Fundamental investment concepts are simple, like common sense
I 01 Overview of investments
I 11 Four commonsense but profound investing principles
I 12 How to think about different kinds of investments
I 21 Historical return patterns
I 22 Sometimes bad things happen for long periods
I 31 Your fundamental investment choices: eat well or sleep well
I 32 Your choice depends on psychological and financial factors
I 33 Sometimes partners have different attitudes towards risk
What are you paying for?
I 41 Active or passive? Three separate issues
I 42 Unbundle the fees
I 43 Is there investment skill? If so, what is it worth?
I 44 Broaden the discussion framework
STAGE I 01: OVERVIEW OF INVESTMENTS
This is Walk 16 in Life Two.
STAGE I 11: FOUR COMMONSENSE BUT PROFOUND INVESTING PRINCIPLES
Where the route takes us
Have you ever been to a casino? Wouldn’t it be nice if the odds were in your favor, so that you’re more likely to win than to lose? How would you behave, if you were in that position? Aha, hold that thought, because it can teach a lot about investing, as this stage shows.
This stage of the tour requires you to use your imagination. It’ll teach you a lot, so it’s worth taking your time over it.
What we’re going to do tonight is to make a trip to a virtual casino, a casino that exists only in your mind. And all of us together are taking over the casino tonight. Yes, it’s our own private function. Even better than that: the good news is that the odds at this virtual casino, unlike at a real one, are stacked in your favor. Does this sound like easy money? We’ll see. Anyway, let’s enter.
What, no slot machines? No, all we see are three doors, cheerfully decorated, with the labels Game 1, Game 2 and Game 3. OK, then, let’s enter into the spirit of the evening and head for Game 1.
Here’s the casino official. He tells us it’s a simple game. He’ll toss a coin. If it comes down heads, every player will win $1,000. If it comes down tails, every player will win $500. Yes please, you’d all like to play! One of you says: “This really is easy money!”
But wait, the casino official hasn’t finished. He adds, “Before you play, I have three questions for you. The first question: would you pay $400 for the right to play this game?”
You’re all still cheerful. “Of course,” you all agree. At that price you’re still certain to win.
“The second question: would you pay more than $400?”
A moment’s hesitation; then, realizing that you haven’t been asked what’s your limit, you all agree: “Yes.” You know that any price up to $499 still results in a certain win.
And so to the third question: “What’s the most you would pay?”
Oh, that’s more difficult. The shout starts: “$401.” “$450.” One wit calls out, “$800!” Everyone laughs: he can’t be serious (or he has such a lust for gambling that he’ll pay anything just to experience the thrill).
The bidding (yes, that’s what it has become) settles down at $749 – just enough to keep the game in your favor, though it’s far from a certain win. (You could win $251 or lose $249, with equal probability.) Some have backed out. It’s hardly worthwhile at $749. They want a better margin in their favor. One in particular says: “That’s too much. The game is still in my favor at $749, but I can get a better return with complete certainty with a bank deposit.” Oh, he’s a spoilsport – he’s making this an investment question rather than fun.
Actually, the game is over at that point. The game was not really to toss a coin. It was to see how much you’d bid and how the bidding developed. Oh, this is a learning game, not a gambling game. How disappointing! Well, we’re here, we might as well continue.
Let’s go to Game 2. Another casino official. He’s going to toss a coin. If it’s heads, every player wins $1,000,000. If it’s tails, every player wins $500,000. Might as well get to the point quickly: what’s the most you would play for the right to play this game?
One of you shouts out: “$740,000.” He pre-empts the bidding. Nobody challenges him with a higher bid. Nobody goes to $749,999, even though the game is still in your favor at that level. You’ve evidently taken the spoilsport’s bank deposit comment to heart; there are easier ways to make money, with much less risk.
The casino official has one more question: “Why do people typically offer to pay less than 1,000 times as much to play Game 2 as to play Game 1?”
One of you says: “Well, Game 2 is like playing Game 1 1,000 times, so I’d be willing to pay 1,000 times as much, as long as the margin was a bit more in my favor, like $650 for Game 1 and $650,000 for Game 2.”
Yes, but you were willing to pay more than $650 for Game 1, weren’t you? “Yes.”
So then, if your limit for Game 2 is $650,000, your bid is less than 1,000 times your bid for Game 1. “Right.”
“OK,” says the casino official, “I accept your offer of $650,000. Let’s play Game 2. Put up the money.”
Our friend says: “It’s virtual money!” No, it needs to be real money. “What d’you think I am, crazy? I’d never risk $650,000 at one time.”
And there endeth the second game.
We’ve already learned two important lessons.
- In a free market, there’s no easy money. As long as people have enough information to understand the game, and anybody can play, the price gets bid up to the point where there’s no easy money, just a risk-versus-reward calculation.
- The higher the potential loss, the higher the potential gain that people demand in order to be willing to play the game. People don’t like losing, but their aversion to losing increases as the potential loss increases, so the bigger the risk, the more they want the payoff tilted in their favor.
Remember, there’s still Game 3 to be played.
Another casino official: “I’m going to draw a card from a standard deck of 52 cards. If it’s an ace, every player loses $100. If it’s any card but an ace, every player wins $100.” That sounds like the odds are heavily in your favor: twelve chances to win, for every one chance to lose.
This might be starting to sound familiar, but no, this time the question is different: “What’s your reaction if you win?”
Several cries: “It was bound to happen.” “This is too easy.” “Let’s play again!”
And one final question: “What’s your reaction if you lose?”
A quick shout: “It’s a fix!” Laughter, then silence. Then several of you say, “Let’s play again!”
Two more lessons.
- Even good strategies can have bad outcomes. Playing Game 3 for no entry fee is clearly a good strategy, because it’s tilted so strongly in your favor, and even if you lose, the loss is bearable. But there’s still a chance that you’ll lose. That’s just bad luck, but bad luck does happen sometimes.
- With a good strategy, the more often you can play the game, the more likely you are to win over the long term. That’s why you said, “Let’s play again!” even if you lost Game 3 the first time it was played. The chances are so much in your favor that you’re highly likely to come out ahead if you play, let’s say, 10 times, and even more likely if you play 100 times.
There you are. Our virtual tour has ended. And, even if you didn’t realize it, you now understand four profound investment principles. We’ll see these principles in action in future stages.
There’s no mystery to investment principles. People behave just the way you’d expect. They’ll play the investment game (many times) if they think they’re likely to win. They don’t like to lose, particularly not large amounts. Put a lot of people together figuring out the chances, and there won’t be any easy money to be made.
