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Ologhai Jones

Calculating A Meaningful Growth Figure

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It's simple enough to work out a growth figure for a portfolio for which there is only an initial deposit, but what about for one to which additional funds will be deposited (at potentially irregular intervals)?

Imagine the following sequence of events:

An initial deposit of £5,000 was made on 01-Jan-2010 and it was used to buy a variety of shares. Then, on 01-Jul-2010 (six months later), an additional deposit of £2,000 was made. Prior to this second deposit, the portfolio's value had increased to £5,500 (taking it up to £7,500 including the second deposit). By 01-Mar-2011 (a further eight months later), the portfolio had grown to a value of £8,250. (And presumably this process of further deposits followed by further periods of growth or decline could continue indefinitely.)

Is there a meaningful way of producing a single growth figure to indicate the performance of the portfolio so far? Normally, one could take the amount of growth of the initial deposit over the time it's taken to achieve that growth, but there isn't just a single initial deposit AND there are (kind of) multiple pots of money (two in my example) that have been growing for different amounts of time.

Any suggestions on a technique?

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Just to follow up:

Having said that it's simple enough to work out a growth figure for a portfolio for which there is only an initial deposit, I was wondering whether it would be useful to treat the multiple-deposit portfolio as if it's multiple single-deposit portfolios. This would produce multiple growth figures that I then don't know quite what to do with.

From my example above:

Growth of £5,000 to £5,500 in six months is equivalent to a yearly IR of (I think[1]) about 21%.

Then growth of £7,500 (previous 'closing' value plus new £2,000 deposit) to £8,250 in eight months is equivlent to a yearly IR of (I think) about 15%.

Are these two growth figures useful? Is there a meaningful way to combine the 21% and 15% to produce an estimate of how well the portfolio is doing represented as something like n AER?

[1] Calculation: POWER(1 + (5500 - 5000) / 5000, 1 / (('01-Jul-2010' - '01-Jan-2010') / 365)) - 1

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Does it need something that sophisticated?

What about:

0 5000

1 5083.333333 0.016666667

2 5166.666667 0.016393443

3 5250 0.016129032

4 5333.333333 0.015873016

5 5416.666667 0.015625

6 5500 0.015384615

7 7500

8 7607.142857 0.014285714

9 7714.285714 0.014084507

10 7821.428571 0.013888889

11 7928.571429 0.01369863

12 8035.714286 0.013513514

13 8142.857143 0.013333333

14 8250 0.013157895

14 0.192034255

* 12/14 16%

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I think I understand the arithmetic up until the last bit, but where did the '0.192034255' come from?

Just totting up the individual percentages over the 14 months then turning into a 12 month figure.

It's an approximation that won't work in a 40 year business plan I grant you!

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Just totting up the individual percentages over the 14 months then turning into a 12 month figure.

It's an approximation that won't work in a 40 year business plan I grant you!

So, you would suggest keeping a note of each month's increase as I go along?

Like this:

Month / Initial Value / Deposit

Month 0 -- Start value: 0 -- new deposit: 5000 -- growth: n/a

Month 1 -- Start value: 5100 -- new deposit: 0 -- growth (100 / 5000): 2%

Month 2 -- Start value: 5176.5 -- new deposit: 0 -- growth: (76.5 / 5100): 1.5%

Month 3 -- Start value: 5343.59 -- new deposit: 1000 -- growth (157.09 / 5176.5): 1.75%

Month 4 -- Start value: 6470.46 -- new deposit: 0 -- growth (126.87 / 6343.59): 2%

Growth calculation:

- <last month's total start value> = <last month's start value> + <last month's new deposit>

- <growth> = (<this month's start value> - <last month's total start value>) / <last month's total start value>

Presumably, this would accurately represent the monthly growth as long as new depositing and trading only took place at the start/end of a month. Then, for each consecutive block of twelve months, I could multiply the monthly growths together to get the yearly growth?

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So, you would suggest keeping a note of each month's increase as I go along?

Like this:

Month / Initial Value / Deposit

Month 0 -- Start value: 0 -- new deposit: 5000 -- growth: n/a

Month 1 -- Start value: 5100 -- new deposit: 0 -- growth (100 / 5000): 2%

Month 2 -- Start value: 5176.5 -- new deposit: 0 -- growth: (76.5 / 5100): 1.5%

Month 3 -- Start value: 5343.59 -- new deposit: 1000 -- growth (157.09 / 5176.5): 1.75%

Month 4 -- Start value: 6470.46 -- new deposit: 0 -- growth (126.87 / 6343.59): 2%

Growth calculation:

- <last month's total start value> = <last month's start value> + <last month's new deposit>

- <growth> = (<this month's start value> - <last month's total start value>) / <last month's total start value>

Presumably, this would accurately represent the monthly growth as long as new depositing and trading only took place at the start/end of a month. Then, for each consecutive block of twelve months, I could multiply the monthly growths together to get the yearly growth?

Yes. I just totted them up rather than multiplying but for one year the difference is minimal.

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http://office.microsoft.com/en-gb/excel-help/xirr-HP005209341.aspx

You can get a resource pack in excel that calculates XIRR : internal rate of return for a schedule of cash flows that is not necessarily periodic.

Thank you. That's very interesting!

For the data I'm playing with, using Frank's month-by-month method (then averaging the monthly growth figures, then deriving a yearly IR from that average) I get a yearly growth figure of: 26.68%.

Using XIRR() produces a figure of: 27.10%.

That's close enough to cause me to think it likely that both are more or less working. I shall proceed to use both approaches for now to see if they remain more or less in touch with each other.

Thanks again.

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