Buffett slams Black-Scholes and 'flat earth' economists

[Andy Nguyen]

A very interesting recap of Buffet's latest letter to shareholders

Buffett said that the accounting obligation to use Black-Scholes, which he sees as deeply flawed, meant that Berkshire had to increase its balance-sheet liability during the year to December 2010 from $8.9bn to $9.6bn, a change that, after the effect of tax accruals, reduced the group’s net income for the final quarter by $455 million. Buffett said,

Both Charlie and I believe that Black-Scholes produces wildly inappropriate values when applied to long-dated options. We set out one absurd example in these pages two years ago. […] We continue, nevertheless, to use that formula in presenting our financial statements. Black-Scholes is the accepted standard for option valuation – almost all leading business schools teach it – and we would be accused of shoddy accounting if we deviated from it.
"Moreover, we would present our auditors with an insurmountable problem were we to do that: They have clients who are our counterparties and who use Black-Scholes values for the same contracts we hold. It would be impossible for our auditors to attest to the accuracy of both their values and ours were the two far apart.

http://www.qfinance.com/blogs/ian-f...slams-black-scholes-and-flat-earth-economists

 

[Yike Lu]

Warren Buffet also said that his ideal holding period would be infinite - it minimizes the costs of trading. He also did a back of the envelope calculation of stock market returns vs aggregate trading costs and concluded that the trading community at large gave whatever profits made from investing back to Wall Street in the form of trading costs.

The guy is a talented investor and sharp, but his perspective is very very skewed to his personal style (value investing). This is no doubt further amplified by a journalist who wants an eye-catching headline.

That isn't to attack his point about Black-Scholes' use in long-dated options. Being somewhat "non standard" options, there must be some issues, especially related to term-structure of volatility.

 

[daleholborow]

Out of interest, do you disagree with either of the first two Buffett points you mention?

And it would seem to me that the aim of investing is to maximise your returns... if Buffett has the best returns over the longest times, wouldn't that suggest he's worth listening to?

 

[financeguy]

hang on, black-scholes is wrong? i better unwind some stuff on monday.

 

[bigbadwolf]

hang on, black-scholes is wrong? i better unwind some stuff on monday.

What's right about it? I'm serious.

 

[Tsotne]

hang on, black-scholes is wrong? i better unwind some stuff on monday.

Come on, since 1973 there have been attempts to design some "sophisticated" methods for pricing options and each one proved to be not useful. How can we say the model is wrong or right?! Look at it and assess the idea it is carrying. BS is ideal method among those which have been created up till now. All the models before and many after it relied on inputs which were unobservable. Buffet seems to be claiming against the reliance on the model if they failed not the model itself.

 

[daleholborow]

Come on, since 1973 there have been attempts to design some "sophisticated" methods for pricing options and each one proved to be not useful.

Search for an article, in fact, I've done it for you: (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075) , in which the authors discuss the ability of traders to price options well before the BS-argument, and I believe they argue, in a more "ideal" manner.

How can we say the model is wrong or right?! [...] Buffet seems to be claiming against the reliance on the model if they failed not the model itself.

Er.... what good is a model if you can't in some way rely on the results it produces? To fall back on a well-worn quote, all models are wrong, but some models are useful It reads to me like Buffett is saying that BS is not applicable/relevant/useful when valuing the components in his portfolio. Is he right? I dunno...

 

[Tsotne]

@daleholborow
That's not what I meant. I have read the first article. If we agree on the assumption of the model which again is the ideal among others till now, then we have no other way to rely on it. It gives inappropriate answer for long standing options he says when he hasn't got a better way. Auditors is another theme, how to regulate and value the ability of a firm engaged in options trading has always been an issue. BS has the exactly the same solution as the heat equation in physics, nothing new.

Er.... what good is a model if you can't in some way rely on the results it produces?

Nobody says it is error-free. But do we have any better model? You can see the Bodie speech in the following video. He also argues that the model is the best one among others invented so far.

 

[daleholborow]

I'm sorry, I don't really understand what point you are trying to make with the first part of this latest post and video? The point is, people (Taleb and Haug, amongst others), very blatantly DO NOT agree with the assumptions of the BS model, and indeed I think they argue that it absolutely IS NOT the best method available.

I think one of the very last sentences spoken in the above video is very telling: "Academics marvelled at it's breathtaking insights and its sheer audacity". The article I link to above, however, suggests that PRACTITIONERS however, were doing just fine without it The appeal of the model is it's simplicity... it has a certain purity and appeal, as though BSM had tapped into a wonderful universal truth for option pricing. In actuality however, authors like Taleb and co. are suggesting it is at BEST a rule of thumb for pricing.... one that occasionally blows up in your face when you trust it too much.

 

[Tsotne]

very blatantly DO NOT agree with the assumptions of the BS model

This is exactly what I am resisting. Many models before and after BSM have proved to be inconvenient for computational purposes since unobservable variables were as inputs or not reliable since they "blew up".

and indeed I think they argue that it absolutely IS NOT the best method available.

So which method is the best available then? BS is misleading sometimes as every model is whether a good or bad approximation. And approximation may come out to be inappropriate in some cases but the way to go is BS. If not, then I really wonder which model is the best, why it is mathematically more sound and accurate and all in all, derivatives business is where the largest amount of money flows, why hasn't that model been such widespread? Interesting...

 

[daleholborow]

*sigh* I really don't want to start a war. I don't have the inclination, nor the experience to comment on what model is "the best". I personally don't know of any other model that HAS blown up and caused damage to the same extent as the BS model (of course, that is possibly due to the massive degree that it was embraced by the market). Although, maybe that's because the other (Bachelier-Thorp?) type models actually DO manage risk better?

But seems to me you've already asked and answered your own question, at least partly: "Why isnt a different model more widespread?".

Precisely because they are more computationally intensive, harder for traders to get instant intuition regarding the results, etc etc. There are already non-parametric option pricing methods that produce arguably "better" results than BS, I know guys who have published them, but they aren't used... because the standard model, the industry default, is BS. In the same way that the US uses imperial units of measure even though they're shit, they're outdated and backward... but they're the standard, what everyone is used to. That doesn't mean there isn't a better way... just that people aren't using it

 

[Tsotne]

Not a war Just discussing.

I personally don't know of any other model that HAS blown up and caused damage to the same extent as the BS model (of course, that is possibly due to the massive degree that it was embraced by the market).

I know many, Ill search in my book where the names and methods are stated that were just idea and nothing more. As for second part of the above quote, I think I partially answered already by saying that no model is exact and BS proves to be misleading sometimes. So when just one model is used you should have know many occasions when BS is false.

But seems to me you've already asked and answered your own question, at least partly: "Why isnt a different model more widespread?".

Nothing asked. Just said that if other models can be a better approximation than BSM, then they would be used intensively. If you claim they are used but for traders who have limited time to follow the complexities of mathematical formulas while BS gives them the shortcut to do the trick, I would definitely ask you the proportion of financial institutions which use those models and not so often BS. They are not traders right?! Have more time. Assume they are not engaged in timely activities when speed is the main concern. I can give you the rude proportion that's somewhere 95% for BS against 5% relying some other methods.

And the most interesting part of your post I found was this:

There are already non-parametric option pricing methods that produce arguably "better" results than BS, I know guys who have published them, but they aren't used... because the standard model, the industry default, is BS.

Tell me the name of those nonparametric models and Ill quickly give you the mathematical proof that they are derived from the BS assumptions and some of them are just the direct extensions of BS taking into consideration constant re-hedging strategies. Fine, let's say it this way. We have common BS model (on which we both agree) and also have binomial model which can also be used for European options but are never used. Since BS gives the exact answer based on the same assumptions right? YES. In infinity binomial model is nothing more than BS calculated premium. They give the same answer. Now consider the parity relationships between puts and calls, from which are they derived from? You can state the binomial proof of everything which holds exactly the same assumptions as BS model. We can safely mean almost all the numerical option pricing methods as binomial. Most of them are derived on the same assumptions so you cannot say that they are better than BS.

That doesn't mean there isn't a better way... just that people aren't using it

I think I also answered this

Best

 

[daleholborow]

Tell me the name of those nonparametric models and Ill quickly give you the mathematical proof that they are derived from the BS assumptions and some of them are just the direct extensions of BS taking into consideration constant re-hedging strategies.

Ahahahahaha....

"Non parametric model" -> in no way related to BS.. which is a distinctly parametric model. For various reasons I'd prefer not to comment on the particular models I am more familiar with, but as some examples, and a particularly relevant abstract, I refer you to the following results of a quick google search:

http://finance.martinsewell.com/option-pricing/Radz.pdf

"Non-parametric and computational methods of option pricing have recently attracted attention of researchers. These
typically include highly data intensive, model-free approaches that complement traditional parametric methods.
Non-parametric and computational methods of option pricing typically include highly data intensive, model-free
approaches that complement traditional parametric methods. One characteristic of such methods is their
independence of the assumptions of continuous-time finance theory."

 

[Tsotne]

@daleholborow

"Non parametric model" -> in no way related to BS.. which is a distinctly parametric model.

Hah...Seems you don't see the point of developing the nonparametric model from parametric one. Who told you that? You must have seen the Sharpe restrictions that's why you deviated from technique (at least as I see). Now, have you heard of the non-parametric adjustments of Black Shoes??? I definitely think you haven't. It's not like the broken bridge between parametric and nonparametric models which cannot be recovered. Again, the assumptions of numerical models and Black Sholes stated exact formula are the same(most of them). Or do you know how to solve or understand the assumption of the differential equation of to derive the outcome of the heat equation??? NO. Can you come up with ways to construct a model from parametric family of models like statistical distributions and relate them by changing parameters to get the nonparametric models. You'd better read copulas or derivations of Archimedesian copulas if you got interested. The assumption is from parametric marginal distributions and the nonparametric joint cumulative distributions are obtained. I would suggest Nelsen's book to walk through. You'd also better to read non parametric adjustment to BS backward movement. Do you know about the Nonparametric Estimation of Scalar Diffusion Models Derived from Black Sholes assumption???

So don't say that non parametric models have nothing to do with parametric ones or are unadjustable . Im gonna provide useful articles for you and Ill post now if you are interested on that particular issue how to construct a nonparametric models from parametric ones and vise versa.

As for the formulas you say you are not aware and cannot state. Look at the video again and listen to Bodie. He talks abot the models that relied on inputs that were completely unobservable like "expectations of investors". And then he says: "How can you come up with the number what i expect?!, or how could you come up with the number that has no any dimension and is expressed in nothing".

Best

 

[daleholborow]

The models I've read (and I'll admit I'm not intimately familiar with them) relied more or less entirely on observable market data.

In general, I'm getting more and more lost reading your replies

I don't know if I'm really misunderstanding your posts, but you seem to be consistently putting words in my mouth? I never said I wasn't aware - I said I preferred not to discuss a couple (for personal/professional reasons). I never said they were "unadjustable", whatever you want that to mean. I'm unsure what you mean by me "deviating from technique"? That is not MY paper, its an example I found for you. I never said I wasnt familiar with your beloved heat equation.

I find it kind of laughable that Bodie mentions investor expectations included in some models, and somehow your project that to apply to all these other failed models? Some models DID use investor expectations. It was found to be problematic. Some models use game theory. It is problematic. The fact that some people look to the stars to plan their future doesn't mean I believe, or even care... sometimes flawed methods are popular, and sometimes probably even useful? What Bodie doesn't comment on, which is the I guess the crux of ALL my comments above, is that BS is used because it's popular, and because it's convenient, and it's popular because it's the standard, and... and.... and the relationship is circular. Lots of other methods are not used, because they are computationally inconvenient, etc etc.

Its like using a P/E ratio to quickly decide if a stock is good value or not. It's a flawed, ridiculous method, but it's utterly ingrained in the finance industry because it's quick to calculate and readily captures the attention of average joe investors that are the targets of financial industry advice-givers.

Copulas don't interest me in the slightest, and no, I can't come up with ways to construct an option pricing model from statistical distributions. I'm not sure what the point would be, even if I could? Haven't you yourself decided that BS is far superior to all other such attempts? That said, I'm always interested in good papers / study resources, so if you have any by all means please post them, but personally, I'm probably more into fixed interest stuff and anything that has been shown to be remotely robust in practise, not rigorous mathematical proofs of flawed models (I probably couldnt understand them anyway ).

In the mean time, this is starting to feel less like a discussion and more like an argument, which was not my intention, so I'll sign off and admit defeat Good luck with your studies.

 

[Tsotne]

In the mean time, this is starting to feel less like a discussion and more like an argument, which was not my intention, so I'll sign off and admit defeat Good luck with your studies.

I still have a feeling we are discussing with arguments - it's normal. No win-loose goals. I really found your arguments interesting whether BS is good or bad. I also read the articles' links provided here. I'll answer your questions and that would be like a summary of my points as you say you are misunderstanding or lost somewhere.

The models I've read (and I'll admit I'm not intimately familiar with them) relied more or less entirely on observable market data.

Zvi Bodie's words: "Previous models relied on inputs that were completely unobservable, like expectations of investors. How can you come up with number what I expect?! Or how could you come up with such number?!" Noway. We can't assign a number to something which has no dimension. He argues that models were unreliable since included on unmeasurable inputs. Agreed. You say you meant models which relied on observable inputs (you don't state the models though - it's ok) some of them were rejected by institutional investors. Those ones which survived and you still think are appropriate in pricing options, are not famous for the reason(as you say) that, black sholes provides a shortcut to compute quickly without digging into mathematical complexity, perfect for traders as you say. OK my answer was that apart from traders, people at large investment banks who have enough time and even more, they also use the BS by far the largest frequency and I provided the proportion of time by how much BS is used and other ones. Also many models to price an option have the same assumptions as BS. For example I said most common one-Binomial model. We can combine all of the numerical methods as the same ones deriving from the same assumption and the assumption is "my beloved" heat equation. If you look at it and compare to numerical option pricing methods you will see the major similarity making the numerical methods' calculated premium exactly the same as BS. For example, again binomial gives the same value as BSM in infinity. Also I mentioned put-call parity and proofs. You can derive them by either method since the assumption is the same - boils down to BS again.

I never said they were "unadjustable", whatever you want that to mean. I'm unsure what you mean by me "deviating from technique"? That is not MY paper, its an example I found for you. I never said I wasn't familiar with your beloved heat equation.

Answer:

Ahahahahaha....

"Non parametric model" -> in no way related to BS.. which is a distinctly parametric model.

We can state nonparametric models and derive their proofs by adjusting the BS parameters to nonparametric. For example holding some of them constant and simulating the remaining observable parameters by MC or historical simulation methods(especially faster when integrating more than 2 parameters, in copulas when underlings are more than 2 assets-credit derivatives case). Good example how to switch from parametric models to nonparametric ones are copula approaches. It is really interesting how they do it with Archimedesian copulas. Nelsen explains really fine.

But as for the Sharpe and what I meant by deviating is that, you probably have read the sharpe restriction while studding nonparametric option pricing methods and that got you confused. Techniques used to derive the nonparametric solution from parametric families of distributions, math formulas(whatever they are) , etc. are different from that explained by sharpe. It's not like an example - just like the first google outcome.

Copulas don't interest me in the slightest, and no, I can't come up with ways to construct an option pricing model from statistical distributions.

I never suggested that and thats pointless. How can you come up with ways to construct option pricing formula from statistical distributions. Which distributions. Never mind...

All in all, I have heard interesting points from you. Thanks for the discussion. Not a war really though we both pushed lots of arguments haha.

Good Luck you also

Regards
Tsotne

 

[daleholborow]

Cheers mate. Sorry, this is the problem with the internet... I read a post and think "Oops, I've upset this guy now", sometimes it is hard to tell the tone of the replies I'm always willing to debate, but sometimes my sense of humour doesn't translate well over the 'net.

 

[Tsotne]

Cheers mate. Sorry, this is the problem with the internet... I read a post and think "Oops, I've upset this guy now", sometimes it is hard to tell the tone of the replies I'm always willing to debate, but sometimes my sense of humour doesn't translate well over the 'net.

It's ok. This is really the case with me too. Very hard to control the tone of the messages Thank a lot.

 

[bob]

Um, okay Warren. He has revealed himself repeatedly as either hypocritical or willfully blind in recent years. A guy who famously called derivatives "financial weapons of mass destruction" sells huge quantities of naked long-dated index puts as a business strategy? (In some ways worse than naked, since the rest of his business is also naturally long the index.) He wasn't complaining about the Black-Scholes valuation when he collected the premium, was he?

I also guarantee you that he would have few complaints about Black-Scholes now if they were marking his positions at a 1% vol. The guy's trying to make his balance sheet look better, and that's really all there is to it. If he proves to have been right, then the PL will show it as the options approach maturity. In the meantime, he's massively short vol--which is merely the Black-Scholes way of saying what anybody with an ounce of common sense would say about this position: He's massively exposed to an adverse market move.

 

[daleholborow]

Bob, I originally agreed with you on this, I was very surprised that the guy who was so vocally against derivatives would chose to issue them. Then, on a bit of reflection, I think that there is a subtlety here that I didn't appreciate originally.

If I can go back to my earlier P/E analogy, the fact that the rest of the market uses some arbitrary method to price a contract (in this case BS for put options), doesn't mean that Buffett necessarily agrees with it, or that the market model and price in any way influenced his valuation? I now see this as an extension of his overall investing methodology: The rest of the market participants chose to value stocks in one way, Buffett in some circumstances disagrees with their conclusions based on his own method of valuation and buys/sells accordingly. So, precisely for that reason, he wouldn't (vocally) disagree with the BS valuation if he thought it overpriced the put options he was trying to sell, precisely because it means people using that model (he believes incorrectly) are willing to buy puts from him (he believes to his advantage).

In this case, the market uses BS model to price puts on an index... Buffett disagrees with the sentiment, and has taken a position (albeit expressed in the mechanism of a WMD as you point out), but in line with Andy's original article, almost certainly isnt actually using the BS model to value his position.

Thoughts?