# Calculating Annualized Average Return

I am currently working on a problem set in a book that asks me to compute the annualized average return for a portfolio, benchmark, and then the relative return from the annual returns reported. I have been using the equation $$Return = (\prod_{t=1}^{T} (1+r_t))^\frac{12}{T}-1$$

The numbers are as follows in %:

Year 1
Port Return: 26.97
Benchmark Return: 24.94
Relative Return: 2.02

Year 2
Port: 16.04%
Bench: 14.03
Relat: 2.01

Year 3
Port: -41.98
Bench: -39.98
Relat: -2


However my book, Trading and Money Management, states if a strategy has a monthly return of $r_t$ in month $t$ within a period of $T$ months, where $T>12$, the annualized average return is the equation above.

My issue arises because it wants monthly returns, not annual returns. Secondly, it states, "Note that the annualized average 3-year relative return is negative even though portfolio beat the benchmark by more than 2% in first two years and only lagged in last year. Explain"

I have tried assuming the returns as monthly and let $T=36$ and got $-5.09, -5.08, and 0.66%$ respectively. I am pretty sure something is wrong, but I cannot figure out what it is.