Why Position-Weighted Returns Ignore Investment Timing
Summary
The document examines a proposed way to summarize the return of a single security position built through purchases at different prices. The method calculates each purchase’s return to the present, weights those returns by the purchase’s fraction of current shares, and adds the weighted values. In the example, this produces a figure distinct from both the return since the first purchase and the return implied by aggregate cost basis.
The central issue is that the calculation weights by share count rather than by the amount and timing of capital invested. Because it ignores purchase dates and cash flows, it does not represent a conventional time-weighted portfolio return or an investor’s money-weighted return. The document poses the question but contains no answer or named method, so it does not settle which performance measure is appropriate; that depends on whether the goal is to describe asset performance or the investor’s realized experience.
Key ideas
- The proposed calculation averages returns on separate purchase lots using their fractions of current share count.
- The method omits purchase dates and therefore does not account for how long capital was invested.
- A cost-basis return, a first-purchase return, and investor-level performance answer different questions.
- Choosing a performance measure depends on whether the focus is the asset’s return path or the investor’s cash-flow experience.
Tags
Full text
# Is a position-weighted sum of nominal returns for a single asset a mathematically sound calculation?
# Is a position-weighted sum of nominal returns for a single asset a mathematically sound calculation?
A friend of mine insists that that the following is a sound method to calculate the performance of a single holding in a portfolio, given that over time more capital has been allocated to that holding. My questions are these
- Is this a theoretically sound way to calculate performance?
- Is there a name for this?
The method is exemplified as follows with shares in a security being held. As additional shares are bought, their total return since purchase is calculated, weighted by the number of shares as a percentage of the total, and summed. No dates are used in the calculation.
```
Shares Price Return to Today Weight Return x Weight
Original purchase 117 $260.91 177.82% 32.14% 57.16%
Add 1 +37 $379.88 90.81% 10.16% 9.23%
Add 2 +172 $541.33 33.90% 47.25% 16.02%
Add 3 +38 $568.56 27.49% 10.44% 2.87%
-------
Today 364 total $724.86 Sum: 85.28%
```
And thus my friend says it is most appropriate to say that the overall return of this holding, given the additional shares bought at a higher price, is 85.28%. He says a cost basis method, which implies a 66% return, is incorrect because it assumes all shares were bought at $438 at the same time. He also says that the total return since the original purchase (178%) is not representative because the shares purchased later did not return this much.
(I am afraid I posted a question earlier that lent itself more to discussion than an actual answer. I hope this is not considered duplicate posting.)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.