a Mutual Fund Gain versus Your Annualized Gain

Here's an interesting thing:

A Mutual Fund says the gain for its Techie Equity Fund was 40% over the past three years (ending April 1, 2001) in spite of the demise of dot.coms and other assorted Hi Tech outfits. They even supply a chart showing the dramatic growth, compared to the Nasdaq. Their Techie Fund had an annualized Return of 11.9%, for this period, while the Nasdaq was down by 0.1%.

Your neighbour has invested $1,000 every six months in this Techie Fund, for the past three years. It's April 1, 2001 and you talk to him over the backyard fence:

You say:
"I guess you're pretty happy with that gain, eh? I mean, if I had listened to you ..."
He says:
"Gain? What gain?"
You say:
"That Techie Fund. Remember when you told me ..."
He says:
"I've put a total of $7,000 into that Fund, the last $1,000 today. It's now worth $6,924."

So you whip out your Excel spreadsheet and calculate, like so
... using the magic XIRR where you keep track of the money that goes in (or out) and when that occurs.

Your neighbour's annualized gain was -0.73%

That's the dark side of Dollar Cost Averaging

See also DCA stuff.

The gain advertised by the Techie Fund looks at some amount of money (say $10K) in the fund at the start of a period (1 year, 3 years, 5 years, etc.) and determines how it has changed. That's called the Time-weighted Return. That's the 11.9% advertised by the Techie Fund.

On the other hand, if you put money in and/or take money out and you take account of these cash flows when calculating the gain (see Calculation of Return), that's called the Dollar-weighted Return.

  • If'n you're unlucky, you buy units when they're HIGH and watch 'em go LOW.
  • If'n you're lucky, you buy units when they're LOW and watch 'em go HIGH.

The two Returns ain't (necessarily) the same.
What are you interested in?
The latter, eh?
In fact, consider this:
  • You invest $1000 in a fund which changes by a gain factor (1+x) over a certain period (a month, a year, whatever).
  • It's worth 1000(1+x) after this first period.
    A 12.3% percentage gain would mean x=0.123 and the gain factor would be 1.123
  • During the next period the investment changes by a factor 1/(1+x).
  • Your $1000 is now worth 1000(1+x)/(1+x) = $1000, again.
  • Compare this with two $500 investments.
  • The first $500 becomes 500(1+x)/(1+x)=$500.
  • The second $500 becomes 500/(1+x).
  • All together they give 500(1+1/(1+x)).
Compare: the market goes DOWN then UP vs UP then DOWN
A 0% gain each period is equivalent to putting your money under the pillow.

Now, if you could just pick the years
when the stock or index went DOWN then UP,
(rather than UP then DOWN)
you'd come out ahead with DCA