How do I interpret weighted and non-weighted gains on a stock portfolio?

[jwburrit]

I have the following stock gains and losses for a stock portfolio. Overall, the portfolio has lost $40 or 28%. But when I calculate weights based on market value, and then calculate the gain/loss based on those weights, I come up with an 8% gain.

My problem is how do I explain the $40 loss (-28%) on a non-weighted market value basis and the 8% gain on a weighted market value basis?

So far, I've just come up with this: The market value weights amplify gains or losses embedded in the total gain/loss. Since the total gain/loss has no weights, you don't see the weighted gain/loss.

But somehow this doesn't sound intuitive.

Furthermore, how do I explain the 8% gain? I understand the math that calculates it. But what is it 8% of?

Any help would be greatly appreciated

[curiouscat408]

%Gain/loss should be weighted by cost, not by current market value. That would be clear if you worked out the mathematics.

See the image below. Ordinarily, I would show you formulas. But apparently, you don't think that's necessary, since you did not show us yours.

Oh well, "two wrongs don't make a right". I've attached the Excel file.

[jwburrit]

Thank you!

[curiouscat408]

@jwburrit, you don't seem to understand that trying to calculate an "average return" by weighting by market value is simply wrong, not just "another kind of average".

At https://www.mrexcel.com/board/thread...eturns.1193430 that you posted today, you ask:

``if an investor wants to use current market weighted returns, the return for the total portfolio is still -28%. But the return for the sum of all stocks on a market-weighted basis is 8%. How would I explain the difference is weighted returns to someone?``

I cannot post a response in mrexcel.com. So I will answer here, as a clarification to my previous response.

The explanation is simple: the market-weighted value is simply __not__ "an" average rate of return. It is simply the wrong answer !

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First, let me explain the concept of "right" and "wrong" by analogy.

If we drive 10 miles in 20 min at 30 MPH and 20 miles in 20 min at 60 MPH, what is the average MPH?

As a youth, my inclination was to weight by mileage. So I would calculate 30*(10/30) + 60*(20/30) = 43 1/3 MPH.

But my father-the-Air Force-navigator always corrected me: we should weight by time. Thus, the correct calculation is 30*(20/40) + 60*(20/40) = 45 MPH.

The fact is: my father was right, much as I hate to admit it.

The correct average MPH is total miles divided by total time (in hours). The total miles is 10+20 = 30. The total time is 20+20 = 40 min, which is 2/3 hours.

So the average is 30 miles / (2/3 hours) = 30*3 / 2 = 45 MPH. QED.

My 43 1/3 MPH is not just "another average MPH". It is simply wrong. It is not a measure of anything. ( Except my own stubbornness. )

In other words, the fact that the miles-weighted method produces the wrong answer and the time-weighted method produces the right answer should be sufficient to explain to anyone that the miles-weighted method is simply wrong.

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Similarly for the portfolio return based on a weighted average. The (only) right answer is to weight by cost.

We can "prove" that many ways. I think the easiest way is to work it backwards.

Given: security S1 with market value M1 and cost basis C1, the return is (M1-C1)/C1, which is equivalent to M1/C1 - 1. Similarly for security S2 and S3.

The portfolio return is total market value divided by total cost basis, which is (M1+M2+M3)/(C1+C2+C3) - 1.

Is that the same as the cost-weighted average return?

Yes. The cost-weighted average return is:

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QED.

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Arguably, we might ask: does the market-weighted average return __also__ return the same portfolio return?

Of course, you already know the answer is "no".

Let's use the same method to demonstrate why not. The market-weighted average return is:

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Hopefully, you can see that bears no resemblence to the actual portfolio return, which again is (M1+M2+M3)/(C1+C2+C3) - 1.

QED.

If that's TMI, it would behoove you to just accept my assertion that the cost-weighted average is the (only) right answer.