STAGE I 12: HOW TO THINK ABOUT DIFFERENT KINDS OF INVESTMENTS
Where the route takes us
If you think about playing cards or tossing a coin, you can learn a lot about fundamental investment principles, and how to think about different kinds of investments.
The lessons of our casino games in Stage I 11 apply to investing for retirement, as we’ll see in this stage.
Here’s a way to think about investing.
Investing has things called asset classes, meaning investment of a particular type. Three of the best-known asset classes are stocks (often called equities), bonds (often called fixed income) and cash (often called Treasury bills).
A little technical detail, just for reference. It’s not necessary to remember this. It’s just general background education. In fact, skip this and go to the next section, if you like.
- Treasury bills are securities issued by governments, typically promising to pay an amount no more than a year from the date of issue. They are issued at a discount relative to the repayment amount, so you get more back than you pay for the security. Typically, government securities are considered the closest to being safe, because the taxing power of governments enables them to get the money they’ve promised to pay. Banks and other institutions buy these securities, and they are very easily traded.
- Bonds are securities typically issued by companies (or Treasury bonds, issued by governments), promising to pay an amount when the bond “matures” some time in the future, and in the meantime to pay interest on the maturity amount at periodic intervals, like quarterly. Company bonds are typically considered less secure than government-issued debt, and they are less easily traded because each bond is typically issued for a much smaller amount than government debt.
- Equities are investments in companies, entitling their owners to the company’s remaining profits, once the company’s bond-holders have been paid (and taxes paid to the government). If a company does poorly, there may be little or no return on the investment, and if it does really poorly, it may go bankrupt and the investment is worth nothing. On the other hand, if the company does well, there’s no theoretical upper limit to the profits to be distributed. A single company’s stock can have very uncertain returns, but when you add up all the companies in a country, the aggregate is usually a good reflection of the prosperity of the country. So mutual funds (also called unit trusts, and sometimes available in a variant called exchange-traded funds) typically invest in many companies, not just one, and if you buy their units, you have a convenient way to diversify your exposure to the country’s prosperity. Stock exchanges (where stocks are traded) conveniently compile an index of all available stocks, so you can invest in the whole lot conveniently. Similarly there’s also a global stock index that reflects the aggregate of the indices available in all the large (and sometimes smaller) countries in the world, so it’s possible to get exposure to the world’s aggregate prosperity.
Those tend to be the biggest and most easily traded asset classes. There are others. For example, real estate (also called property), or the stock of small companies in a small country. But those aren’t easily traded (they’re called “illiquid” assets, liquidity referring to the notion that they’re easily sold), so they tend to be found only in the portfolios of institutions that provide financial services. (An exception is your own home, of course, which may be the biggest investment you own.) Anyway, let’s ignore the illiquid ones and consider the three asset classes I mentioned at the start.
Here’s a big question: how should you think about these asset classes?
My answer may surprise you. Think of them as being casino games, with different payoff patterns. But there are a couple of significant differences between our previous casino games (in Stage I 11) and these asset class investment games.
- Unlike our casino games, these investment games don’t just have two “either/or” outcomes. They have a continuous range of intermediate outcomes.
- And unlike our casino games, these investment games don’t come with precise odds and payoffs known in advance. History is all we know. That’s an obvious starting point, but there’s no guarantee that the future will be like the past.
Nevertheless, as we’ll see, all four lessons that we learned in our virtual casino apply to these asset classes. Let me be explicit about how those four lessons apply.
- In publicly traded markets, where it doesn’t cost much to make a trade and for which lots of research about different analysts’ views about the future are available, there’s no easy money. These markets are called “efficient.” That doesn’t mean that people are always right about the future – that’s impossible, because there’s no crystal ball. Efficiency refers only to the ease of trading in the market and the wide distribution of information. In efficient markets, most of the time (as we’ll see in Stage I 43) it’s pretty difficult to beat others. That’s not true of inefficient markets, in which research is sparse and therefore good research really does create superior money-making opportunities, or in which the cost of trading is so high that most people stay out of it.
- As the potential loss increases, you want a disproportionately big increase in the potential gain before you’re willing to play the game. Consider those three asset classes. We’ll find (in Stage I 21) that the potential losses from investing in equities are higher than in the other two asset classes. So it makes no sense for investors to buy equities, unless the potential gains when equities do well are also higher than in the other two asset classes, in fact disproportionately higher.
- Even good strategies can have bad outcomes. Over the long term, equities have done well more often than they’ve done badly (as we’ll see in Stage I 21), so from that perspective investing in equities is a good strategy. But it can also have bad outcomes, meaning that equities frequently (though historically, less often than half the time) involve losing money. How much of a bad outcome you can tolerate as you seek those more frequent and large good outcomes is a crucial question, often called your “risk tolerance.” We’ll get into this in Stages I 31 and I 32.
- With a good strategy (like investing in equities), the more often you play, the more likely you are to eventually win. (Or at least, that’s been what has happened, historically.) What does that mean, to play the game often? Think of it this way: the younger you are, the more often you can play, because it’s the passage of time that constitutes a play. As we’ll see, over time the likelihood increases that you’ll come out ahead when you invest in equities. But that is only a likelihood, not a certainty. In fact, there’s still a (relatively small) chance that you’ll lose persistently – and that can mean ruin. Again, dealing with this chance, and how to avoid it before it hurts you too much, is a fundamental question we’ll examine.
Already you can guess that investments have two fundamental characteristics, both of which are desirable, but which are invariably in conflict with each other. One characteristic is safety: don’t lose, be predictable. The other characteristic is growth: keep going up, make my investment worth more and more. And since there’s no easy money and even good strategies can have bad outcomes, there is no investment – absolutely no investment, no matter how appealing its prospects and no matter what anyone may tell you – that will assuredly give you both growth and safety.
Basically, that previous paragraph is all you need to know about investing. The rest is about studying history and applying the principles of safety and growth to your own situation.
Investment professionals will tell you that I have grossly oversimplified this stage of the tour, and that investments are much more complex and much more nuanced than in my simple overview. And they’re right. But it needs to be complicated only for those experts who are immersed in investment markets all day long. For the average investor, the average retiree, all you need to remember is that investments involve varying degrees of safety and growth, and your “asset allocation” (the mixture of investments that you hold, divided across different asset classes) reflects your risk tolerance, that is, your tolerance for giving up some safety in search of growth.
