<blockquote>
<p>How is so-called &quot;true price&quot;, &quot;fair price&quot; or &quot;rational price&quot; defined in the literature? Is that the same as the &quot;fundamental price&quot; of an asset?</p>
</blockquote>
<p>There is no definition in literature for &quot;true price&quot; or &quot;rational price&quot;. That is not term used in literature at all. Both <a href="https://link.springer.com/search?facet-eisbn=978-1-349-95121-5&amp;facet-content-type=ReferenceWorkEntry&amp;query=true%20price" rel="nofollow noreferrer">Palgrave Dictionary of Economics</a> and <a href="https://www.oxfordreference.com/search?btog=chap&amp;q0=true+price&amp;source=%2F10.1093%2Facref%2F9780198759430.001.0001%2Facref-9780198759430" rel="nofollow noreferrer">Oxford Dictionary of Economics</a> have 0 entries for &quot;true price&quot; or &quot;rational price&quot;. Google scholar also shows no notable mentions in economic journals of these terms. There seems to be no history of term &quot;true price&quot; or &quot;rational price&quot; commonly (or even at all) used in economic literature.</p>
<p>When it comes to &quot;fair price&quot; is defined as the <em>ethical</em> price or price that people subjectively consider &quot;fair&quot; (see <a href="https://journals.sagepub.com/doi/abs/10.1177/002224377801500208" rel="nofollow noreferrer">Huppertz, Arenson and Evans 1978;</a> <a href="https://academic.oup.com/qje/article-abstract/114/3/817/1848113" rel="nofollow noreferrer">Fehr and Schmidt 1999</a>; <a href="https://www.aeaweb.org/articles?id=10.1257/aer.90.1.166" rel="nofollow noreferrer">Bolton and Ockenfels 2000</a>; <a href="https://journals.sagepub.com/doi/abs/10.1509/jmkg.68.4.1.42733" rel="nofollow noreferrer">Xia et al 2004</a> and  <a href="https://www.nber.org/system/files/working_papers/w10915/w10915.pdf" rel="nofollow noreferrer">Rotemberg 2004</a>). However, since there is no clear dominant ethical framework any price could be fair. Some authors do narrow the definition down a bit. For example, Huppertz, Arenson and Evans (1978) define fair prices as
involving an</p>
<blockquote>
<p>equitable distribution of the benefits</p>
</blockquote>
<p>But the definition is generally not accepted. Discounted value of future cashflows would be considered fair price under some moral framework that would consider such pricing ethical.</p>
<p><strong>Fair value</strong>, not to be confused with fair price, does not have definition in traditional economics, since in economics proper value is defined in terms of marginal utility (hence fair value is bit of an oxymoron since defining value in terms of marginal utility makes value fully subjective) but in <em>finance</em> when talking about financial assets fair value is defined according to  <a href="https://www.oxfordreference.com/view/10.1093/acref/9780198294818.001.0001/acref-9780198294818" rel="nofollow noreferrer">Moles  and Terry (2005)</a> as:</p>
<blockquote>
<ol>
<li>The transaction price for assets or securities in which no ready market exists  The assumption is that both parties know the value of what is bought and sold ( cf. arm's length transaction ; open-market value</li>
</ol>
</blockquote>
<blockquote>
<ol start="2">
<li>The value of a derivative instrument derived from an analytical model</li>
</ol>
</blockquote>
<p>In the paper you cite by Andrews they clearly use the second meaning of a value based on some model of how economy works (that is why they talk about fundamentals etc). Consequently if we would value stocks with some analytical model, such as for example Gordon stock pricing model fair value <span class="math-container">$V$</span> would be:</p>
<p><span class="math-container">$$V =  \frac{D}{r-g}$$</span></p>
<p>Where <span class="math-container">$D$</span> is the expected dividend, <span class="math-container">$r$</span> interest rate and <span class="math-container">$g$</span> growth rate of an economy. Had we use different analytical model fair value might be different.</p>
<blockquote>
<p>Does efficient market hypothesis (EMH) by Fama assume that current/spot price of an asset (e.g. stock) in the market equals to its &quot;true&quot; or &quot;fundamental&quot; price, and efficient markets do not allow mispricing?</p>
</blockquote>
<p>No it doesn't since the terms &quot;true&quot; or &quot;fundamental&quot; price are not used.</p>
<p>EMH assumes that the prices reflect all available information <a href="https://link.springer.com/chapter/10.1007/978-1-349-20213-3_13" rel="nofollow noreferrer">(Malkiel, 1989)</a>. EHM would imply that, assuming no market imperfections, assets are traded at prices equal to their <strong>fair value</strong>, that is value given by some model of what the price should be given by expected value of fundamentals (parameters of an economy) that the model assumes are relevant for valuing particular asset.</p>
<blockquote>
<p>What are causes for mispricing, i.e. divergence from &quot;fair price&quot;? I assume, information asymmetry, bubbles, etc.</p>
</blockquote>
<p>Divergence from &quot;fair price&quot; is caused by people having different moral frameworks.</p>
<p>Divergence of prices of assets from a price that would equal their <strong>fair value</strong> as defined in finance, can be caused by various reasons. As mentioned in the article you  cite by Andrews et all it could by due to market overreacting to bad/good news and similar behavioral reasons. Furthermore, it could be caused by market imperfections and market frictions. For example, liquidity constraints, low capital mobility, leverage of financial intermediators or issues like constraints on informational processing etc (e.g. see <a href="https://www.nber.org/papers/w23231" rel="nofollow noreferrer">Lewis et al 2017</a>, or <a href="https://academic.oup.com/ej/article/124/575/245/5076975?login=true" rel="nofollow noreferrer">Brown 2013</a> and works cited therein for more examples)</p>

CC BY-SA 4.0
2022-05-11T07:23:01.383Z
Thanks for this, helped a lot! Btw, I have edited my question providing some context and my reasoning.
Sane
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2022-05-10T20:43:10.253Z
2022-05-10T20:49:34.147Z
2022-05-10T20:49:34.147Z
1muflon1
<p>A paragraph from the article <a href="https://www.sciencedirect.com/science/article/abs/pii/S0304405X21001471#!" rel="nofollow noreferrer">Asset Mispricing</a>:</p>
<blockquote>
<p>One of the central doctrines of modern financial theory is that the price of a security should equal the present value of its cash flows. Recently, however, this paradigm has been challenged by evidence of asset prices that appear to diverge from their fundamental values, particularly during financial crises and major market events.</p>
</blockquote>
<p>Or in the article <a href="http://web.mit.edu/Alo/www/Papers/EMH_Final.pdf" rel="nofollow noreferrer">Efficient Market Hypothesis</a>, Andrew Lo puts the follwing statement:</p>
<blockquote>
<p>A common explanation for departures from the EMH is that investors do not always react in
proper proportion to new information. For example, in some cases investors may overreact to
performance, selling stocks that have experienced recent losses or buying stocks that have
enjoyed recent gains. Such overreaction tends to push prices beyond their <strong>‘fair’</strong> or <strong>‘rational’
market value</strong>, only to have rational investors take the other side of the trades and bring prices
back in line eventually.</p>
</blockquote>
<p>In this context, I have 3 questions:</p>
<ol>
<li><p>How is so-called &quot;true price&quot;, &quot;fair price&quot; or &quot;rational price&quot; defined in the literature? Is that the same as the &quot;fundamental price&quot; of an asset? By saying &quot;true/fair price&quot; I understand the price which reflects an asset's intrinsic value/price. I do believe &quot;true/fair/rational&quot; price can be defined as the dicounted expected cash flow.</p>
</li>
<li><p>Does efficient market hypothesis (EMH) by Fama assume that current/spot price of an asset (e.g. stock) in the market equals to its &quot;true&quot; or &quot;fundamental&quot; price, and efficient markets do not allow mispricing?</p>
</li>
<li><p>What are causes for mispricing, i.e. divergence from &quot;fair price&quot;? I assume, information asymmetry, bubbles, etc.</p>
</li>
</ol>
<p>Any answer and links/sources/papers will be highly appreciated.</p>
<hr />
<p><strong>EDIT</strong> Here I would like to provide some context for my question. Off the top of my head, I have the following <em>theoretical</em> definition (no practical implication possible) for &quot;true price&quot;, even though this terminology does not exist in the literature:</p>
<blockquote>
<p>Suppose we have an asset, and we do have some &quot;time-machine&quot;, which allows us to move to future and see asset's future cash flow stream, which I assume is deterministic (I know that it is not realistic). Therefore, the discounted cash flow stream I would define as the &quot;true price&quot; of the asset. WHY? Because I am paying for it, what I am going to get in the future, like for fixed income securities (bond). Since in reality there is no time-machine, I want to understand how I can evaluate &quot;true price&quot; of an asset, as I defined above? One can say - &quot;look at the market, and take the price&quot;! But the market is not perfect, and the market merely has an expectation about future cash flow stream, and the information set which generates expectations dynamically changes over time.</p>
</blockquote>

CC BY-SA 4.0
2022-05-10T05:07:52.523Z
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.
Giskard
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2022-05-10T19:00:17.960Z
@Giskard Could you please indicate which question of the above listed is not specific? As far as I understand, I clearly put specific questions.
Sane
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2022-05-10T19:02:58.417Z
"limit it to *a* specific problem", so please post your *three* questions in three separate questions. That way people can answer each individually, with 1/3 of the effort.
Giskard
CC BY-SA 4.0
2022-05-10T19:04:28.120Z
As 1muflon1 points out, perhaps you could also define "true/fair price" or state where exactly it was in your referred text?
Giskard
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2022-05-10T19:13:21.373Z
@Giskard I have edited question by adding a reference for "fair/rational" price of an asset.
Sane
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2022-05-10T19:13:35.940Z
@1muflon1 I have edited question.
Sane
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2022-05-10T19:21:01.623Z
@Sane value in econ $\neq$ price.
1muflon1
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2022-05-10T19:54:02.953Z
@1muflon1  If you read the paragraph from the paper of A. Lo clearly, it says that usually value in econ = price, but overreaction tends to push prices beyond their ‘fair’ or ‘rational’ market value sometimes.
Sane
CC BY-SA 4.0
2022-05-10T19:55:26.053Z
@Sane my point is you are asking what is so called true price/rational price... so called by who? If you are the only person using the term its not "so called", nobody uses those terms in literature yet you want reference to their definitions
1muflon1
CC BY-SA 4.0
2022-05-10T19:57:28.913Z
@1muflon1 I have already mentioned an example -- Andrew Lo in this paper he uses true/rational price terminology: http://web.mit.edu/Alo/www/Papers/EMH_Final.pdf
Sane
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2022-05-10T19:58:37.247Z
@Sane the paper has 0 mentions of true or rational price.
1muflon1
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2022-05-10T20:22:20.653Z
@1muflon1 True price is what reflects asset's true value.
Sane
CC BY-SA 4.0
2022-05-10T20:24:19.527Z
@Sane and what is true value? That is term that again has zero hits in that paper...
1muflon1
CC BY-SA 4.0
2022-05-11T05:19:29.313Z
@Sane The phrase 'true values' appears exactly once in the [linked paper](http://web.mit.edu/Alo/www/Papers/EMH_Final.pdf#page=14), and it does so in quotes. Clearly this is not a well-defined phrase.
Giskard
<asset-pricing><efficient-markets>
Definition of "true price" of an asset and connection with efficient market
Sane
# Definition of "true price" of an asset and connection with efficient market

(Asked by: username_0 on 2022-05-09)

A paragraph from the article [Asset Mispricing](https://www.sciencedirect.com/science/article/abs/pii/S0304405X21001471#!):

> One of the central doctrines of modern financial theory is that the price of a security should equal the present value of its cash flows. Recently, however, this paradigm has been challenged by evidence of asset prices that appear to diverge from their fundamental values, particularly during financial crises and major market events.

