Using Monte Carlo simulation to teach finance

[Jamal Munshi]

I wrote a paper on teaching undergrad finance courses with simulaton instead of formulas and would be grateful for some feedback. My experience is that most undergrads hate math.
Here is the link to the paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2512091

 

[bigbadwolf]

There's probably something to this and it's not confined to finance. The use of high-powered mathematics obscures insight into fundamental processes wherever it's used. The math serves as crack cocaine that addles the mind but lends the appearance of power. Go back to Newton's Principia. He is using geometric arguments although he was familiar with the shortcut method of "fluxions" (which later became the calculus). But today undergrads get taught their first course in classical mechanics using calculus, without the physical understanding and intuition the earlier proto-scientists had. Undoubtedly the same thing is happening with the use of stochastic calculus in finance. It's not even clear that it's necessary. But it's teachable in the sense that it can be delivered through a set of lectures, which can be packaged and sold as an MFE program. The lemmas and theorems can be sold and it looks like something is happening when the prof works through them rapid-fire in the lecture hall. That the finance intuition isn't developed, remains stunted, or dies newborn, is considered irrelevant.

 

[Jamal Munshi]

There's probably something to this and it's not confined to finance. The use of high-powered mathematics obscures insight into fundamental processes wherever it's used. The math serves as crack cocaine that addles the mind but lends the appearance of power. Go back to Newton's Principia. He is using geometric arguments although he was familiar with the shortcut method of "fluxions" (which later became the calculus). But today undergrads get taught their first course in classical mechanics using calculus, without the physical understanding and intuition the earlier proto-scientists had. Undoubtedly the same thing is happening with the use of stochastic calculus in finance. It's not even clear that it's necessary. But it's teachable in the sense that it can be delivered through a set of lectures, which can be packaged and sold as an MFE program. The lemmas and theorems can be sold and it looks like something is happening when the prof works through them rapid-fire in the lecture hall. That the finance intuition isn't developed, remains stunted, or dies newborn, is considered irrelevant.

billiant comment. thank you bigbadwolf.
i think that many of the social sciences suffer from the so-called "physics envy" which causes them to seek legitimacy of their curriculum and pedagogy by injecting math into them. unfortunately for most undergrads, the math actually gets in the way.

 

[Daniel Duffy]

There's probably something to this and it's not confined to finance. The use of high-powered mathematics obscures insight into fundamental processes wherever it's used. The math serves as crack cocaine that addles the mind but lends the appearance of power. Go back to Newton's Principia. He is using geometric arguments although he was familiar with the shortcut method of "fluxions" (which later became the calculus). But today undergrads get taught their first course in classical mechanics using calculus, without the physical understanding and intuition the earlier proto-scientists had. Undoubtedly the same thing is happening with the use of stochastic calculus in finance. It's not even clear that it's necessary. But it's teachable in the sense that it can be delivered through a set of lectures, which can be packaged and sold as an MFE program. The lemmas and theorems can be sold and it looks like something is happening when the prof works through them rapid-fire in the lecture hall. That the finance intuition isn't developed, remains stunted, or dies newborn, is considered irrelevant.

It is prevalent in Mathematics: the Bourbaki school and it distaste for anything that is not axiomatic.

 

[yetanotherquant]

Hi Jamal,

though I generally also preach for Monte Carlo, I always encourage my "congregation" to learn math, if possible. And I always warn about pitfalls of the Monte Carlo (just try to calculate the price of an European knock-out; let alone the options with early exercise). The problem with math is not its difficulty per se but rather a dogmatic teaching without motivating examples. Proper mathematical insight can ignite even skeptical (but not lazy) students!

As to your paper, after a quick look I see some critical points:

1) "Risk is operationalized in financial theory as the standard deviation of value computed either from historical data or from subjective probabilities" Sorry, the standard deviation != the risk. If I (somehow) have only positive returns - sometimes large, sometimes small - the standard deviation will also be large but there is no risk.

2) You use Excel. Since even simplest Monte-Carlo simulations usually require a lot of paths, Excel is definitely suboptimal from the practical point of view.

3) (Just my personal opinion) If you are an undergraduate, you may write formulas in whatever you want. But if you teach (even undergraduates), you should write at least the formulas in LaTeX

 

[Salvatore R. Gulino]

I wrote a paper on teaching undergrad finance courses with simulaton instead of formulas and would be grateful for some feedback. My experience is that most undergrads hate math.
Here is the link to the paper. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2512091

The problem with applying Monte Carlo and alike risk models in the global financial markets: Gaming behaviors are more constant than those of the borrower. Thus, such models cannot possibly predict the future behaviors of borrowers for they can, and will change in an instant . This is due to the fact, inflation out paces median income causing Housing Cost To Income rise. Unlike the gambler, which can walk away from the table at any time, Borrowers are forced to keep playing /paying despite not being able to afford to do so, because they are locked into the game/mortgage for as long as 30 years.

