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.

Look, I hate to be that guy, but I've got a PhD in Mathematical Statistics. This stuff is my bread and butter. If you've got questions I'll be happy to try and answer them. But I'm not going to argue about basic definitions.

The definition of risk in finance is and always has been the expected loss with regard to some measure, or in other words: the expected value (or integral) of some loss function that is defined by your strategy. This is not a probability, it's a value. A value which can be positive, negative or zero to indicate respectively the average loss, profit or no change over

*many* repetitions of the same strategy.

The probability that returns deviate from expectation can be measured in different ways, but none of those is what is understood as "risk" in this field.

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.

No, they do not. Risk exclusively a measure of your proposed strategy. Volatility is a market phenomenon that does not in any way depend on your strategy.

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."

No, I'm still not talking about moving averages and you are still completely misrepresenting what I've said.

To cut it short, it was probably my bad for assuming you weren't, but you're clearly just using terms very loosely and with a naive colloquial understanding as opposed to their actual definitions.

If you're not going to do anything with these things that's fine I suppose. But you should still be aware of your misunderstanding of the subject.

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.

No, they still aren't strongly correlated. The level of correlation depends exclusively on your strategy, capacity, and infrastructure and not on the volatility. They have virtually nothing to do with each other.

You can by the way have two different definitions or objects that are equivalent to each other.

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.

It's called an academic example. Which is more than fit to illustrate points about an already abstract field like finance.

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.

No, I'm not. Risk and volatility are not equivalent and in fact not even correlated until an individual, specific strategy introduces correlation.

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?*Yes, you can. You can have a company that doesn't ever grow, returns the same dividends and keeps the same asset value. Until an asteroid wipes it out of existence and reduces it to zero.

*As I've already said, in finance the risk of a strategy (e.g. "buy Bitcoin") is the expected loss of that strategy. This is a statistical measure. And because Bitcoin's potential returns are so extreme this becomes an example of an asset with negative risk, e.g. expected returns, despite not guaranteeing any profit.*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.

Good, that's why this makes a perfect example if you actually want to understand what's going on.

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**.

See the dice example. I'm not. Risk is a "before-the-fact" measure.