Knowing the Mathematics of Investing Hurts More Than It Helps

Beyond Buy-and-Hold #18

By Rob Bennett

Do you know what alpha is?

Do you know what beta is?

No, me neither.

The investing experts think they are a big deal. I do not. I could look up the terms on Wikipedia and write something here that would make it look like I know what they are. But if you really want to know, you could do that yourself, right? So what?s the point?

I don?t want to talk about alpha and beta. What I want to talk about is why they don?t matter. And why the experts talk about them as if they do. That I believe you really must understand if you are to stand much of a chance of knowing what is going on in stock investing today.

The single dumbest thing ever said about investing

I?ll start by telling you the single dumbest thing that I have ever heard anyone say about investing. It is William Bernstein, the author of The Four Pillars of Investing, who said it. Before I tell you about the dumb thing, I need to tell you that I have the greatest respect for Bernstein. He?s a smart guy and a good guy. Chapter Two of his book is the best chapter of any investing book that I have ever read. I have read that chapter so many times that the pages of that section of my copy of the book are falling out. You wouldn?t think that this fellow would have said the dumbest thing that I have ever heard about this subject. But he did.

What Bernstein said is that most ordinary people cannot hope to become good investors because they do not understand math well enough.


It?s not like that.

What makes this so dumb is that precisely the opposite is so. All you need to become a successful investor in the days of index fund is common sense. You do not need to understand mathematics. Not even a little bit. Bernstein is wrong.

I think he?s sincere. I think he came up with this idea because he has seen so many investors ruin themselves by becoming too emotional and because he thinks that the way to overcome emotionalism is to understand the mathematics behind investing. I believe that just the opposite is so. It is the belief that mathematics can save you from emotionalism that is causing the emotions of so many to go out of control.

I?ll point you to a recent thread at the board to show you why turning investing into a mathematics exercise is the worst thing you can possibly do. Please take a brief look at this discussion of the analytical errors that were made in the studies that financial planners use to help us plan our retirements and one investor?s reaction to learning that the odds are good that his plan will fail.

I first pointed out that the Old School safe withdrawal rate studies get the numbers wrong in a post I put to the Motley Fool site over eight years ago. Lots of investors who possess ten times the numbers skills that I possess didn?t want to hear it. Read the words of the poster who goes by the name of ?Drip Guy? and you?ll see that the self-deception is still going strong today.

The safe withdrawal rate is a mathematical calculation. Wade Pfau, an Associate Professor at the National Graduate Institute for Policy Studies in Tokyo, is telling the Bogelheads that the numbers they used to build their retirement plans are wildly wrong. How many of the thousands of people who participate in discussions there care? Only two posters put forward comments. One of them essentially asked Pfau for permission to ignore what the data says rather than take the warnings to heart. Huh?

The REAL purpose of mathematics in investing

That?s par for the course. Investing is primarily an emotional endeavor. Nine out of ten investors use mathematics not to develop sound strategies but to develop rationalizations for making emotional choices that they couldn?t bear to follow if not the for the ?support? offered by mathematics. Investing mathematics is not real mathematics. It?s a game. The aim of investing mathematics is not to uncover realities. It is to cover up realities.

Investment experts employ mathematics for a similar reason. The experts worry about the responsibility that goes with telling people what to do with their retirement money and do not feel confident about the advice they give. They create elaborate tables and calculators and studies and formulas as a means of easing their consciences over offering what they worry may be dangerous advice.

We all need to move away from the mathematics. We need to face our emotions and come to terms with them. You don?t do that by putting long lines of numbers in pretty tables. Any energy spent on the mathematics of investing is energy that could have been directed to more productive purposes.

The only number that truly matters in investing

In the old days, there was a need to understand some mathematics to become a good investor because you needed to study annual reports to know which companies enjoyed good prospects. In the days of index funds, that is no longer necessary. The only number you need to know to become a highly effective investor is the P/E10 level that applies at the time you buy the fund.

