Monday, June 04, 2007

Stocks vs Bonds: A Puzzle and Half a Solution

On average, buying stocks gives you a better return than buying bonds. That has been true for a long time. The return from stocks is less predictable than that from bonds, but the difference in return is large enough to make risk aversion an inadequate explanation. That, at least, is my understanding of the conclusion of those who have studied the question.

This presents an obvious puzzle to an economist. If stocks provide a better return than bonds, investors should shift to stocks. Once prices have adjusted to the shift, the future return on stocks should be lower than before, on bonds higher, and the process should continue until the returns are roughly equal, allowing for the different risks of the two kinds of investment. Yet that does not seem to have happened.

Some time ago I came up with a solution. Unfortunately, there is a serious problem with it. The purpose of this post is to explain the solution in the hope that someone else can see how to patch the hole.

I start with a simple assumption: All investors have inside information. Someone who works in a company knows a little more than outsiders about the prospects for that company. Someone who has made a career in an industry has a feel for what is happening in the industry. An enthusiastic customer in some niche market knows better than most which products are good and which firms are likely to prosper. One of the functions of the stock market is to put together all of this dispersed information and come up with stock prices.

Suppose I have expert knowledge of the industry I work in and money to invest. Investing all of it in that industry is risky, especially if I work in that industry, since I don't want the risk on my investments to correlate with risks to my income. So I invest some of it in the industry, taking advantage of my special information to do so, and the rest elsewhere. On the margin I am getting the return of an uninformed investor, on the average something between that and the return of an expert investor. Since everyone else is doing the same thing, everyone is getting that result.

What about investing in bonds? Since I have already invested as much as I want in the area of my expertise, investments in bonds substitute for the uninformed part of my investment. So, in equilibrium, the return on bonds will (ignoring any risk premiums) equal the return on my marginal investment in stock and be lower than my average return on stock--explaining why, on average, stock gives a better return than bonds.

The problem with this is that it depends on my uninformed investment giving a worse result than investing at random, since random investments ought to pay me the average return on stocks.

Anyone with a good solution? It's worth noting that the problem applies to other and more conventional views of the stock market. In order for clever investors to do better than average, someone has to do worse.

26 Comments:

At 4:11 PM, June 05, 2007, Anonymous Anonymous said...

Owners make more money than loaners - they HAVE to because they take way more risk. Now, not ALL owners make more money than loaners but on average they do because of the way capitalism is set up. Now just replace "Owners" with "People who invest in equities" and replace "Loaners" with "People who invest in bonds." As an equity investor, you can use smart diversification and suddenly you own two or three hundred of the best companies in the world. Using this strategy, and including EVERY SINGLE catastrophic event in modern history, an equity investor has averaged about a 10% annual rate of return vs bond holders at about 5.5%. Take away inflation (3%) and now equity investors have increased their purchasing power by 7% vs. bond holders at 2.5% - equities win by over twice as much. Who knows what will happen going forward but one thing is for sure: over the long run, owners will make more than loaners.

 
At 4:15 PM, June 05, 2007, Anonymous Anonymous said...

Oh, and volatility is your friend. Volatility is simply the price you pay for superior returns over bonds in long-term investing. Read this book: Simple Wealth, Inevitable Wealth by Nick Murray.

 
At 4:29 PM, June 05, 2007, Anonymous Anonymous said...

The key ingredient in investor success is not investment performance but investor behavior. The reason some equity investors do better than other equity investors is because they buy and hold a properly-diversified portfolio of equities EVEN WHEN THEIR PORTFOLIO DROPS 30-40% which is what it will do on average every 4-7 years.

 
At 6:36 PM, June 05, 2007, Blogger Patri Friedman said...

This explanation does not seem to fit the data, which is that the equity premium applies to index funds too. The only information you need to beat bonds is what stocks are in the S&P 500, which is not exactly inside information :).

There is a ton of academic literature about the equity premium paradox, if you are interested in it - lots of smart people have spent lots of effort on the subject.

 
At 9:43 PM, June 05, 2007, Anonymous Anonymous said...

David F. concludes: "Anyone with a good solution? It's worth noting that the problem applies to other and more conventional views of the stock market. In order for clever investors to do better than average, someone has to do worse."

Sadly, this is my role...

:-)

 
At 10:54 PM, June 05, 2007, Anonymous Anonymous said...

@ David Friedman
What a huge subject! There is NO Holy Grail.....
But here are a few thoughts from a poorly qualified but NOT naive trader.
I will dissect your Blog item just a little to help define the space for discussion.
Your quotes:
"On average, buying stocks gives you..." ... a ballpark figure where the profit 'lies in the detail' + timing. An average is a historical event with all the time lag inherent in gaining the data (or insider information).
It is already out of date. If for some reason it were predictive then there are a
zillion traders better placed than you to profit from any extrapolation.

"That has been true for a long time...." False, from around 1904. Extraordinary events like wartime are exceptions (unfortunately including about 36 hours following the 911 event).

"....to make risk aversion an inadequate explanation." Risk aversion = FEAR, has a twin which is GREED, acting in the opposite direction BUT AT A DIFFERENT, BUT VARIABLE, TIME FRAME.

"...the process should continue until the returns are roughly equal, allowing for the different risks of the two kinds of investment. Yet that does not seem to have happened."
It DOES happen each and every day 6 days a week some where on this planet.
But the professional trader dances between stocks, structured groups of stocks and fund arrangements, futures, commodities, index fluctuations, gold silver platinum etc, risk funding 'over night borrowing, as well as Bonds.
The dance routine is so rapid that there is not any leveling of returns. The professional trader is always seeking a difference and actively works with others to create difference.

"...All investors have inside information." Not so, the Retail trader while wishing to be an investor is in fact a member of the 'Herd', and is correctly regarded as naive and should be encouraged as He/She is there to provide the margin that the MarketMaker(s) require to feed the 'Market'...

"..One of the functions of the stock market is to put together all of this dispersed information and come up with stock prices." Heh, way wrong. The MarketMaker(s) are required by statute to provide an "Auction" process for Stock, Bonds, Futures, etc., in the majority of countries around the world. To make this facility sustainable they have been granted certain privileges, like no commision charges, not direct taxation, are permitted to trade in their "Own Account" and "On Behalf" through the same "books". They must be Heh Ha Ha LOL... "open and above board", but they are infact publicity averse and price information is only accurate for about 15 seconds, and volume data can be delayed "until a "contract had been run to conclusion"..
This may be as much as 90 hours.

"..Since everyone else is doing the same thing, everyone is getting that result." That is only true if everyone else is doing the same thing, AT THE SAME TIME!
Remember the MarketMaker is able to alter the Bid/Offer price at any time during the trading day and frequently do. The actual contract price is only good for 15 secounds, and the overnight price can change dramatically in either direction without notice.

"..explaining why, on average, stock gives a better return than bonds." Wrong again.
Refering now to Retail stocks investors; there is a widely held industry view that 95% of the Herd make a loss, some even rebuild a kitty and loose that maybe 2 or 3 times before the dream evaporates.

"...since random investments ought to pay me the average return on stocks." If you hold this view you should be physically restrained from investing in Stocks by your dependants.. LOL..
The Market may well be "Chaotic" but it is definately NOT random.

"..In order for clever investors to do better than average, someone has to do worse.."
The Herd is by definition the group that have to do worse and estimates vary but between 80 and 95% comply or learn to act in a less naive manner..

The following are a brief couple of points that may help you comprehend the enormity of your problem.

a) The MarketMaker actively seeks 'buy' and 'sell' orders from corporate executives, Government agencies, IMF, National and Local Banks, Managed Funds meeting their legal credit backing requirements, Managed Funds and Endowment Funds adjusting their portfolio, etc.
These financial organisations do not pay the usual commissions and buy in the open as the scale leads to pricing problems so they get the MarketMakers to do this quietly, and out of sight.

Note that the MM will seek to have the SAME stock from several sources on BOTH SIDES of his books from a variety of soucres, both buy and sell but with instructions to meet certain price objectives and at certain cost constraints.

The MM during this process has prior knowledge of business events which will eventually become investor news.
He will invariable, as of right, TIME the stock pricing moves to his abvantage.

Remember the MM has no commission fees and is doing invisible service for many very large professional investor organisations.
The only competitor for the MM is another MM, though when a contract is too large for an individual MM they will work together briefly.

The Herd is there only to pay for the process, they are not expected to get away with much of the margin.

b) Insider information about a Stock. Not refering to illegal Director activity where a Company Stock is misrepresented or dividends or splits are planned or a patent is confirmed.
More about how a stock price is changed.

Supply and Demand drive the pricing. Therefor the large investor can accumulate any loosely held stocks slowly and quietly without raising attention over time and WITHOUT RAISING THE PRICE.
Release of any 'bad news' to help the accumulation is not an accident.

The MM know of his instructions in his order book and sets about to make them happen, frequently "Testing for supply". When the Supply tests low the MM will then set about foster and encourage that price rise to the Herd.
This is when timeing of 'good news' is helpfull, and quite rapidly Distribution of all the Accumulated stock goes out at a profit.

The Herd finally will notice the price rise and rushes in to buy a climax, just in time to make a substantual loss in favour of the MM.

This comment is way too long.

If you want "Market is not chaos but simply Human Behaviour" let me know..

regards db..

 
At 4:04 AM, June 06, 2007, Anonymous Steve Dekorte said...

Is it possible you are underestimating the risk of default associated with bonds? Long Term Capital made this mistake...

 
At 6:25 AM, June 06, 2007, Anonymous Perry E. Metzger said...

Could it be a time preference issue?

Stocks provide higher returns over the long term, but that's useless to you if you need your money tomorrow. If you're retiring, you generally move your money from stocks to bonds to reduce risk and gain more predictable income. If you're managing money for short term use (say, operating capital for a corporation), you again tend to leave it in fixed income or even money market (short term expiry fixed income) securities.

Maybe the difference is explicable by risk premium alone, assuming that what people are interested in under some circumstances is not maximizing income but increasing predictability.

Another possibility comes to mind, but none of us would like it. Perhaps irrational fear of the stockmarket has kept the market inefficient. I would not be too quick to dismiss this possibility -- it is important that a scientist constantly check his basic beliefs.

 
At 11:12 AM, June 06, 2007, Anonymous markm said...

1. How was the risk premium estimated? It's likely that investors are more risk-averse when it comes to slapping down real money in large quantities than when they take a poll, participate in a market simulation, or even invest small amounts. Also, perhaps institutional investors (people investing other people's money) tilt towards bonds too much because high-rated bonds satisfy fiduciary duties to protect your client's capital pretty near automatically, while stocks almost always carry a risk of tanking and leaving you to explain why you picked the wrong one...

2. Time value, as Perry mentioned. No bondholder ever starved while waiting for a better market to sell...

3. Investor laziness. To buy stock intelligently requires all kinds of research, or else trusting someone else's research - and trusting that their report wasn't biased by an interest in selling you the stock. To buy bonds, you just need to know that the issuer is very unlikely to go under. This affects not only individual investors, but also corporate money managers who may have a lot of cash to park and limited time to find a large number of places to spread it around.

 
At 3:48 PM, June 06, 2007, Anonymous Anonymous said...

"I start with a simple assumption: All investors have inside information."

Even if that is true in a weak sense, almost everyone is better off not acting on their "inside information", because what little a person knows that the financial experts don't is more than canceled out by what the experts know that the "insider" doesn't.

 
At 1:26 AM, June 07, 2007, Blogger Amit said...

You write, “Once prices have adjusted to the shift, the future return on stocks should be lower than before,” but this is only true for dividends, no? People also buy stock in order to sell it at a higher price later, and the shift will affect both the buying price and the selling price, meaning the non-dividend returns will not be changed. Perhaps the shift has already occurred, and dividends play less of a role now.

 
At 6:00 AM, June 07, 2007, Blogger Marcus said...

How was the risk calculated? Is it based on the US market only? I ask because if there has been a conclusion that there is a return above and beyond what can be explained by risk aversion then that should be the first clue that the risk has been under-estimated.

In the long run stocks ride the ever rising tide of wealth where as bonds ride the ever rising tide of inflation (stocks too have an inflation component built into them but I'm simplifying).

The generation of wealth is vulnerable to many risks that bonds, especially government bonds, are not, such as socialist policies and/or protectionist policies and regulations. Stock prices are just a vote of Congress away from collapse. Bonds, especially government bonds, are not nearly as vulnerable to changing government policies (not that they don't have their own set of risks).

In general, if the data is based on primarily the US market, then to a large degree these risks have not been realized. There have been times worth looking at though. How did bonds fair against stocks in the 70's?

Hence, it is my argument, that your puzzle is caused by under-estimating the risk.

 
At 10:51 PM, June 07, 2007, Anonymous arthur b. said...

