Volatility vs Risk

[ironchef]

IMHO, volatility is the std dev of returns, but risk is something different. Risk is the std dev of the residuals of your “model.” When you have no model, then volatility and risk end up being the same thing since the residuals become the returns around the mean (or 0 if there is no expected drift).

The above difference between vol and risk is based on the assumption that we can model the returns of an instrument. This shouldn’t be a stretch as we’ve been relying on models such as CAPM and the factor models from Fama-French, etc. for a long time. Let’s say that you’re using a single factor model (it’s easier to visualize), perhaps using the momentum factor. So you load up on positive momentum stocks and short negative momentum ones. In our idealized example, the positive momentum stocks may have high volatility due to the fact that their prices go up a lot and the negative momentum stocks may have high volatility because their price depreciates a lot. But, in this highly unrealistic and for illustrative purposes only scenario, the “risk” experienced by your model would probably be much lower than the volatility in the associated stocks. Your model would have nice (positive) returns since it went long the appreciating stocks and short the depreciating ones. There would be a distribution to the returns generated by your model over some time period (think daily returns over a 20 year span). And, these returns generated by your model would not match exactly the returns “expected” by your model; in some time periods, your model would expect higher returns than it produced and vice versa. The difference between the returns the model generated and expected is the residuals. The std dev of the distribution of these residuals gives us an idea of the “riskiness” of the model.

Of course, everything I’ve said above is easier said than done and is based on some assumptions that we know don’t really hold in practice. For one, it assumes that we can actually create an unbiased model of the underlying process; I’m not sure that I’ve actually ever seen this. Certainly it would mean that our model is free from any data snooping, look ahead and any other biases; no curve fitting Another issue is that we’re using std dev, which really only works well on normal distributions and we know that market returns (even log returns) are not normal. But, IMO, despite practical implementation challenges, the above mental model is useful when thinking about the difference between volatility and risk.

I agree volatility of the stock price is represented by standard deviation.

When I day trade, risk and volatility are essentially the same.

But as a long term investor, my #1 risk is the probability of the company going out of business. Of course there are also other risk, like I may not get all of my money back...

It is often very complicated, different from just the volatility of the stock price?

Anyway, it is beyond my pay grade, my capability, to define risk.

 

[mbquant]

In general, the investment/trading community equate volatility to risk, at least to first order.

Two questions for you:

1. Do you agree?

2. Over most 3 decades windows, QQQ > SPY. Does it mean the more volatile QQQ is not really higher risk?

It's more nuanced.

Risk is commonly defined as the possibility of something bad happening.

And since this "something bad" is unknown, we tend to use volatility as an alias for it.

When you're investing, longer your investment horizon (holding period), more can you treat daily, or even weekly volatilities as noise.

And when you invest for the long term, you should simply put your money and forget that it's there (provided you've run due dilignce on the long term growth prospects of the investment). This way, any drawdowns won't make you divest and you''ll enjoy your LTCG.

Now coming to trading, the major aspect of risk management is to have proper stops/trail stops in place. But since every stock has periods of high and low volatilities, you should adjust your stops accordingly, and not just have them at fixed positions.

The essence of risk management is to ensure zero or minimal loss of capital. And when the above mentioned things are in place, your risk is mitigated.

Volatility is just an attempt of quantifying risk. There are other methods as wel, for example, the likelihood and severity matrix, the VaR, and many others. Then there's the Sortino which takes into account ony the negative volatilities.

Depending on your objectives (to create more wealth, to be risk averse, or to have a combination of both), you can choose to employ the metric that serves your investment or trading strategy best.

 

[ironchef]

It's more nuanced.

Risk is commonly defined as the possibility of something bad happening.

And since this "something bad" is unknown, we tend to use volatility as an alias for it.

When you're investing, longer your investment horizon (holding period), more can you treat daily, or even weekly volatilities as noise.

And when you invest for the long term, you should simply put your money and forget that it's there (provided you've run due dilignce on the long term growth prospects of the investment). This way, any drawdowns won't make you divest and you''ll enjoy your LTCG.

Now coming to trading, the major aspect of risk management is to have proper stops/trail stops in place. But since every stock has periods of high and low volatilities, you should adjust your stops accordingly, and not just have them at fixed positions.

The essence of risk management is to ensure zero or minimal loss of capital. And when the above mentioned things are in place, your risk is mitigated.

Volatility is just an attempt of quantifying risk. There are other methods as wel, for example, the likelihood and severity matrix, the VaR, and many others. Then there's the Sortino which takes into account ony the negative volatilities.

Depending on your objectives (to create more wealth, to be risk averse, or to have a combination of both), you can choose to employ the metric that serves your investment or trading strategy best.

Thank you. Very helpful.

 

[CannonTrading_Ilan]

might a bit too simple to share but here is a good read in general: https://www.cannontrading.com/riskopportunity