If I had a portfolio with one stock with an initial value of 100 and the next day the stock gained 5 and I added 50 too, would I adjust the log return this way: ln [(155-50)/100]?


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Yes, the log return on your portfolio is the log percentage chance in the value of your portfolio, including the value of all assets and cash.

If you initially have an asset valued at 100 and no cash, and then next day you have an asset valued at 105 and 50 cash, then the log return is

$$ R = \ln \left( \frac{105 + 50}{100} \right) $$

Typically you would want the 50 in cash to be a cashflow derived from the asset (e.g. a dividend or a bond coupon) for this to make sense. If you have an account that holds stock and cash, and you are just paying an extra 50 into the account, it doesn't make much sense to consider that as part of the return.

  • $\begingroup$ But if you're computing a daily ending day return and you want to adjust for that transfer in, would you subtract the transfer in the numerator or is there another way to adjust the return? $\endgroup$ – user52443 Jan 18 '17 at 21:58
  • 1
    $\begingroup$ Look up "time weighted returns" to see how cash inflows and outflows in a portfolio are handled. The returns between such events are computed and then "spliced together" (geometric linking) to find the overall TWR. Example: At start of year you have stock worth 100, on Feb 18 it is worth 105; the log return is ln(105/100). On this day you add 50, and at end of year you have stock worth 175. The log return for the second part of the year is ln(175/(105+50)). The logarithmic TWR for the year is the sum of these two log returns. $\endgroup$ – Alex C Jan 19 '17 at 0:55

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