Investment outcomes aren’t as predictable as tossing a coin or drawing a card, where the odds are known and the number of possible outcomes is limited. But there are still similarities. And the odds help us to decide whether an investment is oriented more towards safety or towards growth.
STAGE I 21: HISTORICAL RETURN PATTERNS
Where the route takes us
How have different kinds of investments performed in the past? Let’s take a look, because history, even though it doesn’t predict the future, is still a good basis for adding to our understanding of investments.
In Stage I 12 we used games to learn about investing. In this stage, let’s consider a calendar year as constituting a play of each game – not because there’s any magic to calendar years, but just because it’s convenient. Figure I 21.1 below shows returns from investing in a pool of large US companies (specifically, it reflects the S&P 500 index returns) from 1928 through 2015. Each year’s return is placed in the appropriate 10-percentage-point range, from -50% (meaning the investment lost half its value) to +60% (meaning it gained more than half of its value from the start of that year).
Notice that the middle portion of the range occurs with the greatest frequency, and the frequency fades away as the returns become more extreme on both the left and the right. If you think that the average annual return over the period is somewhere in the 10%-20% range, you’d be right: it’s actually 11.4%.
There’s a statistic called the “standard deviation” that is often used for distributions with this sort of shape. It leaves out the extremes on the two sides, and searches for the range that covers roughly the middle two-thirds of the results. In this case the standard deviation is 19.8%. (Never mind how it’s calculated.) This is a neat way of saying that roughly two-thirds of the outcomes were in the range from 11.4%+19.8% (which adds up to roughly 30%) to 11.4%-19.8% (adding up to roughly -10%). Check it out: yes, most of the annual returns are indeed between -10% and 30%.
Another interesting result is that 64 of the 88 years resulted in a positive return (that is, 73% or roughly three-quarters of the time).
The same source also gave me the numbers for inflation each year, and I calculated the “real” returns, which is a jargon expression meaning the excess of each annual return over that year’s inflation. The average real return was 8.2%, and since the shape of the distribution is pretty much identical, it’s not a surprise that the standard deviation is an almost identical 19.7%. But the proportion of positive years shrinks a little, to 67%. That is, roughly two-thirds of the time the annual return exceeded the year’s inflation.
In fact, most of the time it’s the real return we’re interested in, because for a return to be really useful, it ought to exceed inflation, so that the investment enables us to purchase more at the end of the year than we could at the start. That’s why we invest. So from now on I’ll discuss only real returns.
How about if we look not at individual years, but at chunks of 5 or 10 consecutive years? Some of the interesting results are shown in Table I 21.1.
Table I 21.1: Summary statistics, S&P 500 real returns, 1928-2015
Best single year 53.7% (1954)
Worst single year -38.0% (1931)
Average return 8.2%
Standard deviation 19.7%
Proportion of positive single years 67%
Best 5 consecutive years (annualized) 25.3% (1995-1999)
Worst 5 consecutive years (annualized) -10.3% (1937-1941)
Proportion of positive periods of 5 consec years 76%
Best 10 consecutive years (annualized) 17.9% (1949-1958)
Worst 10 consecutive years (annualized) -3.8% (1999-2008)
Proportion of positive periods of 10 consec years 88%
With 5 and 10 year chunks, the best and worst aren’t nearly so extreme as the one-year numbers. The proportion of positive periods increases – but still doesn’t reach 100%. I even tried 15-year periods, and the positive proportion goes up to 96% – but that’s still not 100%.
Observe that, if you think of investing in US equities as a good strategy, you find that the longer you play, the more likely you are to win (that is, achieve a positive average real return), but even a good strategy can have bad outcomes – and to find, after 10 or (worse) 15 years that your returns still haven’t matched inflation will undoubtedly result in a very bad feeling. Yes, there are no guarantees, and no easy money.
How about if you invested more broadly than the US equity market: in the developed markets of the world, including the US? I analyzed the results of investing in the MSCI World Index from 1970 (when the index was first compiled). The results are shown in Table I 21.2. Of course, this is a shorter period. But two things make the numbers worth showing. One is that they’re not dramatically different from the US numbers over the same period. (Take my word for it, even though I haven’t shown the US results for that period.) The other is that they’re not dramatically different from the US numbers over the longer period starting in 1928.
Table I 21.2: Summary statistics, MSCI World real returns, 1970-2015
Best single year 31.3% (2003)
Worst single year -40.5% (2008)
Average return 6.8%
Standard deviation 17.7%
Proportion of positive single years 70%
Best 5 consecutive years (annualized) 23.5% (1985-1989)
Worst 5 consecutive years (annualized) -7.0% (1970-1974)
Proportion of positive periods of 5 consec years 71%
Best 10 consecutive years (annualized) 14.1% (1980-1989)
Worst 10 consecutive years (annualized) -2.7% (1999-2008)
Proportion of positive periods of 10 consec years 86%
OK, we’ve looked at investing in equities (growth assets) in some detail. How about the supposedly safe assets, Treasury bills?
It won’t surprise you to know that the equivalent of Figure I 21.1 for Treasury bills is just two columns. The mammoth one is the range 0%-10%, and there are also a number of years in the 10%-20% range, reflecting years in which inflation was high. Again, let’s focus on real returns, that is, the extent to which Treasury bills produced returns that outpaced inflation. The results are shown in Table I 21.3.
Table I 21.3: Summary statistics, Treasury bills real returns, 1928-2015
Best single year 12.8% (1931)
Worst single year -8.9% (1941)
Average return 0.5%
Standard deviation 3.9%
Proportion of positive single years 61%
Best 5 consecutive years (annualized) 8.7% (1928-1932)
Worst 5 consecutive years (annualized) -6.0% (1942-1946)
Proportion of positive periods of 5 consec years 61%
Best 10 consecutive years (annualized) 3.8% (1981-1990)
Worst 10 consecutive years (annualized) -5.0% (1941-1950)
Proportion of positive periods of 10 consec years 60%
Let’s interpret these results.
Treasury bill real returns (for annual, 5-year and 10-year periods) are all in a much narrower range than those of equities, and their standard deviation is also very much smaller. Both of those observations demonstrate that they have been more predictable (and in that sense, safer) than equity real returns. To compensate for that, their average return has been very much smaller than that of equities. In fact, on average T-bill returns are close to zero, relative to inflation.
This shouldn’t be a surprise. Given how much greater is the scope of equity investing to produce a serious loss, why on earth would you invest in equities unless the compensation is a potential gain that’s very much greater than for T-bills? And that too is one of the principles we derived in Stage I 11: the higher the potential loss, the higher the potential gain that investors demand in order to be willing to invest in equities.
