could keep you busy enough to displace Netflix. His home studio is ridiculous and he can sidestep getting blocked by music labels since he can easily just demonstrate the music being discussed on his own.

A great place to start:  “What Makes This Song Great?” series (Link)

Here’s a look at his other playlists. His son Dylan has perfect pitch and gets his own playlist full of his own party tricks.

Facing A New Decade

Facing A New Decade

With a new decade looming you are being bombarded with listicles, resolutions, and all manners of reflection. We can’t help but pause when faced with a year ending in a zero. Ascribing significance to base 10 years seems a bit arbitrary, but I’ll play along for a moment.

Taking Inventory

At the start of this decade, I was living in Long Island City. I had my own trading business by then, banked more money than I could have imagined possible just a decade earlier (trust me this says more about my 21-year-old imagination than my 31-year-old paychecks), and very recently married. Facebook was still new to me. We were mailing DVDs with Netflix. If I go back and look at my Google photo album from 10 years ago, it’s sparse. I looked back at my Google calendar from 2010. Crickets.

A lot changes in a decade. I don’t even have a DVD player now. I have been in the Bay Area for 8 years. My Nextdoor profile rhetorically wonders “How long do you need to live in CA before you’re no longer a New Yorker?”. After recently celebrating my 10 year wedding anniversary and 17th year overall with Yinh, I have now spent an equal amount of time with my partner as my nuclear family pre-college. In 2010, our circle of friends had very few babies. Today my 3-year-old is one of the runts of our friends’ combined litter. Today my life is rich with kids, so many nieces and nephews by both blood and bond.

But the passage of time carries everyone forward. My parents, wife’s parents, aunts and uncles, and yes even one of each of Yinh and my grandmothers are 10 years older.

We are children of a generation who gave birth young. We will be much older grandparents than our parents are today. We spent some extra time in our 20s hustling maybe. Or just having selfish fun. Tradeoffs I suppose but no sense in regrets. It’s natural to consider what I might be writing 10 years from now. When I’m 51. My oldest son will be taking the SAT. I’m already older than my mom was when I took the SAT! I’ll be shuttling Max to and from his freshman year of high school in between my doctor-recommended prostate exams and colonoscopies.

Another Year, Another Whisker

Projecting your life forward is never sentimental. Mawkishness only works in reverse. When you are young, looking forward is about ambition and hope. More money. More freedom. A house of your own. But when you cross your actuarial midpoint, the exercise drifts towards melancholy. We’ve seen enough to realize that joy balances on the head of a pin. The unannounced wind will invariably come. If you haven’t heard it whip yet, you’ve heard the tales of its force.

If this sounds sad, it’s because you compared this outlook with the illusions of youth. When you were young, you were naively impervious. I suspect this is a design feature. A timed release of feigned wisdom which you had not yet earned. Of physical beauty which belied your insecurity. When a 24-year-old bro advertises his fitness as a mate, we know nature’s mimicry transcends snakes and butterflies. When you are older, you can spot the fake.

If your beliefs from ten years ago embarrass you, congratulations. You’ve grown. Growth is paradoxical. It comes with both assuredness and humility. It must be humbling. You just learned how wrong your past self could be. But it’s also a hint. You don’t need to pretend anymore. It’s ok to be wrong. More than ok actually. Do you ever wonder what beliefs you carry today that will make future-you cringe? Squirm if you must, but let yourself grow.

A Gift Lies Ahead

Herein lies the beauty of looking ahead — grace.

You may get to be someone’s shelter from the wind. An honor to which even a precocious youth can find no shortcut. It’s as if life’s greatest privilege is reserved for the aged. For those who see their chance to serve as a reward for the mistakes they’ve made. When getting older makes you realize everything is ephemeral, then you can finally enjoy it. When you think you have forever, the present never feels urgent. If you could live forever, nothing would matter. Scarcity, far from a constraint, is actually liberation.

So rather than lament what you will inevitably lose, do what you can today to enhance the memories which are yours forever.

I say all of this knowing that in 10 years I will look back and think about how stupid I was about some things I think today. But that’s just another thing to look forward to.

Is There Actually An Equity Premium Puzzle?

