Under the Hood of Buying & Selling Predictions

How do those futures markets like Betfair and Intrade work?

The managers of a prediction market decide upon a finite number of prediction contracts. A contract is essentially a description of some hypothetical future event. For example, a contract might be “Fadebook trades at least $50 per share in 2012.” Another important aspect of the contract specification is the anticipation and preemptive resolution of ambiguity. If Fadebook does a 2:1 split, does the event become “…at least $25 per share?” What if the asking price for Fadebook shares reaches $50, but the bid price does not? Contracts also specify an expiration date, a time by which the event must occur. In the case of the Fadebook contract, the obvious expiration date would be January 1st of 2013. For other contracts, the expiration will be arbitrary to allow for a final decision on the event’s occurrence or nonoccurrence.

Virtual Currency
A prediction is a single user’s opinion on the likelihood of the contract’s event occurring. The prediction market encourages users to form opinions about contract events, and encourages users to wager virtual currency on a contract. Users purchase virtual currency (henceforth “credits”) with real money, or perhaps are granted an amount of virtual currency in a freemium offering.

Contract Size
Each contract also specifies a size, which is both the minimum number of credits a user can wager on a contract, and the marginal increase in the size of a wager. If the prediction market choose a size of “5 credits” for the Fadebook contract, then an individual user can wager only 5, 10, 15… credits on the contract. Contract sizes are necessary in order better match both sides of the wager. Somewhat confusingly, experienced traders refer to each increment of the contract size as “a contract.” If I wager 15 credits on the Fadebook contract with a size of 5 credits, then I am said to be wagering “3 contracts.”

When making a wager on a contract, the user specifies the number of credits she will risk, in contract size units, and the direction of the wager. If a user believes the event is certain to occur and the user is eventually proven correct, she will profit from buying a contract whenever its likelihood is less than 100%. If a user believes an event is certain not to occur and turns out to be right, the user will profit from selling the contract when its likelihood is greater than 0%. The buyer of a contract is said to be long and the seller of a contract we call short.

When the contract’s event occurs, the long side earns the contract size in credits for each contract, less the likelihood level where she initially make the wager. So if Fadebook’s stock hits $50 in October of 2012 while I am long 3 contracts bought at 25% likelihood, then the prediction market would immediately close the contract and credit my account with 5 credits (size), times 3 contracts, less 25% of the total, or 11.25 credits. The opposite also occurs for the short side. In this case, the 3 contracts the short side sold are closed out worthless at 0%, and the short’s account is reduced by 5 credits size, times 3 contracts, times 25% of the total. Again this is 11.25 credits but deducted from the short side of the wager.

If the contract expires as the year 2012 comes to a close, and I shorted 2 contracts at 60% back in February of 2012, then I will earn a profit of 5 credits size, times 2 contracts, times 60% or 6 credits. This is exactly what the long side of those 2 contracts would lose. The long side may be 1 user, or 2 different users each long 1 contract.

By definition, the long and short sides of a contract will always balance. A user is not able to be long a contract unless another user is short. This would be similar to a real futures contract traded in Chicago or New York, but where the long side is committed to “buying” the event for 100% if it occurs.

The current likelihood (henceforth “price”) of a contract is determined by looking at the contract’s order book on the prediction market. Order books are how buyers and sellers of contracts are matched, and indicate a prediction contract’s current price or likelihood. An order book is an ordered list of buying and selling prices. If there is no market in a contract and a user wishes to make a wager, her estimated likelihood becomes the best buying or selling price for the contract. From now on we drop the price or likelihood’s percent sign for brevity.

Say the Fadebook contract has just been listed and publicized on the prediction market. If I believe the event is very likely to occur, then I might offer 99 to anyone willing to sell at 99. If I am correct, then I will eventually earn 1 credits per contract for my trouble. I will have paid 99 for something that will earns me 100. Though perhaps I want to leave myself more room to profit, and instead offer 25 to anyone willing to sell at 25. This would mean a profit of 75 per contract when it expires. The prices at which every user is willing to buy forms one side of the order book, the buying prices or bids.

A similar process happens on the selling side. I want to be short a contract when I do not believe the event will occur. So I would sell to anyone for more than 0 likelihood or price. If I end up correct in my prediction and the event does not occur when I went short at 90 likelihood, then I earn 90% of the contract size for each contract. The collected prices at which all users are willing to sell forms the other side of the order book, the selling prices or asks.

