And in that time period the US market was a unique market. If you look at the history of markets over time, it was the most mean reverting, stable market of all time. And when you take the most mean-reverting, stable market of all time, all kinds of mean reversion are going to work for you.

Maybe twenty years ago, my answer would have been different. For me, was the dividing line where I think there was a structural break in the global markets. I am less and less trusting of mean reversion on a daily basis. VH: You write annually about long-term expected returns of the market as a whole. Can you give us a brief description of how you come up with your long term expected return for say, the US equity market, or the global equity market? AD: I do it on a monthly basis, and I think again this goes back to what I said earlier about mean reversion.

So I solve for an internal rate of return every month, and that becomes my expected return for stocks. Because if stocks always win in the long term, you know what should happen to your equity risk premium as your time horizon extends? It should go to zero. We think of one hundred years as a lot of data. And then on top of it, being a professor and getting all these awards for best professor at NYU, best business school professor in the whole country.

But almost everything I do spills over into almost everything else I do. I put it up on Friday afternoon. VH: Thank you so much for making time to share your clear and insightful thoughts with us. No Advice The information contained on this page has been provided as general market commentary and for information purposes only. It does not constitute any form of advice nor recommendation to buy or sell any securities or adopt any investment strategy mentioned therein. It is intended only to provide observations and views of the author s at the time of writing, both of which are subject to change at any time without prior notice.

The information contained in the commentaries is derived from sources deemed by Elm Partners to be reliable but its accuracy and completeness cannot be guaranteed. This material does not have regard to specific investment objectives, financial situation and the particular needs of any specific person who may read it. It is directed only at professional investors as defined by the rules of the relevant regulatory authority. Any views regarding future prospects may or may not be realized. Hardcover , pages. Published January 31st by Sociables Publishing first published January 17th More Details Other Editions 2.

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## Future value

Wayne P. Mar 24 at pm. Greg G Mar 24 at pm. Scott Packard Mar 24 at pm. Richard Fulmer Mar 24 at pm. Daniel Barkalow Mar 24 at pm. Dallas Weaver Ph. Mar 25 at pm. Mike Gomez Mar 25 at pm. Here is how I make sense of it: Fat tails are about how the values of outliers affect our picture of the distribution of a random variable. Lio Mar 25 at pm. As usual, an interesting discussion.

One day the US will not come back as well inflation adjusted — another peeve… — Tax policies — Believe it or not, modern portfolio theory tells you to put your IRA into the riskiest assets possible. No matter how much testing you do, fundamental market changes MAY ruin it: — A thirty year bull market in bonds cannot continue forever. Joel McDade Mar 26 at pm. He claims stock returns are a Levy distribution — not normal or log-normal. David Hurwitz Mar 26 at pm. Thank you for another thought provoking episode.

In response to the two posts above: Misbehavior is one of the best books ever written on the markets. Igor F Mar 26 at pm. The following episode came do mind as I was digesting this excellent discussion: A colleague recently described watching a film made by a Christian preacher where states that certain Astrological phenomena have throughout history coincided with significant events in the Jewish calendar.

George Mar 26 at pm. George, Maybe in when that was written, but these days Buffett has much easier ways of making money — rent seeking. JakeFoxe Mar 27 at pm. David Hurwitz Mar 28 at am. George Mar 28 at am. Anyway, on too long again. David Hurwitz Mar 29 at pm. Josh Marvel Mar 30 at am. David Hurwitz Apr 1 at am. Gav G Apr 4 at pm. Gav, Since you asked, I would start with: Misbehavior of Markets — Mandelbrot Evidence based Technical Analysis — Aronson Trading Risk — Grant Schwager on Futures — Schwager In addition, there are thousands of research papers and reports on the web for free, after reading a number of them, you will quickly be able to decide which are useful and which are not.

Robert Ferrell Apr 8 at pm. David Hurwitz Apr 16 at pm. Comments are closed. Enter your email address to subscribe to our monthly newsletter:. Campbell Harvey's Blog. Journal of Portfolio Management , August 25, American Economic Review , March PDF file. William F. Concise Encyclopedia of Economics.

