You have 10 years of daily “X&Y Index” total return observations, 256 trading days each year.

The mean return per day on the X&Y index is 6.37 basis points.

The standard deviation per day on the X&Y Index returns is 113 basis points

What is the annual standard deviation in % (2 decimal places e.g. 1.23 for 1.23%)?

We can calculate the annualized standard deviation using the following formula:

Annualized standard deviation = Standard deviation per day * ( Numer of periods per year ) ^1/2

Given:
Standard Deviation per day = 113 basis points or 1.13% ^{^}
(^ 1% = 100 basis points)
Trading days each year =  256

Trading days each year is the number of periods per year.

Applying the given values in the formula:

Annualized standard deviation = 1.13% * (256)^1/2
= 1.13% * 16
= 18.08%

Therefore, the annual standrd deviation is 18.08%