# 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

1. Is this a theoretically sound way to calculate performance?
2. 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.)

• Why don't you use IRR? – Neeraj Mar 5 '16 at 9:38