# Longer measurement intervals lower volatility

What is the logic behind: Longer measurement intervals result in lower estimates of volatility (e.g. annualised standard deviation of daily returns is higher than of weekly returns).

It is smoothing of returns. Consider the following case of the price of a stock where S(i) is the price of the stock in period i.

S(1)=50

S(2)=75

s(3)=25

s(4)=50

If you measured the standard deviation from start to end of periods 1,2,3, and 4, you would get a standard deviation of 17.6.

If you measured that standard deviation from start to end but only using the two end periods, you would get a standard deviation of 0.

This is an extreme example of ocurse, but hopefulyl illustrates the point.

You lose a lot of noise, as dwheats illustrated.

I thought it’s the other way round, longer intervals means higher volatility. Disperse intervals have more differing characteristics than close intervals. Eg, taking readings every day in the 4th quarter, vs every 3rd day. Volatility would be higher in the second scenario especially if the sampled days coincide with cyber Monday, black Friday or get closer to the holidays (not smoothed by nature).

If what was meant is longer duration vs shorter duration, then volatility increases by a factor of SQRT of the units of duration. Eg, Daily SD = 1.5%, annual = 1.5 X SQRT (250).

If what was meant is volatility of the whole period is less than the sum of the units of the period, then this is correct -smoothed by SQRT(units of the period)-

Please correct me if I’m wrong.

We may be conflating two ideas here:

• Ten years of monthly returns will likely have a _ higher _ standard deviation than five years of monthly returns.
• Ten years of annual returns will likely have a _ lower _ standard deviation than ten years of monthly returns.

So essentially, the more returns we have, the higher the volaility/Standard deviation. Ten years of monthly returns (120 returns) will likely have a _ higher _ standard deviation than five years of monthly returns (60 returns). Ten years of annual returns (10 returns) will likely have a _ lower _ standard deviation than ten years of monthly returns (120 returns). Is that correct?

The key word is “annualized” . Annualized weekly volatility is less than annualized daily volatility.

Couldn’t copy the tables of daily vs weekly volatilities/ annualized vs not annualized. Here’s the link

http://www.investopedia.com/articles/04/021804.asp

It is also helpful to think of this in terms of NAREIT (higher vola) and NCREIF (lower vola).

^ this is somehow different. This is for a lack of frequent data not for reduced frequency of available data.

But all in all, it helps in understanding the different effects on volatility