## Wednesday, July 10, 2013

### Why Even a 0.5% Difference in Fees Matters

DEAR INVESTOR JUAN

Dear Investor Juan,

Your blog is really a good find and very helpful for educating newbies. Thank you very much! Now I am seeking some opinion from you. While checking the UITFs of BDO, BPI and Metrobank, I came to know that BDO have the lowest fee - 1% while Metrobank charges the most at 2% plus others. Am I correct in this or I am missing something?

Regards,
Jovy

Dear Jovy,

Perfect timing, I've been planning to discuss the effect of differences in fees in investment returns. Maybe this illustration can help convince you that even a "small" difference in management fee matters.

Say there are two equity funds (UITF or mutual fund), A and B. The returns of the two funds, before management fees, in years t = 1, 2, 3... are as follows:

Fund A:

rA1, rA2, rA3, ...

Fund B:

rB1, rB2, rB3, ...

So that after 1 year, an investment in A will have grown by 1 + rA1 times, in 2 years by (1 + rA1)(1 + rA2) times, in five years by (1 + rA1)(1 + rA2)(1 + rA3)(1 + rA4)(1 + rA5), and so on.

If A charges an annual management or trust fee of 1%, then the after-fee value of an investment in A after 1, 2, and 5 years are:

After 1 year: (1 + rA1)*(1 - 1%) = (1 + rA1)*0.99
After 2 years: (1 + rA1)*0.99*(1 + rA2)*0.99 = (1 + rA1)(1 + rA2)*0.99^2
After 5 years: (1 + rA1)(1 + rA2)(1 + rA3)(1 + rA4)(1 + rA5)*0.99^5 = (1 + rA1)(1 + rA2)(1 + rA3)(1 + rA4)(1 + rA5)*0.95

Which means that if you invest in the fund for 5 years, 5% of the value of your investment would go to management fees. And if you invest in A for 30 years, your investment will have the following value at the end of the period:

(1 + rA1)(1 + rA2)...(1 + rA30)*0.99^30 = (1 + rA1)(1 + rA2)...(1 + rA30)*0.74

Let's say B charges a 1.5% management fee. A 30-year investment in the fund would result in:

(1 + rB1)(1 + rB2)...(1 + rB30)*0.985^30 = (1 + rB1)(1 + rB2)...(1 + rB30)*0.64

Assuming that the performance of an equity fund does not depend on the skill of the fund manager so that the long-term return (e.g., 30 years) of two equity funds on any given year is the same,

(1 + rA1)(1 + rA2)...(1 + rA30) = (1 + rB1)(1 + rB2)...(1 + rB30)

This means that compared to a fund that charges 1% per year, investing in one that charges 1.5% results in a 14% loss in value (0.64/0.74 - 1) over a 30-year holding period.

The table below compares the effects on value of different combinations of fees and holding periods.

 Holding period 1.00% 1.50% 2.00% 3.00% 4.00% 5.00% 5 .9510 .9272 .9039 .8587 .8154 .7738 10 .9044 .8597 .8171 .7374 .6648 .5987 20 .8179 .7391 .6676 .5438 .4420 .3585 30 .7397 .6355 .5455 .4010 .2939 .2146

So to answer your question, for a 30-year investment, a 2% fee will reduce the value of the fund to 55%, compared to 74% for a 1%-fee fund. It means if you invest in the 2% fund, you'd be losing 26% more (55/74 - 1) of the value of your fund.