<p>An important field in current research is the yet unexplained</p>

<h2><a href="http://efinance.org.cn/cn/fm/The%20equity%20premium%20puzzle.pdf" rel="noreferrer">Equity premium puzzle</a></h2>

<p>originally published by <a href="https://www.academicwebpages.com/preview/mehra/pdf/The%20Equity%20Premium%20A%20Puzzle.pdf" rel="noreferrer">Mehra, Prescott (1985)</a>. Considere a multiperiod investment consumption equilibrium model (CCAPM) with its important result:
$$E_t\left[m_{t,j}\right]=\frac1{\left(1+R_{F,t+j}\right)}$$
where $E_t\left[m_{t,j}\right]$ donates the expected value of a <em>stochastic discount factor</em> (sometimes also referred to as a <em>pricing kernel</em>) and $R_{F,t+j}$ a riskless rate of return.</p>

<p>The model states, that the maximized Sharpe-Ratio $SR_{max}$ can be represented as the ratio of the standard deviation of the optimal stochastic discount factor $\sigma_{m^*}$ to its mean:</p>

<p>$$SR_{max}=\frac{\sigma_{m^*}}{\overline m}$$ </p>

<p>Linking this result with common time separable power utility function shows, that the above equation is approximately the risk-aversion coefficient times the standard deviation of the logarithm of consumption.</p>

<p><strong>The problem</strong></p>

<p>The average risk premium of the market measured in units of risk is far too high to be explained by any consumption-based representation of the stochastic discount factor. As <a href="http://ecsocman.hse.ru/data/018/648/1219/finbook.pdf" rel="noreferrer">Cochrane(2001)</a> notes, the Sharpe ratio measured in real terms has been about 0.5 on the basis of the past fifty years (in the US). This implies, that investors are very risk averse, with a coefficient of risk aversion at least <em>50</em>.</p>

<p>What does that number mean? Suppose an individual faced with a 50-50 gamble of doubling or halving his savings. With a level of risk aversion of 50, he would pay 49% of his savings to avoid the loss of 50%. This individual would forgo a 50% chance of doubling his money and accept a certain loss of 49$ to avoid losing an additional 1% more.</p>

CC BY-SA 3.0
2017-09-21T09:39:36.557Z
2017-09-21T09:39:36.557Z
skoestlmeier
<p>Another unsolved puzzle in economics is the</p>
<h1>Dividend puzzle</h1>
<p>studied first by <a href="http://www.iijournals.com/doi/abs/10.3905/jpm.1976.408558?journalCode=jpm" rel="nofollow noreferrer">Fischer Black(1976)</a>, which evolves from the <a href="https://www.jstor.org/stable/1809766?seq=1#page_scan_tab_contents" rel="nofollow noreferrer">Modigliani-Miller</a> theorems.</p>
<p>Considere well known models for equilibrium in capital markets like the CAPM or the Fama-French 4-factor model. In the latter, return <span class="math-container">$r_i$</span> of any asset <span class="math-container">$i$</span> is explained by the risk of <span class="math-container">$i$</span> towards given portfolios:
<span class="math-container">$$r_i=R_f+\beta_3(K_m-R_f)+b_s\cdot\mathit{SMB}+b_v\cdot\mathit{HML}+\alpha$$</span>
where <span class="math-container">$R_f$</span> is the risk-free return rate, and <span class="math-container">$K_m$</span> is the return of the market portfolio. <span class="math-container">$SMB$</span> and <span class="math-container">$HML$</span> are given portfolios (for futher information see <a href="http://www.sciencedirect.com/science/article/pii/0304405X93900235?via%3Dihub" rel="nofollow noreferrer">here</a>).</p>
<p>Besides these models for equilibrium, return <span class="math-container">$r_i$</span> can be calculated by Discounted Dividend Models (DDM) like the <a href="https://www.jstor.org/stable/2977577?seq=1#page_scan_tab_contents" rel="nofollow noreferrer">Gordon-Groth-Model</a>, which do not aim on the whole market. The valuation of a single share is determined by discounting all further dividends, taking into account increasing dividends in the future:
<span class="math-container">$$ P_i= \sum_{t=1}^{\infty}  {D_0} \frac{(1+g)^{t}}{(1+r_i)^t}$$</span>
where <span class="math-container">$P$</span> is the observable stock price, <span class="math-container">$g$</span> the infinite growth rate of dividend payments and <span class="math-container">$D_0$</span> the value of current dividend payment (absolute value). Adjusting the formula gives the adequate <span class="math-container">$r_i$</span>.</p>
<p><strong>The problem</strong></p>
<p>The dividend a corporation pays, should not affect its valuation. Its clear for equilibrium models, since there is no term in the formula representing dividend payments. Lets look at the Gordon-Growth model: Dividends (and their growth rate) are included within the formulas, but what happens around the payment day? The price of the share drops on the ex-dividend date exactly by the amount of the dividend (besides transaction costs or taxes). It just drops the whole range of possible stock prices by that amount.</p>
<p>Empirical studies show (a good overview can be found <a href="http://www.emeraldinsight.com/doi/abs/10.1108/03074350710715773" rel="nofollow noreferrer">here</a>), that investors reward dividend-paying companies with higher valuation. Its evaluated by many researchers in the fields behavioral finance, asymmetric information, or taxes, but its not fully explained yet.</p>

