The Fallacy of Forecasting

[Amahrix]

The Fallacy of Forecasting:

1) Being right on a random variable X does not mean making money off it.

2) Payoff function f(x) needs to be aligned with what you're forecasting.

3) In fact, payoff function f(x) is never X and f(x) can be very complicated.

4) In real life, most people who think you have to focus on X are academics or idiots.

5) Payoff function f(x) is what you focus on when you make a decision.

6) It's much easier to understand the function of your random variable than the random variable itself.

7) You don't have to be right about the world, you have to make decisions that are convex... decisions that make sense.

8) Paranoia is entirely justified if your payoff function f(x) is concave.

9) Overpricing or underpricing probabilities is not what matters, its your payoff function that matters.

Source:

This is very important to understand.

 

[Amahrix]

@SunTrader I believe this can be of benefit to you, if you can put your disdain for me aside for a few minutes.

 

[Amahrix]

It doesn't matter if you are right or wrong about what you forecast. Getting the forecast right or wrong is actually not the point. You need a payoff function aligned with the forecast. & it's this very payoff function that decisions are(should) be based off of in life.

It's really simple concept, but many forget. Many are focused on win rate and believe if they have a high win rate that this is enough. Too narrow-minded.

Payoff function example:

Disclaimer: Simple statistical concerns are often well clarified through the use of gambling examples.

Example from "The Business of Options" by Martin P. O'Connell, pg. 5

Suppose I would like to bet that I can roll a 4 in a single roll of one die. Of course, if you insist on even odds, I'm not going to bet because I know I only have one chance in six of winning.

On the other hand, if I can get 10-to-1 odds, I am going to make that bet. I am going to make it fully expecting to lose, and I am still going to think about it as a business.

Suppose I make the 10-to-1 bet and roll the die and get a 2 instead of a 4. Was I wrong? Of course not. I'm no dumber than before the roll, and also no dumber than if I had rolled a 4. If I had rolled a 4, the result might make me feel brilliant. That feeling would be simple emotional weakness. To be statistically passive is not just to make a trade without thinking I know the result. It also requires ignoring the temptation to think that the result indicates the quality of the trade.

Learn more here: https://www.elitetrader.com/et/threads/are-you-too-anxious-to-win.334884/

 

[padutrader]

how is any of this relevant to trading.?
you have opened a discussion in 'trading'

 

[Amahrix]

how is any of this relevant to trading.?
you have opened a discussion in 'trading'

You don’t think payoff function is relevant in trading?

You get worked up over the most trivial of things.

The video highlights a trade, albeit a bad one.

 

[padutrader]

You don’t think payoff function is relevant in trading?

You get worked up over the most trivial of things.

The video highlights a trade, albeit a bad one.

let us see what the moderators think about it

 

[pipeguy]

It also requires ignoring the temptation to think that the result indicates the quality of the trade.

We simply get the observations to plot some function then which is "true" in asymptotical case, because randomness starts to follow patterns in the long run. The only problem is that classical probability should be fine tuned because sample outcomes are not equally likely. That's it.

 

[gaussian]

This is a lot of fluff around gambling probabilities. Your example at the bottom more or less hits your point in far fewer words and using something like "payoff function" just makes you sound pompous.

The even simpler explanation of this is that if your expected value of the game is positive proper risk management will insure a profit since the EV is average expected return. This is the meaning behind "having enough capital to survive the drawdown". As you explained as long as your EV is positive, a loss isn't an indicator of a bad play. Variance is where you lose your ass though. Higher variance demands a significant capitalization to make the EV work in your favor.

Of course calculating the odds of a play in the stock market is not like calculate the discrete EV of a table game. However, it's close enough the math can readily generalize. A closed form solution relies on the work of Kolmogorov, which is far too much work for a practitioner.

 

[Amahrix]

Financial returns typically have infinite variance.

When a movie studio predicts the profits a movie will make before it’s released, the error is practically infinite. “The average revenue earned by all motion pictures is dominated by a handful of rare blockbuster movies, rare movies so improbable in a Gaussian World that they should never occur (De Vany. 2004).” De The paradox here is that while the infinite variance distribution is a good model for movie profit prediction, a prediction that has an infinite margin of error is no prediction at all.

Src: https://www.statisticshowto.datasciencecentral.com/infinite-variance/

 

[gaussian]

Financial returns typically have infinite variance.

I would be interested in how you arrived at this conclusion. The infinite Variance argument based in "well the instrument could go to infinity or 0 tomorrow" is only theoretically true. In practice, there is no evidence I am aware of that indicates the divergence of Variance on any equity or instrument. While theoretically true in a pure model sense, the reality of the situation is this is patently false. You must temper your market model with doses of reality - otherwise you arrive at these nice-in-a-journal-paper-but-wrong-in-reality solutions.

Your example of the movie studio is also misguided. We can only MODEL the future. If I took Spielbergs history and built a model for it I could find the conditional variance of his past and, with relatively good accuracy, be able to construct risk bands for his next movie.

In practice the Variance of a log return series is well defined. You can pick your favorite economic explanation but supply and demand holds the most water.