Web Pages and Resources: "Significant". XKCD comic. Do jelly beans cause acne? Sharpe Ratio. Warren Buffett. Search for the Higgs boson. Campbell Harvey on Randomness, Skill, and investment Strategies.

Featured EconTalk Extras Complementary questions for further thought and discussion on this episode. Garden of Econ, August Blog post. Economic Significance. Tien89, March 5, Ed Leamer on the State of Econometrics. May September EconTalk episodes with Nassim Taleb. Bogle on Investing. April Fama on Finance. January Time Podcast Episode Highlights. More EconTalk Episodes.

As a jumping off point, though, we're going to use a recent paper you wrote with Yan Liu, "Evaluating Trading Strategies," which was published in the Journal of Portfolio Management. And we may get into some additional issues along the way. Let's start by reviewing the standard way that we evaluate statistical significance in economics for example or other applications of regression analysis.

You'll hear people talk about a t-statistic being greater than 2. And what does that represent? What are we trying to measure there? What are we trying to assess when we make a claim about significance of, say, one variable on another? Guest: So, the usual procedure--we actually think about trying to minimize the chance that a finding is actually a fluke. And it comes down to a concept called the p-value or probability value. And often this is quoted popularly, in surveys and things like that, [? Russ: And this is a convention in economics, that 2 standard deviations, two sigma is therefore probably not a fluke.

And I want to add one other important point before we go on: when we talk about significance, all we mean in this technical conversation is 'different from random': that there is some relationship. It doesn't mean what it means in everyday language, which means important. So a finding can show a relationship between two variables that's significant but quite small. So it's significant statistically but insignificant in real life.

Guest: Yeah. There's two different concepts and both of them are important.

## Invest in Optimism: A Conversation With Keith Fitz-Gerald - U.S. Global Investors

We're talking about statistical significance by a two sigma rule. There's another concept that's equally important called economic significance : is this fact really a big deal or is it small in terms of the big picture of things? And for many people that sounds--and many economists accept, that that's like, well, if it's only 1 in 20 then it's probably real.

We've ruled out the likelihood that this is just a fluke. But as you argue in your paper--and we're going to talk about some different examples of this--when the number of tests that we're making starts to increase, that statistical technique is not as convincing. So, to set that up I'd like you to talk about the Higgs boson. Which seems far away from finance, but I found that to be a fascinating example to help us think about it.

Guest: Yeah, certainly. So the Higgs discovery was complicated. It was complicated for many reasons. But once it was constructed, they knew what they needed to find. And this was a particular decay signature that would be consistent with the Higgs boson. But the problem was that that same signature could arise just by random chance.

And the number of collisions that they were doing and signatures that were being yielded was on the order of 5 trillion. So, just a huge number of possible false findings for the Higgs. Russ: And we're looking for--we are trying to identify the Higgs--a particular subatomic particle. Guest: Exactly. So, what they had to do was, given the extreme number of tests, they had to have a very different sort of cutoff for establishing a discovery or establishing statistic significance.

And instead of using the two sigma rule, they used a five sigma rule. So, way different from what we're used to. And this reflects just the number of tests that were actually being conducted. Russ: So the idea--try to give me the intuition of this. I'm going to collide a lot of things--I'm going to collide particles many, many times, trillions of times.

And we know that's going to generate lots of false positives, decay signatures that look like the Higgs but are not. Guest: That is correct. So you have to be really[? Russ: So, shouldn't I just--isn't the 'really sureness' just the fact that this is easily confused rather than--what do you mean by the number of tests? Guest: Well, really what we're talking about in the Higgs example are the number of collisions that are taking place. And I'm simplifying what they actually did at the collider.

There are many different tests actually going on. But the fact is that sometimes you would get a signature that looked like the Higgs but really wasn't the Higgs. So, in order to actually--and nobody had actually discovered the Higgs. This was the first opportunity. So, they had to be really sure that they were not being fooled by the random sort of occurrences of something that looked like the Higgs. So, to do this they had to be, as I say, five-sigma confident that it really existed. Russ: Now, it's a little bit, for non-statisticians, 5 versus 2, is actually a little bit misleading, right?

### Nouveauté Livre

That sounds like, okay, so it's a little more than twice as big; so we're requiring the result to be a little more comfortable. But as we move numbers of sigmas away from zero, it's a much smaller chance than say a little more than twice as likely that it's by chance? That means that 1 out of 20 will be a fluke. So, for a 5-sigma, it's 1 divided by 1. So, this is a very small-- Russ: But it could still be a fluke. Guest: Yes, it could be. Russ: It's a weird thing, because you'd think you either see it or you don't. But I guess it's elusive, and there are things that look like it but aren't it, is what you are really saying.

So can I give another example that I think is going to further intuition? Russ: Sure.

### What expectations do you have about valuation?

Guest: It's the famous Jellybean comic. Have you seen that before? Russ: I have; and we'll put a link up to that. It's one of my all-time favorites. So, yeah, describe it. Guest: So, this is a famous cartoon called "Significant. So, somebody makes a statement: I think that jelly beans cause acne. So, they said, okay, scientists: Go investigate.

So the scientists go and do a trial. And the trial would involve I guess giving some people jelly beans and other people without the jelly beans. And then they would test to see if there was a significant difference between, I guess, the number of pimples for people that took the jelly beans and ones that didn't. And the test comes back, and there's no difference. There's no significant difference between the two. So basically the next frame of the comic is, well, maybe it's not the jelly bean itself, but the color of the jelly bean.

So, then, the comic goes and the scientists test different colors of jelly beans. So, again, the trial would be, let's say a group of people get some red jelly beans and others don't get any jelly beans. And they go through all of the colors. So, red, there's no effects, there's no difference in the amount of acne. And orange, yellow, purple, brown, black, Russ: Fuchsia, mauve. The 20th test is green.

And they find that there's a relation with the green. So they declare that green jelly beans cause acne, and that's what actually gets into the headlines of the media the next day: Green Jelly Beans Cause Acne. Guest: That is true. So that's what the significance means in this particular case. So, everybody knows that there shouldn't be a significant effect, because it doesn't make any sense, what they're actually doing; the original test was the correct test: jelly beans versus no jelly beans. But, the more tests that you actually do, it's possible to get a result that is just a fluke.

It's something random. Russ: And if you do 20, you expect one of them to, by chance, show that relationship. Guest: That's right. So that's why, when you do 20 tests, you can't use the 2-sigma rule. So by the 2-sigma rule, if you try 20 things, then the odds are that something is going to come up as a fluke, as a finding that really isn't a true finding.

So, if you are going one test--so the original test that they did, in the comic, were they tested a group of people; they gave them jelly beans and the other group, no jelly beans. In that test, two sigma is fine. That's a single test. But once you start doing multiple tests then you run the risk that something is going to show up as a fluke, and two sigma is not good enough.

Russ: So, let's take the example you give in your paper, which is really beautifully done. And although there are some technical things in the paper, I think the average person can get the idea of what you've done there, which is: You present, at the beginning, a particular trading strategy. Meaning a way to "beat the stock market," make a lot of money. And the strategy that you show, you of course tested over a long period of time, because people know that, in a short test, maybe by luck you would just do well.

But it's over many years. And although it doesn't do so great in the first year, it then does very, very well consistently, including through the financial crisis of , when many people lost their shirts and other pieces of clothing. And it looks like a fantastic strategy. And you evaluate that with the Sharpe Ratio. And talk in general terms if you can about what the Sharpe Ratio is trying to measure as a way of evaluating in particular stock trading--investment--strategy. Guest: So, the Sharpe Ratio is basically the excess return on the strategy.

Just think of it as the average annual return on the strategy divided by the volatility of the strategy. So, the higher the Sharpe Ratio, the more attractive the strategy is. And, indeed, there's a direct link, a direct relationship between the Sharpe Ratio and the t-statistic that we were just talking about. So, they are mathematically linked, and a high Sharpe Ratio means a high t-statistic.

Which means that the strategy is a strategy that generates a return that is significantly greater than zero. Russ: And that's actually relative to a so-called risk-free return--Treasuries? Guest: Yes. Usually you subtract out a benchmark, so just a risk-free. Russ: And I might want to be comparing it to, say, a different benchmark. Say an index mutual fund, which a lot of people hold. That's not risk free but it's relatively cheap, low cost, because it's automated. Is that correct? So it's often used to look at excess performance.

