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What kind of math nerd job should you have?
Say you’re a math nerd, finishing your Ph.D. or a post-doc, and you’re wondering whether academics is really the place for you. Well I’ve got some advice for you! Actually I will have some advice for you, after you’ve answered a few questions. It’s all about fit. Since I know them best, I will center my questions and my advice around academic math vs. hedge fund quant vs. data scientist at a startup.
By the way, this is the advice I find myself telling people when they ask. It’s supposed to be taken over a beer and with lots of tongue in cheek.
1) What are your vices?
It turns out that the vices of the three jobs we are considering are practically disjoint! If you care about a good fit for your vices, then please pay attention.
NOTE: I am not saying that everyone in these fields has all of these vices! Far from it! It’s more like, if one or more of these vices drives you nuts, then you may get frustrated when you encounter them in these fields.
In academics, the major vices are laziness, envy, and arrogance. It’s perhaps true that laziness (at least outside of research) is typically not rewarded until after tenure, but at that point it’s pretty much expected, unless you want to be the fool who spends all of his(her) time writing recommendation letters and actually advising undergraduates. Envy is, of course, a huge deal in academics, because the only actual feedback is in the form of adulating rumor. Finally, arrogance in academics is kind of too obvious to explain.
At a hedge fund, the major vices are greed, covetousness, and arrogance. The number one source of feedback is pay, after all, so it’s all about how much you got (and how much your officemate got). Plus the isolation even inside your own office can lead to the feeling that you know more and more interesting, valuable, things than anyone else, thus the arrogance.
Finally, at a startup, the major vices are vanity, impatience, and arrogance. People really care about their image- maybe because they are ready to jump ship and land a better job as soon as they start to smell something bad. Plus it’s pretty easy in startups as well to live inside a bubble of self-importance and coolness and buzz. Thus the arrogance. On the flip side of vanity, startups are definitely the sexiest of the three, and the best source by far for good karaoke singers.
Okay it turns out they all have arrogance. Maybe that’s just a property of any job category.
2) What do you care about?
Do you care about titles? Don’t work at a startup.
Do you care about stability? Don’t work at a startup. Actually you might think I’d say don’t work at a hedge fund either, but I’ve found that hedge funds are surprisingly stable, and are full of people who are surprisingly risk averse. Maybe small hedge funds are unstable.
Do you care about feedback? Don’t work in academics.
Do you care about publishing? Don’t work outside academics (it’s sometimes possible to publish outside of academics but it’s not always possible and it’s not always easy).
Do you care about making lots of money? Don’t work in academics. In a startup you make a medium amount of money but there are stock options which may pan out someday, so it’s kind of in between academics and Wall St.
Do you care about being able to decide what you’re working on? Definitely stay in academics.
Do you care about making the world a better place? I’m still working on that one. There really should be a way of doing that if you’re a math nerd. It’s probably not Wall Street.
3) What do you not care about?
If you just like math, and don’t care exactly what kind of math you’re doing, then any of these choices can be really interesting and challenging.
If you don’t mind super competitive and quasi-ethical atmospheres, then you may really enjoy hedge fund quant work- the modeling is really interesting, the pay is good, and you are part of the world of finance and economics, which leaks into politics as well and is absolutely fascinating.
If you don’t mind getting nearly no vacation days and yet feeling like your job may blow up any minute, you may like working at a startup. The people there are real risk lovers, care about their quality of life (at least at the office!), and know how to throw a great party.
If you don’t mind being relatively isolated mathematically, and have enormous internal motivation and drive, then academics is a pretty awesome job, and teaching is really fun and rewarding. Also academic jobs have lots of flexibility as well as cool things like sabbaticals.
4) What about for women who want kids?
Let’s face it, the tenure clock couldn’t have been set up worse for women who want children. And startups have terrible vacation policies and child-care policies as well; it’s just the nature of living on a Venture Capitalist’s shoestring. So actually I’d say the best place to balance work and life issues is at an established hedge fund or bank, where the maternity policies are good; this is assuming though that your personality otherwise fits well with a Wall St. job. Actually many of the women I’ve met who have left academics for government research jobs (like at NASA or the NSA) are very happy as well.
Three strikes against the mortgage industry
There’s a great example here of mortgage lenders lying through their teeth with statistics. Felix Salmon uncovers a ridiculous attempt to make loans look safe by cutting up the pile of mortgages in a tricky way- sound familiar at all?
And there’s a great article here about why they are lying. Namely, there is proposed legislation that would require the banks to keep 5% of the packaged mortgages on their books.
And finally here’s a great description of why they should know better. A breakdown of what banks are currently doing to avoid marking down their mortgage book.
Historical volatility on the S&P index
In a previous post I described the way people in finance often compute historical volatility, in order to try to anticipate future moves in a single stock. I’d like to give a couple of big caveats to this method as well as a worked example, namely on daily returns of the S&P index, with the accompanying python code. I will use these results in a future post I’m planning about errorbars and how people abuse and misuse them.
Two important characteristics of returns
First, market returns in general have fat-tailed distributions; things can seem “quiet” for long stretches of time (longer than any lookback window), during which the sample volatility is a possibly severe underestimate of the “true” standard of deviation of the underlying distribution (if that even makes sense – for the sake of this discussion let’s assume it does). Then when a fat-tailed event occurs, the sample volatility typically spikes to being an overestimate of the standard of deviation for that distribution.
Second, in the markets, there is clustering of volatility- another way of saying this is that volatility itself is rather auto-correlated, so even if we can’t predict the direction of the return, we can still estimate the size of the return. This is particularly true right after a shock, and there are time series models like ARCH and its cousins that model this phenomenon; they in fact allow you to model an overall auto-correlated volatility, which can be thought of as scaling for returns, and allows you to then approximate the normalized returns (returns divided by current volatility) as independent, although still not normal (because they are still fat-tailed even after removing the clustered volatility effect). See below for examples of normalized daily S&P returns with various decays.
Example: S&P daily returns
I got this data from Yahoo Finance, where they let you download daily S&P closes since 1950 to an excel spreadsheet. I could have used some other instrument class, but the below results would be stronger (especially for things like credit default swamps), not weaker- the S&P, being an index, is already the sum of a bunch of things and tends to be more normal as a result; in other words, the Central Limit Theorem is already taking effect on an intraday basis.
