Optimal Behavior

I’m occasionally participating in an on-going forecasting competition (Forecast World Events), and the financial forecasts in particular are interesting. Today I received a request for a forecast relating to the S&P500:

What will be the largest single-day GAIN or LOSS for any trading day between 2012-2-06 and 2012-02-10?

Allocate 100% probability across these categories:

1. <1%
2. 1% to 1.99%
3. 2% to 2.99%
4. 3% or more

The status right now is below:

Unless you have very precise estimates of what will happen over the next 5 trading day, a good estimate would come from history. So using the incredibly convenient R program (code below), I pulled historical data on the S&P500. We can check this question in history a couple of ways:

1. Using all week periods since 1980
2. Using all week periods in February since 1980

The results are surprisingly consistent with history. As of Feb 4, 2012, the consensus was expecting the upcoming week to be more volatile than history, with double the odds of seeing a 3%+ movement up or down, and double odds of a movement between 2 and 3%. The modal historical outcome of between 1% and 2% is underweight by about 13%, not a massive difference.

What would be interesting is seeing how “common” this view is, i.e. is the consistency with history because the majority of people are close to history, or are a majority of extreme positions cancelling each other out?

R Code:

rm(list=ls())
install.packages(quantmod)
library(quantmod)<
sp500<- getSymbols("^GSPC",auto.assign=FALSE,from="1980-01-01")
rets<-periodReturn(sp500,period="daily")
cat.rets<-as.data.frame(rets)
str(cat.rets)
cat.rets$ret.cat=NA
cat.rets$ret.cat[abs(cat.rets$daily.returns)<0.01]=1
cat.rets$ret.cat[abs(cat.rets$daily.returns)>=0.01]=2
cat.rets$ret.cat[abs(cat.rets$daily.returns)>=0.02]=3
cat.rets$ret.cat[abs(cat.rets$daily.returns)>=0.03]=4
cat.rets$year<-as.POSIXlt(as.POSIXct(strptime(as.character(row.names(cat.rets)),format="%Y-%m-%d")))$year+1900
table(cat.rets$year,cat.rets$ret.cat)

cat.rets$dow<-cat.rets$dow<-as.POSIXlt(as.POSIXct(strptime(as.character(row.names(cat.rets)),format="%Y-%m-%d")))$wday
#Using Monday as anchor, define greatest return over the next 5 days

cat.rets$max.week.ret<-NA
for (i in 1:nrow(cat.rets)) {
  if (cat.rets$dow[i]==1) {
    j=i+5
    cat.rets$max.week.ret[i]<-max(cat.rets$ret.cat[i:j],na.rm=TRUE)
  }
  else next
}

table(cat.rets$max.week.ret)
prop.table(table(cat.rets$max.week.ret))

################################
#Just Februaries
nrow(cat.rets)
cat.rets$month<-as.POSIXlt(as.POSIXct(strptime(as.character(row.names(cat.rets)),format="%Y-%m-%d")))$mon
table(cat.rets$month)

cat.rets$max.feb.week.ret<-NA
for (i in 1:nrow(cat.rets)) {
  if (cat.rets$month[i]!=1) {
  if (cat.rets$dow[i]==1) {
    j=i+5
    cat.rets$max.feb.week.ret[i]<-max(cat.rets$ret.cat[i:j],na.rm=TRUE)
  }
  }
  else next
}
row.names(probabilities)<-c("<1%","1-2%","2-3%",">=3%")
prop.table(table(cat.rets$max.feb.week.ret))
probabilities<- cbind(c(.13,.37,.32,.18),prop.table(table(cat.rets$max.week.ret)),prop.table(table(cat.rets$max.feb.week.ret)))

An article in the most recent JDM makes two valuable points – sometimes winning is losing, and we’re ok with that. Some individuals are more likely to over-bid, purchasing a lottery for more than it’s best possible value. Why might they do this? Because to some people, very competitive people, it seems that “winning” is as (more?)  important than making a genuine profit.

This effect is probably reinforced in circumstances that meet the Winners Curse, in which optimism about ones incomplete information is compounded by a desire to “win”. The very word winning has such positive connotations, how could we not want to win an auction?

For some people, the joy of winning is worth over-paying. And these are the people you DEFINITELY want to invite to your poker game.

The second half of last year was not kind to my waistline. Between getting married and leaving the UK there were many causes for dinners and drinks out, which always seem to be less healthy than those at home. So when I got settled in the US, I was very disappointed to see I was about 20lbs (1.5 stones, or 9kg)  overweight.

