You may have heard that “filter bubbles” are a source of tension. People are silo’d in their little worlds and don’t know or understand the views of others who think differently. If that’s the correct diagnosis for what is happening around us, then exposure and education are the prescriptions.

I’m skeptical.

I recently listened to an interview with philosopher C. Thi Nguyen, author of *Games: Agency As Art* on physics Sean Carroll’s Mindscape podcast. It was one of those interviews I listened to twice and wrote notes on.

You can check out the conversation and see my notes:

*Notes From C.Thi Nguyen Interview About Games and Society (*14 min read*)*

Feel free to skip to the parts you are interested in. The lessons feel like they confirm my skepticism. It ties back to how our minds feel when we play games and, provocatively, some really basic human needs.

I won’t say too much because it’s worth at least skimming the takeaways, but I’ll share a single thought I have crystallized in the past few months:

What ideologies lack in rightness, they make up for in tidiness and convenience.

Of course, if you internalize Nguyen’s views, you can also see why my thought is deeply ironic.

Give it a listen.

**Money Angle**

This week I published:

*Solving A Compounding Riddle With Black-Scholes* (14 min read)

It’s a bit longer than a usual post as I try to balance ELI5 with dragging things out too much.

I’ll do a quick overview here.

It starts with:

We have 2 stocks: A and B.

Both are at $100 today.

A rises 10% each year.

B either rises 30% or falls 10% each year — with 50/50 probability.

So, in any one year, B “averages” (30 – 10)/2 = 10%, the same as A.

After 10 years, what’s the probability that B is higher than A?

— 10-K Diver (@10kdiver) November 13, 2021

If you have read about “volatility tax” or geometric returns, you can quickly dismiss choice #4 in the poll (click the tweet to see the choices). Over 2k people (30%) of respondents picked the one that requires doing no work.

There are still 3 answers to choose from. Since N was only 10 years it was easy enough to pen and paper the binomial tree. But before you even do that there’s another insight you could have.

Just like any 3,5,7 or odd-game series, there must be a winner…so if Stock B has more up years than bad years it will probably outperform A. The odds of that are 50/50.

But…this question is about year 10. An even year. That means Stock B could experience 5 up years and 5 down years. The “volatility tax” will punish that scenario (“volatility tax” in a nutshell: .90*1.10*$100 = $99)

So in a 10-year horizon, B loses to A if B has:

0 ups, 10 downs

1u,9d

2u,8d

3u,7d

4u,6d

and crucially… 5u, 5d

We can draw Pascal’s Triangle to see the coefficient for the middle term: 5u, 5d

[The coefficient is the number of ways an outcome can occur or =combin(10,5) in Excel]

252/1024 = 24.6%

24.6% of the time the volatility tax causes A > B.

The remaining paths represent 75.4% of the paths and those have a clear winner that is evenly split between A>B and B>A.

75.4% / 2 = 37.7%

So volatile stock B only outperforms stock A **37.7%** of the time!

Part of the reason the post is long is that I explain much of this stuff slowly and contextualize it with a discussion of geometric returns. This is just basic stuff, so far.

The better part follows.

It starts with a problem in my process, even though it’s the right answer…

*My logic doesn’t scale as N grows.*

Here’s why:

What can we do now?

The annual compounding, binomial framework lent itself to simple binomial-formula-chugging or tree-building. But if we switch to a continuous compounding framework we can use option math!

**Put Your Options Hats On**

The first thing I did is just approximate the volatility of Stock B with a round number…20%. (you make 30% or lose 10% each year. 20% vol is good enough for this context)

The original question using 20% vol:

*What’s the probability that stock B with its 10% annual return and 20% volatility outperforms stock A with its 10% annual return and zero volatility in 10 years?*

Now let’s rephrase the original question as an option’s question:

*What is the probability that a 10-year call option on stock B with a strike price of $271.83 expires in-the-money?*

[*$271.83 is the bogey set by stock A derived from continuously compounding $100 at 10% per year for 10 years (ie Seʳᵗ)]

Often when people hear “probability of expiring ITM” they think, “that’s delta”. Not quite. The post has some refresher on why.

Don’t worry, Black-Scholes still has the answer to our question. Here’s why:

So what happens when we compute N(d2) or “probability of expiring ITM” for Stock B at a strike of $271.83.

Boom.

37.6%

Respectably close to the answer we got from the binomial brute force.

This makes sense because the compounding effect on the payoff distribution is almost identical and Black-Scholes’ underlying distribution is the assumption of continuously compounded (ie log) returns.

This summary pic is the coup-de-gras but I explain how I built it (again the post is intentionally tedious, so if you are experienced, feel free to skim/skip)

Finally, I toss in some intuition for why skew is often counterintuitive:

And then I circle back to props to @10kdiver because I’m a fan of the effort he puts into explaining. He’s got beaucoup skills, so it gives me something to aspire to as far as trying to communicate concepts better.

Please check his threads here: https://10kdiver.com/twitter-threads/

**Perth Tolle’s Interview On Yinh’s Growth From Failure Podcast**

Fintwitters and folks in asset management likely already know Perth Tolle, founder of Life & Liberty Indexes and creator of the Freedom ETF, which tracks the freedom-weighted emerging markets index.

One of the neat things about Yinh’s podcast is she tends to find people with interesting stories who are relatively unknown, many of them having never been interviewed before. Perth, on the other hand, is well-known in the finance world. She has been interviewed in many places and is a regular on CNBC.

And yet, she still had this to say which I will leave as its own teaser:

Listen to the interview here:

https://www.growthfromfailure.com/podcast/perth-tolle

In this episode:

– Perth’s first exposure to censorship

– Moving from China to the US

– Delaying law school to move to Hong Kong

– How she became interested in finance and investments

– Creating the Freedom ETF

– Her “Grand Design”

To learn more about Perth, the Freedom ETF or Life and Liberty Indexes, you can visit:

**Job Opportunities**

**TradFi**

[Re-posting. This led to some amazing inbound last week. I hear some people charge for this kinda thing.]

An awesome team (I can’t overstate awesome here) is looking for a **junior full-stack developer**. You will learn from seasoned quant PM and be part of building a HF from the ground up.

Requirements:

- Ability to work on full-stack including DevOps
- Python, JS/React, SQL, Redis

Good to have:

- C# and experience with distributed systems

This group is very groovy, if you’re hungry and eager to learn and build, it will be an amazing opportunity.

Hit them up here: omk.jrdev@gmail.com

**Crypto**

My friend Charlie Graham is a successful tech entrepreneur and world-class puzzle creator and solver. After our sons’ basketball game yesterday he mentioned that he’s trying to find a senior Elixir developer for his latest venture, Hawku.

Hawku is a well-funded startup that is:

building a marketplace that is focused on the specific needs of gaming and utility NFTs. Our vision is to provide prospective buyers with the real-time data they need to research, buy and sell utility-based assets.

Hawku already has a platform that provides the key information players need to research, buy and sell horse NFTs for the popular Zed.run game platform. In the four months since it launched, Hawku has already reached 3M monthly page views and has built an avid following.

This is a list of the open positions: https://jobs.hawku.com/

This is the post for the senior/lead Elixir dev.

Have a groovy week!

Kris