The Mathematics of Investing Is Not Difficult, But It Is Flat-Out Intolerable

The Mathematics of Investing Is Not Difficult, But It Is Flat-Out Intolerable
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I am a big fan of the following quote from Rob Arnott regarding true value of stocks: ““Returns are for the most part a matter of simple arithmetic…. Much of our industry seems fearful of basic arithmetic of this sort.”


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These are such strange words. The experts in the investment advice field are fearful of simple arithmetic. That cannot be so. Yet I know from personal experience that it is so. So it is an exciting reality that Arnott worked up the courage to tell it like it is.

Why are people afraid of arithmetic? Because numbers-based arguments have a power that word-based arguments do not. If I say “I believe that stocks are more risky than usual today because of the high valuations that apply,” people on the other side can dispute the claim. They can say that the high valuations are justified for all sorts of reasons. But if I point out that high prices have been correlated with low returns for as far back as we have records of stock prices, what can be said? I suppose that someone could say that they believe that it is all going to turn out different this time. But that’s not a terribly compelling argument. Math cuts to the chase. It’s objective. We tend to distrust subjectivity, so arguments that are math-based are given extra points.


The numbers show that Buy-and-Hold strategies are a bad idea. There is a strong correlation between today’s CAPE level and the return that stocks will provide for the next 10 years. So we know that stock investing risk is not static but variable. Investors who want to maintain the same risk profile over time must be willing to engage in market timing to do so.

Why don’t we just tell everyone that? Wouldn’t that be the obvious way to go?

Yes, but for one troublesome reality.

The number on the bottom line of our investment portfolio reveals whether we will be able to retire at the age at which we hope to retire. If valuations affect long-term returns, we need to divide that number by two (since stocks are today priced at two times fair value) to identify the true value of our stock holdings. What’s the fun in that?

Our rational minds tell us that we are better off knowing the true value of our stock holdings. But the Get Rich Quick urge that resides within all of us tells us that the inflated Buy-and-Hold numbers possess much more appeal. If we could just make that numbers-based stuff go away, we could have what we want. So we don’t take kindly to experts who make it a practice to employ numbers-based arguments. They are disappeared. And all the others who see what happens to the ones who stick their necks out become “fearful” of making use of numbers-based arguments themselves.


When I am trying to understand the crazy realities of the investment advice world, I find that it helps to make analogies to other fields of human endeavor in which people are asked to come to terms with clear but very much unwelcome information bits. A man is deeply in love with his fiance and his friends show him evidence that she is cheating on him. Does he thank them for helping him out before he gets deeper in a jam? Or does he strike out in anger at the ones seeking to bring an important truth to his attention?

If Arnott worked in the relationship advice field, he would be noting that experts are fearful of photography. Many of us are capable of deceiving ourselves into believing that our fiance is loyal until we are presented with photographic evidence that this is just not so. Seeing undeniable evidence makes us angry, as often as not at the people who presented the undeniable evidence.

The human has been described as the reasoning animal. We certainly are capable of engaging in reasoning. But I think that it might be more accurate to describe us as the rationalizing animal. We employ out reasoning powers to avoid facing important truths as often as we use them to uncover important truths.

Reason and true value of stocks

Additionally, we use reason when we sense that it will take us to a place where we want to go. We use our reasoning powers to step out of the way of reality when we sense that reality is something other than what we want it to be. Investment experts are fearful of arithmetic because arithmetic makes it too concise and too clear that the numbers on our portfolio statement are not a good reflection of the realities. We don’t want to be informed, we want to enjoy sleeping a while longer. And math has the annoying habit of insisting on the recognition of reality.

I like math. I don’t much enjoy working numbers and I am much more a words guy than a numbers guy. But I like it that arithmetic can cut through the marketing slogans that dominate much of the discussion in this field and reveal in a clear and frank way what is going on. The risk of stock investing is that it is so easy for the investor to kid himself about the true and lasting value of his stock holdings. That horrible math stuff makes it a lot harder to walk down that dark (in the long run) path. I love arithmetic for its truth-telling power even though I get it that it is not the easy way to the turning of a quick buck.

