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How Survivorship Bias Can Skew Your Views on Mutual Fund Performance

It’s important to avoid treating the market like a popularity contest by chasing out-performers or running away from the underdogs. But neither do most investors want to go into the market entirely blind. For that, there are database services that track and report on how various fund managers and their offerings have performed.

Besides ample evidence that past performance does not predict future returns, there is another reason we advise investors to proceed with caution when considering past performance: Many returns databases are weakened by survivorship bias.

With respect to mutual funds and similar investment vehicles, survivorship bias creeps in when only the returns from surviving funds are included in the historical returns data you are viewing.

Here is what happens: As you might expect, there is a tendency for outperforming funds to survive, and for under-performers to disappear. When a fund is liquidated or merged out of existence, if its poor returns data disappears as well, overall historic returns tend to tick upward.

As such, you may end up depending on past performance data that is optimistically inaccurate.

Here is an article that further explains how survivorship bias works. In addition, consider the following illustration from Dimensional Fund Advisors’ report, The US Mutual Fund Landscape 2016. It illustrates how survivorship bias can skew your view on fund performance. This video also explains their research report.






In the beginning – in this case January 1, 2001 – there were 2,758 US equity mutual funds. Now fast-forward 15 years to December 31, 2015. By then, only 43% of those funds (roughly 1,186 funds) had survived the period. Out of the survivors, only 17% (about 469 funds) had both survived and outperformed their benchmark over the 15-year time-frame.1

In the illustration above, you can readily see that the small blue box in the lower-right corner represents relatively low, less than 1:5 odds that any given fund in January 2001 went on to outperform its peers by the end of the 15 years.

If a database instead eliminates the “disappeared” funds from its performance data, the larger gray box disappears from view as well, as in the illustration below. Without this critical larger context, you may conclude that those 469 outperforming funds only had to compete against the 1,186 survivors, versus the actual universe of 2,758 funds. While it may seem as if nearly half of the fund universe has done well, in reality, the less than 1:5 odds have remained unchanged.




But wait, maybe you could “take a look at the past performance, pick the funds that have outperformed after the first 10 years, and pile up on those seeming winners. Dimensional’s report also shares the results from that exercise:




The left-hand side of this diagram shows the funds that outperformed (in blue) and under-performed (in gray) during the first 10 years of the 15-year analysis.2 You can see that 20% outperformed their respective benchmark then. The right-hand side of the diagram shows what happened to that outperforming subset during the next five years. Only 37% of the initial “winners” continued to outperform. This demonstrates that is it is extremely hard to predict “winning” mutual funds based on past performance. Your odds are even worse than what you can expect from a basic coin toss!

So let’s take a moment to reinforce our ongoing advice: Invest for the long-term. Instead of fixating on past performance, focus on capturing future available returns within your risk tolerances and according to the best available evidence. Aggressively manage the factors you can expect to control (such as managing expenses) and disregard the ones that you cannot (such as picking future winners based on recent past performance).

These principles guide the actions we’ve advised all along. We will continue to embrace them unless compelling evidence were ever to inform us otherwise. They are the ones that serve your highest financial interests, which is our highest priority as your advisor. 


1.  Beginning sample includes funds as of the beginning of the 15-year period ending December 31, 2015. The number of beginners is indicated below the period label. Survivors are funds that were still in existence as of December 31, 2015. Non-survivors include funds that were either liquidated or merged. Out-performers (winners) are funds that survived and beat their respective benchmarks over the period. Past performance is no guarantee of future results. See Mutual Fund Landscape paper for more information. US-domiciled mutual fund data is from the CRSP Survivor-Bias-Free US Mutual Fund Database, provided by the Center for Research in Security Prices, University of Chicago.

2.  The graph shows the proportion of US equity mutual funds that outperformed and under-performed their respective benchmarks (i.e., winners and losers) during the initial 10-year period ending December 31, 2010. Winning funds were re-evaluated in the subsequent five-year period from 2011 through 2015, with the graph showing winners (out-performers) and losers (under-performers). The sample includes funds at the beginning of the 10-year period, ending in December 2010. The graph shows the proportion of funds that outperformed and under-performed their respective benchmarks (i.e., winners and losers) during the initial periods. Winning funds were re-evaluated in the subsequent period from 2011 through 2015, with the graph showing the proportion of out-performance and under-performance among past winners. (Fund counts and percentages may not correspond due to rounding.) Past performance is no guarantee of future results. See Data appendix for more information. US-domiciled mutual fund data is from the CRSP Survivor-Bias-Free US Mutual Fund Database, provided by the Center for Research in Security Prices, University of Chicago.


Robert J. Pyle, CFP®, CFA is president of Diversified Asset Management, Inc. (DAMI). DAMI is licensed as an investment adviser with the State of Colorado Division of Securities, and its investment advisory representatives are licensed by the State of Colorado. DAMI will only transact business in other states to the extent DAMI has made the requisite notice filings or obtained the necessary licensing in such state. No follow up or individualized responses to persons in other jurisdictions that involve either rendering or attempting to render personalized investment advice for compensation will be made absent compliance with applicable legal requirements, or an applicable exemption or exclusion. It does not constitute investment or tax advice. To contact Robert, call 303-440-2906 or e-mail This email address is being protected from spambots. You need JavaScript enabled to view it. .

