Volatility Value Range
Can volatility be greater than 1? This is one of the typical questions concerning the possible value range of volatility (in finance).
First I give you a short answer: Yes, it can be greater than 1.
When people are asking this question, they actually usually mean if volatility can be greater than 100%, because it is common to measure and quote volatility of investment returns in percent per year (the same units as used for the investment returns themselves).
Volatility can theoretically reach any value from zero to positive infinite.
This means that it can be greater than 1%. It usually is, because 1% p.a. is very low volatility – such stock would be almost not moving at all.
It also means that it can be greater than 100%, although that is much less common. You can see more details and examples here: Can Volatility Be Over 100?
In any case, volatility can not be negative. Here you can find an explanation (actually two explanations: a common sense one and a mathematical one): Can Volatility Be Negative?
Volatility Values in Reality
A typical long-term average volatility of a stock index (such as the Dow Jones Industrial Average or the S&P500) is 15-25%. It is usually lower (below 10% is not uncommon) when stocks are rising and there are few concerns about the economy. It is higher (even 100% or more in rare cases) in times of recessions, financial crises, and stock market crashes (stocks usually fall much faster than they rise).
Individual stocks can of course have much higher or lower volatility than the stock indices, based on industry, the business model of the particular company, and its financial situation.
Most currencies usually have lower volatility than stocks (around 10% p.a. or lower).
Bonds also tend to have lower volatility than stocks. The shorter the duration of the bond, the lower its volatility (because higher duration means higher sensitivity to interest rate moves). High yield bonds typically have higher volatility.
Some commodities can have very high volatility, as their prices are prone to supply shocks. Their volatility also tends to change in time significantly (the volatility itself is volatile).