Mutual Funds, ETFs, and Hedge Funds
4.3 Active vs. Passive Management
When buying a mutual fund or an ETF, an investor has a choice between a passively managed fund that is designed to track an index such as the S&P 500 and an actively managed fund that relies on the stock selection and
timing skills of the fund manager. Actively managed funds tend to have much higher expense ratios. A key question therefore is whether actively managed mutual funds outperform stock indices such as the S&P 500.
Some funds in some years do very well, but this could be the result of good luck rather than good investment management. Two key questions for
researchers are:
1. Do actively managed funds outperform stock indices on average?
2. Do funds that outperform the market in one year continue to do so?
The answer to both questions appears to be no. In a classic study, Jensen (1969) performed tests on mutual fund performance using 10 years of data on 115 funds.5 He calculated the alpha for each fund in each year. (As explained in Section 1.3, alpha is the return earned in excess of that
predicted by the capital asset pricing model.) The average alpha was about zero before all expenses and negative after expenses were considered.
Jensen tested whether funds with positive alphas tended to continue to earn positive alphas. His results are summarized in Table 4.3. The first row shows that 574 positive alphas were observed from the 1,150 observations (close to 50%). Of these positive alphas, 50.4% were followed by another year of positive alpha. Row two shows that, when two years of positive alphas have been observed, there is a 52% chance that the next year will have a positive alpha, and so on. The results show that, when a manager has achieved above‐average returns for one year (or several years in a row), there is still only a probability of about 50% of achieving above‐average returns the next year. The results suggest that managers who obtain positive alphas do so because of luck rather than skill. It is possible that there are some managers who are able to perform consistently above average, but they are a very small percentage of the total. More recent studies have confirmed Jensen's conclusions. On average, mutual fund managers do not beat the market and past performance is not a good guide to future
performance. The success of index funds shows that this research has influenced the views of many investors.
Table 4.3 Consistency of Good Performance by Mutual Funds
Number of Percentage of
Consecutive Years Number of Observations When of Positive Alpha Observations Next Alpha Is Positive
1 574 50.4
2 312 52.0
3 161 53.4
4 79 55.8
5 41 46.4
6 17 35.3
Mutual funds frequently advertise impressive returns. However, the fund being featured might be one fund out of many offered by the same
organization that happens to have produced returns well above the average for the market. Distinguishing between good luck and good performance is always tricky. Suppose an asset management company has 32 funds
following different trading strategies and assume that the fund managers have no particular skills, so that the return of each fund has a 50% chance of being greater than the market each year. The probability of a particular fund beating the market every year for the next five years is (1/2)5 or 1/32.
This means that by chance one out of the 32 funds will show a great performance over the five‐year period!
One point should be made about the way returns over several years are expressed. One mutual fund might advertise “The average of the returns per year that we have achieved over the last five years is 15%.” Another might say “If you had invested your money in our mutual fund for the last five
years your money would have grown at 15% per year.” These statements sound the same, but are actually different, as illustrated by Business
Snapshot 4.1. In many countries, regulators have strict rules to ensure that mutual fund returns are not reported in a misleading way.
BUSINESS SNAPSHOT 4.1
Mutual Fund Returns Can Be Misleading
Suppose that the following is a sequence of returns per annum reported by a mutual fund manager over the last five years (measured using annual compounding):
The arithmetic mean of the returns, calculated by taking the sum of the returns and dividing by 5, is 14%. However, an investor would actually earn less than 14% per annum by leaving the money invested in the fund for five years. The dollar value of $100 at the end of the five years would be
By contrast, a 14% return (with annual compounding) would give
The return that gives $179.40 at the end of five years is 12.4%. This is because
What average return should the fund manager report? It is tempting for the manager to make a statement such as: “The average of the returns per year that we have realized in the last five years is 14%.” Although true, this is misleading. It is much less misleading to say: “The average return realized by someone who invested with us for the last five years is 12.4% per year.” In some jurisdictions, regulations require fund managers to report returns the second way.
This phenomenon is an example of a result that is well known by mathematicians. The geometric mean of a set of numbers (not all the same) is always less than the arithmetic mean. In our example, the return multipliers each year are 1.15, 1.20, 1.30, 0.80, and 1.25. The
arithmetic mean of these numbers is 1.140, but the geometric mean is only 1.124. An investor who keeps an investment for several years earns a return corresponding to the geometric mean, not the arithmetic mean.