It is well known that we **investors are full of biases when making investment decisions** (loss-aversion, trend-chasing, …), but what is the real impact of these biases on our performance? In this post we will try to answer this question quantitatively, and we will also compare the average investor returns with the average mutual funds returns. Do you want to know how good is the investors “timing” with their inflows/outflows? Keep reading!

## Return measurement

There are two standard ways of measuring performance:

**Time-Weighted Return (TWR)****Money-Weighted Return (MWR)**

The aim of this post is not to explain both methods in detail, so in summary we will say that the TWR is used to measure the profitability of your portfolio without it being affected by the contributions or withdrawals of money, while the MWR does take into account the amount and date of these inflows and outflows.

Imagine that you as an investor put 100€ into an mutual fund today, and a year later the fund rises by 50%, at which point, seeing the good performance of the fund, you decide to make an inflow of 350€ (with which you would have invested 500€ in total), and then the fund falls by -20%, so that the final return of the fund (TWR), after those two years, is +20% [(1+0.5)*(1-0.2)-1=0.2], but your real return (MWR) has been negative, you have ended up losing 50€! [100€*0.5 + 500€*-0.2=-50€].

The TWR is a good measure to compare the performance of a fund against other funds.

The MWR is a good tool to determine your account performance and the impact of your investment activity decisions.

If you are still not entirely clear about the differences between the two methods, and you want to go deeper into their mathematical formulation, I recommend you read this other post.

## Experiment

Now that we know how to calculate the performance of a fund and that of its investors, we are going to check with real data whether or not the average return of a fund’s investors is similar to the return of the fund itself. Namely, we are going to examine if mutual fund investors make good investment decisions with the *timing* of their cash flows.

The data we will use for this experiment are the NAVs and AUMs, on a weekly basis, of **more than 15,000 listed mutual funds**. With them we will estimate the inflows/outflows that have occurred each month. And from these data we will calculate three different returns, which we will label with the following names

**MWR**: annualized money-weighted return that the average investor of each fund has obtained, according to the*timing*of the aggregate inflows/outflows.**TWR**: annualized time-weighted return of the mutual fund.**MWR_INV**: money-weighted return that an investor would have obtained by making the opposite flows to the flows made by the real average investor.

For prevent biasing the results due to some anomalous flows, we will clip the larger flows to a maximum of ±30% of the total AUM. Furthermore, this adjustment is mandatory for simulating the MWR_INV, because, obviously, inverting the inflows bigger than the 100% AUM is not possible (making a -150% AUM outflow do not make sense).

ThePython codeto calculate the TWR and MWR from the NAV and AUM time series is available in this GitHub repo. As well as a notebook with some real examples of the ones we are going to see next.

#### Example

Before analyzing the aggregate results, let’s look at a specific example. The following chart shows the evolution of the NAV (black line) and the AUM (light blue line) of a mutual fund listed in Spain, as well as its monthly flows (blue bars).

The first thing we see is that the fund has performed very well, going from trading at 100€ to 200€, which gives an annual return of 10.45%. But if we look at the flows, we see that the biggest inflows were made right at the peak of profitability at the end of 2017, and then after the sharp fall in 2020 (COVID) there were quite a few outflows, which therefore did not take advantage of the great upward rally that followed in 2021. All this means that **the real annualized return (MWR) that the average investor in the fund has obtained is only 3.24%!!**

In the example we have just shown, investors probably made their investment decisions driven by euphoria in 2017 and fear in 2020, which has resulted in a poor return (despite the good performance of the fund itself). But is this common to all investors/funds? Are these effects greater in higher volatility funds? How profitable would it be to systematically make the opposite flows to those made by the average investor? …

### Analysis

First of all, let’s look at the average returns obtained in the aggregate of the 15,000 funds analyzed, depending on whether we had made the flows of the average investor (MWR), if we had not made any flows (TWR, return of the fund itself), or if we had made the opposite flows to those of the average investor (MWR_INV):

Our suspicions are confirmed! **Investors’ flows timing decisions reduce their average returns by 0.53% annually**. Conversely, following the opposite timing would have improved returns by 0.83% per year.

But what happens if we divide the results according to the risk family in which each of the mutual funds analyzed invests:

We can observe how the pattern repeats itself, and moreover it does so with an astonishing consistency. We can also see how the **differences in returns are considerably greater in the higher risk/volatility families (Equity and Alternative), which is not surprising **because it is well known that volatility accentuates investors’ biases.

Finally, we wanted to check whether there is any correlation between the average mutual fund TER and the underperformance of investors in their inflows/outflows decisions. To do so, we are going to analyze only Equity funds, so that the fees between them can be comparable (Fixed Income funds tend to have much lower fees):

We see that there is indeed a high correlation between the level of fees of the mutual funds and the “quality” of their investors. One explanation for this could be that more experienced investors, or those less susceptible to the aforementioned biases, are very aware of the impact that fees have on their returns and consciously seek out funds with lower fees. But, conversely, newer investors, who are more driven by their emotions when investing, are the ones who end up investing in funds with the highest fees.

## Conclusions

- For calculating the real investors returns we need to use the
**Money-Weighted Return**. - The Investors returns are systematically worse than the Mutual Funds returns in which they invest. This underperformance is due to the
**poor**, which are consistent with their trend-chasing behavior.*timing*of its inflows/outflows