BYes Jared dillian

School is in session. Let’s talk math.

Go back to your high school arithmetic class. You take the derivative of Yes in regards to X. You find the sensitivity to change in function versus a change in argument. Concretely, it is the slope of a line or the speed of an object.

Then take the derivative of the derivative, the second derivative. Concretely, it measures the curvature of a line or the acceleration of an object. It turns out that people have a hard time with the second derivative.

The second derivative is everywhere in finance. It is the convexity of bonds or the gamma of options. When someone explodes in the financial world, it’s usually a failure to understand the second derivative. Human beings think linearly and statically. You might be familiar with your exhibit here, but you might not know it there.

Some second derivatives, such as convexity and gamma, are measurable and known. Some of them are hidden and unknown. I have talked about that gamma hidden before in The 10th man, which we saw in March 2020, when people are liquidating their positions and the selling is accelerating.

Once you see the second derivative, you can’t hide it. It’s everywhere you go. And then you are on the prowl.

The second derivative produces graphs like this:

And then people wonder what happened.

Actions have convexity

The first thing to understand is that stocks have convexity. Some actions are positively convex and others are negatively convex.

If that sounds Greek to you, here’s an easier way to think about it …

  • A positively convex action rises faster than it falls.
  • A negatively convex action falls faster than it rises.

Many stocks, like banks, were negatively convex in 2007. Banks had sold a lot of optionality, which made them drivers of negative convexity. They went up slowly and went down quickly, which is pretty much the payoff of a short option.

You can see it with Citigroup Inc. (C) in the following table.

In general, technology stocks and biotech stocks are positively convex. But there are exceptions. And there are positively convex stocks in many other industries, including retail, energy, and mining.

This doesn’t mean that you can’t have a negatively convex stock in your portfolio, but overall your portfolio should be positively convex. If bad things happen to the market, you want good things to happen to you.

A lot of people don’t realize that stocks have convexity built in – they look at the chart and it looks pretty straightforward. Actions go up and down. But sometimes they go up or down very quickly.

Most of the analysis I do on stocks is not about static financial statements. It examines how the underlying business can evolve in a convex fashion.

The convexity ends deceive most people – they’re buying something linear that ends up being non-linear in a smart way. It is a difficult concept to understand.

Many people reject actions even like GameStop Corp. (GME) and AMC Entertainment Holdings, Inc., but there is a lot of convexity there, and gigantic opportunities. The convexity certainly fooled people who were short on GME.

Convexity is also created by liquidity, which I understand correctly, having worked on a program trading desk. If you own a stock that trades at 500,000 shares per day, try to imagine what would happen if it traded at 50,000,000 shares in one day. There is no other place to go than up or down.


I had positions in preferred equity and high yield bond funds until recently. I sold them because of the massive negative convexity.

I try to keep it as simple as possible: the high yield can’t go up much more, but it can go down a lot. One way to win, many ways to lose.

The coupon you get on high yield bonds is like the premium you get for selling options. Sometimes (when the Fed is not involved) that premium is large and bonds become more attractive. People who understand income investing intuitively know the negative convexity present in these strategies.

One of the tragedies of the zero interest rate policy is that it has forced retirees to take on negative convexity in search of income, usually in the form of corporate bonds and dividend stocks. high.

It used to be that you could leave money in the bank, which was essentially zero convexity. If you look at a chart of the average retiree’s portfolio, it’s a series of slow climbs with breathtaking declines. The Federal Reserve, of all, does not understand convexity.

Once you start to think of your portfolio in terms of convexity, your results will improve. And I’m not just talking about returns, I mean risk-adjusted returns.

Of course, the best way to add positive convexity to a portfolio is to simply buy options. But for most people, it’s best to leave it to the experts.

Originally published by Mauldin Economics, 10/6/21

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The views and opinions expressed herein are the views and opinions of the author and do not necessarily reflect those of Nasdaq, Inc.

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