And that's a strategy on its own. And the question is: Do you get a return, an average return on that strategy, that is significantly different from zero? Russ: Say that again? Guest: Is significantly different from zero. So, that's basically, if it's different from zero--if it's above zero, that is an indication of skill: that the strategy actually has something that the market doesn't recognize and leads to some positive return, on average.

And that's what we all seek. We seek to beat the market. Russ: I'd say it in a different way. We are very--it's easy to be seduced. We do seek it, but we also, we desperately would love to have sort of that inside path, the secret strategy: 'The suckers, they're just, they're accepting that mediocre return; but I've got the genius advisor running my money, giving me financial advice, and so I'm making a premium. We definitely want to be better than the average. And this is a prime target.

And we want to allocate our money to managers that we believe are skilled. And skill means that you can outperform the market. Russ: And one of our lessons today, for me, thinking about these issues is how difficult it is to measure skill. So let's--in your particular example, this strategy which you start off the paper with, it has a significant Sharpe Ratio, right?

It's much better than the average return. Guest: It looks really good. You look at it--it is significant. It is like 2. So it means that with the usual statistical test, you would declare this strategy to be true. And that this is something that actually does beat the market. Russ: And here I am, naively investing my portfolio in a lot of index funds, and I obviously should switch. I'm losing money. I'm a fool, because I should be doing this. Guest: That's what it looks like. Russ: Yeah. But explain how you generated that fabulous strategy and why it's a bad idea.

Or at least not significantly proven to be a good idea, even though it's way more than 2 standard deviations above the likelihood that it's random. Guest: Sure. So the opening panel of my paper shows this great strategy. Very impressive, 2. The second panel of the paper shows that strategy, plus other strategies. And it turns out that what I did was I generated random numbers. I'm sorry. You cut out there for me, anyway. Guest: I generated random numbers. Basically it's completely--there's no real data.

And on this graph, I plot the cumulative returns of these strategies. And you can see that on average, the deliver about a zero return over the year period. But on the tails , you can see the original strategy that I presented, that had a 2. And you can see on the other side the worst strategy, which had a 2. So, basically, what appeared to be a great strategy, was purely generated by random numbers, had nothing to do with beating the market.

And again, this is a situation where you've got random strategies. Some of them are going to look significant when they are not significant. Every single one of these strategies by definition had zero skill. Because I fixed the return, when I'm simulating the numbers, to have an average of zero. Russ: Let's do one more example, then we'll get to what the implications are. So, the other example you give, one of my favorites, is--I'm going to use the football example. I get an email from a football predictor who says, 'I know who is going to win Monday night.

I know which team you should bet on for Monday night football. I'm not going to pay any attention to it. But it turns out to be right; and of course who knows? It's got a chance. But then, for the next 10 weeks he keeps sending me the picks, and I happen to notice that for 10 weeks in a row he gets it right every time.

And I know that that can't be done by chance, 10 picks in a row. He must be a genius. And of course, I'm a sucker. So this is a classic example. So let me set up what actually happens. So, let's say after those 10 weeks in a row you actually subscribe to this person's predictions. And then they don't do so well, after the 10 weeks. And the reason is that the original strategy was basically: Send an email to , people, and in 50, of those emails you say that Team A is going to win on Monday.

And in 50, you say Team B is going to win on Monday.

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And then, if Team A wins, the next week you only send to the people that got the correct prediction. So, the next week you do the same thing. And you continue doing this. And the size of the number of emails decreases every single week, until after that 10th week, there are 97 people that got 10 picks in a row correct.

So you harvest 97 suckers out of this. Russ: Who are willing to pay a huge amount of money, because you've got inside information, obviously. And I can make a fortune, all on your recommendation. And the fact is, that this is basically a strategy of no skill. Basically, every single week. There's no skill whatsoever. But it looks like skill. So, again, when you realize what is actually going on, you can't use the same sort of statistical significance. Because, in the usual case, to get 10 in a row, that is highly significant. But, given what you know has happened, it can't be significant.

It's exactly what you expect. Russ: So, that leads us to the deep question: Is Warren Buffett a smart man? I mean, he is called the 'Sage of Omaha. He makes a lot of money relative to his competitors.