#101: The Paradox of Increments

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A few months ago, a friend of mine came for lunch. He is a quantum physicist and loves brain teasers. He was pretty excited to try one on me. It essentially goes like this:

Friend to me: “How much would you want to be paid to run across the USA?” (you can pick any scenario.)

Me: “$5 million.”

Friend to me: “Would you do it for $4,999,999?”

Me: “Sure.”

Friend to me: “How about $4,999,998?”

Me: “Okay.”(This continues with him reducing the amount by $1 each time.)

Friend to me: “So, by your logic, if we keep reducing by $1, you would eventually do it for free.”

Of course I put up a protest, and so did others at the table; it obviously felt wrong. His whole argument to me was one of logic. He wanted to show me that if you follow the natural course of logic, the answer has to be that you will do it for free in the end.

The problem with the brain teaser is that, in reality, there is a psychological threshold. There will be a point where it just won’t work from a psychological point of view, and the paradox becomes impractical.

My friend is one of the smartest guys I know, and I decided to let the whole setup marinate in my mind for a few months, as I knew he doesn’t share things like that just for the sake of sounding smart. After all, he is always the smartest in the room. I was sure I had solved it from a psychological point of view and disproved the paradox along the lines of the subjective psychological threshold we all have.

However, a few days ago, I was thinking about how this idea of the incremental paradox has validity in a trading or investing context. When we lose money slowly, our logical minds, what Daniel Kahneman calls System 2, rationalise the loss. For example, when we lose $2k in our $100k account, we say, Okay, that wasn’t nice, but its not the end of the world. The next week, we lose another $2,000 and go through the same rationalisation process. I have seen this process unfold personally and with others thousands of times. Before we know it, we have rationally become irrational and blown the whole or a large part of the account. Based on this, we could argue that the paradox holds from a logical and psychological point of view.

Conclusion: upfront, before the mind starts to play its tricks, you need to set a stop-loss limit.

S2N Observations

I will spare you any deep analysis of the shocking assassination attempt on Trump yesterday. I have been commenting over the last few days that I believe Biden is finished. Even Trump’s most ardent critics acknowledged that the way he responded with courage and passion was presidential and probably won him the election.

A few days ago, I shared an analysis of the Fed Funds Rate at the beginning of the year and the SP500 performance over a year. A linear regression produced no result that suggested any forecasting ability based on the interest rate. I decided to try and see what the results would look like with the return over the next 5 years. I am happy to say there is somewhat of a relationship. The higher the rate, the lower the next 5-year return. The confidence bands are extremely wide, so do not read too much into this study. I think it is probably safe to say that interest rates do not have as much of an impact on stock returns as we think.

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