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.

Oh great, the 'ol "appeal to authority." Out of all the logical fallacies I did not expect that one first.

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.

Let's use a more definitive

source:

Risk is defined in financial terms as the **chance that an outcome or investment's actual gains will differ from an expected outcome or return**. Risk includes the possibility of losing some or all of an original investment.

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.

Volatility can be used as a measurement of risk, however incomplete it may be. I feel like you didn't even take a look at this

link I posted earlier, which provides a good summary of volatility vs. risk:

Volatility is a statistical measure of the dispersion of returns for a given security or market index. **In most cases, the higher the volatility, the riskier the security.** Volatility is often measured as either the standard deviation or variance between returns from that same security or market index.

...

Volatile assets are often considered riskier than less volatile assets because the price is expected to be less predictable.

...

Volatility often refers to the amount of uncertainty or risk related to the size of changes in a security's value.

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.

How so? It seems like you are altering the definition of the word "constant" to suit your purposes. A measurement which faces any sort of volatility cannot be constant. It can only be constant on average, not in its actual movement.

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?

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.

Every single asset on the planet faces this exact same risk. There is no chance of losing money in this example (outside of the same meteor event that could wipe out all investments), thus it is zero risk.

*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.*

Okay. If that's the case, all I've really learned here is that your definition of risk is useless.