# Why is volatility in a positive direction clubbed in the same risk category as volatility in a negative direction?

Let's say a stock's price has been steadily rising for the last 6 months.

It's going to have (a relatively) high volatility.

Let's say another stock's price has been falling steadily for the last 6 months.

It's going to have high (a relatively) volatility.

High volatility = High risk.

Assuming both stocks have the exact same volatility, ceteris paribus, both will have the same risk.

To my (perhaps non-sophisticated) brain, this doesn't make sense.

Is there a measure of volatility that weighs movement in the positive direction differently than movement in the negative direction? Shouldn't there be one?

Or am I thinking this wrong?

• Keep in mind that there are other forms of risk besides price risk, even in the stock market. Volatility may not speak to these forms of risk directly, if at all. May 19, 2014 at 22:04
• Neither of the stocks you describe has a high volatility. Volatility is measured on the historical returns, not the historical price. (Or to put it another way, it is measured on the "de-trended" price). Aug 6, 2014 at 5:32
• @jjanes Return seems to refer to realized profit or loss. A sale will need to be made to calculate return. Do you have a link to support your contention? Aug 12, 2014 at 3:01
• For frequently traded stocks, returns can be calculated from the reported prices which represent actual trades, there is no reason for them to be your trades. You would have to adjust for splits and dividends. For links, see investopedia.com/terms/v/volatility.asp and en.wikipedia.org/wiki/Volatility_(finance) The wiki site talks a lot about prices in the vague, but when getting down to brass tacks always reverts to "returns". Aug 13, 2014 at 9:21

Mostly, when an equity's price rises, its statistical and implied volatilities fall and vice versa.

The reason why is a mathematical phenomenon mixed with the reality that a unceasingly falling asset price will soon not exist, skewing the results with survivorship bias.

Since volatility is standard deviation of price indexes, a security that changes in price by the same amount every day will have lower volatility, so a rising price will have lower implied volatility because its mostly experiencing positive daily price change while a recently falling price will have higher volatility because factored together with the positive price changes, the negative price changes will widen the standard deviation of the securities price index.

Quantitatively, any change, in or out of one's favor, is a risk because change is uncertain, and any uncertainty is a risk.

This quantitative interpretation while valid runs almost totally counter to the value opinion, that a lower price relative to value is a lower risk than a higher price relative to value, but both have their place in time.

Over long time periods, it's best to use the value interpretation, quantitative for shorter. Using the opposite has hastily destroyed many a fund manager.

• Take out the last statement. Personal opinion shouldn't be included, unless you have data to prove your point. May 19, 2014 at 22:27