Rob’s bio is here.

Updated on

Rob Bennett’s A Rich Life blog aims to put the “personal” back into “personal finance” - he focuses on the role played by emotion in saving and investing decisions. Rob developed the Passion Saving approach to money management; Passion Savers save not to finance their old-age retirements but to enjoy more freedom and opportunity in their 20s, 30s, 40s, and 50s - because they pursue saving goals over which they feel a more intense personal concern, they are more motivated to save effectively. He also developed the Valuation-Informed Indexing investing strategy, a strategy that combines the most powerful insights of Vanguard Founder John Bogle and Yale Professsor Robert Shiller in a simple approach offering higher returns at greatly diminished risk. Tom Gardner, co-founder of the Motley Fool web site, said of Rob’s work: “The elegant simplicty of his ideas warms the heart and startles the brain.”
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  1. I am saying that every investor should practice market timing. The aim should be to keep your risk profile roughly constant over time. When valuations move up dramatically, you have to lower your stock allocation. When valuations move down dramatically, you have to increase your stock allocation. Wade Pfau and I co-authored peer-reviewed research showing that this approach greatly diminishes risk while also greatly increasing return. That’s been so for as far back as we have good records of stock prices.

    I also say that any journalist who is placed in circumstances in which he happens to fall upon a story one-tenth as big and important as this one would be a fool not to pursue it for the remaining years of his life. Stock crashes cause huge amounts of human misery. If we can do away with stock crashes (and we can do that today by permitting widespread discussion and exploration of the far-reaching implications of Shiller’s Nobel-prize-winning research findings), we change the world in a very positive and exciting and life-affirming way. Please mark me down as being in favor of us doing that and as being humbled to have been able to have played the role that I have played in turning this amazing breakthrough in our understanding of how stock investing works into a reality.

    I hate the bad stuff that we have seen. But the good stuff that is waiting over the horizon is so good that I don’t believe that hardly anyone is even going to remember the bad stuff once we make it together to the other side of The Big Black Wall of ignorance and indifference that is holding us back today.

    We’ll see.

    My best wishes.

    Life-Affirming Rob

  2. I agree that 17 years is a long time.

    If you include the value of the book that I could not have written had I not taken this path, then my nest egg value is off the charts. I have not converted that value to cash as of today. But I see the value there very, very, very clearly. So that’s what I have to go by.

    If a fellow had discovered the cure for cancer and people who worked in cancer treatment centers harassed him for 17 years and kept him from earning an income, would you conclude that the value for the cure for cancer was zero? I would not. I would conclude that the people harassing him saw the great value in what he was putting forward or they would not be bothering with the harassment.

    Everyone should be timing the market. Not because of anything that happened to me and not because of anything that I say. Everyone should be timing the market because there is 38 years of peer-reviewed research in this field showing that market timing is required for long-term investing success. If valuations affect long-term returns (Shiller was awarded a Nobel prize for showing this), then stock investing risk is not stable but variable (depending on valuations). Investors seeking to keep their risk profile roughly constant over time MUST engage in market timing. To fail to do so is to fail to practice price discipline, which is obviously not at all a good thing.

    It will be interesting to see how things play out in the days following the next price crash, Sammy.

    I do wish you all good things, in any event.

    Well-Wishing Rob

  3. Like all the other humans, I was given skills that permit me to add value to the world. It is by being compensated for the value that I add to the world with those skills that I am able to cover my costs of living and pursue happiness for myself and my family. Following the principles that I describe in my book “Passion Saving: The Path to Plentiful Free Time and Soul-Satisfying Work,” I elected to leave my safe corporate job to do work that would pay less in the short term but that had the potential to permit me to add much more value and thus earn much more income in the long term.

    That plan worked like a dream, Sammy. In the short-term, it worked horribly. I have not earned a penny since I left my job. That’s of course a catastrophe. But look at the other side of the ledger — look at the value that I have added to the world that will bring in compensation in the days following the next price crash. The shift from Buy-and-Hold to Valuation-Informed Indexing is the biggest advance in the history of personal finance.