The equity risk premium, or ERP, is defined as the excess return you get for investing in stocks over the risk-free rate. Simply, it’s the premium return you earn in exchange for dealing with path. The fact that you might experience a 20% drawdown every few years (with U.S. equity markets currently sitting on all-time highs it’s hard to believe that just 1 year ago the SP500 had a 20% drawdown). I admit this “no pain, no gain” explanation sounds a bit weird.

Student: Hey prof, why do I get paid extra for buying stocks instead of t-bills?

Master: Because if you weren’t offered a discounted price to buy stocks you wouldn’t. Duh.

Proof by induction can be unsatisfying. To be fair, my use of the word proof is straining its English definition. Instead, it’s typical to hear ERP referred to in the context of a puzzle since some economists with calculators decided that this roughly 6% historical premium has been excessive compared to what they would expect even risk-averse investors to demand.

Enter the Witch

But what if I told you that there is actually no ERP and therefore no puzzle. Well, you’d accuse me of heresy since I’m directly contradicting widely accepted financial orthodoxy. After all, I’m ignoring the fact that equities have in fact outperformed t-bills by a wide margin.

Let’s look at that assertion again — equities have outperformed t-bills by a wide margin.

Well, what do we mean by equities? Single stocks or indexes? This is where I let the witch take over. The heretic, BreakingTheMarket who states:

The Equity Premium Puzzle has lasted for 37 years without anyone recognizing the market index doesn’t represent stocks.

Mistaken Equivalency

Turns out the existence of an ERP depends on your definition of equities and an index of equities is just not just equities. It’s a strategy. An index is a rule-based weighting that rebalances intermittently. The difference cannot be overstated. Why?

“Stocks” and the “Stock Market Index” are not the same thing and never have been. One is an asset class, the other is a trading strategy of that asset class. They don’t behave the same and don’t have the same properties, return, or standard deviation. You can’t use one to replace the other.

The math makes it clear.

When you compare the geometric return of stocks not a stock index you do not find an ERP!

The key here is that the historical volatility or standard deviation of single stocks is .33 which is about twice what it has been for U.S. stock indices. He makes the case that a .55% premium is much more in line with what economists would predict or just dismiss it as noise.

Enjoy the full post Solving the Equity Premium Puzzle, and Uncovering a Huge Flaw in Investment Theory. (Link)

How This Ties Together With What We Have Learned In The Past

As you digest this, there should hopefully be a comforting reinforcement of past ideas, namely:

  • When we deal with multiplicative processes, like returns that compound wealth, we care about geometric or logreturns not arithmetic returns because of the “volatility drain”. (Link)
  • Portfolio components are not perfectly correlated so when we rebalance, we capture a premium geometric return. (Link)
  • The imperfectly correlated aspect of a portfolio contributes to what Fernholz called the excess growth component that diversification earns when you are in logreturn space. (Link).

If we presume stock index volatility is only 17% (as opposed to the 33% for single stocks), we can use napkin math to make additional observations.

  • Index ERP is closer to 6% – .5 * (.17^2) = 4.56%…the extra 4% represents Fernholz’s “excess growth rate”. This is why some pros refer to diversification as the only “free lunch” in investing.
  • The average cross-correlation of stocks in an index can be approximated by the ratio of index variance to average weighted stock variance. Using our estimates (.17^2) / (.33^2) = .27 which is in the ballpark of where long term average SP500 index correlations have realized (although option folks know how spikey that number can be, especially on short measures).

Summing Up

ERP doesn’t exist if you look at stock; only stock indexes!

  • Researchers commonly mistake equivalency between a single asset and a portfolio:
    • Treasury bills (and bonds) are a single investment item. An equity market index (SP500 for the original study and many others) is a portfolio of many investments, who’s composition changes all the time. They are not the same thing and shouldn’t be compared as if they are!

A Final Note

I chat with BreakingtheMarket on Twitter and follow his discussions with quants. So much of the merit of Twitter, and the internet in general, is the beauty of being able to learn and engage in conversations with talented, curious people whom you may not have found otherwise. Breaking the Market is not in finance. He’s an engineer with a strong math background who approached markets with a “beginner’s mind”. I don’t think it’s an accident that two of my favorite finance writers on the internet are from scientifically minded people from a different field. I think the best finance blog is PhilosophicalEconomics.com which is penned by another finance outsider, the pseudonymous Jesse Livermore. Jesse did his first interview this year and it’s worth checking out, along with his widely influential writing. (Link to interview with my notes)

How Much of Momentum Is Caused By Randomness?

