PDEs are very hard to solve.
I heard it claimed that it's very lucky, if you're someone who does mathematical finance, that the Black-Scholes partial differential equation, when used to price a call option, has a closed-form solution. (Well, if you include the error function in "closed form".)
The payoff of the thing being priced gives the initial condition for the Black-Scholes PDE and for a simple perturbation of that, there is probably not such a simple solution. And options markets probably would have developed very differently if there hadn't been an exact solution, because solving such an equation numerically, while possible, is a lot slower.
A friend of mine who knows more about PDEs than I do said that, basically, the set of exactly solvable PDEs has measure zero. Of course this isn't a theorem, but the point is that people who study PDEs don't expect there to be exact solutions.
Showing posts with label finance. Show all posts
Showing posts with label finance. Show all posts
20 October 2008
08 October 2008
Conditional probability is subtle
From 60 Minutes on Sunday, video here: the banking crisis is the fault of the mathematicians and physicists, who went to work on Wall Street and invented some complicated models. The "financial expert" says that "you can't model human behavior with math". That may be true with our current mathematics, but I suspect the fault doesn't lie with the modelers so much as with the people who went ahead and thought the models were perfect.
Although there are rumors that a lot of the models basically worked on the principle that defaults on mortgages were independent, which is so obviously false that you'd fail a freshman who said it. (Basically, when the economy gets bad, more people can't pay their mortgages. The effect is larger because there are adjustable-rate mortgages, and everybody suffers roughly the same adjustments.) I would not be surprised to learn that the problem here is that Conditional Probability Is Subtle; the quants may very well have known their models were flawed, but the suits didn't want to hear it.
I just hope this meme dies out quickly and doesn't gain traction. Our PR already isn't so good.
Although there are rumors that a lot of the models basically worked on the principle that defaults on mortgages were independent, which is so obviously false that you'd fail a freshman who said it. (Basically, when the economy gets bad, more people can't pay their mortgages. The effect is larger because there are adjustable-rate mortgages, and everybody suffers roughly the same adjustments.) I would not be surprised to learn that the problem here is that Conditional Probability Is Subtle; the quants may very well have known their models were flawed, but the suits didn't want to hear it.
I just hope this meme dies out quickly and doesn't gain traction. Our PR already isn't so good.
15 May 2008
Well-intentioned money advice
Suze Orman, "internationally acclaimed personal finance expert" (actually the title of her web page!),, said yesterday on myphl17 News At Ten something like: "you are not to spend your economic stimulus check. you must save it." (Don't ask me why I ever watch this newscast. It consists of recycled press releases, news that someone got shot and somebody's house burned down, and sports scores. The only score I care about is the Phillies and I usually know how that turned out anyway.)
Anyway, Orman's advice seemed to be based on the idea that because the economy as an aggregate is doing poorly, we all must be suffering. There are surely some people who have had a very good year and don't need the six hundred bucks. And there are surely some people who have had a very bad year and for whom six hundred bucks is just a drop in the bucket.
I'll call this the "distributional fallacy" (does it have another name) -- assuming that any individual must be representative of some sample from which they're drawn. Not a horrible assumption in the absence of other information -- but I know more about my financial situation than someone appearing on my television!
But "if times have been bad and you don't have money saved up, you should save the money -- and maybe you should save it even if things have been good for you, because they might turn bad" doesn't have the same ring to it.
I'm not arguing that people shouldn't save their money, because life has a way of causing people trouble. But to assume that everybody is going through hard times is kind of short-sighted. Then again, if you tell people "some people should save their money", that American instinct to consume will kick in and people will assume that "some people" doesn't include them.
(For the record, I will be saving my economic stimulus check. I think. It's hard to say, because money's fungible, and I stand to have negative cash flow this summer because I won't be teaching like I have the last two summers. So it'll go into savings, but then I'll spend "it" later. Money is money, it all mixes together. It's a scalar, not some sort of crazy vector in a non-Euclidean space as some people would probably like you to think.)
Anyway, Orman's advice seemed to be based on the idea that because the economy as an aggregate is doing poorly, we all must be suffering. There are surely some people who have had a very good year and don't need the six hundred bucks. And there are surely some people who have had a very bad year and for whom six hundred bucks is just a drop in the bucket.
I'll call this the "distributional fallacy" (does it have another name) -- assuming that any individual must be representative of some sample from which they're drawn. Not a horrible assumption in the absence of other information -- but I know more about my financial situation than someone appearing on my television!
But "if times have been bad and you don't have money saved up, you should save the money -- and maybe you should save it even if things have been good for you, because they might turn bad" doesn't have the same ring to it.