Market Orders
When a wager occurs at a price matching one of the buy or sell orders currently available in the market, the order is instantly made complete by matching a long and a short side of a wager. If I want to buy the Fadebook contract at 30 or 35 and there is already a user with a selling price or ask of 32, my wager will be immediately matched. In this sense, my order never actually appears in the prediction market order book for the contract, since the wagers are instantly matched.

Often a user will want to buy or sell at whatever likelihood or price the market is currently offering. In this market order, the user takes whatever happens to be the best price available at the time. Market orders are risky because the user may not know the exact price at which she commits to the wager. Market orders are also said to leduce liquidity in the market, and may be considered less healthy for the prediction market than regular limit orders.

Trading Out Early
The fundamental advantage to prediction markets over traditional oddsmaking is the option for a user to exit out of a profitable or loser wager early, before the contract event’s expiration. A user who is currently long or short a contract is free to trade the position to another party at any point, even if the user has only held the contract for a few minutes. This is advantageous for a user who wants to cut their losses early on a losing contract, or wants to take their profit early on a contract that becomes profitable.

If I went long 5 of the Fadebook contracts at 35 a few months ago, but that contract now has an order book centered around 50 bid/ask, then I can sell the 5 contracts for a 15 profit per contract right now. I do not need to hold my Fadebook contracts until 2013. This is not going short the contract, but selling to a willing buyer in order to net out my position with a profit.

Liquidity & Accurate Predictions
The more users are actively participating in wagering on a contract, the more accurate the collective estimate of likelihood. The most recent trade price or likelihood of a very busy and popular contract is an excellent estimate of the real likelihood of the contract event occurrence. If a single user believes a contract has a 35% likelihood, but a thousand other users are trading that contract around 75% likelihood, chances are the first user is wrong!

Prizes & Incentives
Prediction markets are more powerful when users are incentivized with real compensation. Therefore even if the prediction market’s virtual currency simplifies the regulatory aspects of the project, credits need to be closely tied to real money or prizes, so users assume actual risk when making wagers. Also any prizes need to incentivize users to make careful wagers and not necessarily “swing for the fences” on each wager. In other words, each bit of virtual currency must contribute to winning prizes.

Users who risk nothing of value when making wagers will not turn out to form a particularly accurate prediction market.

Sequential Learning Book

Things have been quiet around here since the winter because I have been focusing my modest writing and research skills on a new book for O’Reilly. We signed the contract a few days ago, so now I get to embrace a draconian authorship schedule over the next year. The book is titled Sequential Machine Learning and will focus on data mining techniques that train on petabytes of data. That is, far more training data that can fit in the memory of your entire Hadoop cluster.

Sequential machine learning algorithms do this by guaranteeing constant memory footprint and processing requirements. This ends up being an eyes-wide-open compromise in accuracy and non-linearity for serious scalability. Another perk is trivial out-of-sample model validation. The Vowpal Wabbit project by John Langford will be the book’s featured technology, and John Langford has graciously offered to help out with a foreword. Therefore the book will also serve as a detailed tutorial on using Vowpal Wabbit, for those of us who are more coder or hacker than statistician or academic.

The academic literature often uses the term “online learning” for this approach, but I find that term way too confusing given what startups like Coursera and Khan Academy are doing. (Note the terminology at the end of Hilary Mason’s excellent Bacon talk back in April.) So, resident O’Reilly geekery-evangelist Mike Loukides and I are going to do a bit of trailblazing with the more descriptive term “sequential.” Bear with us.

From the most basic principles, I will build up the foundation for statistical modeling. Several chapters assume statistical natural language processing as a typical use case, so sentiment analysis experts and Twitter miners should also have fun. My readers should know computers but need not be mathematicians. Although I have insisted that the O’Reilly toolstack support a few of my old-school LaTeX formulas…

What is There to Eat Around Here?

Or, why clams are bourgeois — the presence of clams on menus is indicative of a place where people spend a lot of their money on housing. This is how I found out.

We have all played the proportional rent affordability game. How much of my income should I spend on where I live? One rule of thumb is “a third,” so if you take home $2,400 per month you aim to spend about $800 on rent or a mortgage payment. Some play the hypothetical budgeting version of the game. We might pay more of our income for housing if it means being able to live in a particularly desirable area.