Randomness In Momentum Everywhere (Link)

This post from Breakingthemarket.com contends that randomness and rebalancing undoubtedly explain SOME of the findings in favor of a momentum effect.

Key Takeaways:

Rebalancing increases a portfolio’s returns

The more often you rebalance the greater the benefit. With the 30 components of the Dow, increasing the rebalancing frequency increases both the portfolio’s arithmetic and geometric returns.

Since most momentum studies examine portfolios which filter and rebalance momentum candidates, we would expect to see improvement over a passive benchmark due to rebalancing alone.

  • Consider one of the original momentum studies by Jegadeesh and Titman:

Their methodology is actually an equal-weight rebalancing scheme, with the 3 month “holding period”, serving as a 3 month rebalancing period, and a 6 month rebalancing period, a 9 month rebalancing period, and finally a 12 month rebalancing period. The finding that “momentum” is strongest over the shorter period and fades as the holding period grows is not a finding about momentum. It’s exactly what you would expect from random behavior when adjusting portfolio rebalancing frequency. Yes the slope of the momentum curve is much higher, but momentum stocks are also much, much more volatile than dow components.

This turns out to be a hint as why momentum is “found everywhere”. The act of rebalancing which is common to all the studies.

  • Note that finance blogger Jesse Livermore got close: momentum failed to work in individual securities but worked in indexes. Recall from Fernholz discussion of EGRs, that portfolios have better logreturns than the weighted average of their components because the cross-correlations reduce the variance of the basket. Arithmetic return and geometric return differ by the the amount of variance.

Momentum is really a volatility screen

  • Imagine two groups of 50 stocks. The first has an average return of 5% but volatility of 25%. The second has an average return of 10%, but a volatility of 15%. If you let the stocks randomly produce returns for a short period, and then select the 10 best stocks, is your sample more likely to come from the first group or the second?
  • Because the first group is more volatile, it is more likely to have extreme losers and winners. Momentum is a gigantic volatility screen, more so than a “momentum” screen. The momentum screen will lean toward picking stocks with higher expected returns. But importantly it will also be filled with high volatility stocks even if they have average or poor returns.

Fading momentum is explainable by geometric return math

Momentum is said to “fade over time” but this is exactly what happens with random returns as “All random compounded returns start out producing returns equivalent to the asset’s arithmetic returns. But with every repetition, the returns will converge toward a geometric return. A portfolio of stocks slows down this degradation of returns toward the geometric return, but it still happens.”

  • Note how a portfolio slows down the process of degradation vs single stocks
  • We already know momentum screens select high volatility stocks. High volatility stocks will inherently have a large spread between their arithmetic and geometric returns. Therefore, the shape of the momentum return stream over time isn’t really an anomaly at all, but is expected…You don’t need stock “momentum” to explain the results of the study. The rules of the strategy alone create the illusion of momentum, even with random coin flips.

Randomness as the benchmark

He concludes:

Technically, I’m not saying that randomness explains ALL of the momentum effect. It may. I’m saying randomness and rebalancing undoubtedly explain SOME of the findings of these papers. The process of selecting high volatility stocks and rebalancing them frequently produces most of “momentum’s” performance. If researchers compared their results to a random data set, they would see this.

Best of Moontower 2019

The Top 11

Spinal Tap style here’s the Moontower posts you seemed to like the most based on my proprietary state-of-the-art analytics which I will only tell you about if you get me drunk.


Is Loneliness A Downside of Connectedness?
Don’t Ignore the Tambourine

Finance and Economics

The Volatility Drain
The Income Inequality Myth
The Disagreeable Investor

The Scooped Midrange
The Homeownership Fetish
How Expensive Human Poop Saved Us All And How High Prices Are Self Correcting

Mind and Productivity

More Shower Thoughts Please
Memories As A Unit Of Time


Number Neighbors

References To Bookmark

Here are writeups you may find useful once they are practically relevant for you:

How To Approach Twitter (Link)
Tips to Optimize Your Reading (Link)
The Investment Experts Bookshelf (Link)
Car Lease Math is Not Obvious (Link)
Correlation Is The Key to Investment Portfolios (Link)

Littlewood’s Law in Media

Check this out.

