Portfolio Returns Explained

Portfolio return is a necessary measure of a portfolio’s performance over an analysis period because its single value is directly related to cash flows including the dollar values at the start and end of the investment period.

In this blog, we define and explain two common return measures and their usage. Real examples show the dramatic differences in the returns, emphasizing the need for care in interpreting a return measure.

The Problem

Out of pocket cash transfers or security transfers from one portfolio to another are a common occurrence and complicate the calculation of a portfolio’s return. The problem is that these contributions and withdrawals seriously affect the calculation of a portfolio’s return performance and can easily result in large errors, depending on the reporting return method. RoboPPA™ correctly handles transfers in calculating portfolio returns.

Common Return Methods

There are two commonly calculated and published portfolio returns for a selected analysis period.

1. Time-Weighted Return (TWR), also called Geometric Mean Return or Holding Period Return (HPR)

This is an analysis period’s annualized portfolio return from portfolio contributions and withdrawals (transfers) that affect the portfolio’s returns in the transfer months. The analysis period’s monthly returns are converted to the overall analysis period return by adding 1 to each monthly return and computing their geometric monthly average. Note that the overall return does not depend on the transfer dates. The monthly return is typically annualized by compounding it 12 times or by multiplying by 12.

This may seem like a non-sensical method but was likely developed initially for reporting the same return on a managed portfolio, such as a mutual fund, to many owners. This avoided tracking the different transfers of individual owners’ rather than just the aggregated transfers, at least for return calculations. This may be justified because the individual transfers and therefore returns represent the different decisions of individuals, whereas the aggregated portfolio return represents the decisions of the manager. The question is, does the HPR represent the correct return to a portfolio’s owner? The answer is yes only if the owner had no transfers.

2. Dollar-Weighted Return, also called Internal Rate of Return (IRR)

This is an analysis period’s portfolio return based on the present value of the portfolio’s cash flows that include transfers. For an analysis period, it is the discount rate (return) that equates the present (discounted) value of cash inflows with the discounted value of cash outflows. The owner’s cash flows are the initial value of the portfolio (outflow), the contributions (outflows) and withdrawals (inflows), and the portfolio's ending value (inflow). The annualized IRR is calculated from the monthly discount rate by compounding it 12 times. In the mutual fund example, the IRR can be calculated at the manager level and at the individual owner level, with the result that the calculated IRRs are different and different from the TWR.

Examples

To demonstrate the difference in the return methods and the problems with the TWR, we show the RoboPPA™ results from a December 31, 2019, $100,000 investment in the market equity index, with a $20,000 portfolio contribution made post crash on March 31, 2020 and also invested in the market index. Therefore, the portfolio was held before and after the March 2020 crash, with a post crash contribution, and calculated over the analysis period starting December 31, 2019 and ending August 31, 2020.

The resulting IRR is 5.31%/year and the corresponding TWR is -1.58%/year, clearly demonstrating the large contradictory portfolio returns in a simple investment. In the case of no contribution, the two returns are identical at -1.58%/year.

The following chart from RoboPPA™ shows comparative returns on an example US domiciled portfolio, the Treasury bill, the S&P500 that is also the user’s selected benchmark.

It shows that the HPR and IRR can be quite different depending on the portfolio, despite having identical transfers.

Conclusion

In the first example, the $20,000 contribution was in the portfolio from March 31, 2020 until August 31, 2020. The portfolio return was positive in every one of those months implying that the contribution must have added value to the portfolio. Therefore, the overall portfolio’s return must exceed the return without the contribution and the positive IRR is a better representation of the return to the owner, than the negative HPR.

In our opinion, the IRR is the preferred measure of a managed portfolio’s return to the owner, and RoboPPA™ calculates it very accurately. However, it also calculates the HPR (TWR), for comparisons.

A significant advantage of RoboPPA™ is that the required inputs for its performance analysis can be saved in its template and updated monthly. This can be done entirely on the user’s computer and never stored on the software’s servers. The software maintains the benchmark databases thereby reducing the user’s work. Finally, the software allows analyses over any selected period contained in the data template’s horizon, providing it exceeds eight months.

Caveats

The analysis and the results in this document are not to be interpreted as representative of real markets and asset classes and are not warranted to be correct or complete. The example is based upon our opinion and interpretation of the data and results, which may be incomplete or incorrect. RoboPPA™ or the data suppliers are not responsible for any damages or losses arising from use of this blog. Details on the performance calculations are available on www.RoboPPA.com.