First let’s take a look at the last 3 years of closes, so starting in the summer of 2008:
Next we can look at the log returns for the past 3 years:
Now let’s look at how the historical volatility works out with different decays (decays are numbers less than 1 which you use to downweight old data: see this post for an explanation):
For each choice of the above decays, we can normalize the log returns. to try to remove the “volatility clustering”:
As we see, the long decay doesn’t do a very good job. In fact, here are the histograms, which are far from normal:
Here’s the python code I used to generate these plots from the data (see also R code below):
#!/usr/bin/env python
import csv
from matplotlib.pylab import *
from numpy import *
from math import *
import os
os.chdir(‘/Users/cathyoneil/python/sandp/’)
dataReader = csv.DictReader(open(‘SandP_data.txt’, ‘rU’), delimiter=’,’, quotechar=’|’)
close_list = []
for row in dataReader:
#print row[“Date”], row[“Close”]
close_list.append(float(row[“Close”]))
close_list.reverse()
close_array = array(close_list)
close_log_array = array([log(x) for x in close_list])
log_rets = array(diff(close_log_array))
perc_rets = array([exp(x)-1 for x in log_rets])
figure()
plot(close_array[-780:-1], label = “raw closes”)
title(“S&P closes for the last 3 years”)
legend(loc=2)
#figure()
#plot(log_rets, label = “log returns”)
#legend()
#figure()
#hist(log_rets, 100, label = “log returns”)
#legend()
#figure()
#hist(perc_rets, 100, label = “percentage returns”)
#legend()
#show()
def get_vol(d):
var = 0.0
lam = 0.0
var_list = []
for r in log_rets:
lam = lam*(1.0-1.0/d) + 1
var = (1-1.0/lam)*var + (1.0/lam)*r**2
var_list.append(var)
return [sqrt(x) for x in var_list]
figure()
for d in [10, 30, 100]:
plot(get_vol(d)[-780:-1], label = “decay factor %.2f” %(1-1.0/d))
title(“Volatility in the S&P in the past 3 years with different decay factors”)
legend()
for d in [10, 30, 100]:
figure()
these_vols = get_vol(d)
plot([log_rets[i]/these_vols[i-1] for i in range(len(log_rets) – 780, len(log_rets)-1)], label = “decay %.2f” %(1-1.0/d))
title(“Volatility normalized log returns (last three years)”)
legend()
figure()
plot([log_rets[i] for i in range(len(log_rets) – 780, len(log_rets)-1)], label = “raw log returns”)
title(“Raw log returns (last three years)”)
for d in [10, 30, 100]:
figure()
these_vols = get_vol(d)
normed_rets = [log_rets[i]/these_vols[i-1] for i in range(len(log_rets) – 780, len(log_rets)-1)]
hist(normed_rets, 100,label = “decay %.2f” %(1-1.0/d))
title(“Histogram of volatility normalized log returns (last three years)”)
legend()
Here’s the R code Daniel Krasner kindly wrote for the same plots:
setwd(“/Users/cathyoneil/R”)
dataReader <- read.csv(“SandP_data.txt”, header=T)
close_list <- as.numeric(dataReader$Close)
close_list <- rev(close_list)
close_log_list <- log(close_list)
log_rets <- diff(close_log_list)
perc_rets = exp(log_rets)-1
x11()
plot(close_list[(length(close_list)-779):(length(close_list))], type=’l’, main=”S&P closes for the last 3 years”, col=’blue’)
legend(125, 1300, “raw closes”, cex=0.8, col=”blue”, lty=1)
get_vol <- function(d){
var = 0
lam=0
var_list <- c()
for (r in log_rets){
lam <- lam*(1 – 1/d) + 1
var = (1 – 1/lam)*var + (1/lam)*r^2
var_list <- c(var_list, var)
}
return (sqrt(var_list))
}
L <- (length(close_list))
x11()
plot(get_vol(10)[(L-779):L], type=’l’, main=”Volatility in the S&P in the past 3 years with different decay factors”, col=1)
lines(get_vol(30)[(L-779):L], col=2)
lines(get_vol(100)[(L-779):L], col=3)
legend(550, 0.05, c(“decay factor .90”, “decay factor .97″,”decay factor .99”) , cex=0.8, col=c(1,2,3), lty = 1:3)
x11()
par(mfrow=c(3,1))
plot((log_rets[2:L]/get_vol(10))[(L-779):L], type=’l’, col=1, lty=1, ylab=”)
legend(620, 3, “decay factor .90”, cex=0.6, col=1, lty = 1)
plot((log_rets[2:L]/get_vol(30))[(L-779):L], type=’l’, col=2, lty =2, ylab=”)
legend(620, 3, “decay factor .97”, cex=0.6, col=2, lty = 2)
plot((log_rets[2:L]/get_vol(100))[(L-779):L], type=’l’, col=3, lty =3, ylab=”)
legend(620, 3, “decay factor .99”, cex=0.6, col=3, lty = 3)
x11()
plot(log_rets[(L-779):L], type=’l’, main = “raw log returns”, col=”blue”, ylab=”)
par(mfrow=c(3,1))
hist((log_rets[2:L]/get_vol(10))[(L-779):L], breaks=200, col=1, lty=1, ylab=”, xlab=”, main=”)
legend(2, 15, “decay factor .90”, cex=.8, col=1, lty = 1)
hist((log_rets[2:L]/get_vol(30))[(L-779):L], breaks=200, col=2, lty =2, ylab=”, xlab=”, main=”)
legend(2, 40, “decay factor .97”, cex=0.8, col=2, lty = 2)
hist((log_rets[2:L]/get_vol(100))[(L-779):L], breaks=200, col=3, lty =3, ylab=”, xlab=”, main=”)
legend(3, 50, “decay factor .99”, cex=0.8, col=3, lty = 3)
Is too big to fail a good thing?
I read this blog post a couple of days and it really got me thinking. This guy John Hempton from Australia is advocating the too big to fail model- in fact he things we should merge more big banks together (Citigroup and Wells Fargo) because we haven’t gone far enough!
His overall thesis is that competition in finance increases as a function of how many banks there are out there and is a bad thing for stockholders and for society, because it makes people desperate for profit, and in particular people increase their risk profiles in pursuit of profit and they blow up:
What I am advocating is – that as a matter of policy – you should deliberately give up competition in financial services – and that you should do this by hide-bound regulation and by deliberately inducing financial service firms to merge to create stronger, larger and (most importantly) more anti-competitive entities.
He acknowledges that the remaining banks will be hugely profitable, and perhaps also extremely lazy, but claims this is a good thing: we would, as a culture, essentially be paying a fee for stability. It’s something we do all the time in some sense, when we buy insurance. Insurance is a fee we pay so that disruptions and small disasters in our lives don’t completely wipe us out. So perhaps, as a culture, this would be a price worth paying?
The biggest evidence he has that this setup works well is that it works in Australia- they have four huge incompetent yet profitable banks there, and they don’t blow up. People who work there are sitting pretty, I guess, because they really are just living in a money press. There is no financial innovation because there’s no competition.
I guess I have a few different reactions to this scenario. First, it’s kind of an interesting twist on the too-big-to-fail debate, in that it’s combined with the idea I already talked about here of having a system of banks that are utilities. John is saying that, really, we don’t need to make that official, that as soon as banks are this huge, we are already done, they are essentially going to act like utilities. This is super interesting to me, but I’m not convinced it’s a necessary or even natural result of huge banks.
Second, I don’t buy that what happened in Australia will happen here- perhaps Australia squelched financial innovation through regulations and the existing boring system, but maybe the people who would have been financial innovators all just moved to the U.S. and became innovators here (there are plenty of examples of that!). In other words Australia may have made it just a bit too difficult to be competitive relative to what else is out there- if everyone tried to be that repressive to financial innovation, we may see people moving back into Australia’s financial waters (like sharks).
