annualized return calculation for the purpose of portfolio performance evaluation

[sharkey]

I'm trying to evaluate the performance of a couple of stock portfolios
and I need to calculate Sharpe,Treynor Ratios, Information Ratio and
also Jensen Measure.
I have a monthly closing prices for all the stocks in a portfolio for
48 months.
My problem is that i'm not sure which rate of return to use in the
ratios..i figured that the annualized rate of return for the 48 months
would be better than just average annual rate of return. How should I
compute the annualized rate of return from the data i have?
I found an article with an example (of what i think I should do) of
calculation of annualized return with the mothly data at
http://www.russell.com/ca/Investor_Services/Personal_Rate_of_Return.asp
But I still don't have a formula and I'm not really sure whether it's a
right way.
Also when I calculate those compound indicators(Sharpe) do I have to
use annualized standard deviaton or is it ok to use just a standard
deviaton of the monthly returns?
Too many questions I know, but I'm kinda lost.
I guess I might as well stick with the average annual rate which would
make things less complicated
Thanx for your help

 

[sharkey]

or do you think it would be ok to convert the average monthly rate for
the whole period to annual rate with this formula (1+avg.m.rate)^12-1

 

[vandenberg p]

Hello:

The general practice is to use holding period returns (HPR) for the period
of the data that you have. But you need dividend information also, since
that is part of the return.

So if you have monthly data you would calculate monthly returns and
monthly standard deviations. (If you had daily data you
would do on a daily basis.) Then you use the average of the monthly returns
so your answers will all be in monthly returns. There is no reason to convert
to annual, in fact it will harm your results. There is some theoretical
arguments for continuous compound returns in your calculations (that
is ln(1+HPR)). In order to calculate the Treynor measure and the Jensen
measures you will also need monthly Risk Free rates, and the betas.
You may want to find a good investment book that goes over the
computations.


Pieter Vandenberg


: I'm trying to evaluate the performance of a couple of stock portfolios
: and I need to calculate Sharpe,Treynor Ratios, Information Ratio and
: also Jensen Measure.
: I have a monthly closing prices for all the stocks in a portfolio for
: 48 months.
: My problem is that i'm not sure which rate of return to use in the
: ratios..i figured that the annualized rate of return for the 48 months
: would be better than just average annual rate of return. How should I
: compute the annualized rate of return from the data i have?
: I found an article with an example (of what i think I should do) of
: calculation of annualized return with the mothly data at
: http://www.russell.com/ca/Investor_Services/Personal_Rate_of_Return.asp
: But I still don't have a formula and I'm not really sure whether it's a
: right way.
: Also when I calculate those compound indicators(Sharpe) do I have to
: use annualized standard deviaton or is it ok to use just a standard
: deviaton of the monthly returns?
: Too many questions I know, but I'm kinda lost.
: I guess I might as well stick with the average annual rate which would
: make things less complicated
: Thanx for your help