And understanding the meaning of the P/E10 number is no more difficult than understanding the meaning of the price tag on a sweater or a cell phone or a box of crackers. When stocks are selling at a good price, you should buy them. When stocks are selling at a bad price, you should not buy them. You don?t need to pass calculus to figure out why that is so.

The focus on mathematics that we see in this field is hurting us, not helping us. We all have a Get Rich Quick impulse lurking within that makes us want to ignore what that P/E10 price-tag tells us. The more time we spend thinking about alpha and beta, the better skilled we become at quieting the voice of common sense that is an investor?s true best friend.

This is one field in which those who are bad at numbers go to the head of the class. That?s me!

Rob Bennett is king of the Investing for Dummy type of article — For obvious reasons! His bio is here.

( Photo by trindade.joao )

6 Responses to Knowing the Mathematics of Investing Hurts More Than It Helps

  1. Hi Rob,
    I have been reading about your method of financial decision making for some time. I have also been following John Hussman.(He seems to have an important emphasis on valuation and particularly uses the Shiller P/E10 . The question I have is if you can direct me to any studies on how using the P/E 10 as a valuation metric to alter the equity allocation in a portfolio is an added value strategy. I have recently read a letter from James Montier who discusses reversion to the mean and he wants to make sure that investors don’t forget about reversion to the mean.
    I am convinced that one should adjust their portfolio to reflect valuation rather than buy and hold as you have well stated in many ways in your work. I would like to be able to defend my position againt opinions such as the recent Pragmatic Capitalist blog that say that P/E is not a good reliable valuation indicator. Can you direct me to any recent or even older studies that would be helpful .Thanks for your help

  2. LR:

    Thanks for your kind words.

    The place to start is The Stock-Return Predictor:

    This calculator performs a regression analysis of the historical stock-return data to reveal the most likely 10-year return for a broad index starting from any of the possible starting-point valuation levels.

    You also may want to check out The Investor’s Scenario Surfer:

    This calculator lets you work your way through a randomly selected, realistic 30-year return sequence. You can change your allocation in response to changes in valuation levels and compare your results with the results you would have obtained by rebalancing to a single stock allocation. My experience is that VII beats Buy-and-Hold in about 90 percent of my tests.

    This article provides links to 20 studies showing that shifting allocation works better than staying with a single allocation:

    A simple graphic that makes the point is here:

    Norbert Schlenker says: “The evidence is pretty incontrovertible. VII…is everywhere superior to Buy-and-Hold over 10-year periods.”

    I suggest you look at the “People Are Talking” section on the left-hand side of the home page of my blog. That contains 85 quotes from big names in the field and regular people who have been won over by these ideas. You need to know that it is not just one guy saying this. Pay special attention to the first one, a quote from an article in the Wall Street Journal where the guy acknowledges that Buy-and-Hold is just a marketing gimmick. The WSJ speaks with a lot more authority than some guy who posts stuff on the internet.

    If you really want to explore this stuff in depth, please check out the RobCasts section of my site. I have recorded 200 podcasts on different aspects of the question. Most provide over 60 minutes of material.

    There are two ways in which it is accurate to say that PE is not a reliable indicator:

    1) P/E1 (the most common valuation metric) is NOT reliable. P/E10 is much better. I have a RobCast (#19, P/E10 Rocks!”) that explains why P/E10 is so much better.; and

    2) P/E10 works only in the long-term. This is the one that throws so many. When you get WHY this is so, the key turns in the lock. In the short-term, stock prices are determined by investor emotion. Emotions are not predictable. So forget about thinking that you can change your allocation and be sure to see a benefit in one or two years. It doesn’t work that way. In the long term, stock prices are determined by the economic realities. These are highly predictable. Long-term timing has ALWAYS worked and it MUST always work (at least on a risk-adjusted basis). To say that long-term timing might not work would be like saying that paying attention to the price of a car you buy might not work. This cannot be. Price always matters.