Or in the article [Efficient Market Hypothesis](http://web.mit.edu/Alo/www/Papers/EMH_Final.pdf), Andrew Lo puts the follwing statement:

> A common explanation for departures from the EMH is that investors do not always react in
> proper proportion to new information. For example, in some cases investors may overreact to
> performance, selling stocks that have experienced recent losses or buying stocks that have
> enjoyed recent gains. Such overreaction tends to push prices beyond their **‘fair’** or **‘rational’
> market value**, only to have rational investors take the other side of the trades and bring prices
> back in line eventually.

In this context, I have 3 questions:

1. How is so-called "true price", "fair price" or "rational price" defined in the literature? Is that the same as the "fundamental price" of an asset? By saying "true/fair price" I understand the price which reflects an asset's intrinsic value/price. I do believe "true/fair/rational" price can be defined as the dicounted expected cash flow.
2. Does efficient market hypothesis (EMH) by Fama assume that current/spot price of an asset (e.g. stock) in the market equals to its "true" or "fundamental" price, and efficient markets do not allow mispricing?
3. What are causes for mispricing, i.e. divergence from "fair price"? I assume, information asymmetry, bubbles, etc.

Any answer and links/sources/papers will be highly appreciated.

---

**EDIT** Here I would like to provide some context for my question. Off the top of my head, I have the following *theoretical* definition (no practical implication possible) for "true price", even though this terminology does not exist in the literature:

> Suppose we have an asset, and we do have some "time-machine", which allows us to move to future and see asset's future cash flow stream, which I assume is deterministic (I know that it is not realistic). Therefore, the discounted cash flow stream I would define as the "true price" of the asset. WHY? Because I am paying for it, what I am going to get in the future, like for fixed income securities (bond). Since in reality there is no time-machine, I want to understand how I can evaluate "true price" of an asset, as I defined above? One can say - "look at the market, and take the price"! But the market is not perfect, and the market merely has an expectation about future cash flow stream, and the information set which generates expectations dynamically changes over time.

**Tags:** asset-pricing, efficient-markets

> **Comments:**
> **username_1**: Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.  
> **username_0**: @username_1 Could you please indicate which question of the above listed is not specific? As far as I understand, I clearly put specific questions.  
> **username_1**: "limit it to *a* specific problem", so please post your *three* questions in three separate questions. That way people can answer each individually, with 1/3 of the effort.  
> **username_1**: As username_2 points out, perhaps you could also define "true/fair price" or state where exactly it was in your referred text?  
> **username_0**: @username_1 I have edited question by adding a reference for "fair/rational" price of an asset.  
> **username_0**: @username_2 I have edited question.  
> **username_2**: @username_0 value in econ $\neq$ price.  
> **username_0**: @username_2  If you read the paragraph from the paper of A. Lo clearly, it says that usually value in econ = price, but overreaction tends to push prices beyond their ‘fair’ or ‘rational’ market value sometimes.  
> **username_2**: @username_0 my point is you are asking what is so called true price/rational price... so called by who? If you are the only person using the term its not "so called", nobody uses those terms in literature yet you want reference to their definitions  
> **username_0**: @username_2 I have already mentioned an example -- Andrew Lo in this paper he uses true/rational price terminology: http://web.mit.edu/Alo/www/Papers/EMH_Final.pdf  
> **username_2**: @username_0 the paper has 0 mentions of true or rational price.  
> **username_0**: @username_2 True price is what reflects asset's true value.  
> **username_2**: @username_0 and what is true value? That is term that again has zero hits in that paper...  
> **username_1**: @username_0 The phrase 'true values' appears exactly once in the [linked paper](http://web.mit.edu/Alo/www/Papers/EMH_Final.pdf#page=14), and it does so in quotes. Clearly this is not a well-defined phrase.  

---

## 1 answers

### Answer by username_2 on 2022-05-10. Score: 1 | Accepted answer

> How is so-called "true price", "fair price" or "rational price" defined in the literature? Is that the same as the "fundamental price" of an asset?

