.chapter17<-function(i=0){
" i Chapter 17: CAPM (Capital Asset Pricing Model)
- -------------------------------------
1 General one-factor linear model
2 Formulae for CAPM
3 market risk, firm specific risk, total risk
4 manually download data from Yahoo!Finance
5 market index (S&P500)
6 closing price vs. adjusted closing price
7 use Fama-French market and risk-free rate
8 An easy way to get risk-free rate
9 How to run a linear regression?
10 T-value and P value
11 R2 and adjusted R2
12 adjusted beta
13 portfolio beta
14 Dimson (1979) beta adjustment
15 Assumption behind the CAPM
16 Several R data sets
17 CAPM an absurd model
18 one-line comments on 'CAPM: an absurd model'
19 Videos
20 Links
Example #1:>.c17 # find out the above list
Example #2:>.c17() # the same as the above
Example #3:>.c17(1) # see the first explanation
";.zchapter17(i)}
.n17chapter<-20
.zchapter17<-function(i){
if(i==0){
print(.c17)
}else{
.printEachQ(17,i,.n17chapter)
}
}
.c17<-.chapter17
.C17EXPLAIN1<-"General one-factor linear model
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1-factor linear model has the following form:
y= alpha + beta *x
where y is the dependent variable
x is the independent variable
alpha is the intercept
beta is the slope
We try to use x plus a and b to explain or predict y
1-factor: since we have just one independent variable
linear : a) if we draw a graph based on y and x,
it is a straight line
b) the power of the independent variable, i.e.,
x is one.
/////////////////////////////////
"
.C17EXPLAIN2<-"Formulae for CAPM
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CAPM
E[R(i)] = Rf + beta *[R(m)-Rf] (1)
where E[] is the expectation
R(i) is for stock i's return
Rf is the risk-free rate
beta is the market risk (slope)
R(m) is the market return
To estimate beta, we run the following regression
R(i,t) = Rf(t) + beta *[R(m,t)-Rf(t)] + e(t) (2)
where R(i,t) is the stock i's return at time t
Rf(t) is the risk-free rate at time t
beta is the market risk (slope)
R(m,t) is the market return at time t
e(t) is a random factor
For example, for IBM, we have the following form.
to make our notation clear, we drop the notation of t
R(IBM) = alpha + beta *[R(m)-Rf] + e (3)
Sometime, we write the following way:
R(IBM)- Rf = alpha + beta *[R(m)0 - Rf] (4)
The interpretation of Equation (4) is clearer.
The left-hand side is the risk premium for IBM
It is the product of two factors:
a) market risk of IBM, and
b) the market risk premium
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"
.C17EXPLAIN3<-"market risk, firm specific risk, total risk
/////////////////////////////////
Total risk = market risk + firm specific risk
sigma: total risk
beta : market risk
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"
.C17EXPLAIN4<-"manually download historical data from Yahoo!Finance
/////////////////////////////////
We have the following steps
Step 1: go to finance.yahoo.com
Step 2: enter a ticker, such as ibm
step 3: click \"historical data\"
step 4: choose beginning and ending dates
frequency
Step 5: click \"Apply\"
Step 6: download to your spreadsheet
/////////////////////////////////
"
.C17EXPLAIN5<-"Market Index
/////////////////////////////////
For the S&P500 index, its ticker (symbol) is ^GSPC
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"
.C17EXPLAIN6<-"closing price vs. adjusted closing price
/////////////////////////////////
When we download daily data from Yahoo!finance, we have the
following format:
Date,Open,High,Low,Close,Volume,Adj.Close
2017-03-09,179.149994,179.25,175.880005,177.179993,5413100,177.179993
2017-03-08,180.75,180.949997,179.300003,179.449997,3520000,179.449997
2017-03-07,180.710007,181.289993,180.199997,180.380005,2930800,180.380005
2017-03-06,179.720001,180.990005,179.570007,180.470001,3180900,180.470001
There are two closing price: close and adjusted close.
The close is the observed closing price while the adj.Close is the
adjusted closing price which considering stock split, dividend
and other distributions.
To estimate our returns, we have to use the adjusted close.
Here is an example. Assume that there is no information or no trading.
John bought one share at $10. At the end of his investing horizon, he sold it at $10.