    Finally, here’s an article called “Market Timing — What Works and What Doesn’t”:

    VII gives significantly higher returns at dramatically lowered risk. It is the Fountain of Youth for stock investors. There is only one big flaw. It works ONLY in the long-term. This will NOT work in the short-term. You should try it out on the Scenario Surfer to get an idea of how it works. Run a few 30-year tests and you will get the idea. I have had cases where at the end of 30 years my portfolio was DOUBLE the size of the Buy-and-Hold portfolio. It’s amazing.

    The reason it works is that you have a virtually sure thing (the price you pay for something MUST matter). That doesn’t mean you always go ahead quickly. It can take some time. But only in very strange return patterns do you not eventually go ahead. Once you go ahead, the Buy/Hold portfolio has little chance to catch up because VII goes with a high stock allocation most of the time. The edge for VII is usually small at the beginning. But compounding works its magic to make it big over time. The moral is: FInd a way to gain an almost certain small edge and it will make a very big difference over an investing lifetime. Compounding is magic. People have a hard time appreciating how big a deal it is is; it is a counter-intuitive reality. But it is a becomes a big deal over time.

    Thanks for your interest. Please shoot back if there are aspects of this that remain unclear.


  3. Thank you Rob for responding to my inquiry. I will work through your suggestions.
    I know you are passionate about this topic and so you have invested a lot of time on it for your personal use.
    I went through the market timing strategies– what works and what doesn’t. This is the sort of thing I am looking for as I want to write down an investment policy plan so it will be somewhat objective.
    I went all equity in April as the P/E10 was approaching 22 and looking back it appears to have been a mistake. In the article it was suggested to not go below 30% and I was surprised by this as I noticed that using one of the calculators it had senario option B that went to 0% when P/E10 was over 24. In addtition I thought I saw somewhere that you were 0 % equities for some time now (I can’t recall where I saw this but think it was on your site and because you were able to get 4% on real return bonds)So, this type of study on the level of the P/E 10 and the amount of the equity in the portfolio for various levels is very important for me.
    Also some of the calculator have a drop down that only allows a few options regarding the market climate. With the P/E 10 now at 23 would I use the 26 bear market as the best starting point for comparison.
    Thanks again for your generous response and direction

  4. I thought I saw somewhere that you were 0 % equities for some time now

    You’re asking a good question, LR. I have been at zero stocks since the Summer of 1996. And, yes, I do not generally advise zero stocks for others in my articles. I’ll try to explain why.

    There is no one stock allocation that matches up with each P/E10 level. We know that stocks are more dangerous at a P/E10 of 25 than they are at a P/E10 of 20 and that 20 is more dangerous than 15 and that 15 is more dangerous than 10 and so on. We know that the return drops and risk increases as the P/E10 level rises. But valuations are not the only factor. So we cannot say that all should be at x stock allocation at y P/E10 level. You always need to consider the other factors. The other factors are: (1) your life goals; (2) your financial circumstances; and (3) your risk tolerance.

    My personal circumstances have called for a zero stock allocation since 1996. But my personal circumstances are highly unusual. I don’t think it is a good idea for most investors ever to go to zero. Even at very high valuation levels, I think an allocation of 10 percent or 20 percent makes sense. It’s good always to have some skin in the game.

    I’ll give you one more link that might help a little. RobCast #137 is titled “Nine Valuation-Informed -Indexing Portfolio Allocation Strategies”:

    None of this is complicated. It is very simple. It SEEMS complicated if all you have ever heard of is Buy-and-Hold because it starts from opposite premises and so it is hard to get used to the new mindset.

    I am concerned by the words in your comment where you talk about a change you made in April and say “it appears to have been a mistake.” There is zero chance that someone could know in December that a change they made in April was a mistake based on performance since April. The short-term is NOT predictable. So you should have known in April that the performance you have seen since then was one of the possibilities. The fact that one of the possibilities happened to turn up tells you nothing you didn’t know starting out. You need to evaluate the change you made in April from a long-term perspective to determine whether it was truly a mistake or not.

