Outline of the Risk-Neutral Probability lessons

I published a new lesson. It’s a big post with 5 embdedded sub-posts and exercises for the reader. It ties together many concepts I write about.

I adapted the Tweet thread I used to promote it into this post to provide an outline for prospective reads.

Understanding Risk-Neutral Probability (Moontower)


To let you build your own understanding, the lesson begins with a progression of simple questions.


From this simple progression, you have actually self-derived a foundation for a key concept that we are going to get some mileage out of. Plus more practice to help you internalize the concept. It will make sense!


For those learning about derivatives or even pros who aren’t academically minded (myself included) there are exploration detours into 2 topics.

Useful Detours

1. Advanced Topic: How To Compute Risk-Neutral Probabilities From A Binomial Tree (Moontower)

That section includes exercises, again so you can own the knowledge, and then a derivation that you will probably have figured out intuitively:

  1. Advanced Topic: ReplicationReal World vs Risk-Neutral Worlds (Moontower)

    This one will be especially fun for traders because it includes:

    💡 What seasoned option traders get wrong

    💡 How divergence between real and risk neutral probability lead to mutual opportunity for speculators & traders

    I give examples from:

    1. Warren Buffet
    2. 2. FX Carry

Returning to the main post

After the detours, we pick up again with the idea of risk-neutrality and make a logical step into the principle of that underpins how investments will be priced:

🧽risk absorbability


This is an underappreciated idea. I can tell because people confess their ignorance all the time when talking about their great investments. They don’t understand that the default assumption should be idiosyncratic risks don’t pay.

Why not?

Consider 2 significant ways that an investing entity can absorb risk and we use simple examples to demonstrate how risky propositions can be rationally priced with no risk premium:

1. Bet Sizing

2. Diversification

Let’s look at each:

Risk absorption by bet sizing


Risk absorption by diversification:


The key takeaway: The more risk you can absorb, the closer your bid approaches the risk-neutral (ie arbitrage-free) price.

Bring it altogether

Now we get to tie all of this together to reason about investing broadly. There’s a short recap before we get to heavier lifting.


Now we’re ready for the real discussion which starts with an an obvious question:

🏗️Why did we slowly build all this theoretical scaffolding?

2 reasons that I categorize as:

1. Instrumental

2. Appreciative

These are essays in themselves.

🔗Instrumental Reasons (aka the practical reasons to learn this stuff)

We divide the audience for this into

a) Traders

b) Investors


I also give an example of the line being blurry between them:


Then we really address the implications for investors which applies to many more people.

We do this in Socratic form.


⚕️Then I offer some prescriptions


That covers instrumental reasons but I am an advocate of financial masturbation. So we also look at the appreciative reasons to understand this stuff.

Like I mentioned, this is an essay unto itself:

🔗Appreciative Reasons

This is the outline:


Followed by some cope:


Then closing comments and links for further reading. This post tied together a lot of material.


🔗Links For Further Reading

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