However, unlike many problems in life, that problem is simple, very solvable and controllable. If you want to lose weight, you must expend more calories than you consume. In many ways, it is like a financial budget – if you want to save (lose weight), you must spend (eat) less than you earn (expend). This is not to say it is always easy, but is is straightforward and doable.

However, how do we track how many calories we consume, and how many we expend? This has historically been the biggest problem with calorie counting diets – they tended to be very imprecise in both foods, and exercise. Many diet programs were based on eating specific foods so that you knew exactly how many calories you consumed. But now, we have a wide variety of applications which can help us to keep track of our calories, both consumed and expended. As an android phone user, I use MyFitnessPal to keep track of calories. I’ve rarely not been able to find the food I was looking for in it.

And these programs lead us to understand exactly the trade-offs we need to make. To lose 1.5 lbs/week, I need to consume, net of exercise, 1520 calories. This doesn’t mean I only eat 1520 calories though – it means I can earn more by exercising. It makes explicit the fact that if I want to drink another beer I need to run for at least 10 minutes. So a night out on the town will cost me about an hour of exercise, which seems like a good deal in both ways. The fact that the approach of equating food to exercise has beneficial effects therefore doesn’t surprise me.

In this way, calorie counting is actually quite useful and allows me to know precisely how much I can eat, or how much I need to exercise at the end of the day. The fact that these trade-offs are made explicit what makes it difficult for us. I have to decide between both drinking a beer and doing 10 min. more exercise, or not doing either.

Because trade-offs are uncomfortable, people seek to trick themselves into this behavior without explicitly counting calories.  They use diets such as only eating meat, eating only during certain hours or the day, or only eat certain foods so that they can achieve exactly the same thing. Almost all forms of diets seek to restrict caloric consumption. Some of them do seek to change your metabolism as well, however at the end of the day if you are losing weight you are doing it by expending more calories than you consume.

This is a clear case the difficulty lying not in knowing what to do, but simply doing it.

However, contrast those budget trade-offs with alcohol consumption. I have no way to earn more alcohol units. I cannot exercise or do any other virtuous behavior the results in being able to drink more and maintain my health. Simply put there is a natural limit which I have no ability to increase. Now being able to make those calorie trade-offs seems great. I have the ability to earn more.

I was very happy to open up my NYTimes this morning, and actually find my own name in Paul Sullivans Wealth Matters column, discussing things to consider as we head into a 2012 with many apparent headwinds.

The conversation continues on the NTimes Bucks blog.

Happy holidays to all.

I’ve wondered about the following question a number of times: How might the fact that we operate in base-10 (0,10,20…100…200) influence our decisions? We all know that we occasionally make decisions based on simply rounding up or down. But do round numbers influence trading in the stock market – for example, when setting stop or limit orders? Consult a new paper in Management Science:

This paper provides evidence that stock traders focus on round numbers as cognitive reference points for value. Using a random sample of more than 100 million stock transactions, we find excess buying (selling) by liquidity demanders at all price points one penny below (above) round numbers. Further, the size of the buy–sell imbalance is monotonic in the roundness of the adjacent round number (i.e., largest adjacent to integers, second-largest adjacent to half-dollars, etc.). Conditioning on the price path, we find much stronger excess buying (selling) by liquidity demanders when the ask falls (bid rises) to reach the integer than when it crosses the integer. We discuss and test three explanations for these results. Finally, 24-hour returns also vary by price point, and buy–sell imbalances are a major determinant of that variation across price points. Buying (selling) by liquidity demanders below (above) round numbers yield losses approaching $1 billion per year.

Utpal Bhattacharya, Craig W. Holden, and Stacey Jacobsen - Penny Wise, Dollar Foolish: Buy–Sell Imbalances On and Around Round Numbers

So would we be better off with a base with a higher or lower modulus? Now that’s an interesting cross-discipline  (economics and pure math) theory PhD waiting to happen. If Krugman hasn’t off-handedly done it yet. 

Robert Frank’s report on what female millionaires want from financial advisors was interesting. It reports on a survey of 550 women millionaires, and sounds like it was particularly geared towards asking questions we’d stereotypically expect women to answer different than men. But…

First, they didn’t ask male millionaires the same questions – we don’t actually know if anything they find is different for women and men. For instance, I think that if you asked male investors if they wanted their advisors to understand their “life pictures” (perhaps with less fluffiness), they’d be happy to. Wealth is a means to an end, and understanding if trust and succession planning is important to you client only comes about when you’ve spoken with them about their objectives.

Second, I don’t get a feeling for what might not matter to women, but might matter lots to men. For instance, beating the market regularly?

