Has the "Equity Premium Puzzle" Been Solved?

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Has the "Equity Premium Puzzle" Been Solved?

Post by SimpleGift » Mon Sep 07, 2015 3:56 pm

Apologies if the paper below, from January 2015, has already been discussed on the Forum.

The Equity Premium Puzzle: In short, the puzzle is the anomalously higher real returns of stocks over the real return of relatively risk-free bonds (chart below). Real returns from U.S. government bonds have been about 1% per year historically, while U.S. stocks have generated real returns of about 7% per year. Utility-based theories of asset prices have a hard time explaining (or fitting, empirically) why the first rate is so low and the second rate is so high — not only in the U.S., but around the world.

The Proposed Solution: In a recent paper (links below), Tsai & Wachter suggest that this high equity premium reflects the rare risk of a severe economy-wide disaster. In other words, the reason why equities generate such apparent outsized returns is that investors are being compensated for bearing the risk of rare, catastrophic market declines during economy-wide (and now global) disasters. Your thoughts?

Summary Article found here: Disaster Risk and Asset Pricing
Full Paper (very math heavy) found here: Disaster Risk and Its Implications for Asset Pricing
Cordially, Todd

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by nisiprius » Mon Sep 07, 2015 4:13 pm

I've done no more than skim the introduction, and don't think I'm capable of understanding or judging the rest, but... this is fascinating. It speaks directly to things that have been bothering me for a long time. The optimists are inclined to suggest that it isn't really fair to count the (supposedly) "ten-sigma events," because nobody could possibly have foreseen them, and they are never going to recur.
Crucial to understanding of rare disasters is to understand when they have not occurred, namely in the postwar period in the United States. A central contention of the rare disaster literature is that the last 65 years of U.S. data has been a period of calm that does not represent the full spectrum of events that investors incorporate into prices.
I really like the idea. Perhaps equity risk premium is not a reward for having to wait an uncertain amount of time to be almost sure of getting it, perhaps it's a reward for a serious honest-to-gosh risk of seriously losing your money and never getting it back.

("Jerry Tsai?" Did anyone else react to that the same way I did? :D I wonder if he's any relation... Gerald Tsai, 1929-2008, often called both "Gerry" and "Jerry" in print, was the man whose success transformed mutual funds from stodgy committee-driven play-it-safe vehicles to the star-manager mutual funds as we know them... or knew them, maybe.)
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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Mon Sep 07, 2015 4:30 pm

- I agree with the unrealized catastrophe theory. From historical data, investors should have typically been 80-100% equity, since over a long enough period they always outperformed bonds. Yet I have trouble rationalizing this allocation in the future since the future contains too much sheer uncertainty.

- Also some of the returns to equity are mere speculative returns, i.e. a bidding up in valuations, over and above the increase in the fundamental earnings. If you only count investment returns, the observed ERP would shrink -- though only by a little. Someone measuring the ERP at the height of the dot-com bubble would have extrapolated a massive ERP. But if they had focused on earnings instead of price they would have better estimated the long-run trend.

- No investor is really choosing between 100% stocks and 100% bonds, but a convex combination of the two extremes. The optimal portfolio is not 100% stocks, even from utility-based theory. The real question should be: given that the theoretically "optimal" equity weight X, why does the average investor hold equity weight Y < X?

- Part of the equity risk premium is a liquidity premium. Stocks can lose their value at any moment and take a decade or more to recover. Thus, investors without certain long run plans would rationally avoid stocks. And no one has truly certain long run plans. Thus even if the average investor actually holds his investment portfolio for an average of say N years, he may be anticipating a holding of n < N to hedge against the risk of a liquidity shock. Thus, ex-post, the portfolio will always be suboptimal, but because of basic risk aversion, grounded in utility theory, it is rational to plan for a shorter-than-average holding period to account for those shocks.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by SimpleGift » Mon Sep 07, 2015 4:34 pm

This paper may also help explain the "excess" volatility of stock prices, compared with forecasts of their future dividends and corporate cash flows. Ever since Mr. Shiller first identified this conundrum in Irrational Exuberance, I've been puzzled about it. "Rare disaster risk" is certainly a more elegant explanation than "animal spirits."
Tsai and Wachter wrote:Another basic question about the stock market pertains to the level of volatility. Various studies, beginning with Shiller (1981) have concluded that the volatility in the stock market is too great to represent forecasts of future dividends or other measures of cash flows of corporations. As memorably described by Shiller, the stock market appears to exhibit ‘excess’ volatility, namely volatility that cannot be attributed to rational factors and rather reflects (in the words of Keynes) the ‘animal spirits’ of investors.
 
Rare disaster models offer an alternative way to understand excess volatility. Rather than reflecting the day-to-day whims of investors, stock market fluctuations could reflect investors' changing views of the probability of a rare disaster. An increased probability of a disaster implies that future earnings are likely to be both lower and more risky. These effects combine to lower equity prices, even if a disaster itself does not take place. Thus, stock returns, which incorporate these probabilities, can be far more volatile than dividends or consumption, which reflect (primarily) the disaster itself.
Last edited by SimpleGift on Mon Sep 07, 2015 4:46 pm, edited 1 time in total.
Cordially, Todd

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by Clive » Mon Sep 07, 2015 4:42 pm

Simplegift wrote:Real returns from U.S. government bonds have been about 1% per year historically, while U.S. stocks have generated real returns of about 7% per year. Utility-based theories of asset prices have a hard time explaining (or fitting, empirically) why the first rate is so low and the second rate is so high — not only in the U.S., but around the world.
Why! If for a down-payment of the value of a piece of land you lend me that land, and later I return that land in exchange for the inflation adjusted down-payment amount then that's somewhat comparable to a cash deposit/bonds.

If I work that land, grow some crops and sell them for a overall profit then the land additionally provides a dividend. The assets (loans/debt/cash) are utilised to generally produce a dividend.

A risk is that valuations are volatile. Whilst generally the broad average provides satisfactory reward, buy a peak, sell a trough and rewards can be poor/negative. For the lucky that buy a trough sell a peak the rewards can be fabulous. To reduce the risk of a peak to trough you might time-cost average the purchase and sale; Or 50/50 and rebalance.

With bonds you lend to the state (or whoever) in return for a reasonable prospect of having the inflation adjusted amount returned at a later agreed date. They utilise that loan for their own potential benefit. With stocks you partake in the business activity and share in any profits risking your capital in the process.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by Clive » Mon Sep 07, 2015 4:54 pm

nisiprius wrote:Perhaps equity risk premium is not a reward for having to wait an uncertain amount of time to be almost sure of getting it, perhaps it's a reward for a serious honest-to-gosh risk of seriously losing your money and never getting it back.
Image

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Mon Sep 07, 2015 5:00 pm

Clive wrote:
nisiprius wrote:Perhaps equity risk premium is not a reward for having to wait an uncertain amount of time to be almost sure of getting it, perhaps it's a reward for a serious honest-to-gosh risk of seriously losing your money and never getting it back.
Image
The original paper was on the S&P 500, not the global stock market. Which is the right benchmark? Based on world returns, you could say the US was just a lucky case where the ERP rolled higher than usual. Therefore it was not known ex-ante that stocks were going to return as well as they did.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by lee1026 » Mon Sep 07, 2015 5:11 pm

Keep in mind that in many of these devastating episodes for stocks, bonds didn't do great either.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by larryswedroe » Mon Sep 07, 2015 5:51 pm

There's really nothing new here, it's long been proposed that the ERP is high because of the risk of stocks doing poorly at the same time labor capital is put at risk. This is old news
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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by Clive » Mon Sep 07, 2015 6:28 pm

Simplegift wrote:Real returns from U.S. government bonds have been about 1% per year historically
Historically pre 1900 UK government bonds rewarded near 4% real.
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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by Clive » Mon Sep 07, 2015 7:35 pm

lee1026 wrote:Keep in mind that in many of these devastating episodes for stocks, bonds didn't do great either.
Bills/notes/gold might have gained stock and/or bond purchase power though i.e. diversification.

An extreme variant of value and time diversification for a investor with longevity/heirs in mind might be to initially weight 50% into short term treasury in anticipation of drawing down such asset value over 20 years and (hopefully) broadly pacing inflation. Combined with a initial 50% in growth. Mindful of the risks, the growth portfolio might be comprised of 25% domestic stock, 25% foreign stock and 16.7% in each of long dated treasury bonds, short dated treasury bonds and gold.

As the income/drawdown basket is drawn down to zero over 20 years (2.5% SWR) and the growth basket grows/accumulates over 20 years that might average a overall equivalent of 18.75% domestic stock, 18.75% foreign stock 37.5% short term treasury and 12.5% in each of long term treasury and gold - that since 1972 lagged 100% total stock market by around 1.4% annualised https://www.portfoliovisualizer.com/bac ... Bond1=12.5

Growth expanding from a initial 50% weighting to being 100% final weighting (after drawdown bonds are spent) is a form of time averaging. Stock/bonds rebalanced is also a form of reactive averaging. With such extreme averaging the broad overall average is more inclined to reflect the broader average and in so doing avoid the worst case outcome.

For a UK investor since 1900 in the rare case when the growth basket didn't at least double in real terms over 20 years (i.e. 3.5% annualised real), typically extending the end date by a few years recovered to have produced a real gain double-up i.e. also averaging the end date nigh on eliminated risk.

If such a value averaged/time averaged, widely diversified choice is considered as the near risk-free rate, and 100% stock since 1972 has provided just a 1.4% higher annualised, then one interpretation might be that the risk-premium of 100% stock was just 1.4% and not the 6% as indicated in the article. That's a relatively small risk-premium in consideration of the risks IMO.

There's a plethora of risks and T-Bills, inflation bonds etc. have their own specific risks. There is no risk-free actual real world asset and as such the next best choice is to value average/time average, diversify in order to increase the prospect of achieving a comparable outcome to the broader average (as that average is generally a good/reasonable outcome).

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by SimpleGift » Mon Sep 07, 2015 8:40 pm

One observation about "rare disasters" is that their frequency and magnitude appears to have declined substantially since the early part of the 20th century (first chart below). After World War I, the Great Depression and World War II, it's a wonder that anyone would dare invest in stocks at all by 1945!
This raises a question whether the decline in the frequency and magnitude of rare disasters worldwide is partly responsible for the decline in the realized equity risk premium over the past century (chart below)? In other words, has an increasingly stable global economy led to less risky stock investments overall and higher equity valuations?
  • Image
    NOTE: Chart shows 10-year, realized equity risk premiums over bonds.
    Source: Seeking Alpha
Last edited by SimpleGift on Mon Sep 07, 2015 8:45 pm, edited 2 times in total.
Cordially, Todd

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by lee1026 » Mon Sep 07, 2015 8:42 pm

Bills/notes/gold might have gained stock and/or bond purchase power though i.e. diversification.
I am not sure what bills or notes you are referring to here. But in many of the countries mentioned, hyperinflation would have zeroed out any savings in bills or notes. Japan, Germany (twice!), Austria (twice!). Even France to a lesser extent.

Gold may have done better; but gold have its own problems. In Nazi Germany, personal ownership of gold was not permitted. I don't believe it was allowed in Imperial Japan either, but I could of course be wrong on that one.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by nisiprius » Mon Sep 07, 2015 8:54 pm

Simplegift wrote:This raises a question whether the decline in the frequency and magnitude of rare disasters worldwide is partly responsible for the decline in the realized equity risk premium over the past century (chart [above])? In other words, has an increasingly stable global economy led to less risky stock investments overall and higher equity valuations?
The more I think about it, the less I believe it. It implies a degree of clairvoyance and rationality that is hard to credit. The marketplace looking ahead through the decades and quantifying the number and severity of upcoming black swans?

In the late 1950s were investors saying "The Soviet threat is fading, the nuclear arms race is just posturing? The number of nuclear warheads will climb constantly up to 30,000 in 1967, but not one of them is ever going to be fired in anger or by accident? There are bound to be things like the Cuban missile crisis ahead but they won't really amount to much? So, now that there isn't much threat of nuclear annihilation, the chances of anything going wrong with stocks are decreasing and we're willing to pay more for them?" That's what was happening in 1957-1970? Really?
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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Mon Sep 07, 2015 9:13 pm

nisiprius wrote:
Simplegift wrote:This raises a question whether the decline in the frequency and magnitude of rare disasters worldwide is partly responsible for the decline in the realized equity risk premium over the past century (chart [above])? In other words, has an increasingly stable global economy led to less risky stock investments overall and higher equity valuations?
The more I think about it, the less I believe it. It implies a degree of clairvoyance and rationality that is hard to credit. The marketplace looking ahead through the decades and quantifying the number and severity of upcoming black swans?

In the late 1950s were investors saying "The Soviet threat is fading, the nuclear arms race is just posturing? The number of nuclear warheads will climb constantly up to 30,000 in 1967, but not one of them is ever going to be fired in anger or by accident? There are bound to be things like the Cuban missile crisis ahead but they won't really amount to much? So, now that there isn't much threat of nuclear annihilation, the chances of anything going wrong with stocks are decreasing and we're willing to pay more for them?" That's what was happening in 1957-1970? Really?
It doesn't need to be perfectly clairvoyant and rational. It can be entirely behavioral. As investors feel more confident in the stability of equity markets, the perceived equity risk premium diminishes. Whether the actual equity risk premium has diminished -- only time will tell.

This is why market crashes happen. The stock price declines a little bit, and perceptions of equity risk go up, so people sell more to get out of risky equities, etc. and it creates a massive feedback loop where an initial price change of -5% amplifies into -50%. It's what Shiller would call "irrational exuberance" or Keynes "animal spirits." No one understands it -- it just happens!

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by Clive » Tue Sep 08, 2015 2:35 am

Simplegift wrote:One observation about "rare disasters" is that their frequency and magnitude appears to have declined substantially since the early part of the 20th century
Paradigm shift. When gold and money were one and the same there tended to be equal amounts of (volatile) inflation/deflation

Image

Progressively breaking away from the gold standard has enabled the value of money to be 'revised' that gives the impression of greater stability. Looked at from a Dow/Gold perspective and volatility (GDP contractions) might be as volatile

http://www.macrotrends.net/1378/dow-to- ... ical-chart

Were their any changes in the GDP calculation? For instance the imputed rent of all properties, owner occupied or not are counted and the proportion has risen considerably (typically representing around 10% of GDP in more recent times (decades)). The concept being that it levels the field, not mattering if a home is owned or rented. Consider if a revision of GDP calculation were also made to include the imputed rent from cars, you buy a car and the imputed cost to rent each and every car for each day might give the impression of greater GDP stability. 40 million cars in the UK, £100/day to rent a car and the UK GDP would be uplifted by close to £1.5 trillion/year and that figure would be relatively stable (number of cars).

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by Clive » Tue Sep 08, 2015 3:07 am

bh7 wrote:As investors feel more confident in the stability of equity markets, the perceived equity risk premium diminishes. Whether the actual equity risk premium has diminished -- only time will tell.
In the 1700's and 1800's treasury bonds paid near 4% real. Money was backed by gold and the risk of default were higher than in the 1900's onwards as money was de-coupled from gold. Nowadays taxes can be raised or more money printed such that the risk of a 'default' is near eliminated and bond yields have dropped more towards 0% real in reflection of such low default risk. The default risk of stocks in contrast persists and as such a premium is required to counter that risk. 6% real is reflective of a 6% default risk - perhaps a 12% chance of only getting half your inflation adjusted money back. Corporate bonds have less of a default risk and might be priced to a 3% real.

Japan 1990, Iceland 2009 ... amongst others, indicate that equity risk is still evident in more recent decades and as such still commands a risk-premium.

The main risk as I see it is that many count survivorship and right tail outcomes as being the average, ignoring the left tail failures/positions, leading to higher expected reward than what might be achieved in practice. Dow for instance created three indexes, two of which have lagged the 'evolved' Dow Industrial. Back in the late 1800's a investor might have invested equally in all three (transport, utility, industrial) and as such lagged the Dow (industrial) 'average'.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by SimpleGift » Tue Sep 08, 2015 3:23 am

Clive wrote:Progressively breaking away from the gold standard has enabled the value of money to be 'revised' that gives the impression of greater stability.
Not sure I understand your point, Clive. Increasing price stability over the decades has been one of the hallmarks of the 20th century. A quick review of the U.S. inflation history (similar to the U.K. charts you posted above):
  • • Prior to the end of the gold standard in 1933: Yearly price growth averaged 1.3%, which seems benign, but it had a standard deviation of 10.9%. Companies would have to expect yearly inflation growth anywhere between -21.1% and +22.3%.

    • From 1950 to today: The CPI averaged 3.7% per year — a much higher growth rate — but the standard deviation was only 2.8%. Businesses would only need to prepare for inflation between -2.0% and +9.2%.

    • Since the Fed tamed inflation in 1982: Yearly CPI gains have averaged 3.0%, with a standard deviation of only 1.3%.
Certainly, inflation in the U.S. has accelerated since the end of the gold standard and the start of Fed management — but the volatility of prices has become much more muted. This has created a much more stable, predictable environment for business investment, the growth of company earnings and, perhaps, lower equity premiums.

PS. Let's kindly not forget that the topic of this thread is rare disaster risk and the equity premium!
Cordially, Todd

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by dumbmoney » Tue Sep 08, 2015 5:20 am

Theory heavy papers should be read as suggestions rather than descriptions. I don't believe for a second that investors are forecasting rare events, but maybe they ought to.
I am pleased to report that the invisible forces of destruction have been unmasked, marking a turning point chapter when the fraudulent and speculative winds are cast into the inferno of extinction.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by JoMoney » Tue Sep 08, 2015 5:27 am

I think the simpler answer to the "equity premium puzzle" is that their measurement of risk is wrong. Why puzzle over why the measure of risk doesn't adequately explain the returns of equities, when it could just be accepted as another empirical example of how the measure of risk is imprecise and perhaps based on a faulty premise to begin with.
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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Tue Sep 08, 2015 6:40 am

Simplegift wrote:
Clive wrote:Progressively breaking away from the gold standard has enabled the value of money to be 'revised' that gives the impression of greater stability.
Not sure I understand your point, Clive. Increasing price stability over the decades has been one of the hallmarks of the 20th century. A quick review of the U.S. inflation history (similar to the U.K. charts you posted above):
  • • Prior to the end of the gold standard in 1933: Yearly price growth averaged 1.3%, which seems benign, but it had a standard deviation of 10.9%. Companies would have to expect yearly inflation growth anywhere between -21.1% and +22.3%.

    • From 1950 to today: The CPI averaged 3.7% per year — a much higher growth rate — but the standard deviation was only 2.8%. Businesses would only need to prepare for inflation between -2.0% and +9.2%.

    • Since the Fed tamed inflation in 1982: Yearly CPI gains have averaged 3.0%, with a standard deviation of only 1.3%.
Certainly, inflation in the U.S. has accelerated since the end of the gold standard and the start of Fed management — but the volatility of prices has become much more muted. This has created a much more stable, predictable environment for business investment, the growth of company earnings and, perhaps, lower equity premiums.

PS. Let's kindly not forget that the topic of this thread is rare disaster risk and the equity premium!
If I'm a long term investor I would prefer to buy a long term bond prior to 1933 than after 1982. Annual volatility is just short run noise that cancels itself out in the long run. What matters is: can I buy a 30 year treasury bond and be assured of its value 30 years from now? Prior to 1933 the answer was 'yes'. Today the answer is 'no'. Inflation has been 1.3% since 1982, but how can we be sure that it won't increase again? The government has after all the power to inflate the money supply at any time completely at will. Do you trust your government to maintain the price level, given its track record? I'm not sure I do.

Fortunately we have TIPS, which if not perfect, preserve wealth much better than nominal treasuries. I would never let nominal assets become more than 20% of my portfolio based on historical returns. Inflation risk is a fat-tailed event -- most decades are fine, but the ones that aren't fine like the 70s are completely devastating to a nominal bond portfolio.
Simplegift wrote:
  • Image
    NOTE: Chart shows 10-year, realized equity risk premiums over bonds.
    Source: Seeking Alpha
This is not a chart of the "equity risk premium". This is a chart of the "equity risk premium minus the inflation risk premium." The realized inflation risk premium was very high coming from the 1970s when inflation fear was high but never materialized.

What you really want is a chart of the returns of equities minus TIPS. Unfortunately TIPS data doesn't go back very far.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by backpacker » Tue Sep 08, 2015 7:14 am

Tsai and Wachter think that the possibility of events worse than the great depression help to explain the ERP. For historical precedent, they point to Austria and France in WWII.
Tsai and Wachter wrote: But the Great Depression was, relatively speaking, a minor event. During the Great Depression, consumption declined by 21%. Compare this to the catastrophic effect of World War II on countries in Europe; consumption declined in Austria by 44% and in France by 58%.
Problem is, government bonds did worse than stocks in Austria and France during WWII. Here's what happened in Austria (from the Credit Suisse yearbook):

Image

Here's what happened in France:

Image

The small risk of extreme financial disasters only explains why stocks beat bonds if, during those disasters, stocks do worse than bonds. The problem is that this is often not the case. If the government confiscates your assets, they confiscates your bonds and your stocks. If your country is conquered by a foreign army, your bonds and stocks are both going to zero. If there is hyperinflation, your stocks are going to be hurting, but your nominal bonds will implode. Whether inflation protected bonds help will depend on the country. I wouldn't trust a country that is hyper-inflating its own currency to treat its inflation protected bond holders very well.
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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by backpacker » Tue Sep 08, 2015 7:25 am

JoMoney wrote:I think the simpler answer to the "equity premium puzzle" is that their measurement of risk is wrong. Why puzzle over why the measure of risk doesn't adequately explain the returns of equities, when it could just be accepted as another empirical example of how the measure of risk is imprecise and perhaps based on a faulty premise to begin with.
Or at least the measure of how investors perceive risk is wrong. I like the idea that prospect theory solves the equity risk problem. The psychological observation is that investors hate small losses about twice as much as small gains, and this generally holds regardless of how much absolute wealth they have. So investors hold less stock than is "rational" and this drives up the price of bonds relative to stocks.
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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by larryswedroe » Tue Sep 08, 2015 7:29 am

backpacker
The more you increase the size of the loss/gain the higher the ratio goes, just ask yourself this question, you might take a bet of your $10 to someone's $20 on one flip of coin, but would you do the same at say $100,000 to $200,000. The greater the amount involved the more risk averse we become and the people who have the most wealth have the least need to take risk so they require a high ERP to invest.
Larry

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Tue Sep 08, 2015 8:59 am

larryswedroe wrote:backpacker
The more you increase the size of the loss/gain the higher the ratio goes, just ask yourself this question, you might take a bet of your $10 to someone's $20 on one flip of coin, but would you do the same at say $100,000 to $200,000. The greater the amount involved the more risk averse we become and the people who have the most wealth have the least need to take risk so they require a high ERP to invest.
Larry

Hi Larry,

So you assume Increasing Relative Risk Aversion (IRRA)?

I have always assumed the opposite: Declining RRA (DRRA) converging to Constant RRA (CRRA). This is consistent with the following 5 pieces of evidence off the top of my head:

1. Empirically estimates of the Stone-Geary utility function [u(c)=(c+a)^(1-b) / (1-b)] have a negative consumption offset (a)
2. The practical wisdom of establishing a cash-only emergency fund before investing in risky assets.
3. There is a theoretical construct known as Precautionary Savings which implies an emergency fund to protect against income or expense shocks.
4. The strategy used by many here of of keeping "N years in bonds, rest in equities."
5. This table from Stigliz (1962) "The Effects of Income, Wealth, and Capital Gains Taxation on Risk-Taking"
Image

Best

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by larryswedroe » Tue Sep 08, 2015 9:50 am

bh
From at least my experience as people get wealthier they switch from playing the game of wealth accumulation to one of wealth preservation, the marginal utility of wealth falls and requires larger and larger ERP to take risk of stocks. That's logical as need to take risk declines as wealth grows. And it's standard utility curve that bends sharply to the right at some point, though never declines.

The early part of the utility curve is very steep as people willing to take risks as even small changes in wealth can make big changes in quality of life, so they have high marginal utility of wealth. But we know for example that happiness isn't any different in US once you get above about on average $75k in annual income, obviously depending on where you live

Larry

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by backpacker » Tue Sep 08, 2015 10:25 am

larryswedroe wrote:backpacker
The more you increase the size of the loss/gain the higher the ratio goes, just ask yourself this question, you might take a bet of your $10 to someone's $20 on one flip of coin, but would you do the same at say $100,000 to $200,000. The greater the amount involved the more risk averse we become and the people who have the most wealth have the least need to take risk so they require a high ERP to invest.
Larry
I think what we're saying is compatible. I agree that marginal utility is generally decreasing. Your first million is usually worth more than your second million, your second million is worth more than your third, and so on. It's generally agreed, though, that decreasing marginal utility on its own isn't enough to explain the ERP.

The insight of prospect theory is that investors anchor their expectations. They pick a portfolio value x and then classify future outcomes as "gains" or "losses" relative to x. And they care a lot about not experiencing outcomes that they classify as "losses". This leads them to be far more sensitive to even small losses than they "should" be.

Another way to think about it: According to prospect theory, once an investor has $2 million dollars, she cares a lot more about having $2 million dollars than when she only had $1 million.
Last edited by backpacker on Tue Sep 08, 2015 10:38 am, edited 1 time in total.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Tue Sep 08, 2015 10:36 am

backpacker wrote:
larryswedroe wrote:backpacker
The more you increase the size of the loss/gain the higher the ratio goes, just ask yourself this question, you might take a bet of your $10 to someone's $20 on one flip of coin, but would you do the same at say $100,000 to $200,000. The greater the amount involved the more risk averse we become and the people who have the most wealth have the least need to take risk so they require a high ERP to invest.
Larry
I think what we're saying is compatible. I agree that marginal utility is generally decreasing. Your first million is usually worth more to you than your second million, your second million is worth more than your third, and so on.

The insight of prospect theory is that investors anchor their expectations. They pick a portfolio value x and then classify future outcomes as "gains" or "losses" relative to x. This leads them to be more sensitive than they "should be" to even small losses.
Just to be absolutely clear: diminishing marginal utility of wealth (i.e. positive risk aversion) does not predict that one would take on less risk as they get wealthier. To be clear, to take on less risk, you need the assumption of increasing relative risk aversion.

The poor guy might not necessarily invest more in risky assets because although his upside is greater than the rich guy's upside, his downside is also much bigger as well. The fact that risk aversion is positive doesn't tell you whether relative risk aversion is increasing or decreasing in wealth. For that you need specific assumptions about the risk aversion curve.

I think there is far more evidence that shows relative risk aversion decreases with wealth. The rich have less need for risk, but their ability to take risk is also greater. The poor have a need for risk, but their capacity is much much less because one bad stock year coupled with sudden unemployment can leave them on the streets. Whereas the rich will have more than enough cash to cover emergencies. The reason Warren Buffet is recommending 90/10 for his wife with $1 billion is because at $1 billion the capacity is basically infinite, as no one individual would even spend 10% of that sum in their lifetime. It has been recommended here that individual's without warren buffet's wealth go with a lower equity allocation.

Yes there could be a sharp "kink" in the utility curve past $75k, but I'm not sure there is any empirical evidence to support that claim. I would certainly like to see it if there is. That's an idea that has been spread a lot in pop journalism but I haven't seen a peer-reviewed academic study support it. But speaking of pop journalism, I have read that most millionaires actually feel like they need approximately double their wealth to "be happy". If they have $1m they need $2m. If they have $2m they need $4m. Happiness is fleeting. Once you're on the hedonic treadmill, it's hard to get off.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by backpacker » Tue Sep 08, 2015 11:03 am

bh7 wrote:
backpacker wrote:
larryswedroe wrote:backpacker
The more you increase the size of the loss/gain the higher the ratio goes, just ask yourself this question, you might take a bet of your $10 to someone's $20 on one flip of coin, but would you do the same at say $100,000 to $200,000. The greater the amount involved the more risk averse we become and the people who have the most wealth have the least need to take risk so they require a high ERP to invest.
Larry
I think what we're saying is compatible. I agree that marginal utility is generally decreasing. Your first million is usually worth more to you than your second million, your second million is worth more than your third, and so on.

The insight of prospect theory is that investors anchor their expectations. They pick a portfolio value x and then classify future outcomes as "gains" or "losses" relative to x. This leads them to be more sensitive than they "should be" to even small losses.
Just to be absolutely clear: diminishing marginal utility of wealth (i.e. positive risk aversion) does not predict that one would take on less risk as they get wealthier. To be clear, to take on less risk, you need the assumption of increasing relative risk aversion.
Ah, right.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by SimpleGift » Tue Sep 08, 2015 1:20 pm

backpacker wrote:The small risk of extreme financial disasters only explains why stocks beat bonds if, during those disasters, stocks do worse than bonds. The problem is that this is often not the case. If the government confiscates your assets, they confiscates your bonds and your stocks. If your country is conquered by a foreign army, your bonds and stocks are both going to zero. If there is hyperinflation, your stocks are going to be hurting, but your nominal bonds will implode. Whether inflation protected bonds help will depend on the country. I wouldn't trust a country that is hyper-inflating its own currency to treat its inflation protected bond holders very well.
One can't argue with your historical facts — but I wonder how much of your (excellent) historical analysis still applies to modern investors in the 21st century. In other words:
  • • Among developed countries, is there really a great risk today of a destructive land war on one's home soil?

    • With modern central banking, is there really a risk of hyperinflation in most developed economies?

    • With the exception of a few state-controlled economies, is there really a risk of asset confiscation in the modern world?
My point is that, with the type of catastrophic risks currently facing investors today (e.g., global pandemics, environmental collapse, deflationary shocks, etc.), it still seems a fairly sure bet that government bonds are safer than stocks — despite the exceptional cases you've identified in the aftermath of World War II.

PS. Personal disclosure: our asset allocation is 50% stocks/50% bonds — and will be for our lifetimes.
Cordially, Todd

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Tue Sep 08, 2015 1:38 pm

Simplegift wrote:PS. Personal disclosure: our asset allocation is 50% stocks/50% bonds — and will be for our lifetimes.
Is that nominal or real bonds? If nominal, do you not worry about inflation risk? Historically nominal bonds have had serious inflation risk. The worst inflation risk over 10+ year periods has actually been more severe than the worst equity risk, with 100% 10y treasury bonds returning -7.2% real in its worst decade but 100% stock returning at least -4.35% real in its worst decade. While 50/50 appears to be the portfolio of minimum 10y risk, in nominal terms, actually 80/20 held the minimum 10y risk in real terms

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by roflwaffle » Tue Sep 08, 2015 1:55 pm

Besides the risk of large scale economic downturns, I imagine part of the equity premium is due to having substantial periods where returns were next to nothing or negative, like 1963-1975. In that case, if you could wait until 1987, your real growth rate jumps from nothing to ~4+%, but not being able to touch an asset for two and a half decades is tough for some folks. :beer

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by siamond » Tue Sep 08, 2015 2:34 pm

Thank you, simplegift, for yet another fascinating thread...
JoMoney wrote:I think the simpler answer to the "equity premium puzzle" is that their measurement of risk is wrong. Why puzzle over why the measure of risk doesn't adequately explain the returns of equities, when it could just be accepted as another empirical example of how the measure of risk is imprecise and perhaps based on a faulty premise to begin with.
Totally agreed...

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by SimpleGift » Tue Sep 08, 2015 2:48 pm

bh7 wrote:
Simplegift wrote:PS. Personal disclosure: our asset allocation is 50% stocks/50% bonds — and will be for our lifetimes.
Is that nominal or real bonds? If nominal, do you not worry about inflation risk?
Oh yes, we worry about inflation risk (probably a bit too much), having come of age in the 1970s.

Since we have an entirely taxable porfolio (we sold a business and started out investing with a lump sum), only about one-quarter of our bond allocation is in TIPS. To inflation-protect the remaining nominal bonds, we generally hold short-intermediate durations and are relying on our equity assets (diversified global stocks and REITs) to cover the rest.

Actually, I worry more about global deflation shocks these days than run-away inflation — but it's always wise to consider both of these "deep risks" in portfolio construction, I believe.
Cordially, Todd

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by swaption » Tue Sep 08, 2015 2:58 pm

nisiprius wrote:I've done no more than skim the introduction, and don't think I'm capable of understanding or judging the rest, but... this is fascinating. It speaks directly to things that have been bothering me for a long time. The optimists are inclined to suggest that it isn't really fair to count the (supposedly) "ten-sigma events," because nobody could possibly have foreseen them, and they are never going to recur.
Crucial to understanding of rare disasters is to understand when they have not occurred, namely in the postwar period in the United States. A central contention of the rare disaster literature is that the last 65 years of U.S. data has been a period of calm that does not represent the full spectrum of events that investors incorporate into prices.
I really like the idea. Perhaps equity risk premium is not a reward for having to wait an uncertain amount of time to be almost sure of getting it, perhaps it's a reward for a serious honest-to-gosh risk of seriously losing your money and never getting it back.
Yeah, this. At this point, maybe now a bit of a Catch 22. Perhaps all those folks in the past were pricing equities correctly for the risk and there is no puzzle after all. So what are we left with, a new premium based on the now numbing disintermediation of index and other mutual funds that helps mask these risks. That is of course until those now ignored risks are realized, which at the risk of pointing out the obvious would likely be too high a price to pay in order to once again get a normalized risk premium. Except of course for the snake oil selling perma-bears who might finally have their day in the sun, which if not for such small matters as starvation and disease, might be the worst part of all this.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by bh7 » Tue Sep 08, 2015 3:40 pm

Simplegift wrote:
bh7 wrote:
Simplegift wrote:PS. Personal disclosure: our asset allocation is 50% stocks/50% bonds — and will be for our lifetimes.
Is that nominal or real bonds? If nominal, do you not worry about inflation risk?
Oh yes, we worry about inflation risk (probably a bit too much), having come of age in the 1970s.

Since we have an entirely taxable porfolio (we sold a business and started out investing with a lump sum), only about one-quarter of our bond allocation is in TIPS. To inflation-protect the remaining nominal bonds, we generally hold short-intermediate durations and are relying on our equity assets (diversified global stocks and REITs) to cover the rest.

Actually, I worry more about global deflation shocks these days than run-away inflation — but it's always wise to consider both of these "deep risks" in portfolio construction, I believe.
Is deflation really a risk? Deflation would be a windfall gain to most portfolios. The only portfolios that suffer are ones with debt or leverage.

The reason inflation is a risk is even if your nominal assets are priced to compensate for expected inflation, you are still facing variance in your real return outcomes, and variance is bad because humans are risk averse.

If inflation expectations are low, that gets priced into the nominal-real yield spread. But you are still facing variance in real outcomes when you go nominal, so going 100% real seems best.

I see your point on taxes though, and by going short-intermediate. But still, do short bonds really protect against inflation? If there's a sudden inflation shock your short term bonds will decline in real value. Now you may argue that interest rates will rise, but if the shock was unexpected, they can't rise before they've already taken the hit. Interest rates try to price future inflation. There's no way you can protect yourself from a one-time unexpected inflation shock with nominal assets, no matter how short you go. The only way they work is if inflation is expected well in advance of when it occurs.

Short Term treasuries didn't do so well 1973-1980. It wasn't until after inflation subsided but interest rates were still high that they boomed during the 80s. The reason they did badly in the 70s was because inflation was above expectation, and interest rates can only price expected inflation. And then in the 80s, inflation expectations were still high because people were extrapolating from the 1970s, and treasuries overperformed because they had high yields but low inflation. An investor who survived the 70s and 80s would have seen a decent 2% return over the entire period, but not without first suffering a -2% return from 72-80 and 5% return from 80-90. In fact an investor in short term treasuries starting 1972 would not have broken even until 1983. 11 years is a long time to wait for what was supposed to be a low risk asset: short term nominal treasuries.

Now apparently TIPS did worse over that period but we only have synthetic TIPS data before 2000 so I don't know how accurate it was. That implies that if TIPS did exist in the 70s, real yields would have been negative. :( But if they were it was only because inflation expectations were so high. Unfortunately what we can't observe is the counterfactual parallel universe in which the Fed didn't control inflation in the 80s. Then we would have seen nominal treasuries do awful and TIPS win out. :)

I've been trying to run simulations in retirement portfolios with TIPS vs TBM, but am not getting clean results. Portfolio Visualizer seems bugged because the success rate of a 100% TIPS portfolio is going down when I add inflation, when it should be inflation neutral :?
Last edited by bh7 on Tue Sep 08, 2015 4:34 pm, edited 1 time in total.