$10 $10
|------------------------------------|
0 1
His return is zero since (10-10)/10 = 0
Assume that the company announced a 2-for-1 split
$10 $5
|------------------------------------|
0 1
What is John's return?
Still zero since (2*5-10)/10=0
What happen if we use closing price to estimate
instead of the adjusted close?
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"
.C17EXPLAIN7<-"use Fama-French market and risk-free rate
/////////////////////////////////
Step 1: go to Prof. French Data Library
Step 2: find data set
Step 3: download
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"
.C17EXPLAIN8<-"An easy way to get Fama-French market and risk-free rate
/////////////////////////////////
Step 1: type
.uu
Step 2: type the following command to see the instruction
.showff3Monthly
Step 2B: type the following command to see the daily data
.showff3Daily
/////////////////////////////////
"
.C17EXPLAIN9<-"How to run a linear regression?
/////////////////////////////////
the function used is called lm(y~x)
set.seed(123)
# note that if we choose the same set of random seed
# we would get the same set of random numbers
x<-seq(1,10,by=0.2)
a<-2
beta=3
n<-length(x)
y=a+beta*x +rnorm(n)
plot(x,y)
lm(y~x)
summary(lm(y~x))
> summary(lm(y~x))
Call:
lm(formula = y ~ x)
Residuals:
Min 1Q Median 3Q Max
-2.01284 -0.65420 -0.03916 0.65827 2.14669
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.06650 0.32731 6.314 1.17e-07 ***
x 2.99539 0.05359 55.892 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.9651 on 44 degrees of freedom
Multiple R-squared: 0.9861, Adjusted R-squared: 0.9858
F-statistic: 3124 on 1 and 44 DF, p-value: < 2.2e-16
/////////////////////////////////
"
.C17EXPLAIN211<-"use Fama-French market and risk-free rate
/////////////////////////////////
We could use the excess market risk premium and risk-free rate
from Prof. French's factor time series
Example #1:>showffMonthly()
DATE MKT_RF SMB HML RF
1 1926-07-01 0.0296 -0.023 -0.0287 0.0022
2 1926-08-01 0.0264 -0.014 0.0419 0.0025
> showffMonthly(-2)
DATE MKT_RF SMB HML RF
1078 2016-04-01 0.0091 0.0084 0.0312 1e-04
1079 2016-05-01 0.0178 -0.0028 -0.0185 1e-04
Example #2: get daily data and save it
> x=showffDaily(0)
> saveYan(x,\"c:/temp/ffDaily.csv\")
[1] \"Your saved file is ==>c:/temp/ffDaily.csv\"
Example #3: get monthly data and save it
> x=showffMonthly(0)
> saveYan(x,\"c:/temp/ffMonthly.csv\")
[1] \"Your saved file is ==>c:/temp/ffMonthly.csv\"
/////////////////////////////////
"
.C17EXPLAIN10<-"T-value and P value
/////////////////////////////////
We should look at the T-value and/or P-value to make a judgement
whether a coefficient is statistically significant.
To get a critical T-value for a given alpha (significant level)
and number of observations, we have the following formula
> qt(0.05,50) # for one sided
[1] -1.675905
> qt(0.05/2,50)
> qt(0.05/2,50)
[1] -2.008559
critical.t <- function(){
cat('\\n','Enter Alpha Level','\\n')
alpha<-scan(n=1,what = double(0),quiet=T)
cat('\\n','1 Tailed or 2 Tailed:\\nEnter either 1 or 2','\\n')
tt <- scan(n=1,what = double(0),quiet=T)
cat('\\n','Enter Number of Observations','\\n')
n <- scan(n=1,what = double(0),quiet=T)
cat('\\n\\nCritical Value =',qt(1-(alpha/tt), n-2), '\\n')
}
source: https://stackoverflow.com/questions/11526041/critical-t-values-in-r
/////////////////////////////////
"
.C17EXPLAIN11<-"R2 and adjusted R2
/////////////////////////////////
R2 is a measure of goodness of a model
adjusted R2 is a better measure since it considers
the number of independent variables.
/////////////////////////////////
"
.C17EXPLAIN12<-"adjusted beta
/////////////////////////////////
The formula is used to adjust our estimated beta.
2 1
adjusted Beta= ---*beta + --
3 3
where beta is our estimated beta
The underlying logic is that beta has a meaning reverting property.
The mean is about 1. This means that if our estimated beta this
year is above 1, there is a good chance that its next year's beta
would be smaller. The opposite is true: if this year's beta is
less than 1, there is a good chance that the next year's beta
is higher, i.e., closer to 1.
/////////////////////////////////
"
.C17EXPLAIN13<-"portfolio beta
/////////////////////////////////
The portfolio beta is the weighted individual stock beta.
beta(portfolio) = w1*beta1 + w2*beta2 + ... + wn*betan
where beta(portfolio) is the portfolio's beta
w1 is the weight for stock 1
beta1 is the beta for stock 1
investment for stock 1
w1= -------------------------
total investment
/////////////////////////////////
"
.C17EXPLAIN14<-"Dimson (1979) beta adjustment
/////////////////////////////////
[note: this is optional material]
Dimson, E., (1979). Risk measurement when shares are subject to infrequent
trading, Journal of Financial Economics, 7, 197-226
http://www.sciencedirect.com/science/article/pii/0304405X79900138
/////////////////////////////////
"
.C17EXPLAIN15<-"Assumption behind the CAPM
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Assumptions:
#1: All investors are risk averse by nature
#2: Investors have the same time period to evaluate information
#3: There is unlimited capital to borrow at the risk-free rate of return
#4: Investments can be divided into unlimited pieces and sizes
#5: There are no taxes, inflation or transactions costs
/////////////////////////////////
"
.C17EXPLAIN16<-"Several R data sets
/////////////////////////////////
http://canisius.edu/~yany/RData/ibm.RData
http://canisius.edu/~yany/RData/dell.RData
http://canisius.edu/~yany/RData/SP500.RData
http://canisius.edu/~yany/RData/daily100.RData
http://canisius.edu/~yany/RData/retDIBM.RData
/////////////////////////////////
"
.EX7P17<-"CAPM: an absurd model
/////////////////////////////////
Pablo Fernandez, Professor of Finance. IESE Business School, University of Navarra
e-mail: fernandezpa@iese.edu. Camino del Cerro del Aguila 3. 28023 Madrid, SpainNovember 3, 2014
On October 2014, I sent the article \"CAPM: an absurd model\" to several professors, professionals and Ph.D. students,
telling them that \"I will appreciate very much your opinion and criticism\". I thank very much all that answered the about 300
interesting comments and criticism that follow. I have learned a lot reading (and thinking about) all of them because are real
opinions of real persons that know finance and have thought about it.
The CAPM is about expected return. If you find a formula that works well in the real markets, would you
publish it? Before or after becoming a billionaire?
The CAPM is an absurd model because not only its assumptions but also its predictions/conclusions have no
basis in the real world. (Absurd means 1. ridiculously unreasonable, unsound, or incongruous . 2:
having no rational or orderly relationship to human life. Meaningless. utterly or obviously senseless, illogical, or untrue;
contrary to all reason or common sense; laughably foolish or false. (Source: http://www.merriamwebster.
com/dictionary/absurd)
With the vast amount of information and research that we have, it is quite clear that the CAPM is neither a
theory nor a model because it does not \"explain facts or events\", nor does it \"describe the past, present, or
future state of something\".
The use of CAPM is also a source of litigation. Users of the CAPM make many illogical errors valuing
companies, accepting/rejecting investment projects, evaluating fund performance, pricing goods and services in
regulated markets, calculating value creation...
It is important to differentiate between a fact (something that truly exists or happens: something that has
actual existence; a true piece of information) and an opinion (what someone thinks about a particular thing).
The CAPM could be described as an uninformed opinion, and not as a sensible opinion.
We may find out an investor's expected return for IBM by asking him. However, it is impossible to
determine the expected return for IBM of the market, because this parameter does not exist. Different investors
have different cash flow expectations and different expected (and required) returns to equity. One could only
talk of the expected return of the market if all investors had the same expectations. But investors do not have
homogeneous expectations.
Valuation is about required return. There are persons, papers and books that mix (or assume that are equal)
expected and required returns.
/////////////////////////////////
"
.EX7P18<-"One-line comments and criticism: on 'CAPM: an absurd model'
/////////////////////////////////
I teach CAPM as a kind of religion/belief. You neither can prove nor falsify it.
I totally agree with the absurdity of CAPM model.
Every professional investor knows CAPM doesn't work. I know of no portfolio manager that actually uses it.
I agree with most of your assertions. In my opinion, CAPM is at best a waste of time.
I share your opinion about CAPM. It has for a long time been a \"taboo\" in financial research and practice.
Why you send this for review which can ruin your reputation?
I myself think that CAPM is overemphasized and blindly used without seeing the suitability even for valuations
CAPM is good for nothing (or it is good for the purpose different from the declared one- to be quite precise).
I have been telling my classes not to use this model for some years now.
I agree about the general uselessness of CAPM for practical applications.
In the U.S. Tax Court case of Gallagher, the U.S. tax court heavily discounted the CAPM model except for large entities.
Finally someone dares say what many sensible people secretly thought. CAPM is not a good explanation.
I couldn't agree more with your paper's title.
Nice work... I will use it with my students in ethics in finance
Welcome to the party of combating bad economists!
I am convinced that CAPM it's one of the most stupid ideas around...
My own opinion is that our inability to separate systematic from idiosyncratic risk is the root problem.
Simply great to see you're trashing this pompous model!
We say \"Beauty is in the eye of the beholder.\" Perhaps we should say \"Beta is in the eye of the beholder.\"
It is a very good fundamental work in the jungle of too much empiricism.
I have never believed in CAPM for circularity in its reasoning.
The IMF carried out an analysis of Banks' profitability based on the CAPM in the last issue of its GFSR! Have a look!
We advocate using multiple measures of estimating cost of equity to ensure reasonableness.
CAPM is absurd, but it has many friends who are not always open to criticism.
I appreciate your demonstration that common sense is the best available shield against phony models.
Quite scary for poor old finance profs. like myself who have to fight the textbooks and rewrite their old teaching notes.
Trying to prove an investment is good or bad based on stock volatility (rather than its basic merits) is silly.
I have always regarded the CAPM as absurd because of all the irrationalities that investors display.
Note that this is a model for which a Nobel Prize was granted.
I would add that the real flaw is in the concept of beta itself. It's like a dog trying to bite its tail!!!
I would suggest focusing more on the recommendation on how to calculate the beta in a sensible way.
I think it has the right findings and it offers a good alternative for estimating the cost of equity.
Your manuscript is impassioned with no reasonable. Every model has limitations and trying to explain (only) something.
I agree that \"there are in fact two things, science and opinion; the former begets knowledge, the latter ignorance\"
I think that your points and arguments are sufficiently strong to demonstrate this absurdity.
I don't agree with any linear pricing models, these include CAPM and any multi-factor pricing models.
It appears that you are saying the emperor has no clothes!
A paper like this had to be written. I am grateful you did.
From my experience economists do not like when somebody criticizes a widely used model.
/////////////////////////////////
"
.EX7P19<-"Videos
/////////////////////////////////
Calculating stock beta using Excel (4m28s)
https://www.youtube.com/watch?v=zlClflcSrM8
What is Beta? - MoneyWeek Investment Tutorials (5m29s)
https://www.youtube.com/watch?v=etlv7qTQUSY
Beta Calculation on Excel (9m48s)
https://www.youtube.com/watch?v=7LiK-qbmPsw
How to Calculate Beta with Excel, Calculation of Beta (18m43s)
https://www.youtube.com/watch?v=LRyFn_T94IU
/////////////////////////////////
"
.C17EXPLAIN20<-"Links
/////////////////////////////////
Damodaran, Aswath, Estimating beta
http://people.stern.nyu.edu/adamodar/pdfiles/eqnotes/discrate2.pdf
Damodaran, Aswath, Estimating Risk Parameters
http://pages.stern.nyu.edu/~adamodar/pdfiles/papers/beta.pdf
Fernandez,Pablo, 2014,2015,CAPM: An Absurd Model,
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2505597
http://www.appraisers.org/docs/default-source/event_doc/2016_bv_presentation_fernandez1.pdf?sfvrsn=2
Ide,Michael,2014,'Absurd' Comments About CAPM Masquerading As Research
http://www.valuewalk.com/2014/12/capm-investing/
Invetorpedio, The Capital Asset Pricing Model: an Overview
http://www.investopedia.com/articles/06/capm.asp
/////////////////////////////////
"