How to break down returns into daily returns net of transaction costs

Hi everyone,

I have a problem that is driving me crazy and after three days of frustration
I thought it would be a good idea to asks somebody brighter than me.

OK, I am trying to derive an asset allocation strategy that tells me on a daily
basis whether to be long in an index (via ETF) or whether to invest in the risk-free
rate (90-day t-bills). So I get something like (in / in / in / in / out /out /in / out).
As you can see, the strategy is telling me to go long in the index on day 1 and stay there until day 4, position will then switch to out-of-the-market and so on.

Now the thing is I would like to calculate the annualized sharpe ratio
for such a strategy and I have no idea how to calculate daily returns net
of transaction costs which is crucial for the sharpe ratio. I know that the simple return from a trade (say the "in"-position for the first 4 days in the example above) is

pi=exp [ sum(t=2)(4)r(t) +log((1-c)/(1+c))] -1

with r(t)=log P(t)-log P(t-1)

Transaction costs obviously occur at day 1 and day 4 . And now comes the trouble:
How can I break down the return from such a trade into daily returns net of transaction costs in order to get the sharpe ratio?

Maybe the answer is obvious, to me it is not so any help is highly appreciated!

You need to either determine each day's performance individually - meaning taking the day's close and incorporate any transaction costs incurred that day - or you need to come up with an average return for those days based on the overall return take for the period.