Two final thoughts.
One is that I’ve said nothing about bonds. That’s because in a sense they’re an in-between asset class, neither particularly growthy nor particularly safe. You therefore wouldn’t be astonished to learn that their statistics are in between those of T-bills and equities.
The other is that there’s actually a fifth lesson that we should see in the numbers (in addition to the four in Stage I 11). The past has not always been a reliable guide to the future.
Here’s something you can try yourself. In Figure I 21.1, find the year of your birth, or the year of a parent’s birth, if it’s no earlier than 1928. See which column it appears in. Then check the following year, and the one after, and so on for 20 years or so. You won’t find a pattern appearing, of good years routinely following bad years (or the reverse), or of two good years followed by two bad ones (or the reverse), or anything that offers a formula for predictability. Too bad. It’s almost as if the pattern is random.
Historically, equities have behaved like a good growth-oriented strategy, Treasury bills like a good safety-oriented strategy. But neither strategy is absolutely safe. And the past hasn’t been a good predictor of the near-term future.
STAGE I 22: SOMETIMES BAD THINGS HAPPEN FOR LONG PERIODS
Where the route takes us
Of course we hope for good outcomes when we invest. But we must consider the possibility that outcomes will be bad, perhaps even over long periods. That’s what risk means. Let’s take a look at history again, this time looking at bad news.
In Stage I 21 we saw that, the longer you play the game, the more likely you are to experience a favourable outcome. But even a good strategy (playing the investment game for a long time) can have a bad outcome. In this stage, let’s focus a little more closely on outcomes that are disappointing even over the long term.
On Route 3, when we take a look at longevity, we’ll note that our own future lifespan is uncertain. If we want to play it safe, we probably ought to plan to make our money last longer than we expect to live – just in case we outlive our life expectancy. For example, suppose people of our age are expected to live, on average, to age 85. (I’m picking a number out of the air here, just as an example.) That means that roughly half of us will live longer than age 85, and half won’t live as long as age 85. Perhaps we might be one of the people living longer than average. It would be wise to plan to make our money last beyond age 85, just to be on the safe side.
How much beyond age 85? We’ll look at two safety margins on Route 3 (though there’s nothing magic about either of them). We can ask: if 85 is the age that half of us will live beyond, what’s the age that only a quarter of us will live beyond? Maybe that’s 89. And what’s the age that only one-tenth of us will live beyond? Maybe that’s 95. (Again, I’m making up the numbers.)
OK, then, we’ll be playing it a bit safe if we plan to make our money last to age 89. Because then, if the future is like the past, there’s only a 25% chance (a quarter) that we’ll outlive our money. And we’ll be playing it even safer if we plan to make the money last to age 95 – because then (if the future is like the past) there’s only a 10% chance (one in ten) that we’ll outlive our money.
Again, there’s nothing magic about “a quarter” and “one in ten” – they’re just different measures of playing it safe.
The same idea can be applied when we project investment returns into the future.
We saw in Stage I 21 what average returns have been in the past. Those are the equivalent of “average life expectancy” figures. If we project our money into the future using those average numbers, we’ll have a 50/50 chance of doing better than we project (if the future is like the past) and a 50/50 chance of doing worse. So, if we want to play it safe, we ought to project lower returns in the future.
How much lower?
I ran the numbers that underlie Table I 21.1 and Table I 21.3 over 10-year periods. (I chose 10 years as a reasonably long term for future projections – again, no magic to 10 years.) First I calculated the average returns over 10-year periods. (I didn’t show them in those tables – never mind.) Half of the ten-year periods had returns higher than those averages, and half of the ten-year periods had returns lower than those averages. (That’s what “average” means, essentially.)
So now I asked a different question. What was the return that only a quarter of the ten-year periods fell below? (Those of you who are familiar with statistics will recognize that I sought the “lower quartile” of the distribution.) How much lower than the average return was this “a quarter” return? If we want to play it a bit safe when we project future returns, we can use the lower number instead of our best estimate of the future.
Here are the answers.
For equities, we should subtract 4.4% from the average annual return, if we want to project with a 75% (rather than a 50%) probability of doing better than our projection (assuming the future distribution of outcomes is the same as in the past). For Treasury bills, we should subtract 1.7% from the average annual return.
And then I also looked at the “one in ten” numbers (the lowest decile, for you techies).
For equities, we should subtract 8.3% from the average annual return, if we want to project with a 90% (rather than a 50%) probability of doing better than our projection (assuming the future distribution of outcomes is the same as in the past). For Treasury bills, we should subtract 4.2% from the average annual return.
Whoa, that means we will be projecting returns that are much, much worse than the historical average! Yes indeed, that’s a good interpretation.
In fact, that’s a reasonable way to look at the risk we’re taking. If the future turns out to be worse than the past, we’ll earn lower returns than the historical average. Will that happen? We simply don’t know. We can’t know, until the future has happened! That uncertainty is one aspect of the risk we take when we invest. If we want to guess how we’ll feel if the risk that we take results, not in the reward we expect for risk-taking, but in a much worse outcome, one way is to project that “much worse” outcome and then try to guess how we’ll react.
And here’s another “in fact.”
In fact, if we don’t do something like that, we’re kidding ourselves. Because then we’ll just believe that investing in equities, with their higher average long-term return, is the answer to all our problems. “Need a higher long-term return? Sure, invest a greater amount in equities. The more you invest in equities, the better the outcomes will look.”
Not so. It’s true that the average projected outcome will look better; but it’s also true that there’s a chance that the actual outcome (which, remember, is necessarily uncertain) will be much worse. And unless we get some kind of estimate about how bad the risk can be, we’re looking only at the good outcomes, not also at the bad outcomes.
If there’s one big lesson to carry into making projections about the future, it’s that we should look at possible bad outcomes as well as possible good outcomes before making decisions. I can’t stress that strongly enough.
To try to guess how we’ll feel if the future is like a bad outcome from the past, rather than just the average outcome, we should also make projections using much lower investment return assumptions than historical averages.
STAGE I 31: YOUR FUNDAMENTAL INVESTMENT CHOICES: EAT WELL OR SLEEP WELL
This is Walk 17 in Life Two.
STAGE I 32: YOUR CHOICE DEPENDS ON PSYCHOLOGICAL AND FINANCIAL FACTORS
This is Walk 19 in Life Two.
STAGE I 33: SOMETIMES PARTNERS HAVE DIFFERENT ATTITUDES TOWARDS RISK
Where the route takes us
What happens when partners find that they have different attitudes to risk? This stage shows that there are many sensible ways to proceed.
Once again I’ve assembled a panel of people I’ve interviewed, and this time I’m asking them to tell you what they told me about partners differing in their attitudes towards risk.
Panelist 6: My husband is a CFA, he’s very conservative, very analytical. That doesn’t mean he’s a good planner. He sits on money, then invests in a big lump sum. I’m more frugal as a spender, but better at regular saving. It took some time for us to communicate successfully as a couple – “How could you do this, it’s our money, yes it really is a big deal” – so now we talk before anything big.
Panelist 7: I’m the husband! And I disagree that I’m not a good planner. In fact, I think I’m a great planner. The thing is, I take my time to make a good plan, then I implement it. That sounds like sitting on it for a long time and then being impulsive, but it isn’t. It’s just being rational and careful. That feels slow to my wife, who is much more emotional. We’ve discovered that we’re close in most of our likes, but we’re different in how we resolve issues, even though we come to the same conclusion. So we try to control what we can, and not what we can’t.
Panelist 8: I’m advising my parents. My father is 74, my mother 73. I worry about whether I’m giving them good advice. My mother is the financial one, with all the documents. She’s the one who wants to know if they’ll be OK. My father is the one who wants to do it all himself. He says his friends all have great money-making investments! I worry about how to be respectful of my father and still reassure my mother.
Panelist 9: I can sleep at night with risk. Maybe I shouldn’t be able to, but big market fluctuations don’t bother me. I make my own stock-selection decisions. I hate to say this to all of you, but my philosophy is that if your spouse is risk-averse, you just don’t tell her. I’m not diversified – 80% in real estate and individual stocks, and of course my real estate is by definition not diversified. It’s been great fun, even though I’m not that good at it – maybe it’s time to start putting money in diversified vehicles. Sometimes you take risks in one area of life and not in others – my risk-taking hasn’t been in life, it’s been in investing.
Panelist 10: My husband is building a plan, and as it builds I start to worry about: what if we aren’t healthy, what if we don’t have enough money, and so on? He does the financial planning. He’s a risk-taker – at least I think so – but I really don’t know! He’s very comfortable with it – I just want to know if there’s a big loss.
Panelist 11: In our case, my wife is much more risk-averse than I am. Her attitude regarding the kids (the kids come first, our future comes a distant second) doesn’t help: the fact is, we need a risky asset allocation to get to where we want! Her own savings before she started working went into a tax-sheltered account 100% in equities; now (to her surprise) its value has doubled. I told her that’s the reward for the risk she took – “If you had been looking at it every day it would never have survived!”
Panelist 12: In my case it’s money shared by multiple branches of our family. It’s clear we all have different degrees of tolerance for risk, but we all have to live with the decisions made by one of us, because that’s how it’s been set up. We’ve talked about it, and we keep saying to one another that we’ll raise the subject at the next family meeting, to see if we can get a discussion going about risk tolerance. But I have to say, I don’t have high hopes of success.
TG: Once again you see not only differences, but how nuanced attitudes are, rather than just big clear-cut differences. And you see how many other factors come into play. Making an explicit decision about how much risk to take is a complex subject, precisely because so much else comes to mind, and because most of us have never had to think about it. You see in this panel the differences between those who think about it a lot and those for whom it’s not exactly an everyday matter. And yet ultimately a decision has to be made, because ultimately your assets are going to be invested in some mixture of assets, and even if the way it all adds up is accidental rather than clearly thought through (let alone agreed to by both partners), it’s still a decision, even if it’s an implicit rather than an explicit decision.
In Stage I 31 I made the trite remark that people are different. One occasion when the differences may be important is when you need to decide where you are on the eat-well-versus-sleep-well spectrum. Let’s discuss what happens if you’ve actually discussed the subject, along the lines in Stages I 31 and I 32, and you’ve come to the conclusion that your risk tolerances are different.
Before I list the five possible ways to deal with it (of which only one is wrong – the other four can all work, depending on the circumstances), let me say that typically the man is willing to take more risk than the woman. And I say this because it’s probably hard-wired into our brains, to be that way.
You’ll read elsewhere that it’s the neurotransmitter (brain chemical) dopamine that drives us to take risks, but that’s not the explanation here, because both men and women have lots of dopamine going through our brains. It’s testosterone that causes men to typically take much more risk than women. It’s a neurotransmitter that drives aggression and risk-taking, and men typically produce ten times as much testosterone as women.
Researchers Barber and Odean wrote a paper about risk-taking in investment. They looked at thousands of household brokerage accounts, and found that men are more overconfident than women, they therefore trade much more frequently, and since there’s no basis for overconfidence their results are much worse. The differences were so stark that, instead of the typical jargon-filled academic title, they called their paper “Boys will be boys.” And they led it off with a lovely quote from nineteenth century American humorist Josh Billings: “It’s not what a man don’t know that makes him a fool, but what he does know that ain’t so.”
OK, enough fun. Let’s suppose you’re both sensible, not overconfident, and disagree about how much risk is tolerable. It’s straightforward to list all five ways you can resolve the difference.
- Go with the one who wants to take more risk. The probable (not certain – nothing is ever certain) outcome is that you will both eat more, and one will sleep less well than he (or more likely she) is comfortable with.
- Go with the one who wants to take less risk. The probable outcome is that you will both eat less.
- Take the average of the two. The probable outcome is that you will eat less well than if you took more risk, but better than if you took less risk; and one will sleep less well than is comfortable.
- Divide the assets according to whatever formula you can agree on, and each invests his or her own portion and lives with the consequences.
- Ask your investment professional to make the decision for you.
I don’t know how you and your partner resolve serious differences, but really those are the options open to you. They’re probably uncomfortable, unless the difference is small and you go with the third option (the average), in which case the impact on the eating and sleeping outcomes may not be large.
The fifth option is the one that’s simply wrong. Why? Because this isn’t an investment issue, as I’ve stressed in Stages I 31 and I 32. This is a personal issue. And, as I stressed in P3 (about being an informed consumer of expertise), in this case you are the experts on the subject of yourselves, and it isn’t investment expertise that you need to resolve this, it’s expertise on the subject of knowing yourselves. That’s not your financial professional’s natural domain.
Perhaps you can find someone else (a member of the family, a friend?) who knows you both almost as well as you know yourselves and can bring some external or objective wisdom to bear on the disagreement.
It’s a tough one.
