Lets say I have a series of daily returns with varying cash outlay. I am trying to take these daily returns to compute the sharpe ratio for the year. my question is about treatment of the weightings.

My initial thought was to do the following

day 1 income- 50,000 outlay - 1,000,000

day 2 income- 120,000 outlay - 500,000

day 3 income- (17,000) outlay - 2,000,000

weight of day 1 = 1,000,000/(1,000,000+500,000+2,000,000)

return of day 1 = ln(50,000/1,000,000)

sharpe =sum (ln(daily return) * weighting based on outlay )/st.dev of returns

the above sharpe * sqrt(252) to annualize the daily returns

I do not think I am treating the weights right. I recall there is a concept of taking the squared value of the weightings


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