What’s your gut reaction?

If Moontower Musings are doing their job then many of you will have smelled a trap and wondered “well how many cardiologists are there?”

The excerpt was taken from a Slatestar’s post Cardiologists and Chinese Robbers (Link). He discusses parallels in “Chinese robbers”, police brutality, and basically any anomaly that can be summed without context to indicate a trend.

Littlewood’s Law

“In the course of any normal person’s life, miracles happen at a rate of roughly one per month”

Applying Littlewood to the news, Gwern writes:

There will be enough ‘miracles’ that all media coverage of events can potentially be composed of nothing but extreme chance chances, even though it would seem like an ‘extraordinary’ claim to say that all media-reported events may be flukes. Given this, it is important to maintain extreme skepticism of any individual anecdotes or stories which are selectively reported but still claimed (often implicitly) to be representative of a general trend or fact about the world.

Inoculate Yourself

He maintains that your best defense remains standard techniques like critical thinking, emphasizing trends & averages, and demanding original sources can help fight the biasing effect of news.

Here’s an easy trick you can use every day. When you encounter cases where anecdotes are used to paint a picture, instead of jumping to horror, retrain your mind to ask “what is the denominator?”

Unfortunately, connectivity combined with the existence of billions of humans will lead to news which distorts reality. I don’t see any supply-side solution to this. Extremes sell. The human love of narrative is a biological backdoor that media holds a key to. It takes mental effort to be constantly critical. To constantly question how stories are framed. For a mild taxonomy of narrative fallacies and how to spot them Art of Manliness gets you started. (Link)

Gwern has some satirical recommendations for the journos. His intentionally naive belief that news is about signal and not clicks is cute. Some of my favorites:

  • Perhaps in one format, discussion could be weighted similar to a meta-analytic weighting of effect sizes: you are allowed to discuss both anecdotes and studies, but the number of words about an anecdote or study must be weighted by sample size. So if you write 1 page about someone who claims X cured their dandruff, you must then write 100 pages about the study of n=100 showing that X doesn’t cure dandruff. That’s only fair, since that study is made of 100 anecdotes, so to speak, and they are as deserving of 1 page as the first anecdote.
  • A “proportional newspaper” might allocate space by geographic region populations, so there’s a giant void with a tiny little 2-line wire item for Africa, while the (much smaller) USA section requires a microscope.
  • Weight by age: If someone is rereading a 50-year-old essay, that should be given more proportionally more emphasis on a social media stream than a 5-minute old Tumblr post.


The Cost of Taking The Bait

The news’ incentives plus our susceptibility to stories strand us in a suboptimal equilibrium. The distortions are insidious and distributed.

How do they darken our world?

1) Healthy skepticism is your best-case scenario

Back to Slatestar’s cardiologist’s example:

If you read Part I of this post and found yourself nodding along, thinking “Wow, cardiologists are real creeps, there must be serious structural problems in the cardiology profession, something must be done about them,” consider it evidence that a sufficiently motivated individual – especially a journalist! – can make you feel that way about any group.

So what are your options?

  • Put no effort into learning how to reason and be an easy mark for charlatans, pseudoscience, ads, politicians.
  • Go to a Penn & Teller show to start a life-long journey into skepticism

Nobody actively chooses to be a sucker, so this is a classic Hobson’s choice. You might not check out P&T but you do try to be critical. So you must find a way to be skeptical without becoming cynical. If my own experience is any indication I’d expect many of you to agree that this is a difficult line to walk.

2) We glorify extremes 

Dr. Oz and the media will highlight whenever a patient appears to benefit from one of his quack remedies. But no story will be written about the patients who did not get better using his tips. Sure that’s frustrating, but by now you are immune to that trick even if the masses are not (given how rich Dr. Oz is I’m pretty sure I’m not underestimating the public here).

But here’s a more speculative cost of glorifying extremes. School shootings. The gun control issue is important, but I’m a seller of it being the entire issue. The social mirroring aspect feels like it is not given enough weight. The question of whether they are contagious, and if so, why and to what extent feels underexplored. Malcolm Gladwell is only a scientist by airport bookstore standards so we know to take him with a heap of salt, but his riot threshold model is worth a peek.

