I think when stating your opinion against 40 years of econometrical research, including multiple Nobel prizes in economy, you should feel enticed to explain your opinion a bit more than "no I don't think so"...

Please quote a Nobel prize (well, there's no Nobel prize in economy, but surely we understand each other) winner explaining that stock prices are, in actual reality, random variables.

> explaining that stock prices are

To be pedantic, stock returns, not prices.

As for the quotes, I encourage you to strongly think about the meaning of the work of Sharpe, Black & Scholes and Markowitz applied to non normal distributions (both Nobel prizes, we understand each other).

In particular, try to articulate the relevancy of sharpe ratios between two non normally distributed portfolios.

Something however has to be said about winning a Nobel prize then using your model to lose billions and send your company into bankruptcy.

The market is incredibly efficient at pricing many things incorrectly and Markowtiz then BSM was no exception.

> To be pedantic, stock returns, not prices.

If one is a random variable, so is the other. It's a simple change of variables. What's your point?

> As for the quotes, I encourage you to strongly think about the meaning of the work of Sharpe, Black & Scholes and Markowitz applied to non normal distributions (both Nobel prizes, we understand each other).

Could you quote the part where they say that actual, real-world stock prices (or returns, whatever) are random?

> If one is a random variable, so is the other. It's a simple change of variables. What's your point?

Not sure I follow your reasoning. Prices are positive only, and non stationary. That is very much not the same for returns. Usually prices are log normal, leading to normal (log) returns.

> Could you quote the part where they say that actual, real-world stock prices (or returns, whatever) are random?

It is not said, but rather implied. Take the Sharpe ratio for instance, it is a measure that:

1) is used to compare different assets / portfolio returns

2) rely on the 2nd moment of the returns.

The standard deviation is less relevant the further away from the normal distribution you go, so since this is a comparison metric, it can only be reasonably applied to compare normally distributed returns.

If you believe the returns are not generally normal, then you reject the use of the Sharpe ratio as a relevant measure of comparison.

I don't have a B&S reference at hand, and I did not read it since 15 years, but I'm pretty sure it assumes lognormals prices as well.

> Not sure I follow your reasoning. Prices are positive only, and non stationary. That is very much not the same for returns. Usually prices are log normal, leading to normal (log) returns.

Perhaps we should take it back to the beginning. What do you believe "random variable" means...?

> It is not said, but rather implied.

I see.

This is absolutely absurd. Economists including Nobel prize winners, including even Eugene Fama who proposed the Efficient Market Hypothesis, does not think the stock market is normally distributed.

At best, using a normal distribution is something that undergrads use as a tool to learn about the stock market and make some simplifying assumptions for pedagogical purposes, but it most certainly is not something that actual professionals or researchers in the field genuinely believe.

Come on, don't create a trial of nitpicking. I am not saying returns are a law of nature meant to teach us normality.

My point is that, for all intent and purposes, you should assume normal distribution of returns.

If you don't, you're obviously on either end of the spectrum: not knowing the subject at all, or nitpicking expertise on the internet.

The subject of the matter here is convincing someone that risk adjusted measures should be considered when comparing portfolios. This is the basic underlying modelisation that 99.99% of the finance world makes, "compare sharpes", "compare volatility adjusted returns".

I'm stating 1+1=2 and you're arguing it doesn't hold in Z/2.

> At best, using a normal distribution is something that undergrads use as a tool to learn about the stock market and make some simplifying assumptions for pedagogical purposes

Implicit normality assumptions are everywhere. I encourage you to think hardly about your model and question whether anything you do would work on non normal distributions, you will most likely find that you have millions of these assumptions in your linear combinations, sample renormalization, regressions, sharpe weighters and optimizations.

Now of course you could refine that with students, lognormals, and whatever, but this is more _refinement_ than anything.