It’s natural for partners to have different attitudes towards risk. It may be difficult to find a single approach that leaves both reasonably comfortable. But remember that this difference is a personal issue, not an issue requiring investment expertise.
STAGE I 41: ACTIVE OR PASSIVE? THREE SEPARATE ISSUES
Where the route takes us
One of the most heated (and therefore potentially confusing) topics in investing is whether to be active (try to choose winners) or passive (just “go with the flow”). In this stage we’ll see that one reason for the confusion is that “active versus passive” really encompasses many different questions.
It’s all very well making plans, whether they’re made by you or by your financial professional. But the rubber has to hit the road. You have to invest the money. And that’s when you get hit by the most expensive issue you’ll face: whether to invest actively or passively. And perhaps the ultimate irony is that you might never face the issue directly, but instead default into active management. Let me explain what this is all about. And I’ll do so by identifying three entirely separate issues that are often confused by being placed under the same heading of “active versus passive.”
Here’s how I’ll do it. First I’ll define active and passive, in case you haven’t come across the terms before, or are less than totally familiar with them. Then I’ll identify the three separate issues. My goal is that, by the end of this stage end, you’ll see that they really are separate issues. And then, in the next three stages, we’ll discuss each of the issues separately. By the end of this mini-tour, you should be pretty clear as to how you’re going to deal with each of the three issues.
OK, definitions first.
Passive management means, in effect, buying all the available securities of a particular type in an investment market. Typically this becomes feasible when there’s an index compiled that reflects most of the investible securities of that type. Examples are the Russell 3000® Index for US equities and the FTSE All-Share Index in the UK. You then buy the index, typically through a mutual fund or unit trust or exchange-traded fund (ETF) that attempts to match the composition of the index. The index itself is typically compiled and periodically updated to reflect the available securities of the kind (typically the asset class) being considered. The goal of passive investing is to find a convenient way to enjoy the returns of everything in the index. Since the index is compiled according to specific rules, matching its composition is usually an easy investment exercise and therefore relatively inexpensive.
Active management means investing in the same asset class, but with the goal of achieving a higher return than the index, by selecting those securities thought to have a higher likelihood of beating the average that the index represents. In other words, get a higher return in good times, and don’t do as badly in bad times. This requires a great deal of research in comparing all the securities available to choose from, and opinions change as time evolves, so trading (selling some securities and buying others) becomes necessary. The cost of research makes the fees charged for active management much higher than for passive management, and the cost of trading systematically reduces returns; so the barrier to winning in the active management game is high. So can the rewards be, of course – as well as the cost of failure to win.
Sometimes active management extends further, in trying to determine which of several asset classes are likely to do better than others in the short or medium term (by which I mean the next few months or the next few years, rather than over your entire post-work horizon), and trading appropriately across asset classes. This used to be called “market timing” until that phrase developed a bad reputation, after which it got called “tactical asset allocation” or something along those lines.
That’s the background.
When you go to an investment professional, sometimes there isn’t much discussion of the issue, and you may be defaulted into one or more funds that are actively managed. It’s always true that active management involves higher fees than passive management; but you may not see the fees explicitly, so you may not realize what you’re paying. It used to be (and may still be, depending on which country you live in) that financial professionals were paid more (by the sponsors of the funds) for placing you in active funds than in passive funds – potentially a conflict of interests, even when the professional sincerely believed that he or she was skillful in being active or in selecting skillfully managed active funds, and so you would benefit from this skill. Clearly, you should have a choice, and it’s best if that’s an informed choice.
Now let me identify the three separate issues involved here.
- Fees: Make sure that you are aware of all the fees you’re paying, directly or indirectly. This is quite separate from whether you’re successful or not with active management. The fact is that fees are certain; success isn’t.
- Skill: Everyone who in involved in active management genuinely professes skill in being active. The thing is, skill here doesn’t just mean getting a good return (passive management can also get a high return); skill means getting a better result than the average of others who also profess the same skill. So it’s not just their skill you’re relying on, it’s also your own ability to find them. Is there such skill? If so, how do you locate it? And if so, under what circumstances should you pay more for it? The fact is that many studies find that fees and skill aren’t correlated.
- Broaden the discussion framework: Typically the issue is discussed as if there’s a right answer and a wrong answer, and it’s your job to find the right answer. That’s unfortunate. The fact is that often it’s best to be partially passive and partially (sometimes necessarily) active (or at least non-passive: I’ll explain the difference in Stage I 44). And you ought to understand when each of those choices is most appropriate for you.
In short, if you understand this framework and the discussion of the issues in the next three stages, you’ll be able to make the choices that best fit your own situation.
Whether to be an active or a passive investor is a discussion that typically confuses three separate questions: how much you pay, what you’re paying for, and whether the choice should be “active and passive” rather than “active or passive.”
STAGE I 42: UNBUNDLE THE FEES
Where the route takes us
What do we pay for the privilege of asking someone else to manage our investments? This stage lists many forms of payment.
Advice or any form of assistance with your post-work financial planning is useful. And so you should expect to pay for it.
A problem is that sometimes it may appear to be free because you are not billed explicitly for it. (And many buyers of services – that is, people like you – prefer it that way; they prefer not to think about it or to have to write a check for it.) Clearly, when you seek advice or assistance the main thing you’re looking for is the competence of the person or firm you hire. But among your search criteria should be that you get a clear understanding of how your professional (or, more generally, your professional’s firm) will be paid. And since there are multiple ways of remuneration, and payments for multiple services may be bundled into a single amount or formula, you should be aware of the unbundled (that is, separate) amounts of remuneration for the difference services. That’s the only way you can compare the charges for the services you’ll receive.
Payments to your professional’s firm tend to be of two main types. One is an explicit fee that you pay directly, of a size independent of the amount of assets under consideration. The other is a commission (or equivalent) paid by an investment manager to your professional’s firm, for directing your assets to that investment manager, typically explicitly tied to the amount of assets under consideration. (Sometimes your professional’s firm is itself the investment manager.) Confusingly, sometimes remuneration is called fee-based, giving the impression that it’s independent of asset size, when in fact it is based on asset size after all. And some forms of remuneration are a combination of fees and commission equivalents. So: buyer beware, and be aware.
The main forms of fee-only asset-independent remuneration that you might pay to your professional’s firm are as follows:
- A one-time fee for a one-time service.
- A flat retainer fee (for example, so much a quarter or a year) for services that will be ongoing.
- An hourly fee for services that will be ongoing.
The main forms of asset-based (which I also refer to as commission-equivalent) remuneration paid by an investment institution or indirectly by you to your professional’s firm are as follows:
- A front-end load. This is an amount paid at the start. Typically it means that the amount that will be invested for you is reduced by an amount related to the front-end load.
- A back-end load. This is an alternative to the front-end load. Under this arrangement the payment is made to the professional’s firm at the start, and the full amount of your assets will be invested. But if you withdraw the investment before some specified period of time, there will be a form of surrender charge applied, to offset the up-front payment.
- A trailer. Under this arrangement the professional’s firm is paid a (smaller) amount periodically (such as every month or quarter or year) as long as your investment stays in the fund into which it is initially placed.
As you will have guessed by now, some commission-type arrangements involve both a front-end or back-end load as well as a trailer.
Asset-based commission-type arrangements have been very popular with advisory firms. They’re virtually out of sight, if they’re taken directly out of the fund. Obviously they have an impact by reducing what would otherwise be the value of your assets, but if all you see is an end-of-year value of assets, you won’t see explicitly how much the value has been reduced because of the professional firm’s compensation. And many buyers of services – that is, people like you – are perverse, in the sense that they will live happily with a concealed asset-based commission but be appalled by a much smaller explicit fee. This makes it much more convenient for a professional firm for remuneration to come from a commission; and since commissions vary from one kind of investment product to another, it is tempting to place your assets in a high-commission arrangement rather than a low-commission arrangement.
In some countries legislation has therefore been passed (for example, in the UK in 2013, in Australia in 2015) banning commission-type remuneration. And there is also legislation that binds the professional to give advice that is solely based on what’s appropriate for you, unconflicted by remuneration arrangements. In the US, for example, the intention of the Obama administration was for a new fiduciary standard to come into force in 2017, meaning that a professional’s actions must be guided solely by what’s in your best interest.
In some countries legislation has therefore been passed (for example, in the UK in 2013, in Australia in 2015) banning commission-type remuneration. And there may also be legislation that binds the professional to give advice that is solely based on what’s appropriate for you, unconflicted by remuneration arrangements. In the US, for example, the intention of the Obama administration was for a new fiduciary standard to come into force in 2017, requiring that the professional’s actions would be guided solely by what’s in your best interest. (But check, as you read this, whether this intention has taken effect.)
I don’t profess to be up to date on legislation (at any stage of this tour); my sole purpose is to educate you so that you know how to think about these issues. And the way to think about the issue of payment to professional firms is simply to be aware of how they are paid in dealing with you.
What has all of this to do with active and passive investing? The connection is that active investing is much more expensive than passive investing, for the investment management company offering it in a mutual fund or unit trust or ETF. It is also typically more profitable, so the company pays higher commissions for active than for passive. The higher cost of active management may be in addition to the remuneration of your professional’s firm. By the time your professional firm’s own fees are added, the total charge to you may be noticeably high. With legislation requiring a fiduciary standard of conduct and explicit fees, commentators predict that buyers of service (that is, people like you) will be more inclined to ask for passive management in order to reduce aggregate visible fees, or that professionals will be more inclined to place you in passive investment products for the same reason.
And so a natural question now is: how can you compare active and passive products? That’s the subject of the next stage, to look at one angle on that issue.
It is reasonable to be charged for financial advice and assistance. You pay for these services in many possible ways, some direct and some indirect. Only if you are aware of exactly what you are being charged can you compare the charges with what others might charge.
STAGE I 43: IS THERE INVESTMENT SKILL? IF SO, WHAT IS IT WORTH?
Where the route takes us
If we make enough choices, some will work out and some won’t. How do we distinguish luck from skill? Is there skill? What is it worth? This stage looks at those questions.
As I said in Stage I 41, everyone who in involved in active management genuinely professes skill in being active. The thing is, skill here doesn’t just mean getting a good return (passive management can also get a high return); skill means getting a better result than the average of others who also profess the same skill. So it’s not just their skill you’re relying on, it’s also your own ability to find them. Is there such skill? If so, how do you locate it? And if so, is it worthwhile for you to pay more for it?
No need for suspense. Let me give you quick answers. Yes, there is investment skill. Locating it is very difficult. Typically it’s not worth paying for it. There, now you know; the rest of this stage gives you my justification for those assertions.
Yes, there’s skill. I have said so on many occasions. At one stage of my career I ran a department that attempted to find superior investment managers, in many asset classes around the world. I published a paper in 1998 documenting my firm’s results. I engaged in a public debate with an Oxford professor at a conference on the issue in 2014, rebutting his assertion that “It’s a waste of time listening to consultants [on the subject of finding good active managers]. It’s a service that’s useless.” I pointed out that his definition of success was the ability to select the manager who finished at the top of the performance rankings, whereas all that a buyer of active management services requires is the ability to beat the passive benchmark – in other words, winning a silver or bronze medal or being an Olympic finalist is success, not just the gold medal – and his own paper actually demonstrated the existence of this level of selection skill. And at another stage in my “post-graduate” years I published a paper providing insights for evaluating active management. So it’s something I have long studied.
But frankly, it’s not enough for there to be historical skill in finding managers who themselves have investment selection skill. This sort of skill gets gradually diluted with time. Investment markets become more efficient with the rapid dissemination of research and greater ease of trading. And so what happens is that persistent added value from skill becomes increasingly difficult to identify. What you always find is occasional added value, and of course it’s precisely after such a period that managers advertise their skill; nobody says: “We’ve been underperforming recently, but trust us, we’re really superior.” And yet advertising is persuasive. Flows into funds that have performed well in the recent past are invariably greater than into funds that have performed poorly.
What’s clear is that there is no simple way to identify future superior performance (which is all that counts – you get no credit for what happened before you became an investor in that fund). And it may surprise you to know that the traditional maxim in other areas of life, that “you get what you pay for,” is typically not supported in the investment field. Let me simply quote from the Investopedia website: “Just about every study ever done has shown no correlation between high expense ratios [i.e. fees] and high returns. This is a fact. If you want more evidence, consider this quote from the [US] Securities and Exchange Commission’s website: ‘Higher expense ratios do not, on average, perform better than lower expense funds.’”
You may think, therefore, that you’ve located skill when you find a fund that has recently outperformed the passive benchmark; but beware the selective presentation of information.
What’s also important is to ask: if there really is skill, how much is it worth paying for that skill? You may find, for example, that over moving 5-year periods a manager (or a fund) has outperformed the passive benchmark 80% of the time. Wow, that’s great! But by how much? And after fees (both the fund’s active management fees for individual investors and the professional’s fees) how much is left for you? Is the amount that’s left for you worth the risk of future underperformance? Perhaps it is, perhaps it isn’t. My point is simply for you to ask the question.