The views, opinion, information and content provided here are solely those of the respective authors, and may not represent the views or opinions of Diversified Asset Management, Inc.  The selection of any posts or articles should not be regarded as an explicit or implicit endorsement or recommendation of any such posts or articles, or services provided or referenced and statements made by the authors of such posts or articles.  Diversified Asset Management, Inc. cannot guarantee the accuracy or currency of any such third party information or content, and does not undertake to verify or update such information or content. Any such information or other content should not be construed as investment, legal, accounting or tax advice.

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The Mathematics of Investing

Tracking the performance of your investments can get confusing, due to the various ways of calculating returns. Whether you prefer to use a calculator or spreadsheet software, the following discussion will help you use and calculate common measurements of investment performance to truly judge your investment results.

Determining Rate of Return

Probably the most basic calculation for investors is return on investment. Total return includes capital appreciation and income components, and assumes all income distributions are reinvested. If you automatically reinvest distributions such as interest or dividends, total return is calculated by taking the difference in an investment portfolio's ending and beginning balance, and dividing that difference by the beginning balance. In formula format, it would look like this:
 
Total Return:
(Calculator or Spreadsheet:)
(Ending Balance [EB] - Beginning Balance [BB])
Beginning Balance

For example, Joe started with an investment of $10,000. After five years, his portfolio's value increased to $12,000. He can determine his portfolio's total return as follows: ($12,000 - $10,000) / $10,000 = 0.20, or 20%. Therefore, Joe can say his $10,000 has increased by 20%.

To annualize this total return, you'll need to calculate the compound annual return.

For example, Jane also originally invested $10,000. However, it took her portfolio only two years to grow to $12,000. If you measure the performances of both Joe's and Jane's portfolios by using the formula above, both increased by 20%. To take the difference in time into consideration, calculate the compound annualized rate of return (you will need a calculator that can raise to powers to calculate this).
 
Compound Annualized Rate of Return =
Calculator: [(EB / BB)^(1 / # of years) - 1]
Spreadsheet: [(EB/BB)^(1/# of years)] - 1

Using this formula to calculate Joe's annual compound return, we take $12,000 / $10,000 = 1.2. Then, we raise 1.2 to the 1/5 (or 0.20) power, giving us 1.03714. Subtract out 1, and we have 0.03714, or 3.714%, which is Joe's annualized return. Jane's portfolio, on the other hand, performed much better, earning 9.54% on average every year. Of course, two different investments should not be judged solely on performance results for short periods of time or for different time periods. The risk of the portfolio must also be considered.

10% Plus 10% Doesn't Equal 20%

You might think that Jane's annualized return should have been 10%, and not 9.54%, since she invested her money for two years and 10% + 10% = 20%, which was her total rate of return. However, here's where the math can get tricky.

Let's just say that Jane's $10,000 did grow 10% each year for two years. At the end of the first year, Jane would have accumulated $11,000. In year one, $10,000 x (1 + 0.10) = $11,000. In year two, if Jane's $11,000 grows by another 10%, this gives us $11,000 x (1 + 0.10) = $12,100, which is more than the $12,000 Jane actually accumulated. This $100 discrepancy explains why Jane only earned a 9.54%, and not a 10%, compound annual return.

Similarly, the math doesn't intuitively make sense when you're losing money. If Jane's $10,000 investment had lost 10% the first year, she would have $9,000 left. In year two, if Jane's investment rebounds by exactly the same amount - 10% - Jane would not break even, as you might expect. In fact, a 10% increase in $9,000 results in only $9,900. Therefore, you need a greater percentage gain after a losing year in order to break even on your investment.

The Rule of 72

If you need an approximation of how your nest egg might grow, you might want to use the Rule of 72. The Rule of 72 can reveal how long it could take your money to double at a particular rate of return. Use the following formula:

Rule of 72
72 / Annual Rate of Return = Number of years it will take for your money to double at a particular rate of return

For example, Jane and Joe want to figure out how long it will take their $10,000 investments to double to $20,000. They use their compound annual rates of return (as figured previously) to estimate how many years it will take to double their money. Joe estimates it will take over 19 years (72 / 3.71% = 19.4 years). However, Jane's portfolio could grow to $20,000 in less than eight years (72 / 9.54% = 7.55 years). It is important to note that the Rule of 72 does not guarantee investment results or function as a predictor of how your investment will perform. It is simply an approximation of the impact a targeted rate of return would have. Investments are subject to fluctuating returns, and there can never be a guarantee that any investment will double in value.