Expensive Housing
Here is a map of income normalized by housing expense, for a bunch of Bay Area neighborhoods. This information is from our Altos Research active market real estate data. More technically, each dot on the map represents the ratio of a zipcode’s household income to the weighted average of single family home list prices and multi-family home list prices. I used median numbers, to minimize the impact of foreclosures or extremely wealthy households. Single and multi-family home prices were weighted by listing inventory, so urban condos matter as much as those McMansions in the ‘burbs. The green dots are areas where proportionally more income is spent on housing, and blue dots are the opposite.

Bay Area Housing Proportional Housing Expense

The data shows that people living in the city of San Francisco spend a much larger proportion of their income on housing than Oaklanders or those in San Jose. If we assume that the real estate market is somewhat efficient, then those who choose to live in certain neighborhoods forgo savings and disposable income. Why is it that housing expenses for living in San Francisco are so much higher than San Jose, even when we control for income disparity?

The Real Estate Menu
Like a proper hack economist, I am going to gloss over the obvious driving factors of proportionally expensive housing, such as poor labor mobility, lack of job opportunities, and a history of minority disenfranchisement. I am a chef by training — culinary arts degree from CHIC, the Le Cordon Bleu school in Chicago — and remain fascinated by the hospitality industry. So instead of diving into big social problems, I focused on something flippant and easy to measure: Where people go out to eat, across areas with different levels of proportional housing expense.

I analyzed the menus of a random selection of 5,400 sit-down and so-called “fast casual” restaurants across the United States. This menu population is hopefully large and diverse enough to represent dining out in general, though it is obviously biased toward those restaurants with the money and gumption to post their menus online. However there is not a disproportionate number of national chain restaurants, since even the most common restaurant, T.G.I. Friday’s, is only about 2.5% of the population:

Restaurant Histogram

Menu Words
The next step in my analysis was counting the common words and phrases across the menus. Here are the top fifty:

1. sauce, 2. chicken, 3. cheese, 4. salad, 5. grilled, 6. served, 7. fresh, 8. tomato, 9. shrimp, 10. roasted, 11. served-with, 12. garlic, 13. cream, 14. red, 15. fried, 16. onions, 17. tomatoes, 18. beef, 19. rice, 20. onion, 21. bacon, 22. topped, 23. mushrooms, 24. topped-with, 25. steak, 26. vinaigrette, 27. spinach, 28. lettuce, 29. pork, 30. green, 31. potatoes, 32. spicy, 33. white, 34. salmon, 35. in-a, 36. soup, 37. peppers, 38. mozzarella, 39. lemon, 40. sweet, 41. with-a, 42. menu, 43. beans, 44. dressing, 45. fries, 46. tuna, 47. black, 48. greens, 49. chocolate, 50. basil

Pervasive ingredients like “chicken” turn up, as do common preparation and plating terms like “sauce” and “topped-with”. Perhaps my next project will be looking at how this list changes over time. For example, words like “fried” were taboo in the 90’s, but more common during this post-9/11 renaissance of honest comfort food. Now-a-days chicken can be “fried” again, not necessarily “crispy” or “crunchy”.

A Tasty Model
Next I trained a statistical model using the menu words and phrases as independent variables. My dependent variable was the proportional housing expense in the restaurant’s zipcode. The model was not meant to be predictive per se, but instead to identify the characteristics of restaurant menus in more desirable areas. The model covers over five thousand restaurants, so menu idiosyncrasy and anecdote should average out. The algorithm used was our bespoke version of least-angle regression with the lasso modification. It trains well on even hundreds of independent variables, and highlights which are most informative. In this case, which of our many menu words and phrases are correlated with proportional housing expense?

Why Clams are Bourgeois

The twenty menu words and phrases most correlated with low proportional housing expense (the bluer dots) areas:

1. tortilla, 2. cream-sauce, 3. red-onion, 4. thai, 5. your-choice, 6. jumbo, 7. crisp, 8. sauce-and, 9. salads, 10. oz, 11. italian, 12. crusted, 13. stuffed, 14. marinara, 15. broccoli, 16. egg, 17. scallops, 18. roast, 19. lemon, 20. bean

Several of these words of phrases are associated with ethnic cuisines (i.e. “thai” and “tortilla”), and others emphasize portion size (i.e. “jumbo” and “oz” for ounce). Restaurants in high proportional housing expense areas (greener dots) tend to include the following words and phrases on their menus:

1. clams, 2. con, 3. organic, 4. mango, 5. tofu, 6. spices, 7. eggplant, 8. tomato-sauce, 9. cooked, 10. artichoke, 11. eggs, 12. toast, 13. roll, 14. day, 15. french-fries, 16. duck, 17. seasonal, 18. oil, 19. steamed, 20. lunch, 21. chips, 22. salsa, 23. baby, 24. arugula, 25. red, 26. braised, 27. grilled, 28. chocolate, 29. avocado, 30. dressing

These words reflect healthier or more expensive food preparation (i.e. “grilled” or “steamed”), as well as more exotic ingredients (i.e. “mango” and “clams”). Also, seasonal and organic menus are associated with low proportional housing expense. The word “con” turns up as a counter-example for Latin American cuisine, as in “con huevos” or “chili con queso”.

