You're talking about a moving average

I am not talking about any moving averages.

Yes, you are. The asset doesn't move perfectly fitted to a "constant trajectory," you said so yourself. A rocket moves at a "constant trajectory." Stocks don't - not even fictitious examples of stocks - unless they completely lack volatility. In your example, you can only be talking about the trajectory of a price as being defined by its moving average. If its not, its not "constant."

Your argument was that volatility is equivalent to risk, which is generally wrong. Neither contains much, if any, information about the other.

Perhaps I shouldn't have used an equal sign to imply that the two are strongly correlated (which they are). They are indeed not equivalents of each other and do not possess the same definition.

To show to you that this is not the case I've tried to give you examples of assets that directly contradict your assertion.

You gave me an example of an asset that doesn't exist.

In the 'basket of all stocks' you have no risk in the long-term, because your expected loss (= risk) is strictly negative and hence your expected return is strictly positive, because the realized total return converges towards 10% p.a. (in the case of the US stock market) over time.

Despite that, the asset itself has been volatile. Hence, volatility does not imply anything about risk nor vice versa. The only thing that matters for risk is your strategy and nothing else.

That's a classic example of an average risk, average volatility asset. Its a benchmark for both risk and volatility. You're proving my point for me.

You can have a perpetually flat asset with high risk, or you can have highly volatile assets without any risk (Bitcoin - which does not mean that you are guaranteed to make money).

No, you can't. "Perpetually flat asset" implies zero volatility and zero risk. How do you lose money on something whose value never changes?

And saying bitcoin has no risk is absurd. Does anybody else feel like bitcoin is a "risk-free" investment?

*You can get volatility and risk in any combination and neither implies the other.*

Okay, I'm willing to concede that they do not imply one another 100% of the time, but as a general rule of thumb, they do.

Risk is a statistical measure, e.g. the expected loss of a strategy, asset or portfolio.

Not quite. Its the probability that a gain or a loss will differ significantly from what is expected.

Just like the expected value of a dice roll is 3.5 = 1/6 times sum of all potential results.

Not trying to troll you but this is a horrible example as you can never roll a "3.5" -- that would be a highly unexpected outcome.

With risk the results are potential price trajectories in the market and the probabilities are obviously different and depend on all sorts of parameters.

Realized returns on the other hand are what you end up with in reality, and while risk can give you an idea of a region that you'll land in, it'll never tell you what will really happen for individual 'games'.

I don't disagree with this.

Here's another attempt to make the point clear.

Assume you have volatility but it's **always** the same. Basically, your price follows a 100% predictable pattern no matter how many people buy or sell. In that case you have volatility, but 100% insight and hence can generate profits without any risk whatsoever.

Obviously this isn't going to happen in real markets (though it does in many games), but it should be sufficiently illustrative to show that volatility and risk aren't related.

Dude. Volatility that is always the same is not volatility. That's stability, and thus not risk. As you said, obviously this isn't going to happen in real markets, and it won't, ever. Nobody has 100% insight into any market.

If your best real-world example of an asset that has high volatility and "no risk" is bitcoin, I'm going to stick by my original assertion that you are just looking at this from an after-the-fact standpoint.