What is Annualization?

First, let’s define what is annualization in terms of return and risk.

Note that there is other term with similar name, but another meaning:

So, in terms of previous example, the main difference between them is that annual return/risk is exact return of an asset for a specific year/risk associated with this return, while annualized return/risk is return/risk over different time periods converted into equivalent annual return.

Another aspect, why annualization is important - is standartization.

Let's define it:

Annualized Returns

Let's assume next notation:

• N - length of time period we are working with in years;
• R - return over entire period of time;
• R_a - annualized return.

Then we can compute annualized return using the following expression:

Alternatively, we can assume that N represents the number of months in our period, which will give us the following expression:

Coming back to the previous example with stocks of Nvidia and AMD, here is a code, which will help us compute annualized returns for them, using corresponding formulas:

Annualized Risk

In terms of risk, which is measured by standard deviation, the annualized value can be calculated using the following expression:

Here:

• σ- basic risk;
• σ_a - annualized risk;
• T - time period, used for computing risk.

So, for example, if σ denotes monthly risk - then T = 12 and annualized risk could be computed using the next expression:

Or, in case of daily risk σ, to annualize we use T = 252, since it is an approximate number of trading days in a year (excluding weekends and holidays), and the following expression is used for computing: