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Mulla Nasreddin, Gaussian Distribution and Capital Asset Pricing Model
Mulla Nasreddin, a 13th century legend lived somewhere between Turkey and Afghanistan (both countries included). I am sure he must have been a kid and a young man in his time but he is remembered as an old man, old and outrageously wise. One evening he was seen looking for some lost article under a street lamp. A passerby inquired what was the Mulla looking for. “My ring”, came the reply . “Now, where exactly did you lose it” the stranger persisted. “Oh, yonder on the commons while grazing my donkey”Mulla replied. The stranger laughed and wondered aloud why the hell was the Mulla looking for the ring on the street then. The Mulla answered, with unshakable patience, "it is too dark on the commons to see anything, on the street there are lamp posts".
Mulla surely knew a thing or two. In 1962, Mandelbrot had demonstrated that asset returns are not normally distributed. Still, our risk models built in nineties (now I guess conclusively proved obsolete but still very much in use) were based on normal distribution of asset returns. Why? Because calculations are a lot simpler with this assumption.
Empirical evidence for CAPM is at best mixed. There are other models that, reportedly, better mimic the returns from risky assets. Still ninety-nine percent (or more) of finance graduates pass out from their schools without trying out any model other than CAPM. Why? Oh, it is so easy (for instructors).
Mulla surely knew a thing or two. In 1962, Mandelbrot had demonstrated that asset returns are not normally distributed. Still, our risk models built in nineties (now I guess conclusively proved obsolete but still very much in use) were based on normal distribution of asset returns. Why? Because calculations are a lot simpler with this assumption.
Empirical evidence for CAPM is at best mixed. There are other models that, reportedly, better mimic the returns from risky assets. Still ninety-nine percent (or more) of finance graduates pass out from their schools without trying out any model other than CAPM. Why? Oh, it is so easy (for instructors).
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Comment by Ali Asad Ghani on August 9, 2010 at 1:46pm -
Great post Sir.
Since i am one of those 90% of finance graduates so i would like to know what are the other better methods for pricing the assets( you can only just name them and i will look for it on the internet).
Regards
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Comment by Chad Ellis on August 9, 2010 at 3:32pm -
Charlie Munger (the acerbic partner of Warren Buffet) was asked about CAPM during a Berkshire Hathaway annual meeting. He said it was only slightly less absurd than most other things being taught in Finance classes about asset valuation. (I'm going from memory so I'm sure he said it more colorfully than I'm remembering.)
Sacha hits on the central point. CAPM is easy to teach, conducive to mathematical analysis, etc. in a way that lets people do a lot of work on and with it without addressing the fundamental question of whether it is useful. (The whole thing reminds me of the bit in The Goal that discusses all the papers about how to optimize batch sizes that don't address whether or not the operation is a constraint and thus are wrong before they start.)
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Comment by Tse Ka Man on August 9, 2010 at 10:45pm
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And it has to do with the fact that business schools are teaching CAPM to perpetuate its dominance over the employment market at i-Bank. You have millions of graduates, teachers and researchers who build their careers based on this flawed ideology. They will not accept anything that will challenge their standing and that's why any alternative explanation would be stymied at its infancy stage and hence you have this self-reinforcing loop.
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Comment by T.Venkataramanan on August 9, 2010 at 11:43pm
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I do not agree with these above observations.It is certainly one of the simple tools available for evaluating risk and capital assets( financial ).A better model is yet to be evolved.How ever EVA based models if any evolved, for asset pricing may be a more realistic one
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Comment by Sachidanand (Sacha) Singh on August 10, 2010 at 2:35am -
Let me put my instructor's cap. I too teach only CAPM and give passing references to F&F's three factors or the multi factor models. Because it is easy. Because the schools do not expect anything else from me and because it was too late by the time I discovered the folly.
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Comment by Sachidanand (Sacha) Singh on August 10, 2010 at 2:36am
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@Venkataramanan
EVA requires cost of capital.CAPM is the model mostly used fro determining that cost of capital.
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Comment by Takamirira Taruberekera on August 10, 2010 at 7:34am
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This is insightful and a brainteaser. Few Finance graduates think beyond CAPM. There are however some reseaches which might lead to an improvement of CAPM (not changing CAPM)
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Comment by sergei on August 10, 2010 at 9:53am -
I believe that copula-based CAPM instead of traditional Pearson based correlation CAPM would be more appropriate. You can apply the most goodness of fit distributions for both market returns and for returns of an asset under consideration and link them by a copula. Perhaps, the Clayton copula is the most suitable for the task. Just use R to make calculations...
http://cran.r-project.org/
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Comment by Sachidanand (Sacha) Singh on August 10, 2010 at 10:02am
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Are you telling it to me? I have already made clear my position in the first comment I posted. I am just lamenting on teh way things are going and having lamented I suppose I will go the same way (as I have done so far).
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Comment by sergei on August 11, 2010 at 9:40am
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I see.
Most people are lazy to construct complex models and they tend to use the simplest one.
At the same time it is difficult to explain the results of, say, copula-based model to managers not having strong education in statistics. And the simulation software, such as ModelRisk, is not readily available.
That is why the CAPM will be popular for a long time yet.
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