Measuring an Asset’s Return Across Multiple Purchases and Sales

Summary

The document raises a performance measurement problem: how to calculate the return on one asset when shares are bought at different prices over time. A simple price return from the first purchase would overstate the experience of an investor who added shares at higher prices. The example illustrates this with successive purchases as the stock price rises, followed by a question about selling part of the holding and valuing the remaining shares later.

The text itself does not provide a resolution or compare calculation methods. It asks whether each purchase should be treated as a separate lot, with each lot’s return weighted by shares, and how a partial sale should affect the result. In practice, the appropriate measure depends on whether the goal is a time-weighted asset return or a money-weighted investor return, and on how cash flows and realized gains are tracked. The document is therefore useful as a statement of the measurement issue, but supplies no answer, evidence, or guidance on accounting conventions.

Key ideas

• Purchases at different prices give an investor a different experience from the asset’s first-to-last price change.
• A single asset return must account for changes in the number of shares held.
• The document asks whether separate purchase lots should be weighted by their share counts.
• Partial sales complicate measurement because realized proceeds and remaining holdings both matter.
• The appropriate return measure depends on the performance question being asked.

Tags

# Computing Overall Return for A Single Asset Given Inflows & Outflows


# Computing Overall Return for A Single Asset Given Inflows & Outflows












I am creating a portfolio tracking model in Excel and have run into difficulty on how to track the overall performance of a single asset, given that over time more and less capital (shares) has been allocated to that asset. I want to determine the most fundamentally sound way to calculate this.

I think an example is best to illustrate this.

- At t=0, 100 shares of ABC stock are purchased for \$100 per share.

- At t=1, 50 shares of ABC stock, which now trades at (costs) \$200, are purchased.

- At t=2, 50 shares of ABC stock, which now trades at (costs) \$300, are purchased.

- At t=3, the portfolio holds 200 shares of ABC stock and ABC's current price is \$400 per share.

So clearly the price change is (400/100–1) = 300%, but this needs to be adjusted for the fact that additional shares were added at a higher price, and so the total return for the portfolio's ownership of ABC stock is lower.

How is this figure calculated in practice? Is it sound to split up the asset into three (original purchase, add 1, and add 2), calculated each's return since purchase, and weight those returns by the number of shares?

Finally, how would I handle selling shares? Say at t=3 I sold 50 shares at \$ 400 each and at t=5 each share (150 in total now) is worth \$ 500.

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