Possibly most important of all is a question that’s rarely asked: Why do you care if your performance is slightly better than passive? If it’s bragging rights you’re after, then yes, you’ll get them. But if the ultimate goal isn’t investment bragging rights, if in fact your investment returns are just a way to get to the lifestyle you desire, then your goal is a lifestyle goal rather than investment bragging rights, and the question is whether active management success contributes much to the probability that you can achieve your lifestyle goals. Whether you’re willing to pay more for active management may ultimately come down to that perspective.
By coincidence, I just came across some comments on a study by Fidelity Investments. Madeline Farber, in Time magazine, summed it up with a great quote:
“Women have long-term goals, and they stick with the plan,” Kathy Murphy, president of personal investing at Fidelity, told CNN. “They focus on saving and investing for retirement or a kid’s college fund, not on outsmarting the market [as men do].”
Good for women! I’m sure this is a relative statement, in the same sense that men tend to be taller than women, but not all men are taller than all women, or women tend to outlive men, but not all women outlive all men; so too the statement is a relative categorization of men and women: not all women and not all men behave according to the quote. But this is the point I’m making: outsmarting the market is only a means to an end, not the end in itself.
Yes, there is investment skill, but locating it is very difficult, and typically it isn’t worth paying for.
STAGE I 44: BROADEN THE DISCUSSION FRAMEWORK
Where the route takes us
After all the analysis, you still have to decide: active or passive. This stage lays out precise reasons that tilt you in one direction or the other — or both.
I said in Stage I 41 that typically the active/passive issue is discussed as if there’s a right answer and a wrong answer, and it’s your job to find the right answer. That’s unfortunate. The fact is that often it’s best to be partially passive and partially (sometimes necessarily) active (or at least not invest in the passive index). And you ought to understand when each of those choices is most appropriate for you. Let me explain.
As you might guess, I’ve written on the subject. My co-author Dr Geoff Warren and I agreed that the (capitalization-weighted) index for an asset class is the natural default potion to start from. What interested us was to identify situations when it makes sense to depart from that default position. We identified three kinds of situations.
The first (call it Reason 1) would be if there isn’t an index that you could replicate in a portfolio. For example, unlisted assets, private equity and real estate (property) are such asset classes. Essentially, you have no choice but to be active. Other relatively illiquid asset classes such as emerging market debt would also qualify.
Reason 2 applies when the weights used in an index aren’t appropriate. Divide this into two parts.
- Reason 2a is when the index conflicts with your purpose. For example, you may want to match drawdowns that are equal over the next five years. No fixed income index matches this series of cash flows. Buying a fixed income index therefore makes no sense; it is sensible, instead, to structure a fixed income portfolio that matches your cash flow needs. Another example is if you have good personal tax-related reasons not to match the index.
- Reason 2b is when you are sufficiently investment savvy to have a well-founded belief that capitalization weighting is inefficient. For example, there are such concepts as equally-weighted and risk-efficient indices that you may believe in as superior constructs. (Or, of course, you may accept your professional’s view on this superiority.)
Reason 3 applies when you believe you can outperform a passive index. This also splits into two parts.
- Reason 3a is the traditional one in which you believe you have superior skill relative to the other skilled investors in the market. This is the one that has been the focal point of the active versus passive debate, the one discussed in Stage I 43. So I’ll say no more about it.
- Reason 3b is when there’s a reason to believe that active management as a whole may outperform passive management. This needs explanation, since it is generally accepted that active management in the aggregate is necessarily the same thing as a well-constructed passive index, and therefore necessarily underperforms after costs are taken into account.
In fact, that last statement is only true when any departure from the index is construed as active management. But it’s more intuitive to think of active management as being defined as intentionally trying to beat the passive benchmark. And that prompts the obvious question: what other reason could you have for departing from the passive benchmark?
Plenty of reasons, as it happens. Investors have lots of different investment purposes (see Stage F 21). Dr Meir Statman notes that investors have three broad purposes: utilitarian, expressive and emotional. The utilitarian purpose is essentially what we’ve been discussing: getting a financial benefit. The expressive purpose is to want the investment to say something about you, such as the egotistical “Look what an exclusive group I belong to, holding this investment,” or (as a more widespread example) “I’m holding this set of investments because I believe strongly in supporting environmental, social and other ethical factors when I invest.” The emotional purpose is when an investment makes you feel good, which might also be true of pursuing environmental and other factors, or just holding an investment for a sentimental reason (like my cousin when he held one share of his favorite soccer team).
So only a subset of investors are genuinely trying to beat the passive index. Their average return may be above or below that of the passive index. And there are many attempts to discover when active (in the sense of deliberately index-competitive) investing may have a tailwind relative to passive. These, then, are times when it may make sense to be active.
Dr Warren and I go into further detail on these angles. Suffice it to say that our conclusion is that, rather than debating the relative merits of active and passive, it seems better to presume that the preferred approach is likely to vary across investors, markets and even time.
Three reasons to depart from passive investing are: (1) It isn’t available. (2) The passive set of investments isn’t consistent with your objective. (3) You really feel you have located active skill.
 This stage is based on a portion of Chapter 4, Ezra et al (2009).
 This stage is based on a portion of Chapter 4, Ezra et al (2009).
 Source: pages.stern.nyu.edu. Retrieved on May 14, 2016.
 This is the arithmetic average, not the geometric average. Most people don’t understand the difference, and it isn’t necessary for our purposes. I mention the difference only for the techies.
 These “annualized” (that is, annual average) numbers are geometric averages.
 Source: https://en.wikipedia.org/w/index.php?title=MSCI_World&oldid=715323098. Retrieved on May 14, 2016.
 For the global investments I used the returns in US dollars and adjusted for US inflation.
 This is the arithmetic average, not the geometric average.
 This is the arithmetic average, not the geometric average.
 Barber et al (2001).
 Ezra (1998).
 Global ICON Conference, Boston, MA, July 2014.
 Sorkin (2013). Retrieved on May 20, 2016.
 Ezra (2011a).
 www.investopedia.com/university/mutualfunds/mutualfunds2.asp. Retrieved on May 20, 2016.
 Ezra (2011a, op. cit.).
 http://time.com/money/4696534/women-better-at-investing-than-men/, viewed March 18, 2018
 Ezra et al (2010).
 Statman (2010).