    It changes everything that we once believed we knew about how stock investing works. In the Buy-and-Hold days, we thought that market timing was a bad idea. As a result of our explorations of Shiller’s research findings. we now know that market timing is the key to long-term investing success. The peer-reviewed research that I co-authored with Wade Pfau shows that investors who incorporate market timing into their investment plan can thereby reduce the risk of stock investing by nearly 70 percent! While increasing their lifetime returns! Is that investor heaven or is that investor heaven?

    And all of this is rock-solid stuff. Shiller was awarded a Nobel prize in Economics for his work. We should have been talking about this going back to 1981. We haven’t been because the advance is so big that it caused us to experience a large amount of cognitive dissonance. And, as the years have passed, the embarrassment felt by the Buy-and-Holders over making a mistake re the critical importance of market timing has grown to a point where many of them cannot stand the thought of people openly discussing what really works.

    What does a society need in circumstances like that? A good journalist to get the word out! That’s what I am! That’s what I do! I am in the process of getting the word out. I wish that I had been getting compensated all along, in which case I would be a multi-millionaire today. But the abusiveness of you and a number of other Buy-and-Holders, which is the only thing holding me back, is not evidence that there is not a mountain of money to be made here. It is evidence that the mountain is so huge that it is hard to comprehend how huge it is.

    Did you notice how excited Wade was in the days when he was doing research on Valuation-Informed Indexing? Those were the happiest days of his life. There are thousands of researchers who would like to experience that feeling. And there are thousands of journalists who would like to be writing about this stuff. And there are thousands of investment advisers who would like to be giving the straight story to their clients. And there are thousands of policymakers who would like to be pursuing policies that would help us all avoid economic crises like the one that we experienced in 2008 (that Shiller predicted in a book published in March of 2000). We are looking at good stuff piled on top of good stuff piled on top of good stuff piled on top of good stuff.

    What’s holding us back? Why haven’t we cashed in all these mountains of good stuff?

    We are afraid. Because we don’t see other people talking about this stuff. We wonder if, given the lack of discussion of the implications of Shiller’s research, we might be thinking about this stuff wrong. Wade told me that he experienced that exact feeling. I experienced that feeling at one time. John Walter Russell experienced that feeling. Everyone who begins pondering these ideas experiences that feeling. We see a mountain of gold in front of us and it is hard to accept that it is real and it is hard to understand why everyone else is not picking up the gold that has been sitting there for 38 years now. It is not the norm in our society for wonderful new ideas not to be widely discussed. But that’s the situation in the investment advice area since 1981. So we are in great need of a journalist to break this one wide open and to help millions of people live better lives by doing so.

    And here I am, you know? That’s the job. It’s been a rough patch of road. These 17 years have been hard, hard, hard, hard, hard. I certainly don’t say different. You’ve got me on that one. But look at the asset that I have built up over those 17 years. I am in the process of writing a book (“Investing for Humans: How to Get What Works on Paper to Work in Real Life”) that tells the entire story in great depth. I expect to see that book change the world in a very positive way.

    Not immediately. My expectation is that virtually no one will read it for so long as stock valuations remain where they are today. But what about after the next crash? I expect that at that time there will be millions of people who will want to know what happened to most of their life savings. And I will be able to tell them the story they want and need to hear in great depth. And tell them how we can all work together to be sure that nothing like this ever happens again.

    That’s my life’s work, Sammy. That’s what I was put on earth to do. I have pulled off something amazing. In ordinary circumstances, I shouldn’t have been able to make one-five-hundredth of the contribution that I have made. Which would of course have meant that I would not have received one-five-hundredth of the compensation that I will receive. I don’t have that money in hand today. I don’t have one penny of it in hand today. But I have the asset that adds to the happiness of millions of people in hand. And I had to be willing and able to give up compensation for 17 years to acquire that asset. So I did what I had to do.

