### Principles

- Investing is a sequential process
- The only goal is to maximize wealth over time. Do not “narrow frame” it to focus only on annual returns.
- A risk mitigation strategy must lower risk and hence increase CAGR (Compounded Annual Growth Rate)

Another example would be a merchant sending 10,000$ worth of goods with a 5% chance of pirates taking it over. Let’s say the merchant has a net worth of 3,000$ and the rest is financed. The expected loss is ~5%. So, an insurance of 800$ might feel expensive.

The better way to look at it is the geometric outcome. Without insurance, the expected per-trip return from 100 trips is ((3000 + 10000)^95 * 3000^5)^1/100 = 12,081$

However, with insurance, the merchant always loses 800$ and gets 10,000$ (either from sale or from insurance), so, the returns are 3000 + 10000 – 800 = 12200$! On the other hand, the insurer makes 800 – 500 = 300$ as well!

**Insurance is not a zero-sum business. The insurance buyer is playing a game of geometric returns while the insurance provider is playing a game of arithmetic returns, so, both can be making money simultaneously.**

One of the book’s core ideas is that investing is a game of sequential investments.

Consider, for example, a simple game where you throw a dice and the returns are

-50% on 1 +5% on 2 +5% on 3 +5% on 4 +5% on 5 +50% on 6

The expected outcome is average of all and that’s 20%/6 ~ +3.3% So, playing this game is a good idea, right? Imagine you play this game repeatedly. Statistically, you will hit all the numbers ~1/6 times each, so, the final returns will be 0.5 * 1.05 * 1.05 * 1.05 * 1.05 * 1.50 ~ 0.91! So, +3.3% arithmetic returns lead to -9%/6 ~ -1.5% geometric returns.

In the game of investing, drawdowns matter a lot.

**The only return that matters is geometric and not arithmetic**.

Leverage in most cases increases arithmetic returns at the expense of geometric returns and that’s how Long Term Capital Management blew up.

The reverse happens when you keep cash on the side. For example, the previous game of dice can be played again. This time, however, you play each round with a fraction of the money you started with. For example, only bet 40% of your wealth in each round and you will end up with a +1.1% arithmetic return and +0.64% geometric return. The 60% cash on the side does not make money but does not lose in extreme scenarios either. This store of value saves you from a major drawdown.

Another even better approach is insurance. Consider this scheme – “invest 91% in the dice game, 9% in an insurance that pays 5X if 1 comes”. This scheme lowers arithmetic return to 3% but increases geometric returns to 2.1%.

**The arithmetic return can go down while geometric returns can go up as the variance in outcomes shrinks**.

Finding safe havens that produce positive returns in the down market is not hard. Finding safe havens that are cost-effective is hard.

Using S&P500 returns for the past 120 years as an example, the author demonstrates that a 99.5% S&P500 with 0.5% allocated to insurance performs better than the S&P500 itself. Gold, bonds, 3-month T-bills don’t even come close! So, what’s that “secret” insurance scheme, well the author does not reveal that. But there are multiple threads on the Internet about what it looks like. For example, this one and this one points out that Spitznagel is buying deep out-of-money PUT options that are cheap enough as insurance.