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Measuring Portfolio Returns Across Trades with Different Holding Periods

Article Quant Q&A · Author: John Faxton
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Summary

The document asks how to calculate and compare portfolio performance when positions are opened and closed at different times. It presents a sequence of stock trades with staggered entry and exit dates to illustrate why simply adding each trade’s annualized return may not represent the portfolio’s overall return over a shared period.

Two suggested approaches are named: internal rate of return (IRR) and modified internal rate of return (MIRR). Another response recommends calculating returns for each position over each time segment, then geometrically linking those segment returns. The discussion gives no worked calculation or comparison of the methods, so it does not establish which measure best suits a particular portfolio. The appropriate choice depends on the question being asked, including how cash flows and the timing of investment capital should be handled.

Key ideas

  • Annualized returns from individual trades cannot simply be summed to obtain a portfolio return.
  • IRR and MIRR are textbook methods suggested for evaluating returns when investments occur at different times.
  • A linked return series can be built by calculating returns for each position during each time segment and geometrically compounding the segments.
  • The discussion does not compare the methods or work through a numerical portfolio calculation.

Tags

Portfolio constructionStatistics
Full text
# Portfolio return for assets held for different lengths of time


# Portfolio return for assets held for different lengths of time












How does one calculate the return on a portfolio if the assets in that portfolio were held for varying periods of time? For Example: $t_0$ Buy AAPL at 100 $t_5$ Buy MSFT at 20 $t_1$$_0$ Sell MSFT at 30 $t_2$$_0$ Sell AAPL at 110 $t_2$$_5$ Buy MSFT at 40 $t_3$$_0$ Buy AAPL at 150 $t_5$$_0$ Sell AAPL at 160 $t_7$$_0$ Sell MSFT at 50

- $t_0$ Buy AAPL at 100 $t_5$ Buy MSFT at 20 $t_1$$_0$ Sell MSFT at 30 $t_2$$_0$ Sell AAPL at 110 $t_2$$_5$ Buy MSFT at 40 $t_3$$_0$ Buy AAPL at 150 $t_5$$_0$ Sell AAPL at 160 $t_7$$_0$ Sell MSFT at 50

Can we simply find the sum of annualized returns for each trade to find out what the annualized portfolio return was at $t_7$$_0$? Could we then do the same for another portfolio to compare the two portfolios from $t_0$ to $t_7$$_0$?

## Answer by KT. (score 1)

https://quant.stackexchange.com/a/22080

IRR and MIRR are probably the two textbook answers to your question.

## Answer by RndmSymbl (score 0)

https://quant.stackexchange.com/a/25679

You would calculate return for each single position and for each segment of time. Following that you would geometrically link all these separate returns.

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