    Did you mean to say that you went to zero stocks in April? Your comment says that you went to all stocks but the context suggests the opposite. Assuming that you meant to say that you went to zero stocks, I will comment on that possibility. Stocks are at dangerous but not insane prices today. The returns on the super-safe asset classes are very low. So the odds are that you will obtain a slightly higher 10-year return on stocks than you would on TIPS or IBonds or CDs. That’s the pro-stock case.

    The anti-stock case is that the odds are strong that we are going to see another crash. Robert Shiller has said that he will not be getting back into stocks until we see a P/E10 level below 10. That’s a 50 percent drop from where we are today. Can you live through that without selling? If you would sell at the bottom, you would be better off in TIPS or IBonds or CDs. Those 10-year returns will end up being imaginary for you.

    I of course am not able to say whether you would sell or not. I think most of us will be selling. So I don’t recommend high stock allocations. But I think the odds of you selling go down as your stock allocation goes down; those with a 30 percent allocation are far less likely to panic than those with a 60 percent allocation. If you hold through the next crash, you will do okay in the long run. So what I am trying to do when I suggest a stock allocation is anticipate how low your allocation needs to go to make the odds good that you could avoid selling in the next crash.

    That’s an element of the story that Buy-and-Holders tend to leave out. They like to present numbers and pretend that that tells us all we need to know. No! The hardest part of the investing project is the emotional side of things. This side must be considered! It makes the recommendations a bit less precise to include this factor (because we do not all have the same emotional setup). But this factor must be considered. So I give somewhat less precise recommendations than the Buy-and-Holders. I would rather be roughly right than precisely wrong!

    I hope that helps a bit. My sense is that you are on the right track but that all of this has not totally clicked in just yet. You need to gain more confidence in it. The way to do that is to work the Scenario Surfer a number of times and also just to let time pass as gaining confidence takes time. Do not worry about results that you have obtained since April! You’re focusing on the small stuff. Investing properly will provide HUGE upside over the long term.

    The key is gaining enough confidence in the ideas to be able to stick with them for the long term. You cannot gain that sort of confidence in a day or a week or a month. That’s another reason why I don’t generally recommend stock allocations of zero. The more extreme your choices, the less likely you are to be able to stick with them. Start with modest adjustments and continue reading and talking and working the calculators. Then, as you gain confidence that this works, you can gradually move to more “extreme” positions (it’s not that the positions really are extreme, just that they seem so to Buy-and-Holders, which dominate the discussion today).

    The ultimate answer is for us all to have a national debate on these questions. It will also help your confidence to hear lots of other smart and good people endorsing the ideas. We don’t see this much today because there is so much marketing money behind Buy-and-Hold. But I have hopes that this will change as the economic crises (caused by the bull market of the late 1990s, which in turn was caused by the promotion of Buy-and-Hold) worsens.


  5. Thanks Rob for your response.
    Your willingness to help is appreciated. You were correct, I should have said zero equity and I know it is short term but it does teach that even though valuations were creeping higher in April that the move to zero equities was most likely too extreme.
    I will continue to look at the suggested links and will follow you on your home site.
    I have over the last 4 years made the decision to manage my own accounts vs using a broker who was doing the “best stock this week” sort of management to the fixed asset allocation using ETF’s based on rebalancing ( that I followed faithfully through the big correction) and am now working on the timing using valuation with P/E10. It was just settling on where one should be at various valuations that once satisfactorily chosen and written down that will help complete the Investment Policy Statement.Hope your New Year goes well

  6. Thank you for this article. It really helps out the guys and girls that are not the best with math and is a necessary confidence boost on investing because you are absolutely right. Although math can be extremely helpful it is not necessary. I hope to write an article on this sometime soon and will link back to yours for reference.

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