I'm not arguing that people shouldn't save their money, because life has a way of causing people trouble. But to assume that everybody is going through hard times is kind of short-sighted. Then again, if you tell people "some people should save their money", that American instinct to consume will kick in and people will assume that "some people" doesn't include them.
(For the record, I will be saving my economic stimulus check. I think. It's hard to say, because money's fungible, and I stand to have negative cash flow this summer because I won't be teaching like I have the last two summers. So it'll go into savings, but then I'll spend "it" later. Money is money, it all mixes together. It's a scalar, not some sort of crazy vector in a non-Euclidean space as some people would probably like you to think.)
14 December 2007
Credit card "points"
I got a credit card today.
Like many credit cards, it comes with rewards "points". I get one point for every $1 I spend. The information that came with the card includes a table that begins as follows, which purports to show "how fast your points... can add up":
(etc.)
What, are people so stupid that they can't multiply by one?
(Of course, there are much more serious quantitative-illiteracy issues involved with credit cards, namely that people don't realize how much they get gouged on the interest rates, or just how long it'll take them to pay off the thing -- and how much interest they'll pay -- if they make the "minimum payment". But I won't go there.)
Like many credit cards, it comes with rewards "points". I get one point for every $1 I spend. The information that came with the card includes a table that begins as follows, which purports to show "how fast your points... can add up":
| Everyday Purchases | Amount | Points |
| Restaurants | $320 | 320 |
| Gasoline | $100 | 100 |
| Groceries | $450 | 450 |
| Miscellaneous | $400 | 400 |
(etc.)
What, are people so stupid that they can't multiply by one?
(Of course, there are much more serious quantitative-illiteracy issues involved with credit cards, namely that people don't realize how much they get gouged on the interest rates, or just how long it'll take them to pay off the thing -- and how much interest they'll pay -- if they make the "minimum payment". But I won't go there.)
22 July 2007
payday loans
When Businesses Can Do Math, from Grey Matters -- interesting links about companies that can do math and use it to rip people off. Check out the fine print to this CashCall.com ad with Gary Coleman:
Yes, you read that right. The interest rate is almost ONE HUNDRED PERCENT. A person taking out such a loan will end up paying back a total of $9,095.10. Their commercial makes it sound like they're lending money because they "trust" people, but that's certainly not the case. I suspect that at least one of the two following things is true:
(Incidentally, I was looking for something to calculate the payments on a loan for me; the first google hit; I wanted to check the payments on the CashCall.com loan. It complains that 99.25 is not in the range from 0.01 to 99 and so I couldn't possibly have meant that interest rate. I did!
Here are CashCall.com's rates; it seems that in states where larger loans are offered, such as California, the interest rates on those larger loans are lower (as low as 21%). Also, for some reason they only offer loans in the amounts of $1,000, $2,000, $2,600, $5,075, $10,000, and $20,000; does anybody have any idea why?
As for the high interest rates, I've heard that small payday loans -- say, the type where someone borrows $100 and has to pay back $115 a couple weeks later -- have to have high interest rates because the cost of doing all the administrative work for the loan needs to be covered. But it seems a lot harder to believe this on loans such as those given by CashCall.com.
This reminds me of the Comcast "Service Protection Plan" I wrote about a few days ago, which I concluded was a ripoff. I was telling my father about this today, and he pointed out that "if they're trying to sell it to you, they expect to make money off of it". The difference is that Comcast was talking about a few dollars a month, whereas payday lenders are giving people a way to really trash their financial lives.
The APR for a typical loan of $2,600 is 99.25% with 42 monthly payments of $216.55
Yes, you read that right. The interest rate is almost ONE HUNDRED PERCENT. A person taking out such a loan will end up paying back a total of $9,095.10. Their commercial makes it sound like they're lending money because they "trust" people, but that's certainly not the case. I suspect that at least one of the two following things is true:
- The people taking out these loans have a very high default rate. And I mean very high; if they were giving these loans at 30% (which is a typical rate for people with credit cards who have made a ot of late payments) then the monthly payment would be $100.69 over 42 months (see this calculator), for a total amount paid of $4,228.98. So I'm inclined to assume that the percentage of people who pay their loans back is less than half of the percentage who pay their credit cards back.
- There's not much competition for this sort of loan; people actually see this commercial and make a phone call without bothering to shop around. This seems pretty reasonable, because the sort of people who would shop around for the best deal are probably less likely to get themselves in this sort of trouble in the first place. Therefore, the loan companies charge the highest interest rate they can legally get away with. In fact, it wouldn't surprise me to learn that in the state where these
(Incidentally, I was looking for something to calculate the payments on a loan for me; the first google hit; I wanted to check the payments on the CashCall.com loan. It complains that 99.25 is not in the range from 0.01 to 99 and so I couldn't possibly have meant that interest rate. I did!
Here are CashCall.com's rates; it seems that in states where larger loans are offered, such as California, the interest rates on those larger loans are lower (as low as 21%). Also, for some reason they only offer loans in the amounts of $1,000, $2,000, $2,600, $5,075, $10,000, and $20,000; does anybody have any idea why?
As for the high interest rates, I've heard that small payday loans -- say, the type where someone borrows $100 and has to pay back $115 a couple weeks later -- have to have high interest rates because the cost of doing all the administrative work for the loan needs to be covered. But it seems a lot harder to believe this on loans such as those given by CashCall.com.
This reminds me of the Comcast "Service Protection Plan" I wrote about a few days ago, which I concluded was a ripoff. I was telling my father about this today, and he pointed out that "if they're trying to sell it to you, they expect to make money off of it". The difference is that Comcast was talking about a few dollars a month, whereas payday lenders are giving people a way to really trash their financial lives.
17 July 2007
Comcast's "Service Protection Plan".
I got my cable bill today.
Enclosed with my cable bill was an ad for Comcast's "Service Protection Plan". Comcast's policy is apparently to charge for "wire-related service calls". The ad says the following:
So this is only a good buy if I expect to have a service call every 22.25/3.30 = 6.74 months (if I'm a video-only customer) or 32.25/3.30 = 9.77 months (if I only have Internet and/or digital voice through them and don't have their television service, which I suspect is quite rare); for those people who might incur both kinds of charges, the relevant quantity is somewhere in between.
In any case, nobody's wiring is that bad, is it, that it needs fixing more than once a year? And if it is, don't you have bigger things to worry about than your cable TV? Comcast is probably making huge piles of money off of this.
You might say that the reason for a customer to buy this is for "insurance", and that my expected value calculation is sort of silly because you're not protecting against the average but against the unusual. And that would be a valid point if, say, they were offering "for a low monthly fee of $330, you'll be covered for charges which are usually $2225 or $3225". These numbers are in the right ballpark for, say, car insurance. But I would hope that people have the good sense to save enough money that an unexpected expense of $22.25 isn't going to hurt them.
(The fine print says that this isn't available to "customers in a residential building with multiple apartments", which describes me.)
Enclosed with my cable bill was an ad for Comcast's "Service Protection Plan". Comcast's policy is apparently to charge for "wire-related service calls". The ad says the following:
"For a low monthly fee of $3.30, you'll be covered for all inside wire-related service calls. Without the plan, regular service call charges will apply. Current service call charges are $22.25 for a video-only service call and $32.25 for a High-Speed Internet or Digital Voice service call."
So this is only a good buy if I expect to have a service call every 22.25/3.30 = 6.74 months (if I'm a video-only customer) or 32.25/3.30 = 9.77 months (if I only have Internet and/or digital voice through them and don't have their television service, which I suspect is quite rare); for those people who might incur both kinds of charges, the relevant quantity is somewhere in between.
In any case, nobody's wiring is that bad, is it, that it needs fixing more than once a year? And if it is, don't you have bigger things to worry about than your cable TV? Comcast is probably making huge piles of money off of this.
You might say that the reason for a customer to buy this is for "insurance", and that my expected value calculation is sort of silly because you're not protecting against the average but against the unusual. And that would be a valid point if, say, they were offering "for a low monthly fee of $330, you'll be covered for charges which are usually $2225 or $3225". These numbers are in the right ballpark for, say, car insurance. But I would hope that people have the good sense to save enough money that an unexpected expense of $22.25 isn't going to hurt them.
(The fine print says that this isn't available to "customers in a residential building with multiple apartments", which describes me.)
13 July 2007
million-dollar waitress update
A few weeks ago I wrote about Mary Sue Williams, who at the time looked like the probable winner of a CNBC stock-picking contest. Basically, she was the best out of those people who hadn't "cheated".
MSNBC reports that she has been declared the winner and presented with an oversized novelty check.
MSNBC reports that she has been declared the winner and presented with an oversized novelty check.
20 June 2007
The Million-Dollar Waitress and stock-picking scams
The Million-Dollar Waitress, from Business Week.