There is no definition in literature for "true price" or "rational price". That is not term used in literature at all. Both [Palgrave Dictionary of Economics](https://link.springer.com/search?facet-eisbn=978-1-349-95121-5&facet-content-type=ReferenceWorkEntry&query=true%20price) and [Oxford Dictionary of Economics](https://www.oxfordreference.com/search?btog=chap&q0=true+price&source=%2F10.1093%2Facref%2F9780198759430.001.0001%2Facref-9780198759430) have 0 entries for "true price" or "rational price". Google scholar also shows no notable mentions in economic journals of these terms. There seems to be no history of term "true price" or "rational price" commonly (or even at all) used in economic literature.

When it comes to "fair price" is defined as the *ethical* price or price that people subjectively consider "fair" (see [Huppertz, Arenson and Evans 1978;](https://journals.sagepub.com/doi/abs/10.1177/002224377801500208) [Fehr and Schmidt 1999](https://academic.oup.com/qje/article-abstract/114/3/817/1848113); [Bolton and Ockenfels 2000](https://www.aeaweb.org/articles?id=10.1257/aer.90.1.166); [Xia et al 2004](https://journals.sagepub.com/doi/abs/10.1509/jmkg.68.4.1.42733) and [Rotemberg 2004](https://www.nber.org/system/files/working_papers/w10915/w10915.pdf)). However, since there is no clear dominant ethical framework any price could be fair. Some authors do narrow the definition down a bit. For example, Huppertz, Arenson and Evans (1978) define fair prices as
involving an

> equitable distribution of the benefits

But the definition is generally not accepted. Discounted value of future cashflows would be considered fair price under some moral framework that would consider such pricing ethical.

**Fair value**, not to be confused with fair price, does not have definition in traditional economics, since in economics proper value is defined in terms of marginal utility (hence fair value is bit of an oxymoron since defining value in terms of marginal utility makes value fully subjective) but in *finance* when talking about financial assets fair value is defined according to [Moles and Terry (2005)](https://www.oxfordreference.com/view/10.1093/acref/9780198294818.001.0001/acref-9780198294818) as:

> 1. The transaction price for assets or securities in which no ready market exists The assumption is that both parties know the value of what is bought and sold ( cf. arm's length transaction ; open-market value

> 2. The value of a derivative instrument derived from an analytical model

In the paper you cite by Andrews they clearly use the second meaning of a value based on some model of how economy works (that is why they talk about fundamentals etc). Consequently if we would value stocks with some analytical model, such as for example Gordon stock pricing model fair value $V$ would be:

$$V = \frac{D}{r-g}$$

Where $D$ is the expected dividend, $r$ interest rate and $g$ growth rate of an economy. Had we use different analytical model fair value might be different.

> Does efficient market hypothesis (EMH) by Fama assume that current/spot price of an asset (e.g. stock) in the market equals to its "true" or "fundamental" price, and efficient markets do not allow mispricing?

No it doesn't since the terms "true" or "fundamental" price are not used.

EMH assumes that the prices reflect all available information [(Malkiel, 1989)](https://link.springer.com/chapter/10.1007/978-1-349-20213-3_13). EHM would imply that, assuming no market imperfections, assets are traded at prices equal to their **fair value**, that is value given by some model of what the price should be given by expected value of fundamentals (parameters of an economy) that the model assumes are relevant for valuing particular asset.

> What are causes for mispricing, i.e. divergence from "fair price"? I assume, information asymmetry, bubbles, etc.

Divergence from "fair price" is caused by people having different moral frameworks.

Divergence of prices of assets from a price that would equal their **fair value** as defined in finance, can be caused by various reasons. As mentioned in the article you cite by Andrews et all it could by due to market overreacting to bad/good news and similar behavioral reasons. Furthermore, it could be caused by market imperfections and market frictions. For example, liquidity constraints, low capital mobility, leverage of financial intermediators or issues like constraints on informational processing etc (e.g. see [Lewis et al 2017](https://www.nber.org/papers/w23231), or [Brown 2013](https://academic.oup.com/ej/article/124/575/245/5076975?login=true) and works cited therein for more examples)

> **Comments:**
> **username_0**: Thanks for this, helped a lot! Btw, I have edited my question providing some context and my reasoning.  

---

