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COMMENT

By Maynard Paton (TMFMayn)
December 17, 2004

How should you calculate your portfolio's 2004 performance? The obvious starting point is the simple return. It's calculated by dividing the portfolio's profit for the year by its starting value and expressing the result as a percentage.

However, things get a bit tricky when -- like most people -- you've put extra money in and/or taken some money out of your portfolio. Here, the simple return can exaggerate or understate your portfolio's actual return.

Take this portfolio performance:

Date Value/transaction
31/12/2003 £10,000 starting value
01/05/2004 £7,000 contribution
01/08/2004 £3,000 withdrawal
31/12/2004 £20,000 closing value

What's the percentage return for 2004?

Outlined below, something called the (Modified Dietz) time-weighted return is perhaps the simplest way of calculating the performance:

```Closing value - starting value - contributions + withdrawals
------------------------------------------------------------
Starting value + contributions - withdrawals           (weighted for time effect on portfolio)```

For the above portfolio, the time-weighted sums go like this (the £7,000 addition is weighted for eight months and the £3,000 withdrawal is weighted for five months):

```  £20,000 - £10,000 - £7,000 + £3,000           £6,000
----------------------------------------   =   -------   =   44.7%
£10,000 + (£7,000 *8/12) – (£3,000 *5/12)      £13,417```

Alternatively, there's what's called the money-weighted return. This calculation requires a spreadsheet and sometimes the knowledge of the internal rate of return function, though a basic understanding of exponentials and a little guesswork will suffice for most people.

For the money-weighted approach -- noting the additions and withdrawals were conveniently made at the start of a calendar month -- basically...

Starting value * ((1+monthly return) ^ months in portfolio) plus
Contribution * ((1+monthly return) ^ months in portfolio) less
Withdrawal * ((1+monthly return) ^ months out of portfolio)

...should equal the closing value of the example portfolio. After deducing the monthly return, the annual portfolio return on a money-weighted basis is then calculated as the monthly return ^ 12.

To cut a long story of guessing short, using a monthly return of 3.16% gives...

Starting value: £10,000 * (1.0316^12) = £14,527 plus
Contribution: £7,000 * (1.0316 ^ 8) = £8,979 less
Withdrawal  £3,000 * (1.0316 ^ 5) = £3,505

... which taken together gives a closing value of about £20,000. The annual money-weighted return is therefore 1.0316 ^ 12, or 45.3%, and very similar to the time-weighted figure.

Finally, if you have a portfolio with numerous cash inflows and outflows, don't get too bogged trying to calculate your 2004 return. Far more important is trying to find the right shares for 2005!