Annualizing Volatility
Overview
Volatilities are most often quoted on an annual basis. However, measuring volatility on an annual basis is hard, primarily
because the returns are calculated as yearly returns, and this will drastically reduce the amount of available data used
to measure the volatility.
More typically, volatility is measured using daily returns and then scaled to an annual basis.
Annualizing Daily Returns
The daily return is calculated as
{% Daily \, Return = ln(P_{t+1}) - ln(P_t) %}
Then, the yearly returns are
{% Yearly \, Return = \sum_i Daily \, Return_i %}
Then, the
Variance of Sum
can be applie to obtain
{% Variance(\sum_0^n X_i) = \sum_0^n Variance(X_i) = n \times Variance(X_i) %}