Third, I think what John is talking about is an example of a general phenomenon, namely that, in the limit as regulations go to infinity, there is only one bank left standing. This is because every additional regulation requires a lawyer to go over the requirements and a compliance person to make sure the rules are being followed continuously. So the more regulation, the more it behooves banks to merge so that they can share those lawyers and compliance officers to save costs. In the end the regulations have defined the environment to such an extent that there’s only one bank that can possibly follow all the rules, and knows how to because of historical reasons. And that one, last bank may as well be a government institution, albeit with better pay, especially for its managers.
But we don’t have that kind of regulatory environment, and hedge funds are alive and well. They have to follow some rules, it’s absolutely true, but it’s still possible to start a smallish hedge fund without a million lawyers.
I guess what I’m concluding is that if we had formed our very few, very huge banks because of a stifling regulatory environment, then maybe we would have an environment that is sufficiently anti-competitive to think that our banks would serve us as slightly overpaid utilities. However, that’s not why we have them – it was because of the credit crisis, and the rules and regulations haven’t changed that much since then.
At the same time, I don’t totally disagree that huge banks do become anti-competitive, just by dint of how long it takes them to make decisions and do things. But I’m not sure anti-competitive is the same thing as low-risk.
Elizabeth Warren: Moses and the Promised Land
This is a guest post by FogOfWar
In Biblical style, Elizabeth Warren (EW) was not nominated to head the CFPB (Consumer Financial Protection Bureau). Having spearheaded the movement to create the institution, pushed to make it part of the otherwise-generally-useless* Dodd Frank “Financial Reform” Bill, and spent the better part of the last two years staffing the actual CFPB and moving it into gear, she has now been deemed too controversial by what passes for a President these days.
One of my favorite EW quotes: “My first choice is a strong consumer agency. My second choice is no agency at all and plenty of blood and teeth left on the floor.” This still remains to be seen, as opposition to the CPFB (and filibuster threats to any appointment to head the Bureau) remains in the face of nominee Richard Cordray. In fact, if one were inclined to be an Obama apologist (I gave up apologizing for Obama right about here), one might view the Warren-Cordray switch as a potentially brilliant tactical maneuver, with the emphasis on “potentially”. If the opposition to the CPFB took its persona in EW, then sidestepping her personally to get the agency up and running would be worthwhile, particularly as Cordray seems at least as assertively pro-consumer as EW (a bank lobbyist described him as “Elizabeth Warren without the charm”).
Barney Frank believes gender bias played a role. Maybe yes, maybe no and the Cordray confirmation will give some evidence to that question. I suspect the Republican opposition isn’t stupid and knows that Cordray will run a good agency. If that’s right then passing over EW doesn’t really serve any purpose.
Hard to tell what a public figure is really like, but my sense is EW doesn’t have any ego attached to running the agency personally. And what she does next is really up to her, I mean who really cares what we think she should do?
Wait—this is a blog! Our Raison d’être is practically making suggestions that no one will listen to, so let’s go…
1. Run for Congress
The biggest idea floated around. Yves Smith thinks it’s a terrible idea. I’m not entirely convinced—there are many ways to make a difference in this world, and being one minority member of a large and powerful body, and thus moving the body incrementally in the right direction can be a very good thing.
Two questions though: can she win (a few early stage polls seemed to indicate no, but do early stage polls really have much predictive value on final election results? Cathy? Fivethirtyeight?), and on which party platform would she run (I vote for running as an Independent)? Any thoughts from the ground from our MA-registered voters?
2. The “Al Gore” option
EW could continue to advocate, lecture and write outside of political office. She’s good television and would be free to speak without the gag order of elected office. Definitely something to be said for this option. Just realized pulling links for this post that EW was the person from the movie “Maxed Out”. Part of me thinks “damn that was effective and she should do more of that because it was so effective” and part of me thinks “wait, that movie came out in 2006 and no one listened and no one will listen”, and then the other part goes “but it can happen—you’ve actually seen social perceptions change in the wake of Al Gore (and yes, lots and lots of other people, but sparks do matter) with real and deep impacts.”
3. The “Colin Powell” option
Y’now, being in the public light kinda sucks ass. Colin Powell passed up a run for President, and largely retired to private life, and doesn’t seem to have any complaints about it. One legitimate option is to say “I did my part, you guys fight the good fight & I’m going to hang out with my grandkids on the beach.”
Any other suggestions?
*-Paul Volker deserves a parallel post of equal length for pushing the Volker Rule through this legislation and similarly receiving the thanks of being sidelined by the TBTF bank-capital-must-increase-even-if-the-peasants-have-to-eat-cake crowd.
Quit your job and become a data miner!?
Today my friend sent me this link, which is a pretty interesting and inspiring video of a talk from a guy from Google named Steve Yegge talking at an O’Reilly conference about how he’s sick of working on uninspiring projects involving social media and cat pictures, and wants to devote himself (and wants you to devote yourself) to more important questions about the nature of human existence. And he things the way to go about this is to become a data miner. I dig it! Of course he’s preaching to the choir at that conference. I wonder what other people will make of his appeal. Can one nerd change an entire culture of endless cat pic collections?
And lest you think that data mining is the answer to everything, here’s an article about how much data mining (in the form of “Value-added modeling”) can screw up other peoples’ lives when it’s misdirected. It’s written by John Ewing, who is the fabulous president of MfA, an organization that trains and mentors excellent college math majors to become effective math teachers in the New York Public School system and beyond- the “beyond” part is partly due to the crazy state of the budgets for new teachers here in NYC- we now have access to these wonderful MfA graduates but have hiring freezes so we can’t hire them. Also, my good friend Japheth Wood, a.k.a. the Math Wizard, is one of the MfA mentors.
I’m planning to post more soon on how crappy the value-added modeling (VAM) system is and how’s it’s a perfect example of mathematics being used to make things seem magical and therefore inaccessible, the exact opposite of what should be going on.
The Bad Food Tax
There’s an interesting op-ed article in today’s New York Times. The author, Mark Bittman, is proposing that we tax bad foods to the point where people will naturally select healthy food because they will be subsidized and cheap.
He has lots of statistics to back him up, and if you’re someone like me who reads this kind of thing widely, nothing surprised me. Of course Americans eat crappy food and it’s terrible for our bodies. We know that, it’s old news.
And we all want to know how to fix this- clearly education about nutrition isn’t doing the trick by itself. And I’m the first person who would love to use quantitative methods to solve a really important, big problem. Moreover, if we start to get rid of the evil farm subsidies that are currently creating a ridiculous market for corn sugar (a major reason we have some much soda on the shelves at such low prices to begin with) as well as screwing up the farmers in Africa and other places, that will be a good thing.
Unfortunately, I really think his tax plan stinks. The main problem is something he actually brings up and dismisses- namely:
Some advocates for the poor say taxes like these are unfair because low-income people pay a higher percentage of their income for food and would find it more difficult to buy soda or junk. But since poor people suffer disproportionately from the cost of high-quality, fresh foods, subsidizing those foods would be particularly beneficial to them.
