Modern portfolio theory has a fair amount to offer: Combining investments with different properties really can outperform a concentrated portfolio
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As Jon commented, I think he assumed the same time frame for both investments, but even still, in investment #1, if you reinvest everything and "let it ride" each time:
For investment #1, lets say the time horizon is 5 years to get to the outcome as you suggested, and in investment #2 it is 1 year.
Hopefully that comes through ok, I'm not going to try to expand the table further. But as you can see, as time goes on, even at the second time step, your chances of having (and keeping!) $0 get quite high. The tools many of the modern portfolio theorists use to evaluate risk include merely the two numbers "mean" and "variance". (Or sometimes only "beta" which they call "risk.")
This means that the guys at the computers don't see the long term difference between #1 and #2 in their computer models. They assume a normal distribution and don't account properly for when it's not. It's not even a matter of being short term greedy -- if they knew, they wouldn't ever pick investment #2, but they just don't know.
One of Jon's other points to me is that, by using too much leverage, you can turn something that seems like a very reasonable investment (assume investment #1 had a 50% chance of 0.9N instead of 50% chance of exactly N) into something that ends badly. Using leverage you can turn #1 into #2 and still have your modern portfolio theory mean and variance intact. Until something strange happens. Then you end up with $0 or worse.
A.I.G. F.P. was already insuring these big, diversified, AAA-rated piles of consumer loans; to get it to insure subprime mortgages was only a matter of pouring more and more of the things into the amorphous, unexamined piles. They went from being 2 percent subprime mortgages to being 95 percent subprime mortgages. And yet no one at A.I.G. said anything about it-not C.E.O. Martin Sullivan, not Joe Cassano, not Al Frost, the guy in A.I.G. F.P.’s Connecticut office in charge of selling his firm’s credit-default-swap services to the big Wall Street firms. The deals, by all accounts, were simply rubber-stamped by Cassano and then again by A.I.G. brass-and, on the theory that this was just more of the same, no one paid them special attention. It’s hard to know what Joe Cassano thought and when he thought it, but the traders inside A.I.G. F.P. are certain that neither Cassano nor the four or five people overseen directly by him, who worked in the unit that made the trades, realized how completely these piles of consumer loans had become, almost exclusively, composed of subprime mortgages.
...
it was simply a bet that U.S. home prices would never fall. Once he understood this, Joe Cassano actually changed his mind. He agreed with Gene Park: A.I.G. F.P. shouldn’t insure any more of these deals. And at the time it didn’t really seem like all that big of an issue. A.I.G. F.P. was generating around $2 billion year in profits. At the peak, the entire credit-default-swap business contributed only $180 million of that. He was upset, it seemed, mainly that he had been successfully contradicted.
...
That’s when Park decided to examine more closely the loans that A.I.G. F.P. had insured. He suspected Joe Cassano didn’t understand what he had done, but even so Park was shocked by the magnitude of the misunderstanding: these piles of consumer loans were now 95 percent U.S. subprime mortgages. Park then conducted a little survey, asking the people around A.I.G. F.P. most directly involved in insuring them how much subprime was in them. He asked Gary Gorton, a Yale professor who had helped build the model Cassano used to price the credit-default swaps. Gorton guessed that the piles were no more than 10 percent subprime. He asked a risk analyst in London, who guessed 20 percent. He asked Al Frost, who had no clue, but then, his job was to sell, not to trade. “None of them knew,” says one trader. Which sounds, in retrospect, incredible. But an entire financial system was premised on their not knowing-and paying them for their talent!
That drifts fairly far from Modern Portfolio Theory itself (that is, roughly the content of Markowitz's PHD thesis). It's a specific way of optimizing returns given a collection of investments of known mean and standard deviation.
If you're pointing out that a lot of Wall Street actors aren't following that model ... that's quite true.
The dual questions of what they're actually doing, and what's a sensible way to maximize return are both interesting. They're also very different questions.
Describing it as not caring is probably inaccurate. Part of the problem is that a lot of financial instruments are quite complicated, and the math to properly analyze them is insanely difficult (if you include systemic effects, as you should). Some of it's a matter of making simplifying assumptions for tractability, some of it's organizational disfunction, and a fair amount is the invisible sledgehammer of regulation knocking things out of balance.
For investment #1, lets say the time horizon is 5 years to get
to the outcome as you suggested, and in investment #2 it is 1 year.
Investment #1
T | possibility | equal possibility
0 | $N
5 | $N | $3N
| / \ | / \
10 | $N $3N | $3N $9N
In 10 years you have a 25% chance of still having $N, a 50% chance of $3N, and
a 25% chance of $9N.