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by larryswedroe » Tue Sep 08, 2015 3:56 pm

bh
I can only speak from my experience, which is fairly extensive, in working with very high net worth individuals for many years, and IN GENERAL, they have increasing risk aversion, not all but most.
Larry

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by staythecourse » Tue Sep 08, 2015 4:04 pm

I will preface this by saying I did not read the paper so apologies if this had been touched on in the original paper. I not sure if I by the argument in the paper (at least without further data) supports his hypothesis. I would think since recency bias is strong in evolution and in finance one would assume the largest forward ERP would have been following an economic disaster. From the graphs that were attached on the OP I am not sure if I can tell if that is true?

The data I would want is to see if the upside volatility of stocks (returns) is HIGHEST following a major downswing in equity prices from recessions and other major disasters.

Is that addressed in the original paper or in other papers?

Thanks in advance.

Good luck.
"The stock market [fluctuation], therefore, is noise. A giant distraction from the business of investing.” | -Jack Bogle

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by Chan_va » Tue Sep 08, 2015 5:07 pm

Interesting paper - thanks for posting OP. I skimmed it and will have to dive into the math later.

I have had a similar hypothesis for a while. That said, I have a question about the "extreme disaster" theory. In almost all previous cases where this has happened, there has been no "risk-less" asset. Bonds and bills have become worthless too. So, why aren't fixed income investors also pricing in the "extreme disaster" risk, and why don't we see similar volatility in the bond price charts?

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by larryswedroe » Tue Sep 08, 2015 5:15 pm

Chan
Actually there is a new paper on corporate bonds that basically says this
A) the credit risk premium is close to zero (even ex ante) and
B) the rest of the yield premium is a disaster premium for what might be called the "jump risk" of systemic risks from "black swans" that cause corporate bonds to act like equities at exactly the wrong time

(note this paper contributes to the literature demonstrating that corporates are really hybrids with little unique risk)
Larry

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by SimpleGift » Tue Sep 08, 2015 7:09 pm

Chan_va wrote:I have had a similar hypothesis for a while. That said, I have a question about the "extreme disaster" theory. In almost all previous cases where this has happened, there has been no "risk-less" asset. Bonds and bills have become worthless too. So, why aren't fixed income investors also pricing in the "extreme disaster" risk, and why don't we see similar volatility in the bond price charts?
Chan, not sure about "extreme disasters" (where bonds and bills become completely worthless), but here is one explanation for the behavior dynamics of government bond prices during garden-variety "rare disasters."

Summary Article found here: Disaster Economics and Bond Yields
Daoud and Brookes wrote:In our framework, disasters hit not only income or consumption but also equities and bonds. Equities do badly because the decline in GDP affects earnings. Bonds suffer because a disaster raises the probability of government default. However, provided this probability remains low, investors will still find bonds attractive as they provide stable and largely safe returns when consumption is low. In other words, when investors fear a disaster, they will be willing to pay a premium to hold bonds because they still view them as safe havens despite the increase in default risk. It is this insurance property that makes bonds attractive when disaster risk is high. Therefore, bonds become riskier but their relative riskiness goes down.
This whole field of rare disaster risk seems to be quite active these days, with lots of recent, interesting research papers to review and ponder.
Cordially, Todd

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Re: Has the "Equity Premium Puzzle" Been Solved?

Post by backpacker » Tue Sep 08, 2015 7:55 pm

Simplegift wrote:
backpacker wrote:The small risk of extreme financial disasters only explains why stocks beat bonds if, during those disasters, stocks do worse than bonds. The problem is that this is often not the case. If the government confiscates your assets, they confiscates your bonds and your stocks. If your country is conquered by a foreign army, your bonds and stocks are both going to zero. If there is hyperinflation, your stocks are going to be hurting, but your nominal bonds will implode. Whether inflation protected bonds help will depend on the country. I wouldn't trust a country that is hyper-inflating its own currency to treat its inflation protected bond holders very well.
One can't argue with your historical facts — but I wonder how much of your (excellent) historical analysis still applies to modern investors in the 21st century. In other words:
  • • Among developed countries, is there really a great risk today of a destructive land war on one's home soil?

    • With modern central banking, is there really a risk of hyperinflation in most developed economies?

    • With the exception of a few state-controlled economies, is there really a risk of asset confiscation in the modern world?
My point is that, with the type of catastrophic risks currently facing investors today (e.g., global pandemics, environmental collapse, deflationary shocks, etc.), it still seems a fairly sure bet that government bonds are safer than stocks — despite the exceptional cases you've identified in the aftermath of World War II.

PS. Personal disclosure: our asset allocation is 50% stocks/50% bonds — and will be for our lifetimes.
Fair enough. The deep risk modern investors face may well be different than the deep risk we saw in the past. My thought was just that to explain the equity risk puzzle, you not only need there to be economic catastrophes in the tails of the distribution, you need economic catastrophes in which stocks are wiped out but bonds are safe. Otherwise we haven't explained the spread between stock and bond returns. There may be such possible scenarios, but the historical examples the authors point to aren't it.

As to your specific points, I think you're right about war. Large scale wars are less likely than they used to be. I find Stephen Pinker's arguments on this mostly convincing.

I'm not sure whether central banks make hyperinflation more or less likely. I don't know enough about this.

Confiscation comes in degrees. Higher taxes rates on capital are the method of choice for developed western countries. (This isn't to say that tax rates shouldn't be higher, just that higher taxes should count as "confiscation" in the relevant sense.)

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