[MUSIC] A natural question to ask is, is bigger better when it comes to mutual fund fees? So you'll see various mutual fund fees across your mutual fund potential investments. You might naturally assume the higher is the fee charge, the better is the quality of the fund. The higher returns are well earned, right? That logic usually serves us pretty well in life, right? When you go to a TV store, you look at various TVs. Some might be priced at 3,000. Some are priced at 2,000. Some are priced at 200, okay? So you usually attribute, if the price is 3,000, it's higher quality than if the price is 1,000 for the TV, okay? That's usually what we think of, the prices reflect quality. How does that logic work if we apply that to mutual fund fees, okay? So remember the Weisbenner Son Funds company here. This was launched last year with my my first course on Coursera. Here, we have Luke looking at the Marketplace page of the Wall Street Journal. And you may recall, for those avid learners, that he charged a 1.5% management fee. Well, now there's an update. Weisbenner Son Funds has become Weisbenner Sons Asset Management. So now the singular son has become plural. And we can see there's a partner here in the mix. And they're really studiously looking at what's happening to the kind of stocks, as kind of displayed here on the financial page. Their annual management fee is now 2%, okay? But there is a squabble as to, what's the split of the 2%? Is it going to be 1.5 for the older brother, Luke, and half a percent for the younger brother, Jay? Will they do a 1% split? But the bottom line for you, as an investor, is the expense ratio has gone up, okay? So the question is, are they earning the extra fee they charge? And just in the interest of full disclosure, some people have questioned their research methods. So just keep that in mind before you invest with them. So let's actually look at this from an academic perspective. So Gil-Bazo and Ruiz-Verdu did a study looking at a lot of mutual funds from the period 1962 to 2005. So they were looking at a ton of data. And they simply asked a question that we're asking right here in this video. What's the relationship between the fees and mutual fund charges and the before-fee performance of the fund? And they're looking at actively-managed equity funds, okay? So I hope you're raring to go for this. And Le Penseur is also very excited, has a question for you here. In equilibrium, what is the predicted relation between mutual fund fees and the before-fee alpha, okay, the gross alpha? Simply, what would you predict as the relationship between the fees charged by a fund and its returns before fees? So you can rephrase a question, just say, should we expect funds with high fees to have higher, the same, or lower alphas than funds with lower fees? So think about that, and then I'll give you my take. So what do you think? If we see a fund with high fees, should it have higher, the same, or lower alphas than funds with lower fees? Well, in equilibrium you'd expect you'd get what you pay for, right? If you get the $3,000 TV, it better be better than the $1,000 TV. So you'd expect, higher fee, higher return before fees to compensate, right? That's what you'd expect in equilibrium. You pay a lower fee, you're getting a lower return before fees, okay? So is bigger better when it comes to mutual funds? Let's go back to this academic study. What do the authors do? Well, for each month, they estimate a 4-factor model or a 3-factor model of the fund's performance over the past 60 months, or 5 years. So for every month t, look at data for that fund over the past 5 years, or 60 months. Estimate this 4-factor or 3-factor model. Take the betas that you get from this past-five-year data. Then actually apply them to the returns that happened during month t. What was the market return minus the risk free rate? What was the return of small stocks minus big stocks, or value stocks minus growth stocks? Take the actual realized factor returns, multiply them by those estimated betas from the past five years. That gets you a benchmark return for the fund. Compare that to the actual before-expense return in month t to calculate the fund's alpha for that month. So take the actual before-expense return of the fund, subtract out this benchmark. And then you have the before-expense alpha of the fund for that month, okay? Pool all this data across all the funds and all the months. And then simply regress these monthly fund alphas on monthly fund expense ratios. So expense ratios are quoted on an annual basis, like 0.5% of assets under management, 0.05% of assets under management, 1.5% of assets under management. So convert these expense ratios into monthly expense ratios and simply do the regression, monthly fund alpha on monthly fund expense ratios. So the key question is, does the coefficient on the expense ratio equal one? When we do this regression across all the funds, that's our equilibrium prediction. So let's go see the results. Quite striking, okay? And there's different models we can use here. So the Carhart row we see here is actually the alpha using a 4-factor model to evaluate performance. The Fama-French row is using a 3-factor model to evaluate performance, okay? So what's our results when we use a 4-factor model? We calculate the alpha of the fund, its risk adjusted performance. It actually turns out that there's a negative relationship. Forget the coefficient being 1, it actually seems to be negative. Funds that have higher expenses seem to deliver not higher returns, but lower returns. So you increase the expense ratio by one percentage point. That predicts the fund underperforms by 0.6 percentage points, where equilibrium prediction was higher fee, higher return. It's exactly the opposite. And these two *s indicate this is a statistically significant negative estimate. And this c here indicates that this is definitely statistically different from our prediction of 1 at the 1% level. Now, when we do a different risk adjustment, use a 3-factor model, the Fama-French model, our coefficient estimate still is negative. It's -0.2, so it suggests the expense ratio goes up one percentage point. The returns to the fund don't go up one percentage point on average. They actually go down 0.2%. That's not statistically different from 0. But remember, our test is, they should go up on a one-for-one basis, a positive one-for-one basis. This c indicates this is definitely statistically different from our prediction of 1. So the bottom line is, our prediction was, this coefficient on the expense ratio should be plus 1. If anything, it's negative. Higher expense funds on average, worse performance than the lower expense fund. And remember, we're looking just at a sample of actively-managed funds. So the results aren't being driven by low-cost index funds. We're just looking at a sample of actively-managed funds. Now, the authors also do an nonparametric analysis, so the earlier results I showed. And we're looking at the alpha, the risk adjusted performance from a 4-factor model. We're just showing the slope of this regression line, okay? And the slope of this regression line is -0.6. But the authors also do a nonparametric estimate where they're looking at, for different expense ratios, what type of alpha do we see? And you can see this black line here is the nonparametric estimate that gives different estimates of the alpha, the risk adjusted performance, for the different expense ratio. It just doesn't assume there's a linear relationship. You see this black line is also declining. And it seems you don't have much data for funds that have expense ratios of 3.5%. That's why you have kind of very noisy, these dots here show the 95% confidence intervals around this estimate. So you can see there's a lot of volatility to this estimate. But let's take this at face value. Even for the funds that have a 3.5 expense ratio, their predicted alpha is maybe 1.5%. So even if we take the best-case scenario, based on these estimates, those funds have a 3.5% expense ratio. They only recover about 1.5% of that on average, in terms of higher returns. So you, as an investor, are still down 2 percentage points. So not great news, kind of the intuition that higher prices mean higher quality doesn't seem to be the case, based on this analysis of the data. If anything, higher expenses are leading to worse performance on a gross basis, before you take into account the expenses. So let's go back to these question. Are these guys earning the extra fee they charge, okay? Unfortunately, no, on average, okay? So, sorry, guys, nothing personal, it's just research. So I really hope I don't come back to regret this presentation. And particularly, if they ultimately do form Weisbenner Sons Asset Management, I'm going to have to go back and burn this video. [SOUND]