Oh, boy, Black-Scholes, brings back a flood of memories. In the early ‘80s I was hired for a Wall Street sales job, and in 1985 I moved to the Mortgage Backed Securities (MBS) trading desk within the Capital Markets department of E.F. Hutton. Having more options knowledge and familiarity than the average MBS trader I rather quickly found myself managing the entire $1bln MBS options book. Due to the fact that mortgage loans can be paid off early - through the sale of the underlying home, refinancing, or the death of the homeowner MBS securities themselves include an implicit (short) call. The security owner receives a slightly better return than the owner of similarly rated government security. (The entire option book was govt. backed MBS.) It became clear fairly quickly to me that Black-Scholes was inadequate to the task of valuing options, especially when the underlying security includes a short call, but then current alternatives were as well. In the mid-90s I was hired by a bank that was later absorbed into BOA and management assured me at hiring that their risk models were “tested to 20 standard deviations.” That Bank virtually closed down its Capital Markets division after horrendous losses on their foreign debt trading desk when Mexico devalued the Peso! Later, In 2003-2004 I danced around with one of the major government MBS agencies for a position as trader/risk manager, etc. I was in an interview with their CFO - who had recently moved from a Wall Street firm (which failed in the ‘08 crash) when I first heard someone in management use the term “fat tails” which I had known about from Mandlebrot. The amount of dollars and man hours that Wall Street had invested in a normal distribution risk model is mind boggling, even after there was some general knowledge that the underlying assumptions were absolutely wrong!
Nice! Like I say, I'm very much coming at it from the academic end of things, so very interesting to hear perspectives from people on that sharp end. My perception is that this heavy-tailed problem was an issue in the Long-Term Capital Management mess (with Scholes and Merton on board of course), but I'm not 100% sure if that's accurate or not!
As someone who coincidentally just finished readying When Genius Failed, covering the rise and fall of LTCM - yes it absolutely was. Lowenstein references this concept in the book several times, so was fun to see it covered more comprehensively in your post here as well! The other major problem that bit LTCM is that Black-Scholes assumes continuous pricing in securities; we all know that this isn't true, liquidity dries up in times of crisis and concern, leading to prices gapping downwards (or upwards, if you're holding a short position, which you could conceive of LTCM's core thesis of spread convergence as).
You know, there were so many “mini-crashes” in sub-sectors of the bond markets in my 30 years in Capital Markets that I lost count and had forgotten about LTCM! I absolutely agree when I learned who was on their board I thought the same thing. An example of a “smaller disaster” can be found in the MBS - CMO market… The original four or five tranche CMOs did - for the most part - served a positive purpose, creating four (or five) new securities with progressively longer call protection. Wall Street’s never heard of “too much of a good idea” where making money is concerned and I can remember Kidder Peabody in particular issuing 50-60 tranche $2bln behemoths. With a four or five tranche deal, one could somewhat satisfactorily reverse engineer the deal with an HP-12C and a yellow pad… but no such luck with the bigger deals. Bear & Kidder (in my memory) were the main culprits in issuing these securities and had the onerous task of unloading the (frankly) toxic waste tranches. They found willing takers in the smaller regional bond firms (Memphis, Little Rock, etc…) who marketed the junk tranches to the unsophisticated portfolio managers of the thousands of community banks, credit unions, insurance companies, and even endowments throughout the country. For instance, a moderate sized Junior College endowment of $100mm in West Texas lost 50% of its value after a bond market sell off. These were all “Government Securities” bearing GNMA, FNMA, or FHLMC names & years before the enormous reliance on “private label” MBS which enabled the entire credit default debacle…
For the sake of accuracy, the College in question was Odessa (Texas) Junior College which had 100% of its $22mm endowment in MBS derivatives, and subsequently sued six brokerages in the Summer of 1994 as the fund had lost 50% of its value. The most immediate cite I could find is in The Chronicle of Higher Education - September 28, 1994. Not huge losses by Wall Street standards, but multiply this by the hundreds of unsophisticated small to medium sized institutions that followed their brokers’ recommendations!