Remember Taxes and Inflation

You should always take into consideration the effects of taxes and inflation when constructing an investment plan to meet your financial objectives. After all, even though Jane earned an average 9.54% on her investments every year, her "real" rate of return will be reduced by taxes and increases in the cost of living.

Depending on Jane's situation and income tax bracket, as much as 39.6% of her 9.54% compound annual return could be paid in federal taxes, leaving her with [9.54% x (1 - 0.396)], or 5.76%.

Then, Jane must figure in the effects of inflation on her earnings. For example, assume inflation averaged 3% over the two years that Jane invested her $10,000, and that she earned a 5.76% compound annual return after taxes, but before inflation. Now, Jane must adjust her after-tax return for the loss of purchasing power caused by inflation. To determine an inflation-adjusted rate of return, use the following formula:

Inflation-Adjusted Return:
(Calculator or Spreadsheet:)
[(1+Rate of Return)/(1+Inflation Rate) - 1] x 100

Jane's inflation-adjusted, after-tax rate of return is [(1.0576) / (1.03) - 1] x 100, or 2.68%. Keep in mind that we've assumed the highest federal income tax bracket (which does not apply to every investor); however, the example does show the impact that taxes and inflation can have on your return.

Bond Yields

Bond investors generally receive periodic income from their investment. The amount of income paid to the holder of the bond is based on the bond's coupon rate. For instance, Jane buys a $1,000 bond that pays a 7% coupon rate and therefore receives $70 a year ($1,000 x 0.07) for as long as she owns the bond. She can determine the income return (or yield) on this bond by taking the coupon dollar amount and dividing it by the purchase price of the bond, or $70 / $1,000 = 7.00%. In this example, the yield and the coupon rate are the same because Jane purchased the bond at its original (or "face") value of $1,000.

However, that yield can fluctuate depending on how much an investor pays for a bond. Let's say Jane's bond cost $1,200. Its current yield is now only ($70 / $1,200), or 5.83%.

Bond prices and yields may change over time with changes in interest rates. As the price of a bond increases, its yield decreases. Conversely, as bond prices decrease, yields increase. If Jane's bond increases in value, her total return (income plus price appreciation) on the investment would be higher than the 7% coupon rate. However, as the yield on her bond changes, the dollar income she receives does not.

Taxable-Equivalent Yield

Municipal bond investors generally receive income that is free from federal and in some cases state and local taxation. As a result, the stated yields on taxable bonds tend to be higher than yields on municipal bonds in order to compensate investors for their tax liability. When comparing bond yields, bond investors must use a taxable-equivalent yield to compare the rate of return on a tax-free municipal bond with that of a taxable bond.

The taxable-equivalent yield on a tax-free bond can be determined as follows:

Taxable-Equivalent Yield:
(Calculator or Spreadsheet:)
Tax-free yield /(1 - investor's marginal income tax rate)

For an investor in a 28% income tax bracket, the taxable equivalent yield for a municipal bond yielding 5% would be 5% / (1 - 0.28), or 6.94%.

No Substitute for Understanding

A financial planner can help you gauge your investments' performance, so you don't have to do the calculations yourself. But it is still your responsibility to understand what it all means. Without that knowledge, you could make potentially unfavorable financial decisions. With a fundamental understanding of the information presented above, you'll be better able to realistically judge your investments.


Required Attribution


Because of the possibility of human or mechanical error by Wealth Management Systems Inc. or its sources, neither Wealth Management Systems Inc. nor its sources guarantees the accuracy, adequacy, completeness or availability of any information and is not responsible for any errors or omissions or for the results obtained from the use of such information. In no event shall Wealth Management Systems Inc. be liable for any indirect, special or consequential damages in connection with subscriber's or others' use of the content.

© 2016 DST Systems, Inc. Reproduction in whole or in part prohibited, except by permission. All rights reserved. Not responsible for any errors or omissions.


Robert J. Pyle, CFP®, CFA is president of Diversified Asset Management, Inc. (DAMI). DAMI is licensed as an investment adviser with the State of Colorado Division of Securities, and its investment advisory representatives are licensed by the State of Colorado. DAMI will only transact business in other states to the extent DAMI has made the requisite notice filings or obtained the necessary licensing in such state. No follow up or individualized responses to persons in other jurisdictions that involve either rendering or attempting to render personalized investment advice for compensation will be made absent compliance with applicable legal requirements, or an applicable exemption or exclusion. It does not constitute investment or tax advice. To contact Robert, call 303-440-2906 or e-mail This email address is being protected from spambots. You need JavaScript enabled to view it. .

The views, opinion, information and content provided here are solely those of the respective authors, and may not represent the views or opinions of Diversified Asset Management, Inc.  The selection of any posts or articles should not be regarded as an explicit or implicit endorsement or recommendation of any such posts or articles, or services provided or referenced and statements made by the authors of such posts or articles.  Diversified Asset Management, Inc. cannot guarantee the accuracy or currency of any such third party information or content, and does not undertake to verify or update such information or content. Any such information or other content should not be construed as investment, legal, accounting or tax advice.

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