My own feeling about the rise in shootings is strongly tied to a vague sense of how social media and traditional media feedback on each other which is highly coincident with how modern the epidemic really is. Gladwell’s theory happened to tie it together in a way that made me feel that I wasn’t alone in thinking social dynamics are the biggest driver.

  • I first caught wind of his take from a 10-minute talk at the New Yorker Festival. (Link)
  • If you prefer a 3rd party take on his theory, Derek Thompson gives it his characteristically balanced treatment. (Link)

If you are new to Moontower, you can find my own views about consuming the news here.

How Math Is Sufficient To Explain Small Stock Outperformance

Takeaways from Diversification, Volatility, and Surprising Alpha by Fernholz et al. (Link)


  • It has been widely observed that capitalization-weighted indexes can be beaten by surprisingly simple, systematic investment strategies including equal and random-weighted portfolios.
  • This outperformance is generally attributed to beneficial factor exposures.
  • It turns out this outperformance needn’t invoke factors. It can be explained by stochastic math where correlation and variance play a larger and more predictable roles than returns.
  • Portfolio logreturns can be decomposed into an average growth and an excess growth component. They argue the excess growth component plays the major role in explaining the outperformance of naıve portfolios.

Some basics

Let’s establish some basic definitions.

Stock Returns

There are 3 types of returns commonly used to describe growth rates. But they are not equal.

Arithmetic returns > Geometric Returns > Log Returns

This is important because only logarithmic returns are an unbiased estimate of expected long term returns.  In other words, arithmetic and geometric returns will overestimate expected growths in wealth.

  • Logreturn of an asset= Arithmetic return – .5 * variance
  • .5 * variance is known as the volatility drag or variance drain. I’ve discussed this here in simple terms.

Portfolio Returns

The logreturn of a portfolio can be decomposed into 2 components:

Weighted avg of stock logreturns  + “excess growth rate” (aka EGR)

Understanding the EGR

EGR = (weighted average stock variance – portfolio variance) / 2

The relationship between stock variance and index variance

Now this part is not in the paper, but taking from my index options experience:

Portfolio variance = weighted average stock variance * average cross-correlation of the stocks

This is a common identity used to price index options. It makes intuitive sense.

  • If all components of the portfolio has a correlation of 1 the portfolio variance would be the same as the underlying stocks.
  • If you had a 2 stock portfolio and the correlation were -1 the portfolio variance would be zero. Iimagine a basket comprised of 50% SPY and 50% inverse SPY. It would never move in price (assuming no fees, frictions, etc) regardless of how high SPY variance was.
  • For an average correlation < 1,  the portfolio variance must be less than the average weighted stock variance.

The key insight: the lower the average correlation between the components the wider the spread between the portfolio and weighted average stock variances!

Back to the paper…

Observations about the EGR

Looking at the formula again:

EGR = (weighted average stock variance – portfolio variance) / 2

  • EGR boosts the portfolio returns beyond that of its components since portfolio variance < weighted average stock variance
  • EGR boosts portfolio returns with lower correlations
  • EGR boosts portfolio returns with high stock variance

Relationships Between Market Cap, Logreturns, and Variance

The authors then use a rank based computation to show:

  • Logreturns of individual stocks do not vary by market cap.
  • Variances of individual stocks do vary by market cap. Smaller stocks are more volatile.

This prompts the great reveal:

Small stocks don’t have higher returns but have higher variances which boost EGRs. The volatility and interaction of the stocks is boosting the portfolios that contain them without any need to rely on factors! The increased volatility of the individual stocks did not earn them a risk premium when considered in isolation, but at the portfolio level they contributed to excess growth.


  •  The authors contend that the excess growth component can be estimated relatively easily, since its value depends only on variances, or relative variances, which are not difficult to determine in practice. The average growth component, however, is more difficult to estimate. 
  • Small stocks are riskier and while this might mean higher single period arithmetic returns long term investors care about logreturns. In logreturn space, individual stocks don’t contribute excess returns. This is at odds with conventional wisdom.
  • Instead, the excess returns are coming at the portfolio level via the small stocks’ contribution to “excess growth rates” (EGRs).
  • They tested the expectations of this stochastic portfolio math on 5 commonly employed weighting strategies, some more diversified and some less diversified than the capitalization-weighted portfolio, confirmed these insights. In general, the more diversified portfolios outperform and the single less diversified portfolio underperforms, because the more diversified portfolios have a higher excess growth rate. This arises from the higher variances associated with the smaller stock exposure in these more diversified portfolios, and not because such stocks have inherently higher returns. This higher excess growth rate, in turn, increases the portfolios’ logarithmic return.

