# Volatility for time periods with little data

When I want the monthly volatility of stock and I only have data for about one month and I do calculation like this:

  Date  Close      Daily Returns   STDEV               STDEV * 24
2015-07-15  162.1
2015-07-14  164.5   0.0148056755    0.0165791585    0.0812209576
2015-07-13  165     0.0030395137
2015-07-10  160.7   -0.0260606061
2015-07-09  158     -0.0168014935
2015-07-08  154.2   -0.0240506329
2015-07-07  154.6   0.0025940337
2015-07-06  157.5   0.0187580854
2015-07-03  160.8   0.020952381
2015-07-02  161.2   0.0024875622
2015-07-01  161     -0.0012406948
2015-06-30  156.1   -0.0304347826
2015-06-29  158     0.0121716848
2015-06-26  162.5   0.0284810127
2015-06-25  162     -0.0030769231
2015-06-24  160.7   -0.0080246914
2015-06-23  162.9   0.0136901058
2015-06-22  159.4   -0.021485574
2015-06-19  156.6   -0.017565872
2015-06-16  157.8   0.0076628352
2015-06-15  156     -0.0114068441
2015-06-12  159     0.0192307692
2015-06-11  158.9   -0.0006289308
2015-06-10  159.3   0.0025173065


So I get 8.1% in monthly volatility. Is this correct calculation or do I have to have one year of data for it to be "correct"? Cheers

• 8.12% is a perfectly reasonable monthly volatility for a stock, it is equivalent to 8.12*sqrt(12) = 28.13% a year, very typical. – Alex C May 30 '16 at 17:36

Not sure why you're multiplying by 24?

EDIT: got confused by your STDEV * 24, you meant (and calculated) STDEV * SQRT(24)

If $X_i$ is random variable representing daily log returns, and assuming that log returns are i.i.d. then volatility of monthly return is

$\sigma_{monthly}=\sqrt{21}\times\sigma_{daily}$

(assuming 252 days a year, i.e. $252/12=21$ per month).

and consequently, the yearly vol is

$\sigma_{annual}=\sqrt{252}\times\sigma_{daily}$

• I think he's actually multiplying by root 24 to get a monthly volatility figure from his daily number. – GodLovesATrier Jun 1 '16 at 9:14
• You're correct - edited answer. – rbm Jun 1 '16 at 9:36