Calculating Portfolio Log Returns When Cash Flows Occur

Summary

The document distinguishes investment performance from cash added to an account. In its example, a stock rises from 100 to 105 while the portfolio also receives 50 in cash. If that cash is an asset-derived payment, such as a dividend or coupon, the total portfolio value is 155, and the log return is computed from the ending value relative to the initial value. This captures the income as part of the investment’s return.

A deposit made by the account holder has a different interpretation: it increases account value but is not generated by the investment, so counting it as return would misstate performance. The response’s calculation assumes the cash flow is properly classified and that the stated beginning and ending values cover the portfolio consistently. It does not explain time-weighted or money-weighted return methods for handling flows during a measurement period, so it offers a simple one-period illustration rather than a general performance-accounting procedure.

Key ideas

• Portfolio log return can include asset-derived cash income in ending portfolio value.
• A dividend or coupon is part of investment performance when it accrues to the portfolio.
• An external deposit increases account value but should not be treated as investment return.
• The example illustrates a one-period calculation and does not cover general cash-flow-adjusted return methods.

Tags

# Adjusting a daily log return for a cash inflow/outflow


# Adjusting a daily log return for a cash inflow/outflow












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]?

## Answer by Chris Taylor (score 1)

https://quant.stackexchange.com/a/31946

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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.