But really, the interesting part was how the commenters reacted. Examining gender differences obviously hits a nerve, as many commenters disliked the premise that men and women might be treated differently by the same advisor. While stereotyping is a good way to lose clients, acting as if men and women are exactly the same is too. Individual differences are important, and your gender makes up a big part of that.

Which isn’t to say that women will accept worse advice or performance, just that what they define as good advice or performance might be different.

Lynne Kiesling makes some points about what market failure isn’t, but doesn’t provide a diagnostic for what it is.. but does say that we’re better off saying “markets fail to exist”. Which reminds me of a problem which has perplexed me lately: why can’t you get a taxi on a rainy night in New York? Many people would pay handily for one….

Assuming we’re asking an economist, there are generally a few answers:

1. Because taxi-cabs are a licensed and therefore restricted service, there is under-supply*.
2. Because prices are fixed, they do not earn enough to make it worth their while, and supply does not expand.
3. Because increases in demand cannot be met flexibly during peak vs non-peak times.

None of those responses rings true to someone who lives in New York. In fact, the common experience is to see many taxies with their “Off Duty” lights on driving around the city at that hour, despite many willing paying customers. So I’d like to add to those options:

• Because taxi drivers do not think like economists

Nothing against taxi-drivers or economists. They just mis-understand one another. Except for Camerer, Babcock, Loewenstein and Thaler, who understand taxi-drivers:

We talked to cab drivers in New York City about when they decide to quit driving each day. Most of the drivers lease their cabs, for a fixed fee, for up to 12 hours. Many said they set an income target for the day, and quit when they reach that target. While daily income targeting seems sensible, it implies that drivers will work long hours on bad days when the per-hour wage is low, and will quit earlier on good high-wage days. The standard theory of the supply of labor predicts the opposite: Drivers will work the hours which are most profitable, quitting early on bad day, and making up the shortfall by working longer on good days.The daily targeting theory and the standard theory of labor supply therefore predict opposite signs of the correlation between hours and the daily wage.

To measure the correlation, we collected three samples of data on how many hours drivers worked on different days. The correlation between hours and wages was strongly negative for inexperienced drivers and close to zero for experienced drivers. This suggests that inexperienced drivers began using a daily income targeting heuristic, but those who did so either tended to quit, or learned by experience t o shift toward driving around the same number of hours every day.

Daily income targeting assumes loss-aversion in an indirect way. To explain why the correlation between hours and wages for inexperienced drivers is so strongly negative, one needs to assume that drivers take a one-day horizon, and have a utility function for the days income which bends sharply at the daily income target. This bend is an aversion to losing by falling short of an income reference point.

To the individual standing on the corner in the rain, willing to pay 1.5x market rate for a ride home, this represents a market failure. The market does generally exist, it just doesn’t exist well when you really want it to.

*I would not let my wife get into an unlicensed taxi-cab – that’s not worth the risk.

Many studies have shown that individual investors do poorly compared to a buy-and-hold strategy… But part of that is that we don’t start out as savvy traders. We have to climb the learning curve. When you start trading, you don’t know if you are good or bad at it, and you have little idea how to do it well. So through time, as people “pay to learn”, they’ll either figure out that they’re good, or trade less. That’s the pattern found by Seru, Shumway and Stoffman in “Learning By Trading”, and the abstract is worth quoting in full:  

We test whether investors learn from their trading experience. Using a large sample of individual investor records over a nine-year period, we analyze both the disposition effect and trading performance at the individual level. Disposition is costly: the median investor who suffers from the effect earns 3.2% to 5.7% lower annual returns on average than an investor with no disposition.

Disposition falls, and performance improves, as investors become more experienced. An extra year of experience decreases the disposition effect of the median investor by about 4%, which accounts for about 5% of the increase in returns earned by these investors. By controlling for survival and unobserved individual heterogeneity, we show that investors in aggregate learn partly by attrition, but that learning at the individual level is also important. We also find that unsophisticated investors and investors who trade more learn faster, and we show that the trading style of investors changes with experience.

 Here’s an interesting thought about estimates of individual investors’ under-performance – the measurements rely on the percentage of your sample which is naïve versus experienced investors. A more experienced sample would be more bifurcated – there would be two types of investors – those who didn’t trade much (because they learned they weren’t very good), and those who traded more (because they’d learned they were good). A sample of only experienced traders could have quite a good record.

But as long as there is flesh blood coming into the market steadily, they average return record could look quite bad – but depending on experience, the average investor could be quite good.

Michael Lewis on Daniel Kahneman

Andrew Oswald’s LSE public lecture on Herding Behaviour (correct spelling, obviously…)

Vanguard – How emotional investing can reduce returns (interactive)

 PNC Cost of Christmas (for some holiday fun). Apparently the items in the 12 days of Christmas have inflated by just over 3% this year. Unfortunately the Maids-a-milking are only on minimum wage…

Benartzi for Allianz: Candor about success and failure builds trust.