Food Crystal Ball
This sort of model for restaurant menus could also be used for forecasting, to statistically predict the sort of food that will be more successful in a particular neighborhood. This predictive power would be bolstered by the fact that the population of menus has a survivorship bias, because failed or struggling restaurants are less likely to post their menus online.

This confirms my suspicion that housing expense is counter-intuitive when it comes to dining out. People who spend more of their income on housing in order to live in a desirable location have less disposable income, but these are the people who pay more for exotic ingredients and more expensive food preparation. Maybe these folks can’t afford to eat in their own neighborhood?


Dorkbot is a semi-monthly meeting of “people doing strange things with electricity.” They have been chugging along in several cities for a decade-or-so. Back in 2005 I presented at a Dorkbot in London, so I have an enduring soft spot for these quirky gatherings. At this month’s Dorkbot in San Francisco, a meteorologist named Tim Dye presented a brilliant visualization called WeatherDots. It summarizes the weather data he collects near his home in wine country.

Inspired by how much time-series information Dye was able to squeeze onto a few pretty circles, I spent the plane ride to ABS East in Miami throwing together a “dot” visualization of the Altos Research weekly active market data. Here is a visualization of a year’s worth of real estate data:

Redots Screenshot

My Redots updates every week, and can be pointed at any of the Altos Research local markets by entering a city, state, and zipcode. Your web browser needs to play nicely with the amazing Raphaël visualization library, or you will just get a blank screen. I recommend using Google Chrome.

The Legend, or What Is It?
Each dot of color represents a week in a local residential real estate market, so each column is a month. The main color of the dot shows the week-on-week change in the median price of single family homes in a particular zipcode. A red dot means house prices have decreased since the previous week (or dot), while green dots are increasing weeks. The summer seasonality effect is pretty clear in our Mountain View, CA example.

The “halo” of a dot is the ratio of new listings to listings in general. If the newest listings coming onto a market are priced higher than the typical listing, then the halo will be green. This suggests a seller’s market, when new listings are asking for a premium. The price of these new listings will be absorbed into the market the following week, so you might imagine a dot’s halo merging with the main color.

A dot’s angle is the year-on-year change in market prices. Aiming northeastward means prices have increased since the year before, while southeast is a decrease. These angles strip away seasonality from the market, and show how secular real estate trends. Our Silicon Valley example is a bit down year-on-year. The thickness of a weekly dot represents the week-on-week change in the number of listings, put more simply, the inventory. Thin dots that are more ellipsoid are a shrinking market, where fewer listings are available for sale at any price.

A Thousand Words
Information visualization is a buzzy field with smart people doing striking work. For me the line between the big data and infovis communities blurs when a pretty picture enables statistical inference without necessarily running the numbers.

A Different House Hedge

Where do stock market winners buy houses?

There are many ways to predict how the price of an asset will change in the future. For stocks, one approach is based on fundamental analysis and another approach uses portfolio diversification theory. A third approach to predicting stock movement is so-called “technical analysis,” which is too silly for more than a mention. There are also statistical arbitrageurs in the high-frequency market-making and trading arms race, who make minute predictions thousands of times per day. If we pretend real estate acts as a stock, we can stretch the analogy into a new mathematical tool for hedging house prices.


Fundamental analysis is usually what people think about when picking stocks. This is the Benjamin Graham philosophy of digging into a company’s internals and financial statements, and then guessing whether or not the current stock price is correct. The successful stock picker can also profit from an overpriced share by temporarily borrowing the stock, selling it, and then later buying it back on the cheap. This is your classic “short,” which may or may not be unethical depending on your politics. Do short trades profit from misery, or reallocate wasted capital?