I think the answer does not lie in financial theory but rather in human behavior and psychology.

If people buy stock and they go down, they will tend to blame themselves for making a decision, although it may just be a pure lack of luck.

Passive investors are not responsible for the move of their portfolio, but small passive investors may be likely to feel responsible for bad performance. Since they want to avoid that feeling, they invest in bonds and are sure to feel good about themselves.

With the rise of mutual funds, this explanation would predict that the investor feels more disconnected from the result, hence invests more, leading to lower stock returns.

 
At 4:56 AM, June 08, 2007, Blogger Marcus said...

Have I misunderstood something here? From reading David's post I'm understanding the claim to be that stocks currently, according to academics, have a return above and beyond what can be explained by risk.

I think that means they have mis-evaluated the risk. I suggest that perhaps it is because their research is biased heavily by the US market.

Even so, the US market gives us clues. I have data going back to 1972. If one was to have invested $10,000 in 5-year treasury bills and another $10,000 in an S&P 500 index fund (had one existed at the time) below is by how much the S&P 500 investment outperformed the bonds (cumulative):

1972: 13.12%
1973: -7.75%
1974: -35.86%
1975: -18.36%
1976: -10.41%
1977: -18.54%
1978: -16.65%
1979: -5.52%
1980: 19.95%
1981: 3.94%
1982: -2.66%
1983: 9.93%
1984: 2.42%

Total value at the end of 1984:
S&P 500: $28,489
Bonds: $27,786

Were researchers claiming there was a premium return above and beyond what could be explained by risk in 1985? I seriously doubt.

Now today, after the longest bull market in history (1985-2006 with the only significant speed bump being the '01-'02 bear market) they claim stocks have a return above risk.

I don't think so. The single biggest risk to stocks are governments but in the US for the past 20-some-odd years this risk has been largely unrealized, biasing the data.

Case and point: Chavez nationalizing the oil industry. Just because Exxon had their property stolen by a government doesn't relieve them at all of their obligations to repay their bonds. Only stocks are effected by such thievery unless the thievery is so extensive it causes the company to go bankrupt.

Again, to a large degree this sort of thing doesn't happen in the US. But it can. We are at all times but an act of Congress away from it. I think stock returns reflect that and I suspect the academic evaluation of the risk doesn't.

 
At 10:22 AM, June 08, 2007, Blogger Taylor said...

David,

Check out Benjamin Graham's "The Intelligent Investor" if you care to understand this more thoroughly.

Worked for Warren Buffett.

 
At 4:47 AM, June 09, 2007, Anonymous DDR said...

When revenue comes into a company, bondholders stand in line in front of equity investors to get their share. Whatever is left after paying expenses (including interest expenses to bondholders) goes to equity investors. Thus, the equity investors get a much more volatile ride. Bondholders get disappointed only after equity investors have lost everything.

Thus, in the short run, bonds will give a much more predictable and reliable return. That predictability and reliability in the near term is worth money. So, the compensating factor is that stocks give a greater return in the long run.

 
At 8:37 PM, June 09, 2007, Anonymous arthur b. said...

@marcus,
did you factor in dividends in the S&P ? Merely looking at the index doesn't represent the actual return to the investor.
Your point about the government suddenly seizing property makes perfect sense, but you would guess that people adapt... I don't think people really expect the US government to drastically change its policy.And similarly, the risk of interference in country with history of interference should be priced in.

 
At 7:14 AM, June 10, 2007, Blogger Marcus said...

Hi Arthur,

Yes, the numbers I gave include reinvestment of dividends.

Of course the market adapts. The price to earning ratios of the S&P 500 in the 70's was less than 10. Today, it is around 17. That is a measure of confidence investors have in the future earnings of these companies.

Claiming that there is a return above risk is essentially the same thing as saying those price to earnings ratios aren't high enough. By who's standards?

Here's what we get to decide between, that A) either the market has mis-priced stocks or, B) that academia has mis-priced stocks. I'm inclined to believe B.

As to the potentiality of the government changing policies, just listen to the proposals of some of the candidates running. There are groups in this country that are actually convinced the economy is doing poorly. This after the kind of performance we've have for the past quarter of a century (thanks in no small part to the efforts of David's father).

It isn't the market that's irrational, it's government.

 
At 10:21 AM, June 10, 2007, Anonymous Anonymous said...

"Here's what we get to decide between, that A) either the market has mis-priced stocks or, B) that academia has mis-priced stocks. I'm inclined to believe B."

The claim of academics, as I understand it, isn't that stock prices are "wrong" but that there is an apparent inconsistency in risk aversion as expressed in stock prices as compared with risk aversion expressed in other contexts. This has nothing to do with differences in opinion over expected returns - you can directly *ask* investors what return they expect. There's no guesswork.

 
At 2:35 PM, June 10, 2007, Anonymous Anonymous said...

Hi David,

I hadn't realized until today that David Friedman the anarcho-capitalist was the same person as David Friedman who posts on rasfc :-)

I don't claim to be very knowledgeable about economics, but I'm curious to understand what you're saying better. When you say that "the difference in return is large enough to make risk aversion an inadequate explanation," can that statement be evaluated in the context of the capital asset pricing model? As far as I understand it, the CAPM says that every rational investor who wants less risk than the stock market's risk is guaranteed to have some money in bonds. It would then seem to me that the difference in price between stocks and bonds would depend entirely on people's preferences about risk, which are simply a matter of personal preference.

-Ben Crowell

 
At 9:51 AM, June 12, 2007, Anonymous Anonymous said...

What is risk? Risk is the possibility that you will outlive your money. If you hold a diversified portfolio of equities with equal parts of large-cap growth, large cap value, small-mid cap growth, small-mid cap value, international, real estate investment trusts and managed futures then you are not talking about risk, you are talking about volatility and they are not the same thing. Embrace volatility, diversify your equities and never sell - you will beet your neighbor who tries to make it more complicated than that. The most difficult part is the "never sell" part - few can actually do it.

 
At 7:02 PM, June 12, 2007, Anonymous Anonymous said...

"you are not talking about risk, you are talking about volatility and they are not the same thing."

That is confused thinking. If the money isn't available when you want it, it's no consolation that the shortfall is "mere volatility".

"The most difficult part is the "never sell" part - few can actually do it."

Few want to. Of course risk is completely eliminated if you never sell, because that implies you never want to spend the money. No desire for money = no risk = infinite risk tolerance.

 
At 12:39 AM, June 13, 2007, Blogger Brandon Berg said...

We know who's buying the bonds, right? Couldn't someone just ask them why they're doing it?

 
At 3:00 AM, June 13, 2007, Anonymous Felix Marian said...

Hi David,

the best explanations I have seen to the equity premium puzzle are myopic loss aversion(Bernatzi and Thaler, i think) and Rational belief theory (by Kurz). The problem with Arrow and Pratts coef. of risk aversion is the underlying assumption of rational expectations, which is far too simplistic and in many cases wrong.

I am not a fan of the insider theory you put forward. Workers in a company may have better information, occasionally, but whats worse is that they bring emotions into the game, which as any successful trader/investor will tell you will in 9 out of 10 cases lose you money.

 
At 6:26 AM, June 13, 2007, Anonymous Felix Marian said...

@Ben Crowell

"When you say that "the difference in return is large enough to make risk aversion an inadequate explanation," can that statement be evaluated in the context of the capital asset pricing model?"

When talking about risk averion we are generally to talking about the Arrow-Pratt coefficient of risk aversion which from experimental economics and observing risky choices is estimated to be around 2 for the average individual(I think). The observed difference in returns however would imply a coefficient of risk aversion of something above ten( I think its even in the region of 16). The underlying assumption here as noted earlier is a rational expectations framework. So the "Puzzle" is to figure out what accounts for this huge difference.

Myopic loss aversion suggests that if individuals "analyse/evaluate" their portfolios every 11 to 12 months, then the difference is almost completely explained. 12 months happens to coincide with the financial year and tax cycles, which would render this a plausible explanation.

Less Behavioural and more traditional economists like Arrow's successor Mordecai Kurz, believes that Rational Expectations is bullocks and that the reality looks a little less perfect. He proposes that while decisions are rational, ie are not contradicted by evidence available at the time, by observing "history", there is no reason why individuals with access to the same exact information should come up with the same expected value for a stock. When opinions are particularly divergent we see volatility and when opinions or rather "Beliefs" are coinciding in the market, then we bubbles or slumps.

Both theories are very interesting and I recommend having a read.

 
At 1:42 AM, December 15, 2007, Anonymous Anonymous said...

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