There is always a debate whether an index fund is better than an active management mutual fund (or even a stock broker). For me, I am biased towards the low cost index funds and ETFs (exchange traded funds). Initially, I went with my parent’s stock broker. Yet, after a few years of disappointing returns, I finally took over the management of my stock portfolio myself and started to convert it slowly into index funds. Here is some of the math that I did to make my decision.

First, an index fund normally has a low expense fee ranging from 0.1% to 0.75% (lower for an S&P500 index fund and higher for an international index fund). While an active management fund can have a 1% to 2% or higher expense fee for their services. For my situation, the stock broker was going to charge me a 2% fee (a reduction from his normal 2.5% fee because he wanted my business). Thus, let’s assume on a $100,000 investment, a 0.5% expense fee on an index fund equates to a $500 cost per year versus $2,000 for a 2% fee for an active management fund/stock broker.

Thus, the manager in this scenario needs to earn 1.5% more than the market on a risk adjusted basis to break-even

Second, an active management fund usually has a higher turnover rate than an index fund. In order to get the higher return to justify his expenses, he (or she) needs to move in and out of the hot stocks of the week (or month). The issue with higher turnover is that for the return is taxed as ordinary income instead of capital gains if the stock is held for less than 1 year. Thus, even though their returns may be higher, so are taxes that you need to pay. For example, let’s assume a 3-year holding period with an 8% investment return and 28% tax rate & 15% capital gains rate:

Index Fund = (1.08) X (1.08) X (1.08) -1
= 25.97% return – 3.90% tax
= 22.07% after-tax return

Mang. Fund = assume 75% long-term holding & 25% short-term holding

Short-term return = 8% return X (1 - .28 tax rate)
= 5.76% per year after-tax return
= (1.0576) X (1.0576) X (1.0576)-1
= 18.29% after-tax return over 3 years Long-term return = 22.07% after-tax return shown above

Overall after-tax return = 18.29% X .25 + 22.07% X .75 = 21.12% return

1% lower after-tax return may not sound like much over 3-years. Yet, it means another .33% return per year that the manager needs to beat the market in this example to break even. Of course, this is not an issue in a 401(k) or IRA (including Roth IRA) because taxes are deferred (or are tax exempt in the case of Roth IRA).

Even if a stock is held for more than 1 year, a higher turnover can still mean higher taxes even though the return is taxed at the lower capital gains tax rate. For example, let’s assume a 10-year holding period where the index fund has no (or little) turnover while the manager turns it over after year 5. Assume a 15% capital gains tax rate

Index Fund = 1.08 ^ 10 years -1
= 115.9% return – 17.4% tax
= 98.5% after-tax return

Mang. Fund = 1.08 ^ 5 years
= 46.9% return – 7.0% tax
= 39.9% after-tax return after 5 years
= 1.399 X 1.399 – 1 = 95.7% after-tax return (2.8% less)

So, even if the manager holds stocks for longer than 1 year, there is still a hurdle they need to overcome for having a higher turnover as they move from sector to sector as they pick what is hot (technology, oil companies, etc.). And, the more turnover a manager has, the higher return they will need to overcome the effect of taxes.

Yet, there are many stock brokers and investment managers that are touting that they can beat the market, so there must still be a way to make a higher return with active management compared to an index fund even after adjusting for these higher expenses and taxes. Right?

Because there are so many factors that affect stock prices, I am sure that there are a few wise investors (maybe Warren Buffet and a few others) that can analyze the market and beat it significantly enough to make a difference. Yet, this is probably a small fraction of those who claim that they can beat the market. For example, let’s assume that I can flip a coin and get heads 10 times in a row; does that mean I am an expert coin flipper and can get heads more often than others at random? No. It means that I can flip and see a head come up ½ of the times. Over 10 flips, I can expect all heads 0.1% of the times. This may seem significant and mean that if I can do 10 heads that I must be an expert because this normally does not happen. Yet if 5,000 people are flipping coins, I can expect 5 people claiming that they are an expert because they had 10 winning years (sorry flips). Yet, for the next flip, they still have a 50% chance of a heads (winning) and 50% chance of tails (losing).

Now there may be 10 expert stock pickers in a group of 5,000 active management mutual funds, yet how can we weed out 5 of the bogus pickers that are just lucky. I have not found a way to sift through the data to find them yet. Being an actuary, I have had clients (usually non-financial people) ask me if the market was going to go up or down before year end. Each time, my boss and I would answered them that if we knew the answer that we would be on the beach in Bahamas with a drink in one hand and a computer in the other and the CFO would just laugh knowing what we meant. Part of this is because if we were confident in beating the market, why would we have to work hard to sell our advice versus sitting back and profiting from it.

Also, out of the 10 expert stock pickers where 5 may have been lucky enough statistically to beat the odds, the odds may be skewed and actually mean that 7 or 8 of the winners just got lucky out of 5,000 total funds. How is this? Mutual funds open and close all the time. Would you invest in a fund that lost 8 out of 10 years? Probably not. So, those mutual funds close up over time and the manager may open a new fund that starts out 5 out of 5. Thus, the hot active management funds stay open while the cold active management funds are forced to close as investors pull out. So if the statistics say out of 5,000 mutual funds, 5 may be lucky enough to appear to be experts, remember that there may have been 8,000 mutual funds over that time and the cold funds closed over the years.

Lastly, I may appear to be bashing active management investment funds and stock brokers a bit. Yet, remember that I am biased to index funds so take it for what it is, just ideas to think about and do your research before picking any fund (index or investment manager) or a stock broker.

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This entry was posted on Friday, September 15th, 2006 at 10:07 am and is filed under Investing. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.