    I say that my plan worked beyond my wildest dreams and hopes. I don’t like the way that things played out. If I were king of the world, we never would have seen a single abusive post. But I didn’t create the circumstances in which the things that happened happened and were tolerated at many, many places. All of those circumstances were in place before I came on the scene. My job is to provide people with the information that they need so that we can all work together to change the circumstances that prevail so that we can all live better lives. I am in the process of doing that.

    Shiller’s research is important, Sammy. That’s why he was awarded a Nobel prize. I don’t think you are going to be able to hold back the History Train forever. I think you are fighting a losing cause. I would say that it is YOUR plan that has failed. But we are just going to have to wait to see how things play out in the days following the next price crash to find out for certain.

    I naturally wish you all the best that this life has to offer a person, dear friend.

    Wildly Successful But Poorly Compensated (For Now!) Journalist Rob

  4. Market timing didn’t work for you, yet you want everyone else to take your advice and time the market.

    The rest of your post is your typical nonsense and lies, which you want me to comment on, so that it distracts people from the main topic in which your timing scheme failed.

  5. For investors following your VII strategy, you are saying they need to write a book and sell it in order to finance their retirement? That’s part of the VII strategy?

    Rob, if any person followed your plan, they would have experienced a failed retirement. It is simple math.

  6. The plan did not work like a dream. We can all see the math. 17 years is not a short term. After 17 years of missing your target, the nest egg is spent down to a level that you can’t recover. You are trying to convince people that they should try to time the market with your VII strategy. Why should they when it failed for you?

  7. Let’s talk about real numbers, Rob.

    In 2002, you quit your job and stated that you had a nest egg of $400k and annual expenses of $30k. You stated you were invested in i bonds, TIPS and CDs. On many occasions, you quoted a real return rate of 3.5%. In 2005, you stated that your expenses were up to $38k, but that the market was returning 7% real and you would be getting bigger returns than that. After 17 years, you have stayed out of the market, so we know your plan failed. You are a shining example as to why you shouldn’t try to time the market. To this day, you refuse to answer the question as to why anyone should take YOUR advice, given your failed track record.

  8. Let’s talk about real numbers, Rob.

    In 2002, you quit your job and stated that you had a nest egg of $400k and annual expenses of $30k. You stated you were invested in i bonds, TIPS and CDs. On many occasions, you quoted a real return rate of 3.5%. In 2005, you stated that your expenses were up to $38k, but that the market was returning 7% real and you would be getting bigger returns than that. After 17 years, you have stayed out of the market, so we know your plan failed. You are a shining example as to why you shouldn’t try to time the market. To this day, you refuse to answer the question as to why anyone should take YOUR advice, given your failed track record.

  9. I don’t consider math stuff to be my string suit. So we are okay re that one.

    I half agree with you that investing is “all about the numbers” and I half disagree. The Buy-and-Holders do not include adjustments for valuations in any of their calculations. Shiller’s work shows that valuation adjustments are required. So the two schools of thought produce very different numbers. If Shiller’s Nobel-prize-winning research is legitimate research, then every calculation that the Buy-and-Holders have ever done is in error. If you leave out the most important factor, your calculations are always wrong, no?

    So who are the real numbers guys? The ones who always ignore the most important factor and get every calculation wrong? Or the ones who says “we better include valuations because we know that valuations always have a big effect.” I do not consider myself strong on numbers but I consider myself strong on emotions and it is investor emotions that cause mispricing (overvaluation and undervaluation). So I think it would be fair to say that I do a better job with the numbers than the Buy-and-Holders. Not because I am great with numbers. Because I am good enough with emotions to know that numbers relating to emotions need to be included and the Buy-and-Holders — who generally are not so strong dealing with emotions — do not.

    I definitely think that it is better to get the numbers right than to get them wrong. I am 100 percent confident re that one.


  10. As you admit, you are not a math guy. With investing, it is all about the numbers. I don’t think, however, it is just your poor math skills that lead to all of your false conclusions. Your retirement plan failed, your market timing strategy failed and the community at large humiliated you and kicked you out. As such, you have to push a false narrative in order to try and save face. As you can see, it’s not working.

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