Need more proof? You only need to look at the effects of past sales pitches of MBS between late 90's to 2007 who provided past performance of MBS from Monte Carlo models to convince their customers just how safe their investments would be in the future. The reassurance of the Monte Carlo and alike models of the 90s proved to be nothing more than a fools paradise, as it was in the 70s and 80's. The past three recessions should be all the proof we need to expose such models as being unreliable at best. I have attached a brief summary of our research which will provide a clearer prospective of the circle of events leading up to greater risk averages.

 

[Jamal Munshi]

a lot of good ideas here that i can use in my follow up paper. thank you all. there are probably better tools for this but excel is something that all business students know very well and so there is no downltime for learning a new tool.

 

[Jamal Munshi]

by the way, in finance the word risk is used slightly differently than in the vernacular. it does not necessarily imply the danger of negative returns. it simply means not knowing. so for example a guaranteed return of 10% is less risky than one in which the returns could be somethere between 10% and 20%.

 

[Salvatore R. Gulino]

Jamal,

Before we get too ahead of ourselves, in terms of finance or investments, in general, risk means chance of, or actual "loss" which could impact overall annual yield/returns. With regard to your example. I do not want you to be misled by blanket statements you may have read about risk. Their are many factors which could make a 20% return less risky than a 10% investment. "Timing" is just one of many factors.

For example: if we are talking about investing in MBS difference tranches are associated with difference levels of "weighed average risk" naturally the higher the risk the higher the return. However, this is not always the case. Here is where timing comes in, if you were to have purchased sub-prime MBS in 2001, the actual default rate or WAR would have turned out to be the same as conventional MBS.

However In 2007 this was not the case . The WAR was actual much higher than Monte Carlo type models had predicted. Why, you may ask? The guidelines in 2001-2007 did not change? The answer is quite simply, timing, just one of a number of considerations Monte Carlo and alike models do not account for.

These types of models can only predict the past not the future. So as you can see, it is possible to obtain a 20% return with the same risk as a 10% returns. Yields are not always related to risk. Monte Carlo and alike models do have their place, but as the examples I have given in this and past post clearly show, their roles should be limited, and in no way at the forefront of financial risk modeling, particularly in MBS as is the case today.

Best

 

[bigbadwolf]

Need more proof? You only need to look at the effects of past sales pitches of MBS between late 90's to 2007 who provided past performance of MBS from Monte Carlo models to convince their customers just how safe their investments would be in the future. The reassurance of the Monte Carlo and alike models of the 90s proved to be nothing more than a fools paradise, as it was in the 70s and 80's. The past three recessions should be all the proof we need to expose such models as being unreliable at best.

Agree with you but financial modeling (including Monte Carlo and econometrics) -- and forecasting in general -- is based on tacit assumptions that the future will in some sense be like the past. In finance, there's a built-in bias to doing this. A chunk of the problem is that there's no working theory of real world processes that are now having an impact on us and -- by implication -- on the world of finance (e.g., rising fuel prices, declining EROEI, et cetera). In brief, the math used has an inherent conservative function: to reassure people that the contours of the future will resemble those of the past. Without this reassurance the world of finance will probably implode.

 

[Salvatore R. Gulino]

BBW,

You have captured my point exactly! Lets stay on your train of thought, for you are on point of how such risk models work "is based on tacit assumptions that the future will in some sense be like the past'' This raises a very basic question, what past? do we set up such risk models for 1929-1945-1970 or 10 years ago.

I submit, none of these options would be correct. Our modern day economy is ever changing. Unfortunately such models can only predict the past. What we need are risk models which can predict the future. I have one I posted that I used with great success.

Unfortunately we are still too dependent on such MC models in MBS to develop tranches and sell bonds. We need more Quants who are willing to jump out of the MC box to develop additional models which are nimble enough to evolve with our ever changing state of our economy.

 

[Jamal Munshi]

good points all. many thanks for your thoughts.

 

[Jamal Munshi]

big bad wolf's comments and a really great paper by mathematician amir aczel of boston u. (in the journal "radiocarbon") inspired me to see if a purely numerical and computational approach would do a better job than analytical models for the statistical analysis of radiocarbon dating data. my answer is "yes". the numerical method is robust. i posted my numerical solution online along with the excel file and would be grateful for your comments. here is the link:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2572966

 

[vertigo]

thank you for taking the time to write your paper and present it to us. the purpose here is, by using simulation techniques, to make finance an easier subject to teach. it is an admirable effort.

that being said, i disagree with nearly everything in your paper. indeed, like a lot (and i mean a lot) of people, you are not aware of what you are really talking about. this confusion comes from talking about mathematics, yet not understanding mathematics. it is amazing - and yes, embarrassing, but it is that simple. this phenomenon is well known and any risk/project manager will blush in his face if you ask him/her about it.

first, as always, we must begin with the basics. you talk about 'monte carlo simulation'.... well, how did monte carlo simulation begin? read into it - and you will see that the creators of monte carlo simulation were the likes of von neumann, feynman, fermi, ulam, hastings, feynman...

take a few minutes to understand what i have just said here. von neumann could calculate an infinite power series in seconds. most people do not know what a power series, nor do they know what infinite is, let alone what an infinite power series is. von neumann was, simply put, a genius. you talk about how "algebra serves to obfuscate"... well, with all due respect, when even von neumann, a master of everything he touched, can not solve a problem analytically, one can understand that it is not the algebra that is obfuscating - it is the problem itself. i think this is difficult to understand. i would recommend taking some time to read this paragraph again. the 'philosopher'/ex trader taleb keeps barking on about this, so.. for more clarification -> read some of taleb's books.

so what did von neumann do when his analytical methods did not work? he supposed that a solution existed and that it would be approximated via simulations. how on earth is that rigorous? it is not. you need deep mathematical tools to prove that monte carlo simulations are rigorous. the most basic monte carlo simulations require knowledge of probability theory, statistical theory and linear algebra. why? because you need the central limit theorem for convergence (probability theory), you need to know which type of estimate you will pick - unbiased, minimum variance (statistical theory)? and of course, you need to know how to implement these (linear algebra). can you see how monte carlo simulation builds on these concepts. it does not avoid them.

how are you going to explain monte carlo simulation without these deep concepts? otherwise, you are the fool that is blind to the black swan - you are using something, talking about it, but you have no real understanding of what is going on. and that is the exact problem that a lot of people have.

concisely put, monte carlo simulation is not a level lower than analytical methods - in fact it is higher, it requires even more thinking. it is bizarre, incredibly bizarre, to me, that you will explain monte carlo simulation before or without analytical methods. i think this would be the worst possible approach.

your article has many mistakes or misunderstandings about finance. i do not have the time to pick on everything, but here are some mistakes.

• the abstract is confusing and i do not agree with any of it - whom are you to say what is right/wrong? some students prefer mathematics, some do not. some people prefer white wine, others prefer red wine. mathematics is a simplification of reality... if you find mathematics complicated, i am scared to think about just how complicated you will find reality. or even worse, you think reality is simple, but mathematics is complicated? do not be sucked into thinking algebra (and that in itself is also an abuse of language, how would you use the word algebra in the context of group theory, or galois theory? it would not make sense, at all) or equations are confusing - they are a way to put into symbols what we know and seek to clarify. that is all. by not understanding the equations, you do not understand the concept.
• risk is not the standard deviation of data. standard deviation, by definition, is a risk measure, which can give some quantitative information about the risk in data, but it is not risk. this is such a huge misunderstanding that it is hard to have confidence in the rest of the paper.
• normality assumptions are not used in everything in finance. var models that use historical simulation do not have any normality assumptions. a lot of time series methods do not have normality assumptions either.
• gaussian parameters? this does not mean anything. do you mean a parameter that has a gaussian prior? a parameter is not a random variable unless you are giving it a Bayesian framework and are treating it as one.
• equations are not complex. nor are they obfuscating. ok - assume that they are. go and show your complex equation to von neumann and see if he finds it complex - i think he will laugh. (ok, he will not because he has passed away, but my point remains). why do i say this? because what is complex is down to interpretation. this is a huge misunderstanding!
• humans have awful intuition. everything we work with, simply put, is rational. in mathematics, the set of rational numbers has lebesgue measure zero - meaning that everything of real interest is irrational. how are you going to put an intuition on that? how are you going to put an intuition on the black scholes equation when people have shown time and time again that you need very careful assumptions to make continuous time trading strategies realistically work in finance. intuition does exist - but it takes time to develop.
• is finance intuitive? this is a deep question. but let us assume that it is intuitive. by having intuition of a process, we know, at a high level, what is going on, without digressing to a low level and looking at everything. when you have financial crashes and trillion dollar losses and many thousands of people losing jobs in finance, i think you can assume that no, finance is not intuitive. or more concisely put, it is intuitive in a sense. but that sense must be developed rigorously.
• i have had some amazing and awful professors teach me finance, statistics, mathematics, etc. the best professors made it very, very clear what a model did and what that meant in conjunction to reality. there is no mention here to 'equation' or 'algebra' or 'computer'. it is simply being able to explain what you are teaching. in order to teach finance well, you must be able to understand the concepts behind finance and teach them. one can not assume that it is the use of equations that makes the teaching difficult for students.
• computational machinery is a tricky subject. any partial differential equation approach or stochastic differential equation approach to option pricing (or statistical analysis, blah blah blah) will suffer a global error. no improvement in computational machinery is going to fix that. what is my point here? by making computers better you can not really fix the 'difficult' stuff. there will never be a time, ever, where by making our computer super fast and super amazing, that algebra becomes easy. again, this is difficult to understand.
• excel is awful for monte carlo simulation.
• "the difference between simulated and analytical solutions is best explained with a simple coin toss example"? are you sure about that? .... tell that to von neumann and the others and they will laugh at you. you are not really understanding what you are talking about here.
• what is a stochastic parameter? in a monte carlo simulation, a parameter being stochastic or not will make a huge difference.

my opinion is simple: to teach finance well, it is sufficient and necessary to teach the concepts of finance well. one can not imply from this that equations are obfuscating and that simulation should replace them. it is that simple.