Fundamental analysis is notoriously difficult and time-consuming, yet it is the most obvious way to make money in the stock market. Fundamental analysis is also what private equity and venture capitalists do, but perhaps covering an unlisted company or even two guys in a garage in Menlo Park. When you overhear bankers talking about a “long/short equity fund” they probably mean fundamental analysis done across many stocks and then managing (trading) a portfolio that is short one dollar for every dollar it is long. This gives some insulation against moves in a whole sector, or even moves in the overall economy. If you are long $100 of Chevron and short $100 of BP, the discovery of cheap cold fusion will not trash your portfolio since that BP short will do quite well. However for conservative investors like insurance companies and pension funds, government policy restricts how much capital can be used to sell assets short. These investors are less concerned about fundamental analysis, and more about portfolio diversification and the business cycle.

Highly Sensitive Stuff

If a long-only fund holds just automobile company stocks, the fund should be very concerned about the automobile sector failing as a whole. The fund is toast if the world stops driving, even if their money is invested in the slickest, most profitable car companies today. Perfect diversification could occur if an investor bought a small stake in every asset in the world. Though huge international indices try to get close, with so many illiquid assets around, perfect diversification remains just a theory. How can an investor buy a small piece of every condominium in the world? How could I buy a slice of a brand like Starbucks? Even worse, as time goes by companies recognize more types of illiquid assets on their balance sheets. Modern companies value intellectual property and human capital, but these assets are difficult to measure and highly illiquid. What currently unaccounted-for asset will turn up on balance sheets in 2050?

Smart fund managers understand that perfect diversification is impossible, and so they think in terms of a benchmark. A fund benchmark is usually a published blend of asset prices, like MSCI’s agricultural indices. The fund manager’s clients may not even want broad diversification, and may be happy to pay fund management fees for partial diversification across a single industry or country. Thinking back to our auto sector fund, they are concerned with how the fortune’s of one car company are impacted by the automobile industry as a whole. An edgy upstart like Tesla Motors is more sensitive to the automobile industry than a stalwart like Ford, which does more tangential business like auto loans and servicing.

Mathematically we calculate the sensitivity of a company to a benchmark by running a simple linear regression of historic stock returns against changes in the benchmark. If a company’s sensitivity to the benchmark is 2.5, then a $10 stock will increase to $12.50 when the benchmark goes up by one point. A sensitivity of 0.25 means the stock would just edge up to $10.25 in the same scenario. A company can have negative sensitivity, especially against a benchmark in another related industry. Tesla probably has a negative sensitivity to changes in an electricity price index, since more expensive electricity would hurt Tesla’s business. No sensitivity (zero) would turn up against a totally unrelated benchmark. Sensitivity has a lot in common with correlation, another mathematical measure of co-movement.

One type of sensitivity is talked about more than any other. “Beta” is the sensitivity of a stock to the theoretical benchmark containing every asset in the world. Data providers like Bloomberg and Reuters probably estimate beta by regressing stock returns against one of those huge, international asset indices. An important model in finance and economics is called the Capital Asset Pricing Model, which earned a Nobel Prize for theorizing that higher beta means higher returns, since sensitivity to the world portfolio is the only sort of risk that cannot be diversified away. Though the CAPM beta is a poor model for real-life inefficient markets, sensitivities in general are a simple way to think about how a portfolio behaves over time. For instance, it turns out that sensitivities are additive. So $100 in a 0.25 sensitive stock and $50 in two different -0.25 sensitive stocks should be hedged against moves in the index and in the industry the index measures.

Back to Real Estate

Prices in certain local real estate markets are bolstered by a rally in the stock market. The recent murmurings of another IPO bubble suggest that newly minted paper millionaires will soon be shopping for homes in Los Altos Hills and Cupertino. We can put numbers behind this story by calculating real estate price sensitivity to a stock market benchmark. If we choose the S&P 500 as the benchmark, the sensitivity number will be a sort of real estate beta. Since real estate is far less liquid than most stocks, I regressed quarterly changes in our Altos Research median ask price against the previous quarter’s change in the S&P 500. Historically speaking, those real estate markets with a high beta have gotten a boost in prices after a good quarter in the stock market. Those markets with a low, negative beta are not “immune” to the stock market, but tend to be depressed by a stock market rally.

Below is a map of the Bay Area’s real estate betas. These numbers were calculated using prices from Altos Research and benchmark levels from Yahoo! Finance. The darker red a zipcode, the greater an increase in the market’s home prices after a quarterly stock market rally. As we might expect, the betas in Silicon Valley are above average. However there are also some surprises in Visalia and Wine Country.

Real Estate Beta, Bