13th Mar 2010
HELP! I am trying to understand CAPM and the cost of equity capital.
I've found plenty of websites that outline the formula, have a
calculator, etc. So I don't want any links. What I need is someone to
please exaplain to me the CAPM concept as if you were talking to a
12-year old. This means, I would appreciate someone walking me
through, step by step, the CAPM formulas as if you were talking to me
and explaining each element rather than presenting a formula for me to
fill in the blanks.
You can assume:
I read and understand English
I'm college educated, but not in finance
I have a 142 IQ
I can operate a calculator and am proficient at Excel
I understand the concept of common stock and investing in general
I understand the concept of risk, including unsystematic and
systematic risk factors
I understand the concept of a diversified portfolio
I understand that there is a direct relationship between higher risk
and the OPPORTUNITY for higher reward
...and.. I suck at math formulas. I am dyslexic, so trying to use the
formula is a barrier to understanding the concept. Once I understand
it systematically, the formula will become embedded and I'll be
golden.
Generous tip if I actually get it the first time through ;-)Margi --
The Capital Asset Pricing Model (CAPM) is used to estimate the cost of
capital to a corporation. Most students are confused because finance
classes take them through the derivation of the formula, assuming
different risk levels for firms with debt and firms without debt.
When you learn that the cost of equity is the same for both, as is the
case in the real world (except for firms on the brink of bankruptcy),
it greatly simplifies the formula.
I?ve included links here ? but only so that you can look at issues or
an example in more depth after reading this answer.
HISTORY OF CAPM
=================
The Capital Asset Pricing Model was developed in the 1960s by William
F. Sharpe and has become the cornerstone of corporate finance. It
also enabled the development of options and futures markets in the
1970s.
Sharpe was awarded the Nobel Prize for the work in 1990:
NobelPrize.org
?THIS YEAR'S LAUREATES ARE PIONEERS IN THE THEORY OF FINANCIAL
ECONOMICS AND CORPORATE FINANCE,? (Oct. 16, 1990)
http://nobelprize.org/economics/laureates/1990/press.html
COST OF CAPITAL
==================
When money is borrowed, there's a cost for the opportunity to use it
month-after-month or year-after-year.
The lowest rate that you?ll see is the rate on Treasury bills, though
even those vary by time. Historically the Treasury bill interest
rate, often called the ?risk free? rate, tracks inflation very
closely. The reason that the U.S. Treasury rates are considered "risk
free" is that if the government runs out of money, it can print more
-- though then inflation rises.
Here are some different interest costs, taken from today?s Wall Street
Journal -- and structured from lowest-risk to highest-risk:
* 6-month Treasury bills: 3.04%
* prime rate: 5.75%
* 10-year Treasury bond: 4.43%
* 25-year Treasury bond: 4.74%
* Freddie Mac 30-year mortgage: 5.58%
* Class A corporate bonds: 4.9-6.0%
* High-yield corporate bonds: 6.7-10%
* Credit card lending: 20-22%
Typically CAPM problems take a long-term Treasury rate, as investors
in stocks are in it for the long-term.
Note that as the Federal Reserve Bank changes its discount rate, all
of these interest rates change. So too, should returns on projects at
Ford or Microsoft. So too, should the returns on stock investments.
Any company still investing to earn a 5% return when inflation has
doubled to 10% is actually
squandering investors' money. ? and the market reacts to it in the stock price.
It turns out that the risk factors are standard for stocks:
? inflation rate
? market risk
? firm risk
CAPM MODEL
============
The CAPM model says that the return to investors (and to the
corporation, Rc) has to be equal to:
? the risk-free rate
? PLUS a premium for stocks as a whole that is higher than the
risk-free rate. This market return premium is (rM ? rf)
? And the market return should be multiplied by the risk factor for
the individual company, termed the ?beta of the corporation? ( c)
Expressed as a formula, it?s:
Rc = rf + c(rM - rf)
Where,
Rc is the company's expected return on capital
rf is the risk-free return rate, usually a long-term U.S. Treasury bill rate
rM is the expected return on the entire market of all investments.
Most measures use a common broad index, most often the S&P500 over the
past 5 or 10 years
c is the company's Beta, based on its covariance with the market.
MEASURES OF BETA
==================
It seems that you understand the firm risk or beta. But it deserves some comment:
* Beta is a measure of the volatility of the company as compared to
the market. A beta of more than 1.0 means that as the stock market
goes up (or down) the firm will move MORE than the market average. A
beta below 1.0 means a ?lower risk? firm that isn?t as dramatically
affected by economic changes. Historically these have been food or
utility companies, where economic or market changes have less impact
on their businesses.
* Most commonly it?s measured as co-variance with the S&P500, as it?s
one of the broadest market indices. However, even then you?ll see
slightly different numbers for a ?beta,? as some methods calculate it
over 1 year, others over 3 years and still others over 5 years.
SOME OTHER STUFF
==================
* Remember when I said that debt was irrelevant? Merton Miller, who
taught at the University of Chicago?s Graduate School of Business when
I was there, was a very funny guy. He and Franco Modigliani developed
the theory behind debt irrelevance. He explains their explanation of
the irrelevance of borrowing
in the capital structure this way, "Say you have a pizza, and
it is divided into four slices. If you cut it into eight slices, you
still have the same amount of pizza. We proved that! Rigorously!"
Arnold Kling -- AP Economics
"Corporate Finance: Leverage and the Modigliani-Miller Theorem" (undated)
http://arnoldkling.com/econ/saving/corpfin.html
** There often are issues in deciding exactly what numbers to use in
the models but I can assure you that financial analysts use these
models extensively in valuing Google and every other company. Here?s
a problem in which someone?s wrestling with Harley Davidson?s cost of
capital and you can see comments on what numbers to use:
Google Answers
?Determine and justify the required rate of return for Harley Davidson
(HDI),? (Omnivorous-GA, April 21, 2005)
http://answers.google.com/answers/threadview?id=511996
IS BETA DEAD?
==============
If you ever wonder what goes on at business schools, a lot of effort
goes into disproving efficient market models like the CAPM. A 1992
paper by Eugene F. Fama (University of Chicago) and Kenneth R. French
(Dartmouth) , two well-known seemed to indicate that small firms don?t
follow the rules for beta and risk. The paper is titled "The
Cross-Section of Expected Stock Returns" and appeared in the Journal
of Finance (1992).
Here?s some interesting background to it but I can assure you that
beta?s not dead and considered in sophisticated options pricing
models:
Google Answers
?Cross-Section of Expected Stock Returns,? (Omnivorous-GA, Nov. 8, 2003)
http://answers.google.com/answers/threadview?id=273817
Google search strategy:
CAPM + beta + WACC
?Capital asset pricing model? + beta
Best regards ? and let me know if you need help with Black-Scholes!
Omnivorous-GADear Omnivorous-ga (I was secretly hoping you would be the one to answer this...)
You said: Expressed as a formula, it?s:
Rc = rf + c(rM - rf)
Where,
Rc is the company's expected return on capital
rf is the risk-free return rate, usually a long-term U.S. Treasury bill rate
rM is the expected return on the entire market of all investments.
Most measures use a common broad index, most often the S&P500 over the
past 5 or 10 years
c is the company's Beta, based on its covariance with the market.
So, if the risk-free return rate is 5%
And the expected return on the entire market is 10%
And, the company's beta is 2
Then:
Rc = rf + c(rM - rf)
Rc = 5 + 2(10-5)
Rc = 5 + 2(5)
Rc = 5+10
Rc = 15%
And the reason why this would be a risk is directly tied to the beta
of the company. Right?
Since holding a diversified portfolio is supposed to insulate me from
the effects of unsystematic risks, and the CAPM is an idealized model
for determining expected return versus systematic risk, what do I do
next? I have this number of 15%. What do I measure against it? What,
exactly, is it telling me?
I guess I'm still missing the context of the formula and CAPM in general.
Does this scenario even make sense? Let's say I've got a presentation
to my board of directors regarding how we are going to use CAPM to
help us determine where to invest, and the goal of our portfolio will
be to create a 18% per year return on our investment portfolio over
all. I've created a CAPM analysis on a variety of potential
institutional buys, and the Rc numbers vary from 11% to 24%. Now
what?
I think the problem I'm running into is that most sources expect that
I already know WHY I'd like to do the CAPM analysis... and the truth
is, I don't. I'm sure I'm exposing my level of understanding (or lack
thereof), and would appreciate your help. You've gotten me this far,
and I'd appreciate your help. In addition to a tip, you can probably
expect a follow on question regarding Cost of Equity Capital ;-)
I'll save Black-Scholes for next time...LOL!
THANK YOU!
-MargiMargi --
You've got the calculations precisely correct. And I'll explain the
implications for you tomorrow. You've picked a high-beta firm, so
this company will make VERY different investment decisions than, for
example, your local bank.
Sorry, I can't answer sooner but I have to go watch my beloved
Cleveland Indians play the Seattle Mariners.
By the way, you can ask for researchers by name if you'd like. And,
this IS the cost of equity. Is your follow-up a question about equity
or perhaps really the Weight-Average Cost of Capital? I'll treat
debt-equity issues slightly in the follow-up clarification but an
extensive discussion really is a whole new question.
Best regards,
Omnivorous-GAI will gladly take you up on your offer of help tomorrow, and good
luck in the game tonight!!! Go Indians!
I'll post the other question separately if I'm not able to master it
this evening. The concept is estimating the cost of equity capital as
it relates to the required return on a firm's common stock, and also
understanding risk-adjusted discount rates.
I'm using HBS's case 9-276-183, but, just like the stuff I'm finding
on the net, it assumes a certain level of baseline context that I
haven't yet been exposed to. While I've been very fortunate to have a
fairly well-rounded career to date, up until now, I've left the finer
elements of finance to those with better initials after their names...
Those days are over, and I'm finding I've got some catching up to do!
Thanks again,
MargiMargi --
You've figured out the required return on equity. It matches what
investors expect from the firm and it's what should be used in
evaluating projects internally.
And that's how it gets used:
* Within financial markets it's used to price stock, options, futures
and even (in some instances) bonds. Today very sophisticated computer
models test pricing of stock vs. the market vs. options vs. warrants
vs. convertible bonds and attempt to find ways to arbitrage a trade
that will make money.
* Within the firm the cost of equity should be used for all business
decisions. I'll give you some examples here and ask you what should
be done. Please use the cost-of-capital that you've already
calculated (Rc = 15%, beta = 2). ANYTHING that has a positive return
or net present value (NPV) should be funded, as it adds wealth to the
corporation. Oh, and for the following, assume that Margisoft has
minimal debt. In fact, think "no debt," just because it should be
clearer.
1. Margisoft is hiring 50 "detailers" who will visit computer stores
to make sure that products are properly promoted and stocked. They'll
need 50 minivans and you've checked on lease rates: they're 8%.
Should Margisoft buy or lease the minivans?
2. Margisoft has $10 million invested in its Bothell printing &
distribution facility, which produces about 2/3's of its manuals,
boxes and CDs. Much of the balance of the printing & box assembly is
done by Kao Corp., a soap and magnetic media company in Japan (I'm not
making this part up!) Judging by price comparisons with Kao,
Margisoft is saving $1 million by printing & assembling its software
in Bothell. Should you continue in the print/distribution business?
3. Kao is willing to buy the print/distribution facility and all of
the assets for $10 million. Kao's beta is 0.70. Should it's
management make the purchase?
4. Real estate on the east side of Seattle has been increasing at
8-10% per year for the past 10 years. Should you okay the project to
spend $25 million to buy 300 acres in Redmond, WA for the Margisoft
campus -- or should you rent? Why might you decide to buy the land
and build the campus anyway?
5. GE Leasing has been using its excellent credit rating to float
bonds at 6% -- and lease software at 10%. They've now approached
Margisoft's major OEMS (Dell, H-P, Sony, Toshiba, Zenith Data Systems)
and offered to finance their $1 billion in annual software purchases
from Margisoft via monthly lease payments instead of the lump sum that
they pay Margisoft each December. Do you care?
6. You read through the GE Leasing bond prospectuses and realize that
you care a lot because the prospectus would have detailed information
about how much business and what you sell to the PC manufacturers.
How would you structure Margisoft Leasing so that you can compete --
and not cost your shareholders wealth?
7. The Margisoft Office group has done a holiday promotion each
December that's resulted in selling an extra 60,000 copies of Office
at $200 to distributors. The bill-of-materials cost of Office is $10
and you'll also need to fund a 3% cooperative marketing fund for the
distributors' purchase. Your advertising costs for radio spots
nationwide will be $10 million. Do you do the promotion?
8. Margisoft Office sales have been running 20% ahead of last year
for six months. Marketing says that you have a 75% chance of selling
an extra 60,000 copies -- but a 25% chance of selling 72,000 extra
copies. Do you do the promotion now?
Best regards,
Omnivorous-GAOh my Lord... It's like having my own personal prof!!!! I didn't
expect additional homework today, though! ;-) And, I like the name of
the company, except that it sounds like we may be a bit marginal.
Perhaps the name is appropriate, because I can't get the leasing
scenario...
(BTW, congrats on the 6-1 over the Mariners)
1. Margisoft is hiring 50 "detailers" who will visit computer stores
to make sure that products are properly promoted and stocked. They'll
need 50 minivans and you've checked on lease rates: they're 8%.
Should Margisoft buy or lease the minivans?
To use my own capital costs me 15% (because my return on my stock, by
definition, is also my internal cost of equity capital). To lease
costs me 8%. I should lease.
2. Margisoft has $10 million invested in its Bothell printing &
distribution facility, which produces about 2/3's of its manuals,
boxes and CDs. Much of the balance of the printing & box assembly is
done by Kao Corp., a soap and magnetic media company in Japan (I'm not
making this part up!) Judging by price comparisons with Kao,
Margisoft is saving $1 million by printing & assembling its software
in Bothell. Should you continue in the print/distribution business?
1/3 (or 33%) of my printing via outsource saves me $1mil. So, if I
were to pay Kao to do the printing, my project costs would increase
33%. This isn't attractive. That $1mil costs me 15% but saves me 33%,
right?
3. Kao is willing to buy the print/distribution facility and all of
the assets for $10 million. Kao's beta is 0.70. Should it's
management make the purchase?
Assuming the risk free and market rates are the same as my prior
example, then their Rc = 8.5%. Their cost of capital at 8.5% measures
favorably against the Rm of 10% and is a good use of capital. ??
4. Real estate on the east side of Seattle has been increasing at
8-10% per year for the past 10 years. Should you okay the project to
spend $25 million to buy 300 acres in Redmond, WA for the Margisoft
campus -- or should you rent? Why might you decide to buy the land
and build the campus anyway?
My Rc is 15% and the value will only increase 8-10%, a 5+% difference,
so, at first glance it's not attractive. I might decide to buy anyway
because rent purely is outlay with absolutely no return, and the
facilities that I build upon the 300 acres may appreciate to more than
make up for the difference, and the land with facilities may be
significantly of higher value than a field of clover. There are
dependencies on how the debt is structured, i.e. % at bank for loan to
build versus my 15% cost of capital.
5. GE Leasing has been using its excellent credit rating to float
bonds at 6% -- and lease software at 10%. They've now approached
Margisoft's major OEMS (Dell, H-P, Sony, Toshiba, Zenith Data Systems)
and offered to finance their $1 billion in annual software purchases
from Margisoft via monthly lease payments instead of the lump sum that
they pay Margisoft each December. Do you care?
I'm not sure how CAPM fits into this. I'm thinking out loud here. 10%
versus my Rc of 15% isn't attractive, but the 15% doesn't acknowledge
that the $1b isn't my cost. BUT, hmmm... cost of capital is still
cost of capital, right? I have a variety of things I could potentially
spend this money on and get a higher return. I know that companies
choose NOT to do this. They let GE Capital and others do the
financing... The answer appears to be that I care, but not enough to
offer the financing myself. What am I missing?
6. You read through the GE Leasing bond prospectuses and realize that
you care a lot because the prospectus would have detailed information
about how much business and what you sell to the PC manufacturers.
How would you structure Margisoft Leasing so that you can compete --
and not cost your shareholders wealth?
I've played with this for an hour and can't figure it out. Again, I'm
sure I'm missing something here with the leasing scenario.
7. The Margisoft Office group has done a holiday promotion each
December that's resulted in selling an extra 60,000 copies of Office
at $200 to distributors. The bill-of-materials cost of Office is $10
and you'll also need to fund a 3% cooperative marketing fund for the
distributors' purchase. Your advertising costs for radio spots
nationwide will be $10 million. Do you do the promotion?
As a marketer, I would never spend $10Mil for a nationwide radio spot
that sells Office to distributors. Is this a trick question?
I'm going to use $190 for my calc.
60K($190) will give me a 14% return on my $10mil at a cost of 15%.
The 3% additional marketing fund for the co-op pushes it further out
of range. It's a no-go.
8. Margisoft Office sales have been running 20% ahead of last year
for six months. Marketing says that you have a 75% chance of selling
an extra 60,000 copies -- but a 25% chance of selling 72,000 extra
copies. Do you do the promotion now?
Not one marketing person (myself included) has ever been able to tell
me if those percentages were all or nothing, i.e. does a 75% chance of
selling 60K copies translate to 45K copies, or is it all or nothing,
like flipping a coin?
75% of 60K is 45K copies for a total just short of $20 mil for my $10
mil investment. It's a go. 25% of 72K is an additional 18K, which
then puts me at close to 50% return. It's also a go.
As you can probably tell, in the past, due to lack of formal trining
in such things, I've usually gone through some sort of thought process
to determine viability versus using a formla. It usually means that I
wind up is some complex weight-valued analysis with a matrix of
considerations. The biggest decision I every made this way was an
investment of $24MM. In theory, CAPM seems clean... but it doesn't
represent every factor that goes into a decision, i.e. making a
strategic investment based on a level of certainty in a future reward.
So I have to wonder if in real life CAPM is used cleanly.
You've been very patient, and I appreciate the help very much. I'd
appreciate it if you would point out the errors in my work so that I
can get this, but I also understand if that's not convenient. Even if
I haven't mastered the topic yet, I've got the gray matter energized.
I don't know if you can post after I've tipped or if it closes it out,
so I'll wait and see if you post today.
I have to say, while I've had great GA experiences (i.e. TaxMamma for
tax questions and PinkFreud on some business and social questions)
this is the first time I've used GA as a way to understand an
academic/study issue better, and I've found it to be very valuable. I
didn't know if it would work, but it does, and I think a large factor
in that is in the WAY you've interacted with me in this forum. Thank
you so much!!!! :-)Margi --
The intent of the questions wasn?t to make you work but to set up some
standard models for analysis ? and show how they work. It was also
meant to deal with some real-world decisions and what ?other? factors
might be. There's a moral lesson in this too (and I say this only
slightly tongue-in-cheek) -- don't let the bean counters do a
simplistic analysis.
By the way, they?re all real world issues too, taken from the play
book of that ?other? Redmond software company.
1. Car lease: easy. If you use cash to buy the cars, each of them
puts $1,750 into the hands of the car dealer that should have been
returned to the shareholders in dividends. (That?s the 7% penalty of
using cash.)
2. It?s a good thing that I don?t write questions for textbooks
because I left some things vague in this one. If your savings on
printing are $1 million on a $10 million investment, it?s a 10%
return. You?ve quite logically said: ?Bring the printing in-house and
we?d save $1.33 million.?
But if you?re already outsourcing, it?s probably because you don?t
have the right equipment or are using vendors to handle peak loads or
maybe that you?re not really very competitive as a printer.
In either scenario, $1 million in savings or $1.33 million you?re not
just making enough, as it?s 10% in the first case and 13.3% in the
second case. Sell the place ? which is exactly what Microsoft did in
the late 1990s. Take the $10 million and try to put Netscape or
Google out of business.
3. What should Kao do? This is actually the one ?trick? question. It
may be that Kao U.S. goes to the capital markets at 8.5% -- and
they?ll make $1 million to $1.33 million on the investment. (After
all, it assures that the Microsoft business isn?t outsourced to RR
Donnelly or another printer.)
It?s definitely a go, with an Rc of 8.5% and returns of 10-13.3%.
But consider another scenario: Kao is a Tokyo Exchange company and the
risk-free rate is 1.375% in Japan due to lower inflation. With a
risk-free rate that low, market returns are probably less than 5%
(that?s a separate topic) ? but we?ll use it for Kao?s Rc = 1.375% +
3.5% = 4.875%
Why not raise the money in the Japanese market and spend it for U.S.
expansion? That?s probably precisely what Kao Finance would do.
4. NPV doesn?t allow for the residual real estate value ? you?re going
to use it as long as the company exists.
However, you?re thinking in the right direction on one aspect: you
could borrow using a conventional mortgage and reduce the costs to the
shareholder. This starts to take us into the area of Weighted Average
Cost of Capital ? and it is a very real reason that corporations have
leasing divisions. But I?ll reserve that for the next couple of
questions.
The real reason that Microsoft has made the decision to build a campus
comes from a strategic decision to keep its teams working closely
together. Even in this corporation ? which starts virtually every
meeting with "why are we here?" ? they recognize that people have to
meet formally and in the hallways to communicate key information. If
you have a team spread out in 3 buildings, it may reduce productivity
by 10%, which would be $10,000 per year for each of your 25,000
full-time employees.
5. The lesson here is: don?t use cash to fund it. It?s a 10% gross
return on your own receivables. But can we structure a way to do what
GE Leasing does?
6. You hire Omnivorous to set up the Margisoft Leasing division in
Reno, NV. Oops, that?s a typo, I meant Margisoft Leasing PLC in the
Bahamas. Yeah, that?s the ticket!
It?ll cost $1 million to set up the corporation and legal structure
and to operate Margisoft Leasing. We?ll use the good faith and credit
of Margisoft to float bonds at 6%, just like General Electric does.
We?ll need $500 million on average (half the year), so it will cost us
$30 million in interest payments. We?ll charge the OEMs 10% or $50
million.
We make $20 million on the $1 million investment, using the value of
leverage. Do you think the shareholders will vote to approve that
plan?
7. The radio spots are intended for pull-through. I simply used the
?distributors? as the example to be structurally accurate.
You?re netting $184 per copy in gross profits ($10 B.O.M. and $6
co-op). You?ll make $11.04 million on a $10M investment. No, don?t
do it, even though it's clearly profitable on an accounting basis.
8. We all deal with forecasts in making business decisions and the
frustrating part of them is that you know in advance that THEY?RE
ALWAYS WRONG! Oh, you also know that you?ll spend a lot of time
preparing for something that?s always wrong . . .
But you can systematically improve your marketing by analyzing what
works; setting numbers to as many decisions as you can (even branding
decisions, where the ?return? might be more ephemeral); then finding
ways to improve.
One way to deal with them is to use ?expected values.?
E(v) of the 75% case is 0.75 * $11.04M = $8.28M
E(v) of the 25% case is 0.25 * $13.25M = $3.31M
E(v) of the Margisoft Office promotion is $8.28M + $3.31M = $11.59M or
15.9%. It would be a ?go? here.
I don?t want to get too much farther into financial discussions here ?
but believe it or not, there are ways to further reduce the risk that
you?ll sell 72,000 extra copies only 25% of the time.
---
I?m not very familiar with the HBR case that you?re working with,
though cost of capital was a constant issue with regulated utilities
like the phone companies until the CAPM became widely accepted.
The CAPM works ? and it?s logical:
The CAPM says that investors expect a premium over T-bills to invest
in stocks. A wide portfolio (actually as few as 9 or 10 stocks) will
provide a ?market? return to investors. The firm will have a risk
premium or not depending on the structure of its business.
----
All of that said, be wary of one thing: the Communications Satellite
Corp. case apparently deals with the cost of EQUITY.
As you?ve seen from the leasing example, we?ve taken the no-debt
Margisoft and tacked on a unit with $500M of bonded debt. The returns
of $20M on a $1M investment were handsome for the shareholders ? but
I?ve changed the weighted-average cost of capital (WACC). The WACC is
a mix of debt and equity. But that?s another question.
And besides it?ll soon be time for baseball again today.
Best regards,
Omnivorous-GAThis isn't a request for clarification. I couldn't find the comment
button (??) Anywhooo... just to let you know that I totally got the
CAPM concept and have even started plans to formally bring it to
practice at my job. The class went very well, and I appreciate your
help tremendously!!! You are awesome! THANK YOU!Margi --
Thank you so much for the comment. (And the RFC works fine because it
actually e-mails me a note!)
Please understand that your comment means more to me even than the tip
involved. To understand how sincerely I mean that, you should
probably know that the true motto of the University of Chicago
Graduate School of Business (my alma mater) is "There's no such thing
as a free lunch" and you were kind enough to provide more than a free
lunch.
At any rate, the CAPM and options theory pricing -- a derivative of it
-- is incredibly important in understanding many, many sophisticated
ways of managing businesses. It is behind even baseball and the
Sabermetric theories of baseball management. You can explore some
interesting ones by searching Google Answers with "omnivorous-ga" +
"CAPM" or "omnivorous-ga" + "Black-Scholes".
And understand too that there are still new interpretations being
developed. (I think that a great question would be "Given the
increases in petroleum prices, what does CAPM and option pricing
theory say that the airlines should do with ticket prices?" But
there are only a handful of GA researchers who wouldn't hit the 'Next'
button before the end of THAT question.)
Researchers sometimes miss the mark with precisely what customers are seeking.
It's always a joy to know when we hit the spot!
Best regards,
Omnivorous-GA#If you have any other info about this subject , Please add it free.# |
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