Mutual Fund Survivorship: The Revenge of Abraham Wald

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Jan 02, 2015

The story of Abraham Wald and the study of WWII bomber casualties is one of the more enlightening stories from the field of operational research. During the early days of the Allied strategic bombing campaign the amount of bombers not returning from their missions reached an unacceptable rate. In a desire to find out why, the USAAF completed a study on where the damage was taking place and where additional armor could be placed to make each bomber safer. Here Wald enters our story. Taking one look at the methodology and findings, Wald told the team they were looking at the problem the wrong way. By studying the planes that came back the researchers were seeing where the planes could withstand damage. The more interesting facts should be about the planes that didn't make it back. By analyzing where all the bullets holes and damage were on the planes that made it back, he proposed strengthening the areas where there were no bullet holes. Through his report thousands of bomber crewmembers were saved through the course of the war. Wald’s report and methodology can be found here.

Wald’s technique would later be summarized quite pithily by Charlie Munger (Trades, Portfolio) when he advised, “Invert. Always invert.” The use of Wald’s methodology can be applied in the investment world in many ways. Perhaps the greatest use is the study of mutual funds. Investors spend an inordinate amount of time studying mutual funds with fantastic records (such as Bill Miller’s Legg Mason Capital Management Value Trust fund during the 1990s). Put in Wald’s context, these are the funds that made it home. But what about all those funds that didn't survive? The funds that didn't make it home? What can be learned from these?

Before we get to that, let’s take a look at the numbers of mutual funds and find out their general survivor rate. In 2013 Vanguard released a study on fund survivorship (which can be found here) studying mutual funds from 1997 through 2011. At the start of the study period there were 5,108 funds available. By the end of 2011, 2,364 of these funds had been closed or merged, leaving 2,744 funds (or 54% of all funds) that survived for the entire period. In that period from 1997 through the end of 2011 roughly 1 out of 2 funds didn't make it home. Of the funds that didn't make it, roughly 80% (or roughly 1,900) were merged away while the remaining 20% (roughly 470) were closed entirely.

It’s how the funds performed where the story gets very interesting. Let’s start with the funds that existed for the entire period (or the funds that made it home). Of the 2,744 funds roughly 1/3 ended up outperforming. During the period of 1997 – 2011 - even if you could divine which fund might actually survive - you still had roughly a two-thirds chance at underperforming the market.

Fund Category # of Surviving Funds % Under Perform # Out Perform # Under Perform
Global Markets 124 35% 81 43
Developed Markets 259 35% 168 91
Emerging Markets 64 53% 30 34
Large Blend 280 65% 98 182
Large Growth 326 66% 111 215
Large Value 261 50% 130 131
Mid Cap Blend 64 94% 4 60
Mid Cap Growth 174 89% 19 155
Mid Cap Value 45 100% 0 45
Small Cap Blend 78 58% 33 45
Small Cap Growth 158 65% 55 103
Small Cap Value 55 56% 24 31
Sector Funds 138 30% 97 41
U.S. Government Bond 220 71% 64 156
U.S. Corporate Bond 379 85% 57 322
U.S. High Yield 119 90% 12 107
TOTALS 2744 983 (36%) 1761 (64%)

Let’s take a look at the funds that didn’t survive the period (or the ones who didn't make it home). Here the story is far more depressing. Roughly 9 out 10 funds underperformed before they were either merged away or simply closed. A loss that would have staggered Wald himself. It’s hard to imagine that trained professionals – with a wealth of technology, analytics and treasure behind them – couldn't exceed the batting average of a Double-A baseball team third-stringer. In fact it’s hard to imagine that throwing darts at a list of stocks and bonds couldn't have produced better results. For the investors who received such terrible returns from their investment managers, all they received was a letter quietly delivered to their mailbox informing them of the merger of their fund with an entirely new – and no doubt exciting and outperforming – investment opportunity.

Fund Category # of Dead/ Merged Funds % Under Perform[1] # Out Perform # Under Perform
Global Markets 106 88% 13 93
Developed Markets 179 79% 38 141
Emerging Markets 54 53% 25 29
Large Blend 286 96% 11 275
Large Growth 283 93% 20 263
Large Value 212 80% 42 170
Mid Cap Blend 56 96% 2 54
Mid Cap Growth 166 100% 0 166
Mid Cap Value 48 95% 2 46
Small Cap Blend 59 94% 4 55
Small Cap Growth 133 83% 23 110
Small Cap Value 30 91% 3 27
Sector Funds 83 72% 23 60
U.S. Government Bond 269 90% 27 242
U.S. Corporate Bond 341 96% 14 327
U.S. High Yield 59 84% 9 50
TOTALS 2364 256 (11%) 2108 (89%)

What would Abraham Wald say?

Wald approached the problem of aircraft losses very differently than the original assessment team. His ability to flip (or invert) the model allowed him to address the problem with an entirely fresh (and as it turns out – correct) approach. If we apply his methodology to the mutual fund industry there are several points that jump out that go far beyond the usual Wall Street talking points.

It’s not about succeeding; it’s about not failing

In the investment world, action represents success. In reality, active management (or action) represents a losing proposition. There’s an old adage that 90% of success is just showing up. It would seem the same rings true in investing – but with a twist; 90% of success is showing up, investing and doing nothing. Actively managed funds have demonstrated they have very little chance at beating the market indices. Indeed, if you add in the silent results of the funds that never made it, the odds of outperforming the markets are roughly 2 in 10. Active management – in general – is a loser’s bet. As personal investors this has equal import. By not making the simple mistakes – overpaying, trading too much, etc. – we can achieve remarkable returns. By not failing, we can provide our investors an invaluable service.

Evaluate an investment backwards

Many of us have a formalized process for evaluating investing opportunities. Some might use a DCF model while others use a dividend discount model. All too often we find comfort in using this process, and we get lulled into a false confidence in our stock picking. At Nintai, we frequently ask ourselves why we wouldn't invest in a certain company. By being the devil’s advocate, we get a pretty good understanding of potential impairments to our investment case. Another tool is to build into your model the exact opposite assumptions and see where you end up. For instance if you project 8% FCF growth over the next 5 years, what would it look like if the company had -8% FCF growth instead. What impact would that have on EPS, balance sheet, etc.? Finally, we step away from our assumptions and become a competitor. What could I do strategically to beat the company? What new products could I develop? Do I have the financial ability to acquire them? All of these (and others) allow us to view our prospective investment from very different angles than our normal proprietary process.


Abraham Wald saved tens of thousands of flight crew lives during World War II. His ability to see things from a different perspective allowed him to solve a critical failing in the Allied war effort. More importantly he demonstrated the power of survivorship bias and how it can lead us to misguided assumptions. For investors – both mutual fund and individual – we can be blinded by our successes and not take sufficient care to understand and protect against the downside. That’s a shame. Sometimes there are more learnings from a mistake than a success. I encourage everyone to take a long, hard look at his or her failed investments and find out what went wrong. Sometimes simply getting these corrected is far more powerful than looking for the next Microsoft. In the final analysis the solution can occasionally be blindingly clear with a simple move to the left or right. Just ask Abraham Wald.

As always we look forward to your thoughts and comments.

[1] Percent underperforming from 01/1997 to close/merge date