I would like to calculate the Yearly Sharpe Ratio on MSCI World index
I have monthly values of the index that falls back up to Jan/1970, hence about: 44 years, 528 months
In order to calculate Sharpe Ratio we need standard deviation of the yearly rate or returns, there are two ways to calculate this:
Which one is the right way to calculate yearly sharpe ratio? 1 or 2 OR 3? And why?
WAY 1) I calculate rolling yearly rate of returns, and then I simply calc the mean and the stddev
Just to make it clear, I calc the rolling yearly Rate of Returns (RoR
) in this way:
RoR1 = (Val(12) - Val(0)) / Val(0)
RoR2 = (Val(13) - Val(1)) / Val(1)
RoR3 = (Val(14) - Val(2)) / Val(2)
...
RoRN = (Val(N) - Val(N-12)) / Val(N-12)
where Val(N)
is the value of the MSCI World index at time N
Hence, we calc about N-12 RoRs
which for my sample is 516 RoRs
Then I would just find the mean (M
) and the stddev
of the previously calulated RoR
s
WAY 2) I calculate yearly rate of returns, and then I simply calc the mean and the stddev
Just to make it clear, I calc the yearly Rate of Returns (RoR
) in this way:
RoR1 = (Val(12) - Val(0)) / Val(0)
RoR2 = (Val(24) - Val(12)) / Val(12)
RoR3 = (Val(36) - Val(24)) / Val(24)
...
Hence we calc about 44 RoRs
WAY 3) we calculate the yearly Sharpe ratio by using the mean and stddev of annualized monthly rate of returns (see for instance this Morningstar paper that explains it).
But this 3rd way adds a bit of complexity (and some arguments about whether is correct to annualize stddev by simply multiplying by sqrt of 12)
And I don't understand why would even someone look at this 3rd way, when way 1 or 2 could suffice.