The Secret Risk Factor That Most Investors Ignore

Have you ever wondered how risky it is to invest in assets that have non-normal returns? Do you know how to quantify the extra return that you expect for taking on more risk? If you are interested in these questions, then this article is for you which was inspired by Bank for International Settlements – BIS working paper titled "The cumulant risk premium" authored by Albert (Pete) S. Kyle and Karamfil Todorov .

Imagine you’re at a carnival, and there’s a game where you can win a giant teddy bear. The game involves throwing a ball at a stack of cans. If you knock down all the cans, you win the teddy bear.

But there’s a catch - the game costs $5 to play.

Now, most people would be willing to pay $5 for the chance to win the teddy bear.

But what if the game operator offered you a deal? For $10, you could throw two balls instead of one. This would double your chances of winning.

This is similar to investing in the stock market. When you buy stocks, you’re essentially paying for the chance to win more money in the future.

But stocks are risky - just like the carnival game, there’s no guarantee that you’ll win.

In the financial world, this is known as the “risk premium” - the extra amount that investors expect to earn for taking on more risk.

Now, let’s say the game operator offers another deal. For $15, you could throw three balls instead of two. This would triple your chances of winning. But it would also increase your risk - if you don’t win, you’ll lose more money.

This is similar to buying a leveraged ETF (Exchange-Traded Fund).

A leveraged ETF is like a regular ETF, but it uses borrowed money to amplify the returns of an asset. So if the asset goes up in value, the leveraged ETF will go up even more. But if the asset goes down in value, the leveraged ETF will go down even more.

The “cumulant risk premium” is a way to measure this extra risk. It looks at how much investors are willing to pay for the chance to earn higher returns, but also take on more risk.

So in our carnival game example, the cumulant risk premium would be how much extra people are willing to pay for the chance to throw more balls and potentially win more teddy bears.

I hope this makes it easier to understand! Here are some key points:

1. The “risk premium” is what investors expect to earn for taking on more risk.
2. Options and leveraged ETFs are two ways that investors can take on more risk.
3. The “cumulant risk premium” measures how much extra investors are willing to pay for this additional risk.
4. Higher-order moments (like skewness and kurtosis) can affect the returns and risks of different investment strategies.
5. Understanding these concepts can help us make better investment decisions.

P.S.: If you were at the carnival, how many balls would you buy for a chance to win the teddy bear? Why? Share your thoughts below!