CC BY-SA 3.0
2017-09-22T15:34:05.033Z
But which is the actual puzzle? In the payment day, you are jumping ahead on period, which means $D_0$ becomes $D_1$, and an unknown dividend is now known, so it is reasonable to expect an adjustment due to expectation error. Surely a very simple model cannot fully capture the problem. I don't quite get why this is a puzzle.
luchonacho
CC BY-SA 3.0
2017-09-26T15:27:43.323Z
The point is, that wether a company pays out dividends or not should not affect its valuation. Its clear for equilibrium models, but needs explanation for DDM (and their derivatives). Its not the expectation error or similar effects. Consider you hold 100% of a company. Paying out financial assets as a dividend or let them within the company is exactly the same situation. But what can be seen in empirical research is: Companies who pay out dividends are far higher rated then those who don't pay dividends. Yet no explanation, e.g. taxes, asymmetries, etc. captures this observation fully.
skoestlmeier
CC BY-SA 3.0
2017-09-22T13:06:06.470Z
2017-09-22T14:29:48.803Z
2020-06-17T09:40:54.643Z
skoestlmeier
<p>A good one is where the equilibrium is on the laffer curve and thus what the level of taxation for a society should be.</p>

<p><a href="https://dqydj.com/laffer-curve-does-decreasing-taxes-increase-revenues/" rel="nofollow noreferrer">https://dqydj.com/laffer-curve-does-decreasing-taxes-increase-revenues/</a></p>

<p>If what you're looking for is all the unsolved questions in economics you're going to have a pretty long list.</p>

CC BY-SA 3.0
2017-09-21T09:22:32.943Z
Thanks, but the question is not asking about unsolved **problems** but unsolved **puzzles/paradoxes**. The list of questions to be answered is of course boundless. In which sense is the optimal taxation level a **puzzle**? What is it about it that makes it apparently contradictory or mysterious?
luchonacho
CC BY-SA 3.0
2018-02-04T16:29:28.950Z
What do you mean by "equilibrium"?
Giskard
CC BY-SA 3.0
2018-02-05T19:19:09.293Z
The laffer curve shows that at a certain level of taxation decreasing taxation will counterintuitively increase tax revenue for the federal government due to decreased avoidance and increased incentive for income. There is some point on the laffer curve where either increasing, or decreasing taxation would cause a decrease in income, this point would be the equilibrium, and a tax policy set at that point would maximize tax revenue.
TheSaint321
CC BY-SA 3.0
2017-09-20T18:52:26.130Z
2017-09-20T18:52:26.130Z
TheSaint321
<p>Science is full of apparent puzzles and <a href="https://en.wikipedia.org/wiki/List_of_paradoxes" rel="noreferrer">paradoxes</a>, some of which still remain unexplained. <a href="https://en.wikipedia.org/wiki/List_of_paradoxes#Economics" rel="noreferrer">Economics</a> is not an exception. </p>

<p>It would be interesting to get a list of  <strong>unresolved puzzles</strong> in Economics. By unresolved I mean there is a considerable divergence of opinions and evidence on what explains the puzzle, or perhaps not sufficient evidence to provide a clear explanation to the puzzle.</p>

<p>As always with these type of question, one puzzle/paradox per answer would be ideal. When doing so, <strong>please back up your answer with references that certify that the issue is currently a puzzle/paradox among academics and researchers.</strong> Resolved puzzles are off-topic (another thread for that might be appropriate).</p>

CC BY-SA 3.0
2017-09-20T19:03:28.630Z
Are such type of questions on topic? I mean the format where many answers are possible. (Probably they are, I am just inquiring.)
Richard Hardy
CC BY-SA 3.0
2017-09-21T09:26:40.790Z
@RichardHardy There is a long list of such questions. Pretty much every [reference request](https://economics.stackexchange.com/questions/tagged/reference-request) question allows for it. Other popular questions with such a setting are [this one](https://economics.stackexchange.com/questions/35/fundamental-equations-in-economics) and [this one](https://economics.stackexchange.com/questions/5305/seminal-papers-that-later-were-proven-to-contain-errors).
luchonacho
<reference-request><research>
Unexplained economic puzzles?
luchonacho
# Unexplained economic puzzles?

(Asked by: username_0 on 2017-09-20)

Science is full of apparent puzzles and [paradoxes](https://en.wikipedia.org/wiki/List_of_paradoxes), some of which still remain unexplained. [Economics](https://en.wikipedia.org/wiki/List_of_paradoxes#Economics) is not an exception.

It would be interesting to get a list of **unresolved puzzles** in Economics. By unresolved I mean there is a considerable divergence of opinions and evidence on what explains the puzzle, or perhaps not sufficient evidence to provide a clear explanation to the puzzle.

As always with these type of question, one puzzle/paradox per answer would be ideal. When doing so, **please back up your answer with references that certify that the issue is currently a puzzle/paradox among academics and researchers.** Resolved puzzles are off-topic (another thread for that might be appropriate).

**Tags:** reference-request, research

> **Comments:**
> **username_1**: Are such type of questions on topic? I mean the format where many answers are possible. (Probably they are, I am just inquiring.)  
> **username_0**: @RichardHardy There is a long list of such questions. Pretty much every [reference request](https://economics.stackexchange.com/questions/tagged/reference-request) question allows for it. Other popular questions with such a setting are [this one](https://economics.stackexchange.com/questions/35/fundamental-equations-in-economics) and [this one](https://economics.stackexchange.com/questions/5305/seminal-papers-that-later-were-proven-to-contain-errors).  

---

## 3 answers

### Answer by username_2 on 2017-09-21. Score: 9

An important field in current research is the yet unexplained

## [Equity premium puzzle](http://efinance.org.cn/cn/fm/The%20equity%20premium%20puzzle.pdf)

originally published by [Mehra, Prescott (1985)](https://www.academicwebpages.com/preview/mehra/pdf/The%20Equity%20Premium%20A%20Puzzle.pdf). Considere a multiperiod investment consumption equilibrium model (CCAPM) with its important result:
$$E\_t\left[m\_{t,j}\right]=\frac1{\left(1+R\_{F,t+j}\right)}$$
where $E\_t\left[m\_{t,j}\right]$ donates the expected value of a *stochastic discount factor* (sometimes also referred to as a *pricing kernel*) and $R\_{F,t+j}$ a riskless rate of return.

The model states, that the maximized Sharpe-Ratio $SR\_{max}$ can be represented as the ratio of the standard deviation of the optimal stochastic discount factor $\sigma\_{m^\*}$ to its mean:

$$SR\_{max}=\frac{\sigma\_{m^\*}}{\overline m}$$

Linking this result with common time separable power utility function shows, that the above equation is approximately the risk-aversion coefficient times the standard deviation of the logarithm of consumption.

**The problem**

The average risk premium of the market measured in units of risk is far too high to be explained by any consumption-based representation of the stochastic discount factor. As [Cochrane(2001)](http://ecsocman.hse.ru/data/018/648/1219/finbook.pdf) notes, the Sharpe ratio measured in real terms has been about 0.5 on the basis of the past fifty years (in the US). This implies, that investors are very risk averse, with a coefficient of risk aversion at least *50*.

What does that number mean? Suppose an individual faced with a 50-50 gamble of doubling or halving his savings. With a level of risk aversion of 50, he would pay 49% of his savings to avoid the loss of 50%. This individual would forgo a 50% chance of doubling his money and accept a certain loss of 49$ to avoid losing an additional 1% more.


---

### Answer by username_2 on 2017-09-22. Score: 4

Another unsolved puzzle in economics is the

# Dividend puzzle

studied first by [Fischer Black(1976)](http://www.iijournals.com/doi/abs/10.3905/jpm.1976.408558?journalCode=jpm), which evolves from the [Modigliani-Miller](https://www.jstor.org/stable/1809766?seq=1#page_scan_tab_contents) theorems.

Considere well known models for equilibrium in capital markets like the CAPM or the Fama-French 4-factor model. In the latter, return $r\_i$ of any asset $i$ is explained by the risk of $i$ towards given portfolios:
$$r\_i=R\_f+\beta\_3(K\_m-R\_f)+b\_s\cdot\mathit{SMB}+b\_v\cdot\mathit{HML}+\alpha$$
where $R\_f$ is the risk-free return rate, and $K\_m$ is the return of the market portfolio. $SMB$ and $HML$ are given portfolios (for futher information see [here](http://www.sciencedirect.com/science/article/pii/0304405X93900235?via%3Dihub)).

Besides these models for equilibrium, return $r\_i$ can be calculated by Discounted Dividend Models (DDM) like the [Gordon-Groth-Model](https://www.jstor.org/stable/2977577?seq=1#page_scan_tab_contents), which do not aim on the whole market. The valuation of a single share is determined by discounting all further dividends, taking into account increasing dividends in the future:
$$ P\_i= \sum\_{t=1}^{\infty} {D\_0} \frac{(1+g)^{t}}{(1+r\_i)^t}$$
where $P$ is the observable stock price, $g$ the infinite growth rate of dividend payments and $D\_0$ the value of current dividend payment (absolute value). Adjusting the formula gives the adequate $r\_i$.

**The problem**

The dividend a corporation pays, should not affect its valuation. Its clear for equilibrium models, since there is no term in the formula representing dividend payments. Lets look at the Gordon-Growth model: Dividends (and their growth rate) are included within the formulas, but what happens around the payment day? The price of the share drops on the ex-dividend date exactly by the amount of the dividend (besides transaction costs or taxes). It just drops the whole range of possible stock prices by that amount.

Empirical studies show (a good overview can be found [here](http://www.emeraldinsight.com/doi/abs/10.1108/03074350710715773)), that investors reward dividend-paying companies with higher valuation. Its evaluated by many researchers in the fields behavioral finance, asymmetric information, or taxes, but its not fully explained yet.

> **Comments:**
> **username_0**: But which is the actual puzzle? In the payment day, you are jumping ahead on period, which means $D_0$ becomes $D_1$, and an unknown dividend is now known, so it is reasonable to expect an adjustment due to expectation error. Surely a very simple model cannot fully capture the problem. I don't quite get why this is a puzzle.  
> **username_2**: The point is, that wether a company pays out dividends or not should not affect its valuation. Its clear for equilibrium models, but needs explanation for DDM (and their derivatives). Its not the expectation error or similar effects. Consider you hold 100% of a company. Paying out financial assets as a dividend or let them within the company is exactly the same situation. But what can be seen in empirical research is: Companies who pay out dividends are far higher rated then those who don't pay dividends. Yet no explanation, e.g. taxes, asymmetries, etc. captures this observation fully.  

---

### Answer by username_3 on 2017-09-20. Score: 0

A good one is where the equilibrium is on the laffer curve and thus what the level of taxation for a society should be.

<https://dqydj.com/laffer-curve-does-decreasing-taxes-increase-revenues/>

If what you're looking for is all the unsolved questions in economics you're going to have a pretty long list.

> **Comments:**
> **username_0**: Thanks, but the question is not asking about unsolved **problems** but unsolved **puzzles/paradoxes**. The list of questions to be answered is of course boundless. In which sense is the optimal taxation level a **puzzle**? What is it about it that makes it apparently contradictory or mysterious?  
> **username_4**: What do you mean by "equilibrium"?  
> **username_3**: The laffer curve shows that at a certain level of taxation decreasing taxation will counterintuitively increase tax revenue for the federal government due to decreased avoidance and increased incentive for income. There is some point on the laffer curve where either increasing, or decreasing taxation would cause a decrease in income, this point would be the equilibrium, and a tax policy set at that point would maximize tax revenue.  

---