A waitress in Ohio, Mary Sue Williams, may win the million-dollar grand prize in a CNBC stock-picking contest. She was in sixth place when the contest ended on May 25. But a flaw in the way the contest was set up meant that, basically, the five people ahead of her "cheated". They found a way to select stocks to buy at, say, $20 -- and then wait until they went up to $25 before pressing the "buy" button. Because of the way the contest had been programmed, they only had to pay $20 in fake money to buy the stock. (I'm putting "cheated" in quotes because although this is clearly against the spirit of the contest -- you couldn't do this in the real market -- perhaps one could argue that the contest is defined by whatever the computer lets people do.)
Furthermore, it's not really clear how meaningful a contest like this is. From what I can tell, the contest lasted for ten weeks; the winner each week won $10,000 and the grand-prize winner won $1,000,000. Although I can't find information about the prize structure, my guess would be that any other prizes were much smaller. So this encourages risk-taking that nobody would take with actual money. Let's say there's a second-place prize, and it's $100,000. In "real life", most people would be happy with that money. But if you bet -- and I'm using "bet" here because this really does feel like gambling -- all your money on some very risky stock, then you have a shot at multiplying your money by ten. But it's probably a lot more likely that you'll lose it all.
Jim Kraber, on the other hand, played legitimately but at one point had 1600 portfolios. This enabled him to take the sort of risks that someone with a single portfolio -- or even a number of portfolios that could reasonably be played with with hard currency -- would never take, because he could afford to just throw out a portfolio that wasn't succeeding.
Williams admits that "Part of this was luck... a lot of it was a gut feeling, some eenie-meenie-minie-moe, and common sense." Now, I'm not saying that she can't pick stocks -- who knows, she might be quite good at it. But this story reminds me of the following scam. I get a mailing list with 64,000 people on it. (I'm not sure whether this should be postal mail or e-mail; the story, which is not mine and which I learned from a book of John Allen Paulos, predates e-mail.) I tell 32,000 of them they should, say, bet on football team A to win this week, and 32,000 that they should bet on the same team to lose. The team either wins or loses. Next week, I take the 32,000 that got the right answer this week, and split them in half. To 16,000 I say that team B will win this week, and to 16,000 I say that team B will lose. I repeat this six times, until 1,000 people have received six correct predictions. Note that when I begin this scheme I don't know which 1,000 people this will be, but I know they'll exist. Then I try to sell these thousand people my "system". Maybe they'd buy it!
A waitress in Ohio, Mary Sue Williams, may win the million-dollar grand prize in a CNBC stock-picking contest. She was in sixth place when the contest ended on May 25. But a flaw in the way the contest was set up meant that, basically, the five people ahead of her "cheated". They found a way to select stocks to buy at, say, $20 -- and then wait until they went up to $25 before pressing the "buy" button. Because of the way the contest had been programmed, they only had to pay $20 in fake money to buy the stock. (I'm putting "cheated" in quotes because although this is clearly against the spirit of the contest -- you couldn't do this in the real market -- perhaps one could argue that the contest is defined by whatever the computer lets people do.)
Furthermore, it's not really clear how meaningful a contest like this is. From what I can tell, the contest lasted for ten weeks; the winner each week won $10,000 and the grand-prize winner won $1,000,000. Although I can't find information about the prize structure, my guess would be that any other prizes were much smaller. So this encourages risk-taking that nobody would take with actual money. Let's say there's a second-place prize, and it's $100,000. In "real life", most people would be happy with that money. But if you bet -- and I'm using "bet" here because this really does feel like gambling -- all your money on some very risky stock, then you have a shot at multiplying your money by ten. But it's probably a lot more likely that you'll lose it all.
Jim Kraber, on the other hand, played legitimately but at one point had 1600 portfolios. This enabled him to take the sort of risks that someone with a single portfolio -- or even a number of portfolios that could reasonably be played with with hard currency -- would never take, because he could afford to just throw out a portfolio that wasn't succeeding.
Williams admits that "Part of this was luck... a lot of it was a gut feeling, some eenie-meenie-minie-moe, and common sense." Now, I'm not saying that she can't pick stocks -- who knows, she might be quite good at it. But this story reminds me of the following scam. I get a mailing list with 64,000 people on it. (I'm not sure whether this should be postal mail or e-mail; the story, which is not mine and which I learned from a book of John Allen Paulos, predates e-mail.) I tell 32,000 of them they should, say, bet on football team A to win this week, and 32,000 that they should bet on the same team to lose. The team either wins or loses. Next week, I take the 32,000 that got the right answer this week, and split them in half. To 16,000 I say that team B will win this week, and to 16,000 I say that team B will lose. I repeat this six times, until 1,000 people have received six correct predictions. Note that when I begin this scheme I don't know which 1,000 people this will be, but I know they'll exist. Then I try to sell these thousand people my "system". Maybe they'd buy it!
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