Investment #2
Hmmm, I'm having a hard time simply representing this, but I'll try. Assume
any payoffs are reinvested.
T | 1/8 | 1/8 | 1/8 | 1/8 | 1/8 | 1/8 | 1/8 | 1/8 | 1/8 |
| $0 | $2N | $4N | Header row
| | | | of probabilities
0 | $N | $N | $N |
1 | $0 | _______ $2N_____ | $4N |
| | ________/ | \_____ | |_
2 | $0 | $0 ___$4N___ $8N | $0 $8N $16N |
| | ____/ | \ / | \ | /|\ /| \ |
3 | $0 | $0 $8N 16N 0 16 32 |0 16 32 0 32 64|
Hopefully that comes through ok, I'm not going to try to expand the table further. But as you can see, as time goes on, even at the second time step, your chances of having (and keeping!) $0 get quite high. The tools many of the modern portfolio theorists use to evaluate risk include merely the two numbers "mean" and "variance". (Or sometimes only "beta" which they call "risk.")
This means that the guys at the computers don't see the long term difference between #1 and #2 in their computer models. They assume a normal distribution and don't account properly for when it's not. It's not even a matter of being short term greedy -- if they knew, they wouldn't ever pick investment #2, but they just don't know.
One of Jon's other points to me is that, by using too much leverage, you can turn something that seems like a very reasonable investment (assume investment #1 had a 50% chance of 0.9N instead of 50% chance of exactly N) into something that ends badly. Using leverage you can turn #1 into #2 and still have your modern portfolio theory mean and variance intact. Until something strange happens. Then you end up with $0 or worse.
--Beth
Reply
(The comment has been removed)
From: http://www.vanityfair.com/politics/features/2009/08/aig200908?currentPage=4
A.I.G. F.P. was already insuring these big, diversified, AAA-rated piles of consumer loans; to get it to insure subprime mortgages was only a matter of pouring more and more of the things into the amorphous, unexamined piles. They went from being 2 percent subprime mortgages to being 95 percent subprime mortgages. And yet no one at A.I.G. said anything about it-not C.E.O. Martin Sullivan, not Joe Cassano, not Al Frost, the guy in A.I.G. F.P.’s Connecticut office in charge of selling his firm’s credit-default-swap services to the big Wall Street firms. The deals, by all accounts, were simply rubber-stamped by Cassano and then again by A.I.G. brass-and, on the theory that this was just more of the same, no one paid them special attention. It’s hard to know what Joe Cassano thought and when he thought it, but the traders inside A.I.G. F.P. are certain that neither Cassano nor the four or five people overseen directly by him, who worked in the unit that made the trades, realized how completely these piles of consumer loans had become, almost exclusively, composed of subprime mortgages.
...
it was simply a bet that U.S. home prices would never fall. Once he understood this, Joe Cassano actually changed his mind. He agreed with Gene Park: A.I.G. F.P. shouldn’t insure any more of these deals. And at the time it didn’t really seem like all that big of an issue. A.I.G. F.P. was generating around $2 billion year in profits. At the peak, the entire credit-default-swap business contributed only $180 million of that. He was upset, it seemed, mainly that he had been successfully contradicted.
...
That’s when Park decided to examine more closely the loans that A.I.G. F.P. had insured. He suspected Joe Cassano didn’t understand what he had done, but even so Park was shocked by the magnitude of the misunderstanding: these piles of consumer loans were now 95 percent U.S. subprime mortgages. Park then conducted a little survey, asking the people around A.I.G. F.P. most directly involved in insuring them how much subprime was in them. He asked Gary Gorton, a Yale professor who had helped build the model Cassano used to price the credit-default swaps. Gorton guessed that the piles were no more than 10 percent subprime. He asked a risk analyst in London, who guessed 20 percent. He asked Al Frost, who had no clue, but then, his job was to sell, not to trade. “None of them knew,” says one trader. Which sounds, in retrospect, incredible. But an entire financial system was premised on their not knowing-and paying them for their talent!
--Beth
Reply
Reply
If you're pointing out that a lot of Wall Street actors aren't following that model ... that's quite true.
The dual questions of what they're actually doing, and what's a sensible way to maximize return are both interesting. They're also very different questions.
Describing it as not caring is probably inaccurate. Part of the problem is that a lot of financial instruments are quite complicated, and the math to properly analyze them is insanely difficult (if you include systemic effects, as you should). Some of it's a matter of making simplifying assumptions for tractability, some of it's organizational disfunction, and a fair amount is the invisible sledgehammer of regulation knocking things out of balance.
Reply
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