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# Volatility question...

Discussion in 'Strategy Development' started by NTB, Feb 8, 2006.

1. ### NTB

Stupid newbie question. X% volatility of annual returns, monthly returns or daily returns, what does that mean in plain English? Example, we make project 2% monthly returns with 5% volatility? We expect 15% annualized with 4% volatility. Can someone translate into plain english. I understand volatility is variance of returns. However, 4% monthly volatility doesn't mean 2% average monthly returns where returns could be between -2% and +6% one standard deviation of the time? Thanks

2. ### NTB

I think I figured it out. Volatilty is expressed as 1 standard deviation from the mean. Mean monthly return of 2% with a 4% volatility means that 68% of all observations will be between -2% and +6% on a monthly basis. 95% of all observations will be between -6% and +10% on a monthly basis. Correct? Or, does it mean that monthly returns will be between -4% and +4% 68% of the time and -8% and +8% 95% of the time? Same principal for daily or annual volatility. Right? When one says the volatilty of the equity market is currently 10% (VIX) that means that there is a 68% chance that the market will finish the year +/-10% of the current price and a 95% chance the market will end the year +/- 20% from current prices. Right?

3. ### emjroll

You've got it. Vol is 1 std. deviation. Also, if you want to translate yearly to monthly/weekly/daily price moves use this formula:

Price * Volatility * 1/(sq. root of time)

for example, if an index is 1000 and has a vol of 20% and you want to know what the normal 1 day price move will be you would use

1000 * .20 * 1/15.8 = avg. daily price move

15.8 is the square root of 252, the number of trading days in one year.

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