28May 2019

Crypto Convexity

by Henrik Andersson

Convexity is an interesting concept that explains why investors should pay attention to crypto as an asset class.

I believe there are actually two ways that crypto has convexity. The first one is more technical and the second one more broadly related to individual crypto assets and portfolio allocation:

  1. Crypto has deeply rooted technical convexity 

As a former options trader, I learned that convexity is the concept of positive gamma. Gamma is the rate of change of the price sensitivity to the underlying price. If you’re ‘long gamma’ you will become more sensitive to price changes as the price goes up. Long gamma is a nice situation to be in, as the price goes up you will make more and more money (Short gamma on the other hand should be avoided like the plague.)

A short gamma trader on Bitmex gets liquidated.

A short gamma trader on Bitmex gets liquidated.

Why is crypto be ‘long gamma’? On a high level, base layer protocols like Bitcoin and Ethereum are creating an immutable ledger where value and contracts can be exchanged between any two parties. That network only has value if the security is strong enough, i.e. the network is only trustless if we don’t have to worry about a rollback of previous transactions.

Since Bitcoin and Ethereum’s miners are paid in bitcoin and ether, the trustlessness of these crypto networks is a direct function of the price of those assets. Put another way, the value of the network as a secure ledger goes up as the price increases. This reflexivity means that 1. the network effect in crypto networks is strong 2. the immutability and thus the value proposition of the network increases with price — this self reinforcing effect is a form of positive gamma!

2. Crypto has convexity both in the micro and macro

On the micro scale, there is a lot of experimentation and competition going on in crypto markets. If you have exposure to a diversified portfolio of crypto assets you are more likely to capture the returns from breakout crypto assets. This is the reason why we are building a portfolio aligned to our investment thesis that is diversified between different verticals and technologies . In option parlance we’re said to be ‘long volatility’. We can view the portfolio as a collection of call options.

Here it makes sense to mention another Greek letter, namely Theta. A call option has a negative theta, meaning that as time passes the value of the call option will decline as optionality decreases. If crypto assets are call options, I’d argue that the theta of a crypto asset is positive. This is due to the Lindy effect, which says the future life expectancy of a non-perishable thing like technology increases with time. Unlike call options that expire at a given time, crypto assets don’t expire. Instead, they prove themselves over time and become more trustworthy as time passes. If Lindy is valid for crypto assets, then they just have to survive to be successful — that’s a convex bet in time.

Secondly, on the macro side of things. By having 5% of crypto assets in your portfolio you are exposed to an asset class with limited downside (all of crypto is only US$150bn, a fraction of one company like Facebook) and with limitless upside. This has the added advantage that you can take much less risk with the rest of the portfolio. Instead of cultivating a portfolio of securities with average risk and average return expectations you can instead construct a portfolio where 90 or 95% of the portfolio has very little risk, maybe just enough to cover inflation while the rest of the portfolio has unlimited upside. Prof. in risk and philosopher Nassim N. Taleb describes this Barbell Strategy this way:

“If you know that you are vulnerable to prediction errors, and accept that most risk measures are flawed, then your strategy is to be as hyper-conservative and hyper-aggressive as you can be, instead of being mildly aggressive or conservative.”

We believe this very asymmetric return profile coupled with the uncorrelated nature of crypto assets makes this a very unusual and attractive asset class. On the contrary if you’re short, you have limited upside (100%) and unlimited downside.

The above reasons summarise why I like to say:

‘Crypto is Convexity for your Portfolio’.

Henrik Andersson

Henrik is the Chief Investment Officer at Apollo Crypto and is the fund manager for the Apollo Crypto Fund. He also acts as the fund advisor for the offshore Apollo Crypto investments funds, the Apollo Crypto Frontier Fund and the Apollo Crypto Market Neutral Fund. Henrik's expertise in traditional financial markets comes from spending a decade on Wall Street as a vice president in institutional equity sales. His exceptional understanding of DeFi comes from co-founding two successful DeFi protocols, mStable and dHEDGE.