The Law of Conservation of Risk


0 reactions 2022-05-16

Disclosure: Personal reflections after the breakdown of Terra/Luna this week, but this is a timeless philosophy I've carried with me since my option trading days.

A very basic principle of financial engineering I learned early on as an options trader is The Law of Conservation of Risk:

Risk cannot be created or destroyed, it can only be redistributed.


I was reminded of this principle when looking over the UST/$LUNA implosion this past week:


That’s a token that starts at $1.30, declines to under $0.2, then over 14 months, soared to $115 in April (making it one of the top 10 cryptocurrencies in the world), and then in one week crashed from $80-$100ish down to 2% of one cent.

Perhaps you might think volatility is part of the game with crypto tokens, and I’d agree, but for the fact that $LUNA backs the TerraUSD stablecoin, which is meant to be.. well… stable:


I’ll leave it to experts interviewed by journalists (like Odd Lots or Crypto Critics Corner) or Jon Wu’s writeup and Do Kwon’s response to explain what happened, since there’s no shortage of explainer content out this week.

What I’m drawn to is the mechanism by which stability was manufactured out of instability. The Terra whitepaper specifically addresses this in the short term and the long term:

Luna also serves as the most immediate defense against Terra price fluctuations. The system uses Luna to make the price for Terra by agreeing to be counter-party to anyone looking to swap Terra and Luna at Terra’s target exchange rate. More concretely:

  • When TerraSDR’s price < 1 SDR, users and arbitragers can send 1 TerraSDR to the system and receive 1 SDR’s worth of Luna.
  • When TerraSDR’s price > 1 SDR, users and arbitragers can send 1 SDR’s worth of Luna to the system and receive 1 TerraSDR.

The system’s willingness to respect the target exchange rate irrespective of market conditions keeps the market exchange rate of Terra at a tight band around the target exchange rate. An arbitrageur can extract risk-free profit when 1 TerraSDR = 0.9 SDR by trading TerraSDR for 1 SDR’s worth of Luna from the system, as opposed to 0.9 SDR’s worth of assets she could get from the open market. Similarly, she can also extract risk-free profit when 1 TerraSDR = 1.1 SDR by trading in 1 SDR worth of Luna to the system to get 1.1 SDR worth of TerraSDR, once again beating the price of the open market.

The system finances Terra price making via Luna:

  • To buy 1 TerraSDR, the protocol mints and sells Luna worth 1 SDR
  • By selling 1 TerraSDR, the protocol earns Luna worth 1 SDR

As Luna is minted to match Terra offers, volatility is moved from Terra price to Luna supply.

As is not news by now, this worked against Terra/Luna’s favor this week when there is sharp selling pressure on Terra (faster than miners can respond and therefore faster than it can adjust) and the protocol mindlessly prints more and more Luna in defense. Once too much Luna was being printed and demand for Luna did not keep up, the Terra dollar peg broke down.

Stability from Instability

There’s a few points of view on the Terra/Luna debacle:

  • The “bank run”: All banks (historically) operate under the assumption that not everybody is going to withdraw their money all at once. Banks usually keep some amount of cash on hand for normal withdrawals, but a bank about to go out of business can suffer a spike in withdrawals, and owe more money than they have liquid. Of course this hasn’t happened for centuries because we have learned to credibly backstop banks, but other forms of “banks” crop up in every financial system - most famously the Bank of England defending (unsuccessfully) its European Exchange Rate agreement. We know that Terra was buying $10b of bitcoin to capitalize itself, but unfortunately the bulk of the stability was based on $LUNA issuance and the run on this “bank” became a self reinforcing loop.