Yes they would, if they could actually buy them in their neighborhood! If he has the idea that the reason poor people buy crappy food is because they go into their neighborhood grocery store with a museum-like display of fresh fruits and vegetables, bypass those foods (because they are too expensive) to go straight to the back and find junk, then I guess his plan would make sense. Unfortunately the truth is, there is no fresh fruit at most of the food stores in poor urban areas – they are typically small and carry long-lasting packaged goods and groceries, from canned evaporated milk to diapers, and don’t have extra space. Moreover, I don’t think a pure price comparison is going to convince them to carry fruit, because it’s not just the higher prices that makes bodegas carry no fruit- it’s also the convenience of packages that don’t go bad. In fact it’s an entirely different business model, which is unfortunately a pretty tough nut to crack, but is essential in this discussion.
In other words, the result of this tax plan would be, for poor people, even higher prices for crappy food, not access to fresh cheap food. Unless the plan has worked out a system for how to get fresh fruit into poor areas, it really is missing the very audience it wishes to target.
Measuring historical volatility
Say we are trying to estimate risk on a stock or a portfolio of stocks. For the purpose of this discussion, let’s say we’d like to know how far up or down we might expect to see a price move in one day.
First we need to decide how to measure the upness or downness of the prices as they vary from day to day. In other words we need to define a return. For most people this would naturally be defined as a percentage return, which is given by the formula:
where 
If you know your power series expansions, you will quickly realize there is not much difference between these two definitions for small returns- it’s only when we are talking about pretty serious market days that we will see a difference. One advantage of using the log returns is that they are additive- if you go down 0.01 one day, then up 0.01 the next, you end up with the same price as you started. This is not true for percentage returns (and is even more not true when you consider large movements like 50% down one day, 50% up the next).
Once we have our returns defined, we can keep a running estimate of how much we have seen it change recently, which is usually measured as a sample standard deviation, and is called a volatility estimate.
A critical decision in measuring the volatility is in choosing a lookback window, which is a length of time in the past we will take our information from. The longer the lookback window is, the more information we have to go by for our estimate. However, the shorter our lookback window, the more quickly our volatility estimate responds to new information. Sometimes you can think about it like this: if a pretty big market event occurs, how long does it take for the market to “forget about it”? That’s pretty vague but it can give one an intuition on the appropriate length of a lookback window. So, for example, more than a week, less than 4 months.
Next we need to decide how we are using the past few days worth of data. The simplest approach is to take a strictly rolling window, which means we weight each of the previous n days equally and a given day’s return is counted for those n days and then drops off the back of a window. The bad news about this easy approach is that a big return will be counted as big until that last moment, and it will completely disappear. This doesn’t jive with the sense of the ways people forget about things- they usually let information gradually fade from their memories.
For this reason we instead have a continuous look-back window, where we exponentially downweight the older data and we have a concept of the “half-life” of the data. This works out to saying that we scale the impact of the past returns depending on how far back in the past they are, and for each day they get multiplied by some number less than 1 (called the decay). For example, if we take the number to be 0.97, then for 5 days ago we are multiplying the impact of that return by the scalar 0.97^5. Then we will divide by the sum of the weights, and overall we are taking the weighted average of returns where the weights are just powers of something like 0.97. The “half-life” in this model can be inferred from the number 0.97 using these formulas as -ln(2)/ln(0.97) = 23.
Now that we have figured out how much we want to weight each previous day’s return, we calculate the variance as simply the weighted sum of the squares of the previous returns. Then we take the square root at the end to estimate the volatility.
Note I’ve just given you a formula that involves all of the previous returns. It’s potentially an infinite calculation, albeit with exponentially decaying weights. But there’s a cool trick: to actually compute this we only need to keep one running total of the sum so far, and combine it with the new squared return. So we can update our vol estimate with one thing in memory and one easy weighted average. This is easily seen as follows:
First, we are dividing by the sum of the weights, but the weights are powers of some number s, so it’s a geometric sum and the sum is given by
Next, assume we have the current variance estimate as
and we have a new return 
Note that I said we would use the sample standard deviation, but the formula for that normally involves removing the mean before taking the sum of squares. Here we ignore the mean, mostly because we are typically taking daily volatility, where the mean (which is hard to anticipate in any case!) is a much smaller factor than the noise. If we were to measure volatility on a longer time scale such as quarters or years, then we would not ignore the mean.
In my next post I will talk about how people use and abuse this concept of volatility, and in particular how it is this perspective that leads people to say things like, “a 6-standard deviation event took place three times in a row.”
Happiest being sad
I’m done with math camp, and I am stopping off in Harvard Square on the way home to New York. I collected my two older sons from their first stint at overnight camp yesterday evening, a two-week middle-of-the-woods experience complete with a cold lake, dirty socks and sticky bunk beds. They were actually happy to see me, I could tell by the way they let me hug them in front of other people. I cried when I realized they had each grown two inches.
The past few days have been incredibly emotional. Somehow I started to pine for the program and for the students at the program before it had ended, and now I seem to miss my kids even though I have them back. I’m a mess of yearning, for a million things at once, and it seems like I’ve set myself up for this.
Of course when I think about it I absolutely have, and I guess the only real question is why I’m surprised. I keep falling in love with people and experiences that often even love me back, and even though I’m an experienced piner it doesn’t get any less painful. And yet it seems like the only alternative, if it is a choice I could even make, would be to close myself off from that openness and compassion and live in a careless void. That is certainly more terrifying to me than the safety of wistful suffering.
My friend Moon came to the program a couple of nights ago and gave a kick-ass talk to the students about the Banach-Tarski paradox. She stuck around that night for dinner and asked the program director, who has been doing this for 40 years, whether I had ever been shy. The director said, “No, Cathy was never shy, but she was memorable for the fact that she always said the same thing whenever someone started a conversation with her.” I had no idea what that could have been, and to tell you the truth I was a little worried what he’d say. So Moon asked, and he said the phrase was, “I love math!” It brought back a clear memory of the passion I had then and still have, and hopefully will always have. I am happy to be this sad.
What tensor products taught me about living my life
When I was a junior in college, I went to the Budapest Semesters in Math. I got really bummed while I was there, and I was thinking of leaving math, when a friend of mine back home sent me Silverman and Tate’s book on elliptic curves. That book restored my faith in math and I decided to become a number theorist. I went back to Berkeley and enrolled in Hendrik Lenstra’s Class Field Theory class, which was the second semester of a grad number theory class, and in Ken Ribet’s second semester grad algebra class. Since I’d missed the first semester of each, I pretty much got my ass kicked. I lived and breathed algebra and p-adics and local-glocal principles for the next three months. It was pretty awesome and incredibly challenging. The moment of my biggest frustration happened when we learned about tensor products over arbitrary rings with zero divisors.
I kept trying to understand these rings, and in particular the elements of these rings. I wasn’t asking much: I just wanted to figure out the most basic properties of tensor products. And it seemed like a moral issue. I felt strongly that if I really really wanted to feel like I understand this ring, which is after all a set, then at least I should be able to tell you, with moral authority, whether an element is zero or not. For fuck’s sake!
I couldn’t do it. In fact all the proofs I came up with involved the universal property of tensor products, never the elements themselves. It was incredibly unsatisfying, it was like I could only describe the outside of an alien world instead of getting to know its inhabitants.
After a few months, though, I realized something. I hadn’t gotten any better at understanding tensor products, but I was getting used to not understanding them. It was pretty amazing. I no longer felt anguished when tensor products came up; I was instead almost amused by their cunning ways.
Every now and then something like that happens in my life. Something that I start out desperately wanting to understand, to analyze, and to own. It’s practically a moral imperative! And I consider myself a person who gets stuff done! How can I let this lie unexplained?
Then after a few days it turns out, no, I still don’t understand it, but it actually makes me like it more. In fact now I look forward to things like that; little puzzles of human existence, where, for perhaps small examples (like when you work over a field) you can understand the issue entirely, but overall you realize it’s harder than that, and moreover you shouldn’t kill yourself over it. You can remain content maybe knowing how to describe some of its properties, while allowing it to maintain its secrets, because life is actually more interesting that way.
Follow up on: math contests kind of suck
I have been really impressed with the comments and thoughts of my first post about how I think math contests kind of suck. Thinking about it some more, I’d like to make two corrections to my original thoughts as well as a clarification.
The first correction is that it’s the MAA, not the NSF, that mysteriously only seems to support contests, or at least for the most part supports contests and not enrichment. The NSF, as has been pointed out in the comments, mysteriously supports primarily college-level math enrichment (through REUs) instead of high-school level stuff, but that’s a different mystery.
The second correction is that, instead of saying about contests “most people don’t get close to winning, and in particular give those people the impression that because they lost a contest they don’t “have it” when it comes to math,” I should have said, “most people don’t get close to winning, and for the subset of people who care about winning, in gives them the impression that because they lost a contest they don’t “have it” when it comes to math.” In other words, I’m not discussing the subpopulation who don’t care if they win. (To those people I’d say: you are rare and you are lucky.)
Except I am discussing them, and this is where the clarification comes in. My point about girls is this: girls are more likely to be in the subpopulation of kids who care, and therefore more likely to be disappointed in themselves. In fact I would add that girls are more likely to underestimate their performance, even if it was great, and moreover they are more likely to do badly in the presence of the negative stereotype that tells them girls aren’t good at math.
These are all statistical statements. In particular, an argument that won’t convince me I’m wrong is something like: I’m a guy and I didn’t care if I won or lost and I loved (or hated) contests. That just means you are not in the population of kids I am talking about. Another argument that won’t convince me I’m wrong goes like this: I’m a guy and I cared and I did awesome. In fact won’t even really change my mind if a woman writes and said she cared and did badly (or well) but loved (or hated) them anyway. Because what I’m talking about is essentially a statistical statement, and idiosyncratic examples probably won’t change my mind.
In fact I’d argue that it’s very very difficult to prove or disprove my claim, at least with comments, because there’s a strong survivorship bias in place, namely that people who got scared away from math won’t be reading my blog at all. In order to give evidence to support or discredit my claim we would have to look at examples of populations which were or weren’t exposed to enrichment, versus contests, versus perhaps something else (like no math outside their classroom) and see who became mathematicians. Oh wait here’s something.
By the way, it’s important to make clear that I’m not suggesting stripping contest math out of the picture altogether. I think there’s a case to be made that they’re better than nothing. But we don’t need to settle for nothing! However, I think we should be creating alternatives that are not competitive or timed. I was very happy to hear about the month-long test and I also heard about a team 24-hour test (does anyone know the name of that and if it still exists?)
Two last tangentially related issues:
- I would argue that any time a bunch of nerd kids get together they have a blast. So we definitely should be getting math nerd kids together. We just shouldn’t be having them compete against each other. I claim they’d have an even better time that way.
- Also, has anyone else noticed the prevalence of girls who are good at competitions and very involved fathers? It’s really interesting. My dad is a mathematician too, and many (but not all) of the women mathematicians I know have heavily involved and/or mathematical dads.
_Love_ you people
I’d like to make a shout-out today to a bunch of people.
First, my readers, who are gorgeous, sexy, and brilliant people. Thanks for reading.
Second, my commenters, who are thoughtful, gorgeous, sexy, and brilliant people, especially when they back me the fuck up. Go, you people! I’m nearly at a 3-to-1 comment-to-post ratio, which makes me feel pretty awesome. I’ve learned a whole bunch and met some pretty amazing people recently through their comments. I’ve actually been please to discover that I really enjoy being disagreed with and argued with- it makes it so much faster to learn. So keep the (constructive) criticisms coming!
Next, I’d like to throw out a bunch of links to blogs which I really like. Actually I recently created a blog roll so there’s that. But in particular I’d like you to check out some of my favorites:
- My good friend Jordan Ellenberg has a wonderful blog entitled “Quomodocumque“, whatever that means (oh wait! it means “whatever” in Latin; I wonder if that is meant sarcastically), in which he muses about math (Rubik’s cubes included!) and… whatever.
- Just in case you’ve somehow missed the whole String Theory Debate, please inform yourself at Peter Woit’s blog called “Not Even Wrong”. When I taught at the Columbia math department, as a Barnard math professor, I used to eat lunch with Peter every day at the Mill Korean on Broadway and 112th. What was adorable about Peter is that every frigging day, and I mean every day, he’d read the menu, look a bit confused, and then order beef fried rice. And then he’d give me his Chiclets at the end of the meal. I’m not sure why this story would recommend his blog to you but it certainly endears him to me. His blog rocks btw.
- Andrew Gelman’s blog titled Statistical Modeling, Causal Inference, and Social Science has a pretty awesome post today about economists (who doesn’t love hating on economists?!).
- I just found this blog, Quantivity, which contains impressively informed finance stuff, and is more technical than what I’m going for.
- Check out a new game theory blog, called Nuclear Chicken Collusion, which comes up with very readable, fun versions of fancy ideas. Their most recent post talks about the probability of there being a god and what it means for you.
High frequency trading: Update
I’d like to make an update to my earlier rant about high frequency trading. I got an awesome comment from someone in finance that explains that my main point is invalid, namely:
…the statement that high frequency traders tend to back away when the market gets volatile may be true, but it is demonstrably true that other, non-electronic, non-high-frequency, market makers do and have done exactly the same thing historically (numerous examples included 1987, 1998, various times in the mortgage crisis, and just the other morning in Italian government bonds when they traded 3 points wide for I believe over an hour). While there is an obligation to make markets, in general one is not obliged to make markets at any particular width; and if there were such an obligation, the economics of being a marketmaker would be really terrible, because you would be saying that at certain junctures you are obliged to be picked off (typically exactly when that has the greatest chance of bankrupting your enterprise).
My conclusion is that it’s not a clear but case that high-frequency traders actually increase the risk.
By the way, just in case it’s not clear: one of the main reasons I am blogging in the first place is so that people will set me straight if I’m wrong about the facts. So please do comment if you think I’m getting things wrong.
High frequency trading
This morning there was an article in the New York Times describing high frequency traders- what they do and how they want people to like them. I’m of the mind that there’s not much to like.
NOTE: Please see update!
High frequency traders are basic, old-fashioned opportunists. They buy somewhere and try to sell somewhere else cheaper. They have expensive technology and colocate next to exchanges to deal with speed-of-light issues to shave off tiny fractions of seconds for their trades. They notice a currency change in Brazil and trade on it in the US before anyone else notices. That kind of thing.
