<p>Market value cannot be negative.  Book value can, but then again, these are outlier companies that can reasonably be taken out of the sample in order to estimate the "normal"/ "average" structure.</p>

CC BY-SA 3.0
2017-08-16T19:59:29.853Z
this create a bias against company with negative book market value. I don't know how you can think this is okay and just dismiss them as outlier.
Lost1
CC BY-SA 3.0
2017-08-16T20:04:46.323Z
@Lost1 Is a negative-book-value company part of a sample that is representative of the population, _as regards the phenomenon we want to study_? This is the question that needs to be answered.
Alecos Papadopoulos
CC BY-SA 3.0
2017-08-16T20:08:45.463Z
what does "representative of the population" really mean here? it is like studying IQ of the population, but we discard people who identify themselves as gay. You can claim people who are gay not representative of the population. Does it have an effect on the result? Perhaps it does not. However, does this mean we discard them from the population we study?
Lost1
CC BY-SA 3.0
2017-08-16T20:10:05.763Z
in any sort of statistics analysis, it is generally safer to discard values when things when they are missing at random. However, here, we are selective discarding them depending on a parameter of the regression. That seems like a very bad practice.
Lost1
CC BY-SA 3.0
2017-08-16T20:34:37.980Z
@Lost1 This is a very big methodological matter. Your concerns are legitimate. The only thing I am pointing out is that the statistical concept of "population" is obtained by certain criteria applied. In this case, why should the population be "all companies for which we have data"? The concept of "outliers" exists exactly in order to capture the possibility that certain observations _reduce_ the degree that our sample is "representative of the population". Certainly, researchers should clearly lay out their argument for excluding observations as "outliers". (CONTD).
Alecos Papadopoulos
CC BY-SA 3.0
2017-08-16T20:36:10.213Z
@Lost1 (CONTD)  In our case, I would say a company with negative book value is not a company that attracts institutional investors - and the paper examines a hypothesis on the behavior and action of institutional investors. So I find it justifiable to exclude such companies. In general, excluding "outliers" is a case-per-case issue.
Alecos Papadopoulos
CC BY-SA 3.0
2017-08-16T20:58:54.343Z
Having looked a few of these companies, this included companies like American Airlines for a period of time. it is possible the negative book value is due to accounting practice. See the discussion here: https://www.gurufocus.com/news/176639/is-negative-book-value-bad
That is why I disagree that this is justifiable.
Lost1
CC BY-SA 3.0
2017-08-16T19:48:59.120Z
2017-08-16T19:48:59.120Z
Alecos Papadopoulos
<p>Well the problem can be dodged by the use of some simple solution of just adding a constant to all values which circumvent issues of taking logarithms of negative numbers. Usually the mean is used as a centering point. If the mean is negative though some other number must be chosen.</p>

<p>Interpretation of such a transformed variable would be different from its regular logged counter part.</p>

<p>These are just some hunches on what could have been done. Its odd that methods aren't mentioned for this case.</p>

CC BY-SA 3.0
2017-08-16T18:22:16.500Z
guess they probably chucked away the data with negative BM value... in this case, it certainly makes no sense to square it. I know you can add a constant but this is a hacky and not data agnostic.
Lost1
CC BY-SA 3.0
2017-08-16T18:24:17.100Z
@Lost1 Ah, I see why you have an issue with squaring it. I messes up ordinality of numbers. Editing now
EconJohn
CC BY-SA 3.0
2017-08-16T18:25:41.333Z
@Lost1 how is adding a constant not data agnostic? it maintains ordinality of the data.
EconJohn
CC BY-SA 3.0
2017-08-16T18:26:41.697Z
if you use a different set of data, with a negative number of bigger magnitude, suddenly your current model breaks again.
Lost1
CC BY-SA 3.0
2017-08-16T18:31:26.310Z
@Lost1 so the constant ends up changing based on the data? That's how all regression models work. estimates and their statistical significance can change as data does. Quantile regression would probably be the best tool in this case to check consistency of the estimates.
EconJohn
CC BY-SA 3.0
2017-08-16T20:03:59.870Z
It isn't really a constant it depends on your data.
Lost1
CC BY-SA 3.0
2017-08-16T20:56:51.573Z
@Lost1 I don't see an issue with that.
EconJohn
CC BY-SA 3.0
2017-08-16T21:02:23.393Z
One test of a good model is that it can be used to test against out of sample data and produce results matching estimated standard error. If we chop the data in 80 / 20 proportion. There is no guarantee that the method you proposed will even produce a number of the out-of-sample data as you do not know whether the BM value is smaller than the constant you add.
Lost1
CC BY-SA 3.0
2017-08-16T21:30:22.867Z
@Lost1 Now you're speaking about using a whole new method (i.e bootstrapping). For the sample you have right now plain old regression would work fine with some centering.  If you want clearer estimates, one would bootstrap the data and run a quantile regression on it, though I think thats a little bit of overkill.
EconJohn
CC BY-SA 3.0
2017-08-16T17:42:42.363Z
2017-08-16T18:24:41.923Z
2017-08-16T18:24:41.923Z
EconJohn
<p>Negative book value is actually a 'bug' that remains unsolved by general accounting principles. It is a problem that we've better not think isolatedly. Any companies that have negative book values can actually 'transfer to' positive ones if alternative accounting principles are considered. But firms are not that flexible to change their ways of recording financial information so that this kinda anomaly exists. Correct me if I am wrong. </p>

CC BY-SA 4.0
2019-08-07T17:42:09.380Z
2019-08-07T17:42:09.380Z
Chong Yu
<p>As noted in <a href="https://economics.stackexchange.com/questions/12522/definition-of-market-to-book-value">this post</a>, the book value of a company is its assets minus its liabilities.</p>

<p>I am reading this paper: "<a href="http://www.sciencedirect.com/science/article/pii/S0304405X09000634" rel="nofollow noreferrer">The price of sin: the effect of social norms on market</a>" by Hong and Kacperczyk. One of the paper's hypothesis is that institutional investors are less likely to hold sin stocks. To demonstrate this, the following initial (Fama-Macbeth) regression was run as a benchmark:</p>

<p>$$IO \sim Logsize + Beta + LOGMB + PRINV + STD+ RET $$</p>

<p>IO is institutional ownership
Logsize is the market cap
Beta is the beta of the sector the stock belongs
LOGMB is the log of the market to book ratio.
PRINV is the inverse of price
STD is standard deviation of monthly return
RET is log of arithmetic of previous year's monthly return.</p>

<p>My question here is that, because the Market book ratio can be negative, how can we take log of this? </p>

<p>It is not specified in the paper how this is treated. I have the strong suspicion that it is likely any company with negative book value for whatever reason is ignored. Surely this would introduce some sort of bias. Does anyone know what is the standard practice?</p>

<econometrics><financial-economics>
Log of a Negative Market-Book Ratio in a Regression Model
Lost1
# Log of a Negative Market-Book Ratio in a Regression Model

(Asked by: username_0 on 2017-08-05)

As noted in [this post](https://economics.stackexchange.com/questions/12522/definition-of-market-to-book-value), the book value of a company is its assets minus its liabilities.

I am reading this paper: "[The price of sin: the effect of social norms on market](http://www.sciencedirect.com/science/article/pii/S0304405X09000634)" by Hong and Kacperczyk. One of the paper's hypothesis is that institutional investors are less likely to hold sin stocks. To demonstrate this, the following initial (Fama-Macbeth) regression was run as a benchmark:

$$IO \sim Logsize + Beta + LOGMB + PRINV + STD+ RET $$

IO is institutional ownership
Logsize is the market cap
Beta is the beta of the sector the stock belongs
LOGMB is the log of the market to book ratio.
PRINV is the inverse of price
STD is standard deviation of monthly return
RET is log of arithmetic of previous year's monthly return.

My question here is that, because the Market book ratio can be negative, how can we take log of this?

It is not specified in the paper how this is treated. I have the strong suspicion that it is likely any company with negative book value for whatever reason is ignored. Surely this would introduce some sort of bias. Does anyone know what is the standard practice?

**Tags:** econometrics, financial-economics

---

## 3 answers

### Answer by username_1 on 2017-08-16. Score: 1

Market value cannot be negative. Book value can, but then again, these are outlier companies that can reasonably be taken out of the sample in order to estimate the "normal"/ "average" structure.

> **Comments:**
> **username_0**: this create a bias against company with negative book market value. I don't know how you can think this is okay and just dismiss them as outlier.  
> **username_1**: @Lost1 Is a negative-book-value company part of a sample that is representative of the population, _as regards the phenomenon we want to study_? This is the question that needs to be answered.  
> **username_0**: what does "representative of the population" really mean here? it is like studying IQ of the population, but we discard people who identify themselves as gay. You can claim people who are gay not representative of the population. Does it have an effect on the result? Perhaps it does not. However, does this mean we discard them from the population we study?  
> **username_0**: in any sort of statistics analysis, it is generally safer to discard values when things when they are missing at random. However, here, we are selective discarding them depending on a parameter of the regression. That seems like a very bad practice.  
> **username_1**: @Lost1 This is a very big methodological matter. Your concerns are legitimate. The only thing I am pointing out is that the statistical concept of "population" is obtained by certain criteria applied. In this case, why should the population be "all companies for which we have data"? The concept of "outliers" exists exactly in order to capture the possibility that certain observations _reduce_ the degree that our sample is "representative of the population". Certainly, researchers should clearly lay out their argument for excluding observations as "outliers". (CONTD).  
> **username_1**: @Lost1 (CONTD)  In our case, I would say a company with negative book value is not a company that attracts institutional investors - and the paper examines a hypothesis on the behavior and action of institutional investors. So I find it justifiable to exclude such companies. In general, excluding "outliers" is a case-per-case issue.  
> **username_0**: Having looked a few of these companies, this included companies like American Airlines for a period of time. it is possible the negative book value is due to accounting practice. See the discussion here: https://www.gurufocus.com/news/176639/is-negative-book-value-bad That is why I disagree that this is justifiable.  

---

### Answer by username_2 on 2017-08-16. Score: 1

Well the problem can be dodged by the use of some simple solution of just adding a constant to all values which circumvent issues of taking logarithms of negative numbers. Usually the mean is used as a centering point. If the mean is negative though some other number must be chosen.

Interpretation of such a transformed variable would be different from its regular logged counter part.

These are just some hunches on what could have been done. Its odd that methods aren't mentioned for this case.

> **Comments:**
> **username_0**: guess they probably chucked away the data with negative BM value... in this case, it certainly makes no sense to square it. I know you can add a constant but this is a hacky and not data agnostic.  
> **username_2**: @Lost1 Ah, I see why you have an issue with squaring it. I messes up ordinality of numbers. Editing now  
> **username_2**: @Lost1 how is adding a constant not data agnostic? it maintains ordinality of the data.  
> **username_0**: if you use a different set of data, with a negative number of bigger magnitude, suddenly your current model breaks again.  
> **username_2**: @Lost1 so the constant ends up changing based on the data? That's how all regression models work. estimates and their statistical significance can change as data does. Quantile regression would probably be the best tool in this case to check consistency of the estimates.  
> **username_0**: It isn't really a constant it depends on your data.  
> **username_2**: @Lost1 I don't see an issue with that.  
> **username_0**: One test of a good model is that it can be used to test against out of sample data and produce results matching estimated standard error. If we chop the data in 80 / 20 proportion. There is no guarantee that the method you proposed will even produce a number of the out-of-sample data as you do not know whether the BM value is smaller than the constant you add.  
> **username_2**: @Lost1 Now you're speaking about using a whole new method (i.e bootstrapping). For the sample you have right now plain old regression would work fine with some centering.  If you want clearer estimates, one would bootstrap the data and run a quantile regression on it, though I think thats a little bit of overkill.  

---

### Answer by username_3 on 2019-08-07. Score: 0

Negative book value is actually a 'bug' that remains unsolved by general accounting principles. It is a problem that we've better not think isolatedly. Any companies that have negative book values can actually 'transfer to' positive ones if alternative accounting principles are considered. But firms are not that flexible to change their ways of recording financial information so that this kinda anomaly exists. Correct me if I am wrong.


---

