Lecture Notes on the Equity Premium: Part I

Lecture Notes on the Equity Premium: Part I
J. Bradford DeLong
March 2, 2006

There is, somewhere, a marginal investor: somebody just about indifferent between stocks and bonds. If the expected return to stocks were a little higher, he or she would move more money to stocks. If the extra risk associated with holding stocks were a little lower, he or she would move more money to stocks. In either case, that increase in demand for stocks would push their prices up, and so push the relative returns on stocks--which are the dividends that will be paid out on stocks in the future divided by the stocks' current price--down. But this marginal investor fears the risk as much as he or she values the return, and so does not move more money into stocks, and that is why the current price of stocks and the current value of the equity risk premium are what they are.

Now let's look at patterns of returns over the twentieth century, and try to figure out what this marginal investor has been seeing and thinking to make the equity risk premium what it has been, and then try to figure out what the current equity risk premium is.

Our first candidate marginal investor is someone who has some wealth that they want to invest for one year, and is considering whether to invest it in (relatively safe) one-year government bills (a "bill" is a short term bond) or in a (riskier) diversified portfolio of stocks. Figure 1 below plots the difference in returns for these two strategies for each year from 1900 to 2004--with the return differentials ranked from lowest to highest. 1931, with its (geometric) return differential of -60% (yes, 1931 was a bad year for the stock market) is at the far left; 1933 (the rich may not have voted for Roosevelt, but they certainly voted with their dollars that his "New Deal" was going to add value to American corporations) is at the far right.

Given this distribution of one-year returns over the twentieth century, the marginal one-year investor looks at it and reasons as follows:

Stocks certainly pay a healthier and higher return on average: over the twentieth century the inflation-adjusted real stock return has averaged 6.6% per year, while the real one-year Treasury bill return has averaged only 1.7% per year for an average gap of 4.9% per year. But look at all that extra risk: there's a 35% chance that you will do worse with stocks than bonds, a 10% chance that you will--relatively--lose more than 1/5 of your wealth if you put it in stocks, and in 1931 the (geometric) relative stock return was -60%! Considering the portfolio positions I already hold, the extra expected return to moving a little more of the wealth I'll need to spend next year out of bills and into stocks is simply not worth the risk.

Thus we understand why a--rational, reasonable, well-informed--marginal investor putting money away to spend in a year would not decide that stocks are underpriced, that the equity risk premium is appropriate. And so such a marginal investor would not put downward pressure on the equity risk premium.

The problem--the reason that the large value of the equity risk premium is called a "puzzle" is that the marginal one-year investor is not the only possible marginal investor. Consider the marginal twenty-year investor: somebody 40 with ten-year-old children who is putting money away to spend on his or her children's college, or somebody 50 saving for expenditures at 70 after they have retired. This marginal investor has to be satisfied with the configuration of asset returns as well. And what does the distribution of twenty-year-returns--either buy and hold a distributed portfolio of stocks (reinvesting the dividends) or buying and rolling over short-term Treasury bonds--look like? The answer is shown in Figure 2, which plots the twenty-year return differential over the twentieth century. The average return differential is (of course) the same: 4.9% per year. Over twenty years that cumulates to a lot: e^{20 x .049} = 2.67. But much more important is the lower tail: only 4% of the time do stocks do worse than bills over a twenty-year horizon. And the worst observation is the twenty years starting in 1965, when investing in stocks yields -0.84% per year less than investing in bills--a relative wealth loss of 17%.

What kind of investor would turn up a 96% chance of gain, associated with an expected more-than-doubling of relative wealth, that carries with it only a 4% chance of any relative loss and a maximum loss of 17% of relative wealth? Where is this twenty-year marginal investor, and what is he or she possibly thinking? All such twenty-year marginal investors should be furiously pulling much more money out of short-term bills and investing it into diversified portfolios of stocks, thus making the equity risk premium lower and stocks less of an overwhelmingly attractive long-run investment. That is the equity premium puzzle.

One possible answer that initially looked promising was that the marginal twenty-year investors had already moved all the money they could out of the short-term money market: that it was hard to short-sell Treasury bills (a large part of the value of them, after all, is certainty of immediate liquidity, which nobody other than the government can promise), and that the holders of Treasury bills are overwhelmingly institutions that needed them for specific institutional liquidity or transaction-cost-minimization reasons. The problem with this possible answer is that the same equity premium puzzle emerges when we look at twenty-year differential returns between diversified stocks and investment-grade corporate or longer-term bonds, which are extraordinarily widely held, and which do not have the special certain-liquid-value properties of short-term Treasury bills. Figure 3 shows the distribution analogous to that of Figure 2, where this time the marginal twenty-year investor is considering the relative returns to investing in a diversified stock portfolio (and reinvesting the dividends) as opposed to investing in a bond portfolio (and rolling maturing bonds over into new issues).

This time the lower tail is even smaller: in only 1% of the years in the twentieth century would investing in bonds for twenty years outperformed investing in stocks; and in that year--1929--the twenty-year returns to bonds would be only 8% ahead of the twenty-year returns to stocks. The equity premium puzzle is not due to the specific liquidity or collateral or other institutional properties of Treasury bills that make them especially valuable.

We have climbed into the box of the equity premium puzzle, which has now been locked and sealed with us on the inside. How are we going to get out of it? There are four possible roads, four possible arguments. They are:

1. The twenty-year-horizon marginal investors are very, very risk averse--so averse to risk that they should be too scared to dare get into the bathtup (Daniel Altman cleaned this up a bit).
2. There are no twenty-year-horizon marginal investors. Institutional features of Wall Street force everybody able to mobilize significant money to have a very, very short time horizon.
3. The distribution of actual returns over the twentieth century does not match the true ex ante distribution of returns: we've been very lucky. If we hadn't been so lucky, relative stock returns would not look nearly so impressive and there would be no equity premium puzzle.
4. Investors over the course of the past century have misjudged the return distribution: the true ex ante long-run return distribution matches the ex post distribution we see in Figures 2 and 3, but for one of a number of possible reasons investors have greatly overestimated the risk associated with lon-run diversified stock market positions.

To be continued...

Comments

[RonK, Seattle]

Got one of those in a logarithmic plot? (Noting that it takes a 25% relative gain to reverse a 20% relative loss, 100% gain to reverse 50% loss, etc.)

[Matt Austern]

Sorry, I'm still confused. What's the x axis?

[Carrie Underwood]

Brad:

A 3D graph, with time as your z-horizon,
would go a long way towards explaining
your conundrum, representing equity data
as a surface in time, rather than a line.

Then inputting that 3D surface into an
animation engine, so that the user can
"fly" the hundred years past leading up
to the present, soaring over the dips
and bubbles and crashes like a roller
coaster, would give you the "gut" that
science now confirms outperforms our
rational mind.

(recent study showing gut choice more
accurate than rational thought-out one)

?Why don't they present equity prices
as topological surfaces within a time-
domain and set chock-a-block with stock
avatars battling in some PS2 animation
investment game, complete with Buy Now?

How would I know? The equity and bond
markets ain't rocket science. More like
snake pits for autonomic reticuloids.

[Robert the Red]

Near the beginning: "If the extra risk associated with holding stocks were a little higher, he or she would move more money to stocks."

Don't you mean "a little lower"?

[anne]

Fine meticulous presentation. What puzzles me considerably is who might the 20 year investors be and how much of the market do they come to? Absent indexing, which begins in 1976 and took hold significantly only after 1990, what are 20 year investors beyond a Berkshire Hathaway or fixed endowments about?

[Nicholas Mycroft]

Still wondering why no one looks at 19th-century asset class returns in re the "risk premium puzzle." Two words: unanticipated inflation. There ain't no puzzle.

[anne]

John Bogle and David Swensen have stressed how few non-timing long term investors they find in individual and institutional circles, and Wall Street has been set up for anything other than long term investment. Also, realized gains from sotck investments are in fact decidedly less than idealized index gains. Then, why should we be surprised at a reluctance to fully and with stability invest a portfolio?

[meno]

Uh,

Maybe this is a dumb question, but what about diversity risk?

I can't invest in the platonic idea of "Stocks", just in some specific stocks. What if I picked the wrong ones?

In 2006 I can buy from Vanguard units of a fund that I'm sure is diverse, because it holds the top 500 stocks.

But was that sort of option readily available to the marginal investor in 1950? Or did she have to add in the risk that her stock portfolio was not diverse?

[Bernard Yomtov]

I also wonder who the 20-year investor is. Anne mentions endowments, but endowments have managers who do not wait twenty years to get their perfomance bonuses.

How many individuals have 20-year horizons? Even young investors may be, often are, looking at shorter periods.

[a]

Add a person's personal capital to his wealth portfolio - and this is probably the largest part of the portfolio for most people. For simplicity say there are three things in the portfolio: stocks, T-bills, and personal capital. I think there is probably a strong correlation between the return on stocks and the return on personal capital, and a less strong correlation between the return on T-bills and the return on personal capital. So people with strong personal capital are simply diversifying their risk. (And those without strong personal capital probably use a time frame which is closer to 1 year than it is to 20.)

[dsquared]

"There exists a marginal investor" is an assumption explicitly stated here, but "There exists an expectation of stock returns" is another assumption and I think it's tacit.

[Bruce Ferguoson]

Suppose someone with real wealth, say maybe 1B. How do you preserve that wealth? All you need do is beat inflation. Pretty much with bonds/time you can do that.
Now let's say you want to invest in a company. How are you going to do that? Well you find a good company with assets you can always sell if need be that needs some cash for some reason. You get them to sell you bonds. Lets say they promise you a 10% return with the option to take payment in options at the current depressed price of say 5$. A year goes by the stock goes to 20. You get the 10% plus the 100% increase via the options. So you dump the stock.

[John Stein]

This was a good presentation. I am 55. I have been invested in stocks for 20 years; for the first 2/3 of that only through my 401k/IRA, all in mutual funds with a small admixture of company stock. A few years ago I started investing in individual stocks (results mixed -- I don't spend enough time on it and may switch back to all funds). I'm not retired yet. So I'm a 20 year investor. Engineer. Financially pretty conservative (no debt except mortgage etc). I can tell you that until about 20 years ago I viewed the stock market "industry" with considerable distaste and distrust: there was a lot of hype, commissions were high (and remained high until online trading took off, as I recall), things did not seem transparent. Maybe there are a lot more folks out there who had a similar view. Maybe the fact that the Crash happened relatively early in the 100 years you plotted has something to do with people's view of the relative risk/reward. I'm not especially trying to defend my attitude -- I would have been better off modifying it sooner. On the other hand, there's no question that if I already had more than ample funds on which to retire, so that I didn't need the hoped-for extra return from stocks, I would stash it all in something safe like a rolling bond ladder, so as not to worry about the volatility. Even though I still have a 20-year horizon (heck, I hope it's a 40-year horizon!), as I get older it will be harder to compensate for unexpected downturns. It may not be that easy to go back to work if I need to, I may have high medical expenses, etc. It's the knowledge that those downturns are POSSIBLE that's the issue -- I don't get to live my life statistically y'know!.

[anne]

By fixed endowment, I mean a fund that must keep a given stock or small set of stocks indefinitely. But, turnover in investment portfolios is remarkable whether individual or instutional. The norm for stock turnover in mutual funds has for years been about 100%. I am continually puzzled by reports of high turnover in institutional funds and returns significantly less than index returns.

[John Stein]

By the way, I have done all that "safe withdrawal rate" modelling using actual stock returns (which include the Crash, the mid-1960s, etc). So I think I'm being as rational about it as I can. Still, this isn't engineering: I'm uncomfortable with the level of uncertainty. It's an effort to overcome my distrust.

[nate]

"I buy expensive suits. They just look cheap on me."

Warren Buffett

http://www.brainyquote.com/quotes/quotes/w/warrenbuff102760.html

[anne]

Remember 25 years ago, we had a price earning ratio for the S&P stock index below 10, while long term interest rates were above 10. Now we have a large cap p/e ratio of about 18, and long term Treasury rates about 4.6%. Interesting choices, and reasons continually given to be wary in 1980 and now of either stocks or bonds.

[nate]

you may need to look at real interest rates in addition to nominal rates. real rates may have been lower.

[nate]

http://economistsview.typepad.com/economistsview/2005/12/the_expost_real.html

see real rates above

[Francis]

Professor: as an overly-educated and overly-cautious investor, i will point out that your selection of a rising line is arbitrary. for those who fear failure more than they anticipate success (which is, apparently, most of us), it would be more accurate to put the best year at zero and show the less successful years (or periods of years) as a declining line from there.

second point: how rational was your marginal investor, over the time period at issue, to fear failure as much as he did? As an investor with a 20-year window ahead of me (just), I have the following significant concerns about investing: very high debt loads among american citizens (meaning they can't buy more stuff or stocks); upcoming retirement of baby boomers (stocks being liquidated); massive unfunded pension liabilities (corporate income diverted to pension obligations); staggering budget deficits (higher taxes coming); staggering trade deficit (recession coming); unprecedented corruption and partisanship in DC (political instability rarely good for stock market) and high p/e ratios (from watching the NASDAQ's fall, it seems that there is a limit to even americans's irrational exuberance, but we're right at the top of it).

maybe i'm being irrational, but it doesn't feel to me like i'm being irrational when i invest conservatively in this market.

[anne]

There's the problem, there is always reason to worry, and when there was a price earning ratio for the S&P stock index that was below 10 from 1977 to 1982, investors including professionals wished all too little to do with stocks. Nonetheless, they should have been in stocks and current worries have not prevented a terrific international bull market from October 2002, that should have swept away the bear market for reasonable investors.

[anne]

Since inception in 1976, the Vanguard S&P index has a 12.15% annual return, and there have been worries all the way through.

[Sam Taylor]

Brad-

Suggest you check out the Ibbetson-Sinquenfield (sp?) graphs from 25-30 years ago. They were much more informative.

Sam Taylor

[C]

How about that the vast majority of investors don't even factor 'expected return' into their decision making process, just whether they have a vague feeling that stocks or bonds are going to go 'up or down'.

And the ones that do consider expected returns and have long term time horizons, large institutional investors such as pensions, make it a policy to spend most of their funds matching their long term liabilities with fixed income investments.

And finally, the institutions and sophisticated investors not so constrained, would be foolish to leverage enough to close the premium, as the volatility in the markets would blow them out, or at least cause their capital to be pulled out from under them before returns were fully realized.

[mauisurfer]

Surprising that a man who owes a mortgage, and buys stocks, calls himself a conservative investor. The return on I-bonds is currently 6.73%, and it goes up with inflation, and can be cashed with almost no penalty (1 quarter's interest lost only if cashed during 1st 5 years). Plus, no state or local income tax. Perhaps I-Bonds should be your baseline to compare other investments.

[reason]

I wonder whether the returns to shares are overstated by "survival bias". That is if you look at indexes you see only firms currently with large capitisations. If a firm goes bankrupt or heads in that direction it disappears from the index. Does your calculation include the 100% loss made by holding ENRON shares for instance?

[glenn]

I'm a portfolio manager of public mutual funds, about $2Billion or so. I've got a finance degree, MBA, CFA, and I'm pretty comfortable with theory and with actual practice. I've given this issue some thought, but not much more than that. I appreciate Brad's analysis.

In my experience with the marginal investor - admittedly limited, I've got just over 10 years of experience in the market - the John Steins (comments above) of this world are in a severe minority, the top 2% or so of individual investors.

I find that many (perhaps most) individual investors cannot express their investment time horizon, their relative risk tolerance, nor their financial goals. Most do not think in terms of "the market" and "structuring a potfolio" or "investment horizon."

Most people want "hot stocks," they want them to work and they want performance, like, yesterday, man.

The CNBCs of this world (and idiotic monkey Kramer) have quickly gone from educating to entertaining. Combine that with a culture of instint gratification, and I get the impression that many people have a Texas Hold'em style investment mentality.

And let's admit, risk-taking and the aove behavior has only been rewarded. Over the past 20 years, the Fed has stepped in religiously, lowered interest rates and/or flooded the market. Almost an entire generation of investors know nothing but the Greenspan Put, get-out-of-jail-free cards for everyone!

I venture that equity risk premiums have come in dramatically during this time frame. And being a strong believer that mean-regression is even more powerful than love, something will cause equity risk premiums to increase again, perhaps gradually, but more likely due to a cataclysmic event.

[anne]

Actually there is a large persisting gap between index returns, or Vanguard returns, and returns from the rest of the investment service companies. The gap is more severe internationally, but is a special problem here. John Bogle has spoken to the gap for years, and now David Swensen of Yale is speaking to the issue. Eliot Spitzer has spoken to the issue and sought with courage to use the Attorney General office to help investors. But, there has been and is a severe problem with reading of returns before costs and realizing far less after.

[spencer]

I keep thinking, why is there an issue here.

Isn't it completely normal that ownership of a real asset should provide a higher return then ownership of a debt issue?

If it were not normal that ownership of a real productive asset provided a greater retun then a debt instrument it would not make sense for individuals of corporations to borrow to finance a capital investment.

But why call this a risk premium and/or assume that it has anything to do with risk?

[NinjaPlease]

Silly Meno, in 1950 women weren't holding stocks, they were busy defending freedom and not giving comfort to the enemy at home while taking valume. You know, when a family could be supported on one income, and people had bank accounts with positive numbers.

[anne]

Meno asks an important question and makes as important a point.

Until Vanguard and 1976, indexing was not possible and even then the use of index investing grew quite slowly. Vanguard did not hold more stock assets than bond assets until 1992. We can trace indexes values to the past, but not use indexes. The middle cap index is not 10 years old. The Vanguard REIT index is not quite 10 years old. The Europe index is just more than 15 years old.

[a]

"I find that many (perhaps most) individual investors cannot express their investment time horizon, their relative risk tolerance, nor their financial goals. Most do not think in terms of "the market" and "structuring a potfolio" or "investment horizon."

anne: this quote above may explain some of the fees. Some people who want and need to invest would be lost with a vanguard account and a 1 800 number. Some of the people on the other phone line at Vanguard do not know you and seem very young and inexperienced.

Spitzer is a government employee in the state of NY. He has done some good things, but he needs to realize who pays his salary, and that he is at the state and not national level (granted, the state with Wall Street so there may be some national implications for state employees of NY). Not everyone who makes a profit in business is a villain. We needed the Spitzer routine around the year 1999 and 2000. The Spitzer may be a little bit late and may have tinges of grandstanding and pandering for popularity.

I prefer terms such as "risk averse" in place of "conservative". You may find some investors who are very liberal in politics and very risk-averse (AAA bonds) in investments. You probably should not call such a person "conservative".

Also, you may find people with "conservative" politics who are risk-neutral or risk-seeking in investments and business (see Enron and Arthur Andersen).

Thus, I prefer investments and behavior to be described as risk-averse ... risk-neutral ... risk-seeking. Utility may also come into play. Some people are very bothered by volatility.

[anne]

Twenty-five years ago, the insurance industry controlled vast amounts of investments in terribly expensive and managed annuity funds. A more competitive mutual fund industry, not including mutual funds controlled by commercial banks on even Wall Street brokerages quickly took over investment volume during the 1980s and 1990s. But, while especially superior to funds controlled by insurance companies and superior to bank and Wall Street funds, investment costs for mutual funds save mainly for Vanguard remain much higher than reasonable.

[anon]

Vanguard is kind of like Wal Mart. Vanguard has done a lot of good and will lower prices. At some point, however, even the Vanguard routine reaches a point of diminishing returns. The Vanguards and Wal Marts of the world take stuff out-of-the product to keep the product cost low. The product (which includes service) ends up cheap and lower quality.

The S&P 500 is not at all-time highs, and has not been for a long time now. Tracking the S&P 500 was a great idea from 1982-2000, but who knows going forward whether this is a great idea.

The insurance industry does well because people do not like volatility. Insurance products often come with some sort of insurance that people (investors) will not lose principal. This means a lot to some people, and they are willing to pay for it. An investor does not want him or his family to face a forced liquidation at a low price.

That being said, I tend to think that some people over-insure because the fear and pain of a loss is greater than the joy of a gain.

[anne]

A, an interesting and important comment.

Eliot Spitzer, by the way, is impressive to me in terms of the necessary distinct and persistent consumer protection orientation given to the New York Attorney General's office.

[anne]

Well, if a person can find a finer fund than the Vanguard health care fund these 20 years or Vanguard energy or long term investment-grade bond fund for 30 years or high yield tax free bond fund, let alone the indexes, and a company offering finer and more transparent service, than I will be most pleased in knowing the industry is competitively improving.

Insurance, by the way, is for protection but surely not for investing :)

[anne]

What might a highly diversified portfolio have looked like over the last decade?

25% American total stock market index
10% middle cap index
10% health care fund
10% energy fund
15% real estate investment trust index

10% Europe index
10% emerging market index

10% intermediate term bond fund, taxable or tax free

[anon]

Anne:

Have you heard of a barbell bond portfolio?

http://www.investopedia.com/terms/b/barbell.asp

Because I know Anne appears to be a fan of Swensen... Anne: do you know what Swensen has to say on bonds? Does he like long-term or short-term maturities in a financial crisis?

http://thumb.shutterstock.com/photos2/thumb_small/3288/3288,1123494721,1.jpg

[anon]

Anne: you might consider "long-term" bonds (in addition to intermediate)

Pioneering Portfolio Management
by David Swensen

P 158
"By holding portfolios of high-quality, long-term, noncallable instruments, investors emphasize the attributes of bonds that provide the great protection in times of financial crisis. When investors seek refuge from the volatility induced by panics, securities backed by the full faith and credit of the U.S. government outperform risky assets, sometimes dramatically."

p171
"Portfolios of long-term U.S. Treasury securities promise to generate a steady flow of returns even in the most dire economic and financial circumstances, defining the fundamental justification for including in a portfolio the relatively low expected return asset class of bonds."

[...]

Only high-quality, long-term bonds perform well in times of severe stress, allowing investors to view the opportunity costs of holding bonds as an insurance premium...

[anne]

Anon, you are quite right about favoring long term bonds and would have been right for 25 years as long as you were keeping to a reasonably constant duration fund. I have always preferred Vanguard's long term bond funds. If you were willing to hold through a duration cycle, no matter the direction of interest rates you would have been better off than with an intermediate or short term bond fund.

Short term duration at Vanguard is 2 years, intermediate is 5, and long term 9 or 10.

[centrist]

Great discussion! Indexing is growing rapidly....I would love to hear everyones positions on the end game for indexing. At what point does indexing lose its advantage, and where would the edge be at that point?

[Michael Cain]

Glenn: "In my experience with the marginal investor - admittedly limited, I've got just over 10 years of experience in the market - the John Steins (comments above) of this world are in a severe minority, the top 2% or so of individual investors."

In a similar vein, a friend who is a financial advisor (who hires me from time to time for some statistical analysis) says that he sees no individual investors who have a real 20-year horizon. Nor, according to him, do most people understand their actual risk tolerance: almost all clients who claim they can tolerate a 20% drawdown will bail after losing 10%.

[anne]

What are the edges in indexing? Low cost in buying or selling a diverse portfolio, low cost of turnover and resulting capital gains taxes, low cost of timing wrongly since the portfolio is fully invested, not setting ourselves against the finest professional investors or traders, no mistaking management stock picking ability.

Why then should the efficacy and advantages of indexing be lost? There is a tillion dollars in hedge funds alone, using all sorts of trading strategies and ranging in success, but interestingly enough as far as research can show hedge funds as a market sector and with especially high costs trail comparable indexes as a sector. Still, hedge funds are the rage and and and there are those that are ever so successful :)

[anne]

What was it Clint Eastwood asked? Do you feel lucky today? Well, do you? Evidently lots of people do, from professionals to the rest. So, there is no reason to assume trading will go out of favor and since there is little competition on cost relative to quality in the financial services industry trading will go on at a cost at which the winners are "in house."

Now, me, I do not feel lucky today :) so I prefer to assume I will not be and invest anyway.

[anne]

I think it was "do you feel lucky, punk?" Nope, the idea for me is not to have to be lucky. Clint would understand :)

[anon]

http://www.bizjournals.com/denver/stories/2005/01/10/focus6.html

Luck favors the well-prepared

So i may not be feeling lucky, yet i should feel lucky.

[anne]

There is then a reasonable way for a non-professional investor to be personally prepared. Apart from whether feeling lucky or an old stick in the mud, a diversified reasonably permanent portfolio of index funds is one way. After all, a few funds and you have an American and international stock portfolio, real estate, for the REIT index serves for real estate, and bonds.

[anon]

i prefer wet blanket to stick in the mud.

http://www.answers.com/topic/wet-blanket

[anon]

let's assume someone out there can beat the index and has beat the index for many consecutive years... (~ 8 or so)

what incentive does that person have to work for "managers" in a legacy organization who do worse than an index (S&P 500 or industry index)? does something sound backward? who should be in management and who should be completing templates assigned by the management?

[J Mitzman]

One alternative reason you missed is that many small investors may believe that, to some extent, the system is rigged against them due to inside information rampant among large-scale investors and their brokers, and, to some extent deliberately bad advice given by all the free sources of guidance. To some extent it pays investment counselors with clients that don't hold a lot of money to deliberately give them bad advice so as to drive down the value of good stocks and drive up the value of one's that are already held in quantity by their larger investors. It's always possible to do market analysis for yourself, but most small scale investors don't really have the time for that, and even so won't do as well as those that have inside information into the market.

[anne]

Ah, but should there be a worry that others have more information than we can have, which is reasonable to assume when we are not professional invetors, there is another reason to index rather than a reason to avoid investing. As long as we have pensions or can save however, we really have no choice but to provide for ourselves by being investors.

[pgl]

My instincts point me to explanation #3. Then again - if #1 is correct, there is a strong case for your Soc. Sec. proposal aka the Great Risk Arbitrage play - but not for the George Bush hope that private investors will make that play on their own. Look forward to the next set of lecture notes!

[Kimmitt]

If index funds came around in 1976, a good test of the "transactions costs" hypothesis might be to see if the equity premium dipped shortly thereafter.

[STS]

Brad, what ever happened to your reading of Martin Weitzman?

Here's the key to that ridiculous "box" you're sitting in (taken from Jobert, Planaria & Rogers at Cambridge):

"Let us now motivate our Bayesian approach to these equity puzzles. In the Mehra-Prescott setup, the agent is assumed to know with certainty the distributional properties of the growth rate of dividends, but this assumption would be hard to defend in the face of the known imprecision in estimating rates of return. An example makes the point.

Example 1 (The 20's example). Suppose you observe daily prices for T years of a stock with an annual rate of return of 20%, and an annual volatility of 20%. You want to observe for long enough so that your 95%(= 19/20 ) confidence interval estimates of the parameters are good to 1 in 20 (that is your confidence interval is (+/-)1%).
(i) How large must T be to give this level of precision in the estimate of the volatility?

(ii) How large must T be to give this level of precision in the estimate of the rate of return?

The answers are: (i) about 11, (ii) about 1550!!

Thus uncertainty regarding the rate of return is enormous, and any analysis which over-looks this is unlikely to sit well with reality."

The full paper is at:
http://www.finance.group.cam.ac.uk/PREPRINTS/EPP.pdf

I think Weitzman & the paper above are saying roughly: "several 20th centuries wouldn't be nearly enough to establish the 96% confidence level you are claiming" -- *poof* goes the puzzle.

[Blissex]

The arguments about the 20 year investors seem plausible except that:

* It is very hard to be sure to be a full 20 year investor.
* The graph above for the 20 year investor is quite misleading.

As to the first point, investing all your funds for 20 years in quality bonds is a no brainer, as they have maturities and redemption values and pay interest. Investing all of them in shares instead exposes one to the huge risks of having to liquidate them at inopportune times, or of not getting income/capital gains for long periods of time. This depresses demand for stocks.

As to the second point is that different 20-year intervals have very different returns, and for several of these investing in stocks has been very bad, just like investing in bonds.

But investors look at absolute returns, not just at the difference between bond and stock returns. Because the risk to them is on the absolute, not relative, side, because while

so if the real returns in both stocks and bonds over some/several 20 year intervals can be (and it has happened) catastrophic in absolute terms, investors will invest in neither, even if stocks return more than bonds, but typically in real estate, which usually then returns more than either. Put another way, when both are doing badly, that returns on stocks are better than on bonds does not mean much.

Besides I would be astonished if that 20 year graph above discounted survivor bias; plenty of companies go bust in a 20 year interval, and indexes change a lot over 20 years, and there is the huge risk of buying a portfolio with an above average number of companies that will disappear...

[liberal]

"The Vanguards and Wal Marts of the world take stuff out-of-the product to keep the product cost low. The product (which includes service) ends up cheap and lower quality."

"Lower quality"? You have any actual evidence that Vanguard's products are lower quality?

[liberal]

Michael Cain wrote, "In a similar vein, a friend who is a financial advisor (who hires me from time to time for some statistical analysis) says that he sees no individual investors who have a real 20-year horizon."

I thought someone did a study and from actual investor behavior figured out that the typical implied time horizon is about...one year!

[Jack]

How does the supposed 20 year return distribution square with option prices?

I believe that long dated options cost rather more than this analysis suggests would be appropriate. Should Swensen and Buffett be selling heavy equity put options on the grounds that they are very overpriced?

[Bond investor]

Anne and Anon,

Your quoting of Yale investor Swensen's support of long-term bonds is incomplete. In his first (more technical) book relating to institutional investors, he notes most of these investors (pensions, foundations) have very long horizons.

In Unconventional Success, his follow-up for individual investors, he unwisely focuses on too short of a time period. (He also relies on very limited anecdotes to pooh-pooh any bond but supposedly default-risk free Treasures.)

The difficulty is that applying just 25 years of history to bond returns will of course give a great return for long bonds. Try doing 35 or 50 years -- not as good.

In general, I agree with you that mean reversion dictates that longer-term bonds should outperform shorter-term bonds, but that conclusion is turned on its head when the yield curve is inverted -- such as now.

Swensen's supposed "safest place" could be cash right now.

The real key is determining what the long-run average yield is on long-term bonds. Do you use 25, 50 or 135 years of history? As JP&R's paper notes (see STS' post above), your need 1550 years of history to be confident of the mean.

So it comes back to every bond investor's key question: does the yield curve move up or down from here?

[anne]

Bond Investor

Agreed :) Though I have not cared for bonds since 2003, for those who wish the relative safety I am only pointing out how safe a Vanguard "constant" duration bond fund will be. An increase of 1 percentage point in short term interest rates, will lower the price of a short term bond bond about 2% since the duration is about 2 year. But, the yield of the fund will increase so an investor will make back even the 2% in less than 2 years. For those who wish to invest in bonds indefinitely, it really makes sense to go intermediate or long and have no care for short term interest rate moves.

[Don]

(A) The assumption that "many" people have a 20-year time horizon might not actually be the case. I don't know about you but most of my friends had hardly a nickel to invest in their retirements until they were 40 years old. They were too busy paying down college debt and competing with other overly SPENDY boomers who blew giant $$$ on homes in good school districts in their 20's and 30's.

(B) All of these arguments rest on the assumption that the past is prologue. This has been proven FALSE countless times with individual stocks, stock funds, and now entire Indexes in the stock market. If we correct stock returns by "reverting dividend payout ratios to the mean (3.5% long term mean)", we are facing something like a 50% drop in stocks, and today's bond investor will look incredibly smart!

[anne]

Forgive me, but thinking the dividend payout ratio will revert to the long term mean seems awfully foolish and woulf already have cost an investor almost 20 years of excellent total stock market index returns, and this includes a 50% bear market decline.