They will tell you that they are useful to the market, because they have set the bid-ask spread smaller than it used to be. Back in the day, there were official “market makers” who would maintain a book of certain instruments, and would be the go-to person for anyone who wanted to buy or sell. In return for the service they would charge a fee, which would be this so-called spread. Moreover, they were required to offer to buy and to sell in all kinds of trading environments (the spreads could get pretty wide of course).
It’s true that those spreads have gotten smaller since high-frequency traders have come to dominate. They have substantially replaced the old-school market makers and claim to be doing a better job. However, it’s also true that high-frequency traders aren’t required to be there. So when the going gets tough they completely vanish. This happens in moments of panic, and it can easily be true that their ability to vanish at will can also create more panics more often (I’d love some evidence to support or deny this theory), since from their perspective, at the first sign of weirdness, they may as well pull out until the dust settles.
The analogy I like to come up with is a little story about chores. Suppose you have someone who comes and helps you with your cleaning, mostly dishes, every day, for a small fee. Since you have kids and a job, the small fee seems to be worth it. After a while someone else comes along and offers to do your dishes every day! for free!! What a deal! You can’t resist. However, it turns out that, if the kitchen actually gets really dirty and needs to be mopped up or seriously cleaned, the free-dishes guy is nowhere to be found and you’re on your own, just when all the kids are sick and there’s a product release at work. Maybe not such a great deal after all.
Math contests kind of suck
I’m going to annoy quite a few people with this post, but I’ve been thinking about this for a while and it comes down to this: I think math contests for kids kind of suck.
Here’s the short version of my argument.
Math contests discourage most people who take them, because most people don’t get close to winning, and in particular give those people the impression that because they lost a contest they don’t “have it” when it comes to math. At the same time, although they are encouraging for a few people, it’s not clear to me that the kind of encouragement they give those kids is healthy. Finally, they are bad for women.
Now I will argue this more thoroughly.
The way math contests are set up nowadays, they start in middle school, at the school level, and if a student does well at a given test they move on to a larger stage, perhaps at the state level, and they typically culminate in a national test, or sometimes even an international test (in the case of the IMO).
This system sets up nearly all the participating students for a feeling afterwards of having not been good enough. It encourages competition over collaboration, which is a huge problem in my opinion, but even worse, it tends to make young people feel like they aren’t smart enough to be mathematicians. It is in fact well-documented that people seem to think that one is either born good at math or not, in spite of the fact that there’s ample evidence that practicing math competition-type problems makes you good at them (why else would Stuyvesant kids consistently beat other kids? Is it really possible that smart people somehow know to be born in New York?). The bottomline is that these extremely young, impressionable kids get early impressions that the contests are measuring their genetic abilities, and that they aren’t cutting it.
When I was in middle school, there were no math contests. I was lucky enough to have a great teacher in 7th grade, who let us nerds debate amongst ourselves for an entire class whether 0.999999… is equal to 1 or not. He put himself in the position of a mediator. It was a great moment for me, and made me realize how much creativity and originality could be involved in the process of making and understanding math.
When I got to high school, I was on the math team, and although I wasn’t bad, I also wasn’t good – and I felt bad about that, consistently. In fact there were definitely moments when I doubted my chances at becoming a mathematician. It is really a testament to my internal love for mathematics, combined with finding this math camp that I’m teaching at now, that motivated me to become a mathematician. If I had not had that 7th grade teacher, and if I had had earlier experiences being so-so at math contests, it’s possible I would have been turned off of math altogether.
Perhaps you are thinking, well of course there’s a selection process for math contests, because they select for people who are good at math! I discussed this with another mathematician today and he refined that argument as follows: some people are good at understanding concepts but can’t work out the details, and some people are good at working out details by rote but don’t understand the concepts- you can’t really be a good mathematician without both, and perhaps the contests select for the details people, but after all you need that aspect.
But I would go further: although I agree you can’t be a good mathematician without both, I don’t think the contests select for the details people. They actually select for people who do or don’t understand the concepts (probably do for the higher level tests) but who in any case are extremely fast at the details. I have never been particularly fast at working out the details of something from the conceptual understanding (for example, it takes me a long time to solve a 7x7x7 Rubik’s cube) but it turns out the Rubik’s cube doesn’t mind. And in fact mathematics in real life isn’t a timed tests- the idea that you need to be original and creative really quickly is just a silly, arbitrary way to select for talent.
I guess if you could have math competitions that aren’t timed then I might start being okay with them. Especially if they were collaborative.
The reason I claim math contests are bad for math is that women are particularly susceptible to feelings that they aren’t good enough or talented enough to do things, and of course they are susceptible to negative girls-in-math stereotypes to begin with. It’s not really a mystery to me, considering this, that fewer girls than boys win these contests – they don’t practice them as much, partly because they aren’t expected by others, nor do they expect themselves, to be good at them. It’s even possible that boys brains develop differently which makes them faster at certain things earlier- I don’t know and I don’t care, because I don’t think that the speed issue is correlated to later deep thought or mathematical creativity.
Finally, I don’t necessarily think that winning math contests is even all that good for the winners either. In spite of the fact that many of my favorite people are mathematicians who were excellent at contests, I also know quite a few people who were absolutely dominant in math contests in their youth who really seemed to suffer later on from that, especially in grad school. From my armchair psychologist’s perspective, I think it’s because they got addicted to the rush of doing math really fast and really well, and winning all these prizes, and when they get to grad school and realize how hard math really is, they can’t stand it.
One related complaint to this rant: it seems like there is way money out there for math contests for young people than there is for math enrichment programs like the program I’m working at now (I’m looking at you, NSF). Why is this? Probably a combination of the fact that’s it’s easier to organize, it seems quantitatively measurably “successful” because there’s a winner at the end, and maybe even because it makes the United States look good compared to other countries to have a winning IMO team- in other words, spin. Booo! How about throwing a little bit of money towards programs that sponsor a sense of collaborative, exploratory mathematics and which encourages women?
Before I get people too riled up, I will say this in favor of math contests: they do tend to expose kids to different kinds of math than is normally offered in their classrooms, which can be really great, and expansive, for kids that have drab math curriculums with drab teachers. Lots of kids first find out there’s math beyond quadratic equations by going to a math contest. That’s cool, but can’t we do it in a better way?
What is an earnings surprise?
One of my goals for this blog is to provide a minimally watered-down resource for technical but common financial terms. It annoys me when I see technical jargon thrown around in articles without any references.
My audience for a post like this is someone who is somewhat mathematically trained, but not necessarily mathematically sophisticated, and certainly not knowledgeable about finance. I already wrote a similar post about what it means for a statistic to be seasonally adjusted here.
By way of very basic background, publicly traded companies (i.e. companies you can buy stock on) announce their earnings once a quarter. They each have a different schedule for this, and their stock price often has drastic movements after the announcement, depending on if it’s good news or bad news. They usually make their announcement before or after trading hours so that it’s more difficult for news to leak and affect the price in weird ways minutes before and after the announcement, but even so most insider trading is centered around knowing and trading on earnings announcements before the official announcement. (Don’t do this. It’s really easy to trace. There are plenty of other ways to illegally make money on Wall Street that are harder to trace.)
In fact, there’s so much money at stake that there’s a whole squad of “analysts” whose job it is to anticipate earnings announcements. They are supposed to learn lots of qualitative information about the industry and the company and how it’s managed etc. Even so most analysts are pretty bad at forecasting earnings. For that reason, instead of listening to a specific analyst, people sometimes take an average of a bunch of analysts’ opinions in an effort to harness the wisdom of crowds. Unfortunately the opinions of analysts are probably not independent, so it’s not clear how much averaging is really going on.
The bottomline of the above discussion is that the concept of an earnings surprise is really only borderline technical, because it’s possible to define it in a super naive, model-free way, namely as the difference between the “consensus among experts” and the actual earnings announcement. However, there’s also a way to quantitatively model it, and the model will probably be as good or better than most analysts’ predictions. I will discuss this model now.
[As an aside, if this model works as well or better as most analysts’ opinions, why don’t analysts just use this model? One possible answer is that, as an analyst, you only get big payoffs if you make a big, unexpected prediction which turns out to be true; you don’t get much credit for being pretty close to right most of the time. In other words you have an incentive to make brash forecasts. One example of this is Meredith Whitney, who got famous for saying in October 2007 that Citigroup would get hosed. Of course it could also be that she’s really pretty good at learning about companies.]
An earnings surprise is the difference between the actual earnings, known on day t, and a forecast of the earnings, known on day t-1. So how do we forecast earnings? A simple and reasonable way to start is to use an autoregressive model, which is a fancy way of saying do a regression to tell you how past earnings announcements can be used as signals to predict future earnings announcements. For example, at first blush we may use last earning’s announcement as a best guess of this coming one. But then we may realize that companies tend to drift in the same direction for some number of quarters (we would find this kind of thing out by pooling data over lots of companies over lots of time), so we would actually care not just about what the last earnings announcement was but also the previous one or two or three. [By the way, this is essentially the same first step I want to use in the diabetes glucose level model, when I use past log levels to predict future log levels.]
The difference between two quarters ago and last quarter gives you a sense of the derivative of the earnings curve, and if you take an alternating sum over the past three you get a sense of the curvature or acceleration of the earnings curve.
It’s even possible you’d want to use more than three past data points, but in that case, since the number of coefficients you are regressing is getting big, you’d probably want to place a strong prior on those coefficients in order to reduce the degrees of freedom; otherwise we would be be fitting the coefficients to the data too much and we’d expect it to lose predictive power. I will devote another post to describing how to put a prior on this kind of thing.
Once we have as good a forecast of the earnings knowing past earnings as we can get, we can try adding macroeconomic or industry-specific signals to the model and see if we get better forecasts – such signals would bring up or bring down the earnings for the whole industry. For example, there may be some manufacturing index we could use as a proxy to the economic environment, or we could use the NASDAQ index for the tech environment.
Since there is never enough data for this kind of model, we would pool all the data we had, for all the quarters and all the companies, and run a causal regression to estimate our coefficients. Then we would calculate a earnings forecast for a specific company by plugging in the past few quarterly results of earnings for that company.
I love math nerd kids
So I’m almost at the end of my second week here at HCSSiM, and the pathetic truth is I already miss these kids. They are so freaking adorable, and of course I miss my own kids so much, that the emotional turmoil of the situation combines to create the reality that I am actually nostalgic for each moment with them before that moment happens. Pathetic!! It’s something about identifying with their nerdy selves finding each other and figuring out that they have a community of nerds that accepts them… whatever, now I’m tearing up. Pitiful.
As for what I’m teaching them, the first week it was number theory, number theory, and more number theory. Can you tell I like number theory? At the end of the first week I looked around and I saw a bunch of earnest faces wondering if I was going to prove yet another thing about relatively prime numbers and solving polynomials modulo n and I thought to myself, these kids are going to think there’s no other examples of proof by induction! How shameless! So this week I talked about graph theory. Next week: I’m going back to number theory. Yes I know, but it’s AWESOME. I’m going to talk about Farey numbers and continued fractions and maybe the Pell equation. They will know all about the golden ratio and maybe we’ll even measure each other’s faces. I can’t wait.
Last night we went to the director’s house and ate corn on the cob (we made the kids husk the corn- did you know teenagers today have mostly never husked corn before in their lives?) and pizza and we played “Mafia,” which was hilarious and sweetly innocent.
This weekend is “Yellow Pig day” at the camp program, which is a day where we celebrate yellow pigs and the number 17. We take this incredibly seriously, including making t-shirts with yellow pigs, having a 4-hour (feels like 17) talk about interesting properties of the number 17, and finally, singing yellow pig carols and eating a yellow pig cake at the end. It’s a wild time for math nerd kids. They will remember this and each other for the rest of their lives. Woohoo!!
Did I mention that I was a minor celebrity last night because I solved a 7x7x7 Rubik’s cube in front of them? This is status at its best. I even showed them my trick, and one of the kids came back to me at breakfast this morning proudly displaying his cube with a 3-cycle. Update: he has solved his entire cube using 3-cycles. Now he’s moving on to a dodecahedron puzzle.
LOVE these kids.
Motivating transparency: what we could do about too big to fail
In this previous post, I promised a follow-up post about how we can devise a system in which large banks are actually motivated to be transparent about what is inside their portfolios. We have also discussed why the current system doesn’t work this way and that the banks have every reason to obfuscate their holdings, and in fact make loads of money by doing so. This makes appropriate external risk management difficult or impossible.
I have actually thought about this problem quite a bit since that post, and I (and a friend in finance) have come up with two quasi ideas, which hopefully together add up to be as good as one complete idea. The first comes under the category, “add stuff to what we have now”, whereas the second comes under the category, “initiate a new system which will over time replace the one we have”. Both of these systems rely on a good understanding of the underlying problem of the current system, namely the concept of “too big to fail.”
If you’re reading this and you have comments about either idea, please do comment. We are hoping for lots of feedback so we can improve the details.
Too Big to Fail
Recall that the way it works when hedge funds want to trade stuff: they have prime brokers, i.e. banks like Deutche and Goldman Sachs and Bank of America (see list of the biggies here). When the brokers don’t like the trade, or think it’s not sufficiently liquid, or think that the hedge fund may fail for any reason, they demand that the hedge funds post margin. That way if the bet goes sour there is a limited amount of risk that the brokerage could lose. As soon as a position starts to look riskier, which could happen because of recent volatility or lack of price transparency, the amount of margin that needs to be posted normally increases, putting pressure on the hedge fund to liquidate suspicious assets.
In other words, there is a real cost to hedge funds for trading in illiquid or complex securities, namely their cash is tied up in bank accounts with their brokers. This is not to say that they don’t take large risks, but there is a limit of how much risk they can take because of the “posting margin” system.
By contrast, big banks don’t post margins. They trade with hedge funds, of course, since hedge funds trade with them, but it’s the banks who demand margin, not the hedge funds (actually there’s a historical exception to this rule, namely Paulson’s hedge fund demanded margin from its brokers during the 2008 financial crisis).
This asymmetrical situation begs the question, why do hedge funds have to post margin but the big banks don’t? Two reasons: first, banks have access to Federal funds, and second, they are deemed to big to fail. [I admit I don’t know exactly why the access to Federal funds is granted to banks, nor do I understand exactly what the effect is. But I do think it’s a pertinent fact which is why I’ve included it here. Please do comment if you know more! Also note it may be a red herring since Goldman Sachs didn’t have access to Fed funds until the crisis.]
This “too big to fail” guarantee is a huge problem, which has only gotten more precise (since we’ve seen the bailout and now everyone knows the guarantee is there) and larger (because, in the end, the net result of all the 2008 crisis is fewer, larger banks) and about which absolutely nothing seems to be getting done. The disingenuous whining of greedy bankers like Jamie Dimon serves as a smokescreen for the fact that, if anything, banks are presumably waltzing into the next phase of their life with more power and fewer checks than they could have dreamed about in August 2008.
Idea #1: make banks post margins
“Too big to fail” means that it is assumed that the bank will be rescued by the government if it makes huge bad bets that threaten to bring them down. Two of the reasons the government can be counted on to bail out banks are first, that the deposits of normal Americans are at risk, which is discussed below in Idea #2, and second, that a bankruptcy would be catastrophically complicated, which we discuss here. One result of the guarantee is that hedge funds don’t bother demanding margins, which makes the banks riskier, which makes the “too big to fail” guarantee even worse.
What if the lawmakers enforced a symmetry of posted margins? We have to be precise, because actually there are different kinds of margins that traders are forced to post.
First, there’s the margin you post in the sense of “keep $x as a deposit for the position”, the thinking being that even if things go south, the broker could liquidate at something better than $x below current marked price in a hurry. This is the initial margin.
Next there’s the “your position lost $10 today, so you need to give me $10” (this is called variation margin). This is the most likely way to get margin called.
The idea here is to require brokers to post initial margin just as hedge funds do now. More precisely, the idea would be to let the two parties negotiate on the initial margin, which could be more for hedge funds since they may well be riskier, but then once it’s set to have complete symmetry of variation margin.
Occasionally, in risky environments, the initial margin of $x is increased, which causes a lot of unraveling, and possibly cascading waves of problems which set off a panic. We’d need to have rules about how often this can happen to avoid the “symmetric of variation margin” rule from being bypassed with lots of initial margin modifications. The symmetry aspect should keep the margin contracts from allowing this to happen too often.
The overall goal would be to devise a system that would:
- Encourage the posting and calling of (variation) margins,
- Encourage sufficient sizing of initial margin,
- Encourage early calls and liquidating if there is doubt that a variation margin call could be met, and
- Simplify the bankruptcy rules on ownership of assets, especially for illiquid or complex assets.
The initial margin can be thought of as the dollar amount a price could move by between a margin call and it being paid. It should not be thought of as an asset for either party (and therefore the accounting of the various margins should be carefully considered, but I’m no accounting expert), and certainly should not be able to be recycled to buy more stuff, i.e. add to ones leverage, or offered towards capital requirements. Moreover, if it is indeed symmetric, that would mean if a bank claims to only need to post n dollars in initial margin, then the hedge fund can turn around and use that same number for that same trade, at least up to an understood discount.
As for bankruptcy, we should start with the following. When a margin call is made by one side and it isn’t met, the person making the call:
- keeps ALL the margin,
- gets the security, and
- is a (super-senior level of seniority) claimaint to the variation margin they posted with the counterparty.
Moreover, rules 1 and 2 above do not go into a bankruptcy filing if one occurs (in particular, if the security is a swap, it’s just torn up). This is a key point since that means the bankruptcy is simplified and at the same time the security is back in liquid hands. All over, this setup, or one like it, encourage hedge funds to margin call frequently (banks already do that), which is a good thing, and as described above is a further incentive to invest in liquid, non-complex securities, which in the end creates transparency.
The above idea doesn’t deal directly with desired property 2, and may well cause margins to be lower. One possibility to encourage margins to be of sufficient size would be to allow either party to “put” the security in question on to the other party at a cost of giving up the initial margin posted.
Idea #2: grow a separate system of utility deposit banks
Besides incredibly complicated bankruptcy filings with infinitely many counterparties, one of the major reasons those banks really are too big to fail is that they hold deposits, and the government doesn’t want people to worry that their life savings are at risk, causing a run on the banks and chaos. Another way to get around this, at least eventually, is to create new “utility banks” at the state level which do not trade securities (beyond very basic one like interest rate swaps and treasuries), don’t take large risks, and have FDIC guarantees on savings.
In order to get consumers to switch to banks like this, the government should intentionally create incentives for people to transfer their deposits from “too big to fail” banks to these utility banks. A list of incentives could start with reasonable, transparent fees, and the eventual loss of FDIC insurance guarantee at non-utility banks. Then people who want to stay with risk-taking banks can do so knowing that, as long as bankruptcy laws eventually get simplified, the “too big to fail” guaranteed will in fact be gone.
Moreover, another layer of separation between depositors and utility banks should be the requirement that, even with the restricted kinds of trades allowed for utility banks, they should be done in separate corporate entities (since banks are always a mishmash of many companies anyway).
This idea is not new, and can be seen for example in this article. In fact it is incredibly obvious: admit that what we have now is a guarantee for a get-out-of-jail card for greedy bankers, and transfer that guarantee to a banking system that we’ve created to be boring, along the lines of the post office.
Bank accounting link
I wanted to share this link with you; it is both interesting and relevant to another post I’m working on (a follow up to this one) that will describe two ideas I’m contemplating regarding how to systematically change the way big banks are motivated to behave in the presence of the “too big to fail” guarantee.
Its goal is to describe how banks will behave in a given situation with a mortgage, but the thought process generalizes quite well to how banks behave in general, and in particular how accounting considerations trump utility to the depositors and even the long-term shareholders. It also explains, to those of us who were wondering, why Obama’s mortgage modification plan was never going to work.
Short Post!
I’ve been told my posts are intimidatingly long, what with the twitter generation’s sound byte attention span. Normally I’d say, screw that! It’s because my ideas are so freaking nuanced they can’t be condensed to under a paragraph without losing their essence!
But today I acquiesce; here’s a short post containing at most one idea.
Namely, I’ve been getting pretty strong reactions online and offline regarding my post about whether an academic math job is a crappy job. I just want to set the record straight: I’m not even saying it’s a crappy job, I’m simply talking about someone else’s essay which describes it that way. But moreover, even if I were saying that, I would only be saying it’s crappy (which I’m not) compared to other jobs that very very smart mathy people could get. Obviously in the grand scheme of things it’s a very good job- safe working conditions, regular hours, well-respected, etc., and many people in this world have far crappier jobs and would love a job with those conditions. But relative to other jobs that math people could be getting, it may not be the best.
Many professors of math (you know who you are) have this weird narrow world view, that they feed their students, which goes something like, “if you want to be a success, you should be exactly like me (which is to say, an academic)”. So anyone who gets educated in a math department is apt to run into all these people who define success as getting tenure in an academic math department, and they just don’t know about or consider other kinds of gigs. It would be nice if there was a way to get a more balanced view of the pros and cons of all of the options.
mathbabe 