My Comments

  • The role of low correlation was not emphasized enough in the paper considering it drives the EGR by setting the gap between portfolio and average weighted stock variances.
  • You should read the paper if you’d like a refresher on computing arithmetic, geometric, and logreturns.
  • You should read the paper to see how they computed rankings since this work established that there was no relationship between logreturns and the market cap of a stock.

Moontower Gift Guide for 2019

It’s the official start of holiday season. I thought this would be a good time to share some of my favorite finds from 2019 including a gift guide in advance of Cyber Monday.

Moontower Gift Guide

Everything in this list is something I have gotten great use out of and found to be reliable. Several of them have been secret Santa gifts I’ve been given. You can’t go wrong buying them for your white elephant exchange or jumping on them if someone else brings it to the party.

1. A car jump starter. I have a VicTsing model (link)

  • Doubles as a high capacity power bank
  • I keep this in my car and have used it many times to give myself a jump without anyone’s help as well as used it to help other motorists. It’s a quicker, easier process than putting 2 cars nose to nose.

2. A 12v/120v power inflator. There are many types to choose from. I have this Bonaire model (link)

  • Set target tire pressure and hit ‘go’. It auto shuts off when the tire is filled. The best part — a digital guage.
  • Comes with regular 120v power cord and the 12v that plugs into your car’s ashtray. I had to use that one on Friday actually.
  • Comes with multiple needles for filling basketballs or bike tires.

3. Asus ZenScreen. My laptop has a 13″ screen but the ZenScreen connect via USB to give you another monitor. (Link)

  • Draws power from your laptop so no need for a separate power supply
  • The included case acts as a stand allowing you position the monitor horizontally or vertically

4. Youtube Premium (Link)

  • I watch more Youtube than I do TV. If you have the same habit, it’s worth the monthly subscription to get rid of the ads. I started paying for it this year and I’m happier for it.

5. Youtube TV (Link)

  • If you are thinking about cutting the cord, I just wanted to share our solution. We switched to Youtube TV in January and we have been happy. It has all the channels we want and there is no lag when you change channel. The lag was always a pet peeve from our Comcast setup. The quality is good and we are saving a little bit of money.

6. Shady Rays Sunglasses (Link)

  • I like their aviator styles. I wrote this summer: I ordered some Aviator style sunglasses from Shady Rays. They are about $60 bucks. If you break or LOSE the glasses up to 2 times they will send you a new pair for the cost of shipping. 

7. A massage gun. I got a Hypervolt (Link)

  • For the person who likes when the masseuse karate chops their back rapidly Street Fighter II- style. They are pricey but if that therapy is your jam, these guns are pretty awesome. Get your kids or partner to do your back. You can do your legs, IT band, etc yourself. There’s 3 intensity settings and it lasts several hours from a single charge.
  • I actually got a knockoff from China for a fraction of the price and it works perfectly. If you are interested and in the Bay Area hit me up and I might be able to help.

8. “Demonslayer” sake (Link)

  • At $50 a bottle this is a treat but it’s very smooth junmai daiginjo. I mentioned a bit about sake from my trip to Japan. (Link)

9. Most practical stocking stuffer

  • White Wizard Spot Remover (Link). We give this to everyone. Takes blood out of white sheets. If you have kids you keep this stuff in a holster. I have no idea if it’s destroying the environment but it’s so good I assume I’m being evil.

10. Games

Boardgames I started playing this year with my 6-year old:

  • Evolution — The Beginning: I wrote about it here
  • Forbidden Island (Link): Simple and fun coop game by the same game designer who brought you Pandemic. The game gets kids to work together and while the replayability for adults is limited there is enough variation in board layout and characters to keep kids engaged. Take about 30 minutes to play and requires no more reading than identifying the names of regions.
  • The Magic Labyrinth (Link): By far the best version of a memory game our household has ever played, No reading required and adults and kids are on equal footing since the game is about trying to remember you and others’ footsteps through a maze with invisible walls. This game was a big hit around here and is one of our favorites to gift since its fun and has few rules to learn.

Boardgames for 10 and up:

  • Settlers of Catan (Link): This was the gateway game that got us into European boardgames 11 years ago. Putting it here because we recently re-discovered it when I took a chance and taught it to Zak. Honestly, unless you are used to playing games for hours it might be a reach for age 6 but I’d feel very comfortable teaching it to an 8-year-old. Teaching someone the rules is the most painful part, but I have yet to meet anyone who did not enjoy playing. Even non-gamers. It’s a gateway game for a reason. While its conflict is economic like Monopoly, it feels less punitive and the entire design is one of the most elegant I’ve seen. Dusting it off was like seeing an old friend and wondering why you let it take so long to connect.
  • Decrypto (Link): A party game like Codenames. Both games are great for teams and so many ages. As word games go Codenames and Balderdash are hall of famers but Decrypto is an instant classic we started playing last Christmas.
  • Acquire (Link): I’m putting this game here even though it’s several generations old. It’s a classic game of M&A and stock ownership using the hotel industry as the theme. Many Moontower readers are finance pros so might appreciate the rec if they didn’t know about it already. It’s in a sweet spot of complexity and has clever market-driven dynamics.
  • A general tip: normal people don’t like reading rule books. Learning rules is best done via Youtube videos. Just search for a tutorial of the game you are interested and use the rulebook as a reference. If you need even deeper rule clarifications I’m 99% confident any question you can think of is covered in relevant BGG forum.

Video Game

  • We just discovered Portal : Bridge Constructor (Link). Available on many platforms including iOS and Android. We are playing it via Xbox Game Pass which has 3 months for a $1 intro rate which gives you access to tons of free games. If you liked Lemmings growing up you will dig this game. The whole house is addicted to structural engineering principles now.

11. Finally, a rec I received from Twitter — Storyworth memoirs (Link)

  • Our knowledge of our parents before we are born is very limited. If you have ever asked them to recount their stories, you may have left the conversation wishing it was written down. And that’s just for the stuff they thought of when they were on the spot or during that evening around the table. Storyworth is a service which prompts them every day with a question that they answer and at the end of the year you can get physical and/or digital copies. I’m sure the efficacy of this depends a lot on your parent’s bandwidth, willingness, and literacy but I thought the concept was worth surfacing here. I actually think they should have a version for family recipes!

Sake Tidbits I Learned While in Kyoto

One of the highlights of the past week was spending a few hours with sake apprentice Jorge Navarette. I will do a fuller write up on his awesome story when I compile a guide to Japan based on our trip but I will just say that Jorge is probably the most knowledgable American citizen on the subject of sake. Meeting him was pretty much an accident as we just took a tour where the hotel concierge sent us but he had only been there since July.

But here’s some knowledge you can use today if you like sake or want to get into it.

  • Premium sake is defined by how much the rice is polished down. So a 60% sake has had 40% of its rice polished down before fermentation. Sake must be below 70% to be considered premium.
    • Jumai: “pure rice” typically 60-70% remaining after polish. Large variation in taste.
    • Ginjo: “fragrant” 50-60%
    • Daiginjo: “super fragrant”. Less than 50%. Very smooth, but less variation in taste
  • To give sake shelf life it is pasteurized. In Japan, unpasteurized or “draft” sake is bottled and kept cold. It is known as “nama” sake. While technically you can drink it within 6 months we learned you really want to drink it in less than 30 days. You can find it in the states but it won’t be the same as fresh namasake.
  • Sake is expensive in the US mostly because of taxes and tariffs. A good bottle of sake in Japan need not set you back more than $7.
  • A word on Japanese whiskey. Jorge could trace the boom in popularity and price spike back to a single month in time. ​November 2014. There were 2 reasons at the same time which created a perfect storm:
    1. The rise of international demand for Japanese whiskey in the wake of The Whiskey Bible ranking Yamazaki as number one in the world and ahead of Scottish brands.
    2. A surge in local demand when a documentary about Nikka Distillery’s founder aired in Japan. It told his incredible story full of passion and suffering as he traveled to Scotland to learn the craft during the WW1 era.

Yamazaki 12 went up 6x in price but this was like table whiskey before that! Jorge had been drinking it for over 20 years when it was 25 a bottle.