What’s a mutual fund worth?

This change raises a question: How much is the broad diversification offered by mutual funds worth? For me, the answer is “a lot.” That’s about what I’d need to be paid to trade the tap in my kitchen for a well in my backyard; my car for a horse; electric lights for tallow candles. My colleagues Mike Nolan, Tyrone Sampson, and I tried to quantify “a lot.” We used a utility function—an economic concept that helps us measure the subjective values of different choices.⁴ The chart below depicts the choices. It displays hypothetical outcomes for a 2-stock portfolio and a diversified fund. Both portfolios have the same average, or expected, return. In other words, if we picked thousands of 2-stock portfolios and thousands of funds, their average returns would be about the same.⁵

The choice between funds and stocks

Notes: This illustration of the likelihood of various investment outcomes is hypothetical in nature, does not reflect actual investment results, and is not a guarantee of future results. The distribution of return outcomes for the 2-stock portfolio and the diversified fund are derived from 10,000 simulations for each portfolio. The simulations use a mean return of 11.4%, which is the average annual return of the U.S. stock market, as measured by the Russell 3000 Index, from 1980 to 2016 (11.40%); the variations around this average return are based on the average volatilities—standard deviations—of 2-stock U.S. portfolios (33.05%) randomly selected from the Russell 3000 Index from 1980 to 2016 and a diversified U.S. stock fund (14.79%) over the same period. Results may vary in subsequent simulations and over time.   The difference is risk. Maybe your 2-stock portfolio consists of Amazon and Netflix. But maybe it’s Enron and Lehman Brothers. In a diversified fund, the best case will never match the Amazon-Netflix combo, but the worst will never be as bad as the Enron-Lehman duo. In our simulation, the 1% of 2-stock portfolios with the worst performance returned, on average, –65%. Some 2-stock portfolios went to 0. In the fund simulations, the bottom 1% returned, on average, –23%. None went to 0.

The value of a fund

If we don’t care about risk, we see no difference between the 2 portfolios. If we love risk—we have a taste for Powerball and Evel Knievel stunts—we place a higher value on the 2-stock portfolio. But most of us are risk-averse. If 2 investments, on average, produce the same return, we place a higher value on the investment with the narrower range of potential outcomes. When we plugged risk, return, and an average risk-aversion score into the utility function, the result suggested that a 2-stock portfolio would need to outperform the diversified fund, on average, by 13 percentage points per year to make the 2-stock gamble attractive to us. (Note: The hypothetical outcomes for a 2-stock portfolio and a fund are based on historical returns and volatilities. Lower volatility estimates would reduce the difference in utility scores; higher numbers would raise them.) At the end of 2018, 57.2 million U.S. households, some 100 million people, owned mutual funds. The average balance in these household portfolios was $150,000.⁶ To simplify the math, let’s assume these funds are stock funds. Utility values are unintuitive, but they can start a conversation about what it’s worth to keep $150,000 in funds rather than a 2-stock portfolio. When we make that choice, as tens of millions of households have, we effectively say that we value the fund’s diversification benefits at $19,500 per year—13% multiplied by $150,000.

Fund technology is improving

Different assumptions yield different numbers, but they all tell the same story. Mutual funds and exchange-traded funds (ETFs) have been a transformative technology, helping us take advantage of the stock market’s potential to improve our financial lives while reducing the risk of ruin. And as with electric lights and cars, fund technology continues to improve. In 1976, when Jack Bogle introduced the first index mutual fund, he kick-started a revolution that’s enhanced our diversification opportunities while grinding down our costs. Today, I can invest in a total world stock index fund that offers exposure to more than 8,000 stocks in every corner of the globe at a total cost of $1 for every $1,000 in my account. Were the bad old days really as bad as I imagine? Or were they worse? And for those who were there, what would you need to be paid to go back?  

¹Federal Reserve Board, 2019; Kimmel, Lewis. Share Ownership in the United States. 1952, Brookings Institute, Washington, D.C.

²Investment Company Institute: https://www.ici.org/faqs/faq/mfs/faqs_mf_shareholders

³Investment Company Institute, 2019; Federal Reserve Board, 2019.

⁴We used the following function to calculate utility scores, in percentage points, for both choices. U = E(r) – (.005)(A)(σ2), where E(r) is expected return; A is a risk-aversion coefficient; and σ2 is variance. The difference between these scores is a measure of how much we value one choice over the other.

⁵In fact, the average return of the 2-stock portfolio would be a little higher because it incurs no operating expenses. Our simulations of fund performance use an expense ratio of 0.55%, consistent with the asset-weighted expense ratio of U.S. stock mutual funds at the end of 2018, according to data from Morningstar. But as Vanguard investors know, it’s possible to pay much less.

⁶Investment Company Institute, 2019.


All investing is subject to risk, including the possible loss of the money you invest.

Diversification does not ensure a profit or protect against a loss.