  • Turkey problem: Terra’s Anchor protocol was a wonderful thing to own for a while - a stablecoin savings account that paid an algorithmically guaranteed 20% yield!! Right up to the point it breaks the $1 USD peg. The Terra chart is a form of Turkey problem:


  • Ponzi scheme: As I’ve written before, all financial assets are reflexive - they only have value to the extent that everyone believes they have value. What tips something over from normal reflexive system to Ponzi is withdrawal of money from the system by insiders. VC and LFG insiders held a large (I cant find a good source but I gather it’s in the 30-40% range) of either the central entity and likely a lot of the token and probably sold on the way up, pulling money out of the system as newer, probably less knowledgeable new investors piled in. Very classic, but also no big deal, lots of people make intentional and accidental Ponzi’s.

What I’m interested in what investors should learn from this whole thing. Usually when you’re presented with something too good to be true, you want to ask “where’s the catch” - the problem is the catch is usually opaquely presented under a mountain of verbiage.

But the mental model of “The Law of Conservation of Risk” can be applied to any analysis that claims to reduce risk in an asset class - in this case, stablecoins.


In this case, the Terra stability mechanism literally transformed standard token volatility from the normal blue curve to the sharper-yet-fatter-tailed green curve, except that the green curve spike was so close to 0 change it was marketed as “stable”.

Aside: yes the curve was also “fat” in the positive direction - for a few months Luna was the best performing crypto in the world, and skeptics note that it was extremely risky to short Luna for the same reason it was prone to collapse. Unfortunately risk of ruin dominates positive tails in long term outcomes.

Other Occurrences in the Wild

Collateralized Debt Obligations

There’s a strong similarity in this outcome with the mortgage boom and subsequent crash of the 2000s, fueled by CDOs and risk models that overfocused on modal outcomes with normal correlations. Again, there are countless, variously biased ways to explain this risk:

But the main thing I’ll focus on is the transformation of low-rated MBS into AAA ratings by sheer financial engineering:


Again, if you don’t look too closely, and under normal conditions, you have created something great from something crappy! Couple this with investor’s well documented risk adverse nature, it means that there is an unlimited demand from financial investors for credible “investment grade” assets that yield more than other alternatives, rather the credibility comes from ratings agencies, the Gaussian copula, or a white paper with a bunch of formulas that proclaims itself stable.

Option portfolio wings vs decay

This is going to be far too technical for anyone who hasn’t been a professional options trader (particularly sellside) but essentially the trick in options portfolio management is having enough gamma that you don’t get wiped out on big moves, while not bleeding out from paying too much in time decay of the options that give you that gamma. One of the best ways to get this “efficiency” is to take advantage of the volatility surface:


The basic components of a vol surface you can exploit for efficiency are:

  • Term structure - longer dated options can (sometimes) have higher implied vol than shorter dated ones, or vice versa
  • Vol skew - downside options can have higher implied vol than upside ones (mostly because of conditional probability - if stock market drops it tends to be more volatile than if stock market rises by same amount)
  • Vol smile - extreme options can have higher implied vol than “normal” ones

Aside: There are more with every option greek but they are comparatively minor unless built up in aggregate.. which I have also seen particularly with long dated options and interest rate risk.

Basically to get more efficiency you sell the higher vol and buy the lower vol. A very efficient portfolio works like a dream in normal times - you are making loads of money from gamma hedging, and paying comparative peanuts in time decay for the privilege.

But what you have done to get here is to basically say the market is wrong in pricing these known risks in time and spot price - and when the market goes against you, you lose money.

Option portfolio efficiency is selling the tail risks in favor of looking good in the normal times. No free lunch - you haven’t really created or destroyed any fundamental risk, you’ve just swept it under a rug.


When presented with something too good to be true, try to understand how the “normal” outcome is being goosed by creating/repackaging more risk in the extremes, and understand the driving factors that lead you to tip towards those extremes.

Peter Bernstein’s 1998 classic Against the Gods tells a lot more versions of our repeated failures to manufacture less risk with no tradeoffs throughout human history, from Greek prehistory to the French Renaissance to modern stock markets.

If you’re a software engineer reading this and tut-tutting smugly at all these financial frauds shoveling risk around, consider how you are minimizing and managing your own technical, career, and yes, financial, risks as well and what tradeoffs you may know now you are making to achieve your relative level of comfort.

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