It looks like 1 and 2 are different portfolios of companies.
1 is a portfolio of dual-listed companies, and
2 is a portfolio of everything in the "market".
Once you have constructed these these portfolios, let's say you put the returns for every time step into a vector, call it
r, then the average return would be
You need some clarification as to what "equally-weighted portfolio" means in this case in order to construct your portfolios. For example, if you simply assume to buy the same # of shares of every stock, you may have a situation like this:
Assume the whole market consists of stocks A, B, and C.
if you buy 1 share of each stock, then your total portfolio will worth 85 dollars, with $50 (59%) being from stock C, $25 (29%) from stock B, and $10 (12%) from stock A. So you can see even if you bought the same % of shares, you do not have an equally weighted portfolio. Your portfolio is much more sensitive to fluctuations in stock C than it is to fluctuations in stock A. If stock A goes to zero, you only lose 12% of your portfolio, but if stock C goes to zero, you lose 59%.
As far as I can tell they do ask you to use log-returns. I don't think it is necessary to use log returns calculate average portfolio returns. If you do use log returns, remember there is a difference between log returns and arithmetic returns: http://en.wikipedia.org/wiki/Rate_of_return#Arithmetic_and_logarithmic_return.
Easiest way to find the returns of the equally weighted portfolio would be to adjust your prices so that start price of each asset is equal to 1. Then you pretend that you buy one of each asset and look at the returns for you time period. This would be the same as assuming that you are investing the same $ amount in each asset regardless of the share price.
If these are your prices for asset A and the first 4 time points:
50.50 @ t = 1
50.75 @ t = 2
50.80 @ t = 3
50.95 @ t = 4
after adjusting the prices you would have
1 @ t = 1
1.00495 @ t = 2
1.00594 @ t = 3
1.00891 @ t = 4
So no you can see that your return for this asset over the first 4 time periods is:
1.00891 - 1 = 0.00891 or 0.89%
Do this for all the assets and you will have your equally weighted portfolio.