“Everyone is entitled to his own opinion, but not his own facts” - Daniel Moynihan

@GregBDavies points me to this article by J.D. Roth. First, let me say I agree with many things in it. Knowledge is not enough, you have to take action, sometimes use of behavioral finance is the most effective way etc..

However, like I state previously, the fait-accompli conclusions that financial literacy doesn’t work is completely unsupported. Strong opinions without facts to back them up are things we should be wary of. To my knowledge most independent evidence points to positive effects of financial literacy programs.

I already touched on how financial literacy interacts with basic financial management, but it also effects investing behavior. Here is van Rooij, Lusardi, and Alessi in the Journal of Financial Economics:

The empirical estimates in Table 7 show that financial literacy matters for stock ownership, even after controlling for a large set of demographic characteristics and income and wealth. Those who display higher literacy are more likely to participate in the stock market. The estimates are also sizable: A one-standard deviation increase in advanced literacy raises stock market participation by more than 8 percentage points. Note that the effect is as large as the effect of formal education and wealth. For example, having a university degree increases stock market participation by more than 9 percentage points. Compared to the first quartile of wealth (values up to 2,300 Euros), having wealth in the second quartile (up to 45,000 Euros) increases stock market participation by more than 7 percentage points. Note also that when we account for basic literacy the estimate of advanced literacy does not change. The estimates in Table 7 indicate that financial literacy affects stock market participation above and beyond the effect of the traditional determinants of stock ownership.

When we devised the module on financial literacy, we took into account the fact that financial literacy is not an exogenous characteristic; in fact, literacy can itself be affected by financial behavior (for example, if individuals learn via experience). To remedy this problem, we have collected additional information (beyond current levels of economic knowledge) that can serve as instruments for advanced financial literacy. To be able to rely on measures of
literacy that are exogenous with respect to stock market participation, we asked respondents about their exposure to financial knowledge before entering the job market. Specifically, we asked how much of their education was devoted to economics. 14 Note that economics is part of the high school curriculum at the majority of schools in the Netherlands and it is possible to specialize in economics/business at the high school level (economics degrees can be pursued in college as well, of course).15 Our strategy is to rely on exposure to economic education in the early stages of life. This measure should be correlated with current advanced knowledge while it should be uncorrelated with stock market participation. As mentioned before, advanced knowledge may be a crude proxy of actual knowledge. Moreover, it may simply reflect how much respondents have learned from their personal  experiences and from their success in the stock market. For example, if financially knowledgeable respondents are more likely to invest successfully and stay in the market, while low knowledge respondents are more likely to lose money and exit the market, the relationship between literacy and market
participations may simply reflect the higher knowledge of those who stay in the market.

The first stage regressions are reported in Table 8. Responses to how much of education was devoted to economics range from “hardly at all” to “a lot” and we construct dummies for different levels of economics education while in school. These instruments have a strong predictive power: Those who have had less exposure to economics education in school are less likely to display advanced knowledge, and this holds true even when we account for basic literacy, which we consider a measure of cognition and ability. The Fstatistic in the first stage regressions is high (with values close to 20) and beyond the values recommended to avoid the weak instruments problem (Staiger and Stock (1997) and Bound, Jaeger and Baker (1995)). The first stage results also continue to confirm the correlation between literacy and demographic characteristics, such as education and gender, reported in Table 4B. The estimates in the second stage reported in the last two columns of Table 7 show that the relationship between literacy and stock market participation remains positive, statistically significant, and is even larger in the Generalized Method of Moments (GMM) estimates. Moreover, the exogeneity test is not rejected. Thus, the OLS estimates do not differ significantly from the GMM estimates. The results of the Hansen J-test show that the overidentifying restrictions are not rejected. Overall, our estimates indicate that financial literacy is an important determinant of stock market participation: Those who have low financial knowledge are less likely to hold stocks.

Financial literacy doesn’t make you into George Soros, sure, but it does improve your debt management, savings behavior, and propensity to invest in stocks.

The core problem seems to be the all-or-nothing assessment. It seems expected that financial literacy acts like a vaccine, and once educated, you are inoculated for life, and you’ll be a perfect trader. Against that impossible standard, programs definitely fall down. But it’s not a vaccine, it’s like most skills you learn – you need to keep using/practicing them to keep your skills up over time. And there are real returns to using it.

And indeed, a combination of being financially literate and using the successes in behavioral finance are most likely to get from where you are to where you want to be. It’s not “or”, it’s “and”.