Cool, thanks! Yes, I think the whole "equivalent martingale measure" thing is very pretty, and should hold regardless of any assumptions about the underlying tails, but it's very interesting to hear about that particular slice of history
I’m not a gambler, though I’m intrigued by people who are, and especially who gamble on tennis (a sport I know well) which is prone to upsets. How would one model event probability there, where there are many, many matches played and upsets (judged by comparative ranking of each player) unlikely but possible? Do you aggregate all the match results, with 1 for expected and -1 for upset (or larger for a bigger disparity: if the No 300 beats the No 7, as happened this week, is that a -293?
I’m just thinking out loud, but there are people who gamble stupid amounts of money on such things, but I doubt they have any model to guide their behaviour.
I agree. I think you could try and model it - if you calculated an Elo rating https://en.wikipedia.org/wiki/Elo_rating_system for each player then in theory it gives you a probability of each outcome for example.
But (and this is not based on any particular players!) I'd have a nagging feeling that there might be people out there who were prepared to take a dive in minor tournaments, or that I might be betting against people who were better informed than me about whose knee just went and so on.
Oh certainly about the “better informed” or dive-taking. The ITIA (tennis integrity authority) is VERY hot on betting patterns around upsets in lower-ranking matches particularly.
Look, I'm just a petty gambler, but it is odd not to mention Kelly.
And the truth for anything financial is that you don't have ever have to have the really funky distributions where you have massive tails against you. You can almost always reasonably limit your loss to a fixed sum - but that's boring to a lot of people because when you do the return profile looks very small.
No, I don't think it's necessary to talk about Kelly here - I tend to think of that stuff as upstream of this. That is, yes, if you are in a situation where (your model of) the underlying probabilities don't match the odds then Kelly can tell you how to exploit that in terms of a strategy. And one result of the strategy would be something like a red or blue payoff curve. But my point is that even a Kelly-optimized strategy needn't be immune to the problems of heavy tails I'm talking about here
Oh, boy, Black-Scholes, brings back a flood of memories. In the early ‘80s I was hired for a Wall Street sales job, and in 1985 I moved to the Mortgage Backed Securities (MBS) trading desk within the Capital Markets department of E.F. Hutton. Having more options knowledge and familiarity than the average MBS trader I rather quickly found myself managing the entire $1bln MBS options book. Due to the fact that mortgage loans can be paid off early - through the sale of the underlying home, refinancing, or the death of the homeowner MBS securities themselves include an implicit (short) call. The security owner receives a slightly better return than the owner of similarly rated government security. (The entire option book was govt. backed MBS.) It became clear fairly quickly to me that Black-Scholes was inadequate to the task of valuing options, especially when the underlying security includes a short call, but then current alternatives were as well. In the mid-90s I was hired by a bank that was later absorbed into BOA and management assured me at hiring that their risk models were “tested to 20 standard deviations.” That Bank virtually closed down its Capital Markets division after horrendous losses on their foreign debt trading desk when Mexico devalued the Peso! Later, In 2003-2004 I danced around with one of the major government MBS agencies for a position as trader/risk manager, etc. I was in an interview with their CFO - who had recently moved from a Wall Street firm (which failed in the ‘08 crash) when I first heard someone in management use the term “fat tails” which I had known about from Mandlebrot. The amount of dollars and man hours that Wall Street had invested in a normal distribution risk model is mind boggling, even after there was some general knowledge that the underlying assumptions were absolutely wrong!
Nice! Like I say, I'm very much coming at it from the academic end of things, so very interesting to hear perspectives from people on that sharp end. My perception is that this heavy-tailed problem was an issue in the Long-Term Capital Management mess (with Scholes and Merton on board of course), but I'm not 100% sure if that's accurate or not!
As someone who coincidentally just finished readying When Genius Failed, covering the rise and fall of LTCM - yes it absolutely was. Lowenstein references this concept in the book several times, so was fun to see it covered more comprehensively in your post here as well! The other major problem that bit LTCM is that Black-Scholes assumes continuous pricing in securities; we all know that this isn't true, liquidity dries up in times of crisis and concern, leading to prices gapping downwards (or upwards, if you're holding a short position, which you could conceive of LTCM's core thesis of spread convergence as).
Thanks for the great post(s)!
Great, thanks for confirming!
You know, there were so many “mini-crashes” in sub-sectors of the bond markets in my 30 years in Capital Markets that I lost count and had forgotten about LTCM! I absolutely agree when I learned who was on their board I thought the same thing. An example of a “smaller disaster” can be found in the MBS - CMO market… The original four or five tranche CMOs did - for the most part - served a positive purpose, creating four (or five) new securities with progressively longer call protection. Wall Street’s never heard of “too much of a good idea” where making money is concerned and I can remember Kidder Peabody in particular issuing 50-60 tranche $2bln behemoths. With a four or five tranche deal, one could somewhat satisfactorily reverse engineer the deal with an HP-12C and a yellow pad… but no such luck with the bigger deals. Bear & Kidder (in my memory) were the main culprits in issuing these securities and had the onerous task of unloading the (frankly) toxic waste tranches. They found willing takers in the smaller regional bond firms (Memphis, Little Rock, etc…) who marketed the junk tranches to the unsophisticated portfolio managers of the thousands of community banks, credit unions, insurance companies, and even endowments throughout the country. For instance, a moderate sized Junior College endowment of $100mm in West Texas lost 50% of its value after a bond market sell off. These were all “Government Securities” bearing GNMA, FNMA, or FHLMC names & years before the enormous reliance on “private label” MBS which enabled the entire credit default debacle…
Really interesting, thanks!
For the sake of accuracy, the College in question was Odessa (Texas) Junior College which had 100% of its $22mm endowment in MBS derivatives, and subsequently sued six brokerages in the Summer of 1994 as the fund had lost 50% of its value. The most immediate cite I could find is in The Chronicle of Higher Education - September 28, 1994. Not huge losses by Wall Street standards, but multiply this by the hundreds of unsophisticated small to medium sized institutions that followed their brokers’ recommendations!
Cool, thanks! Yes, I think the whole "equivalent martingale measure" thing is very pretty, and should hold regardless of any assumptions about the underlying tails, but it's very interesting to hear about that particular slice of history
I’m not a gambler, though I’m intrigued by people who are, and especially who gamble on tennis (a sport I know well) which is prone to upsets. How would one model event probability there, where there are many, many matches played and upsets (judged by comparative ranking of each player) unlikely but possible? Do you aggregate all the match results, with 1 for expected and -1 for upset (or larger for a bigger disparity: if the No 300 beats the No 7, as happened this week, is that a -293?
I’m just thinking out loud, but there are people who gamble stupid amounts of money on such things, but I doubt they have any model to guide their behaviour.
I agree. I think you could try and model it - if you calculated an Elo rating https://en.wikipedia.org/wiki/Elo_rating_system for each player then in theory it gives you a probability of each outcome for example.
But (and this is not based on any particular players!) I'd have a nagging feeling that there might be people out there who were prepared to take a dive in minor tournaments, or that I might be betting against people who were better informed than me about whose knee just went and so on.
Oh certainly about the “better informed” or dive-taking. The ITIA (tennis integrity authority) is VERY hot on betting patterns around upsets in lower-ranking matches particularly.
Look, I'm just a petty gambler, but it is odd not to mention Kelly.
And the truth for anything financial is that you don't have ever have to have the really funky distributions where you have massive tails against you. You can almost always reasonably limit your loss to a fixed sum - but that's boring to a lot of people because when you do the return profile looks very small.
No, I don't think it's necessary to talk about Kelly here - I tend to think of that stuff as upstream of this. That is, yes, if you are in a situation where (your model of) the underlying probabilities don't match the odds then Kelly can tell you how to exploit that in terms of a strategy. And one result of the strategy would be something like a red or blue payoff curve. But my point is that even a Kelly-optimized strategy needn't be immune to the problems of heavy tails I'm talking about here
This is very interesting - thanks!
Gambling where you come out ahead?
Sure. Insurance. The ookies are called actuaries.
Legal. It's socially useful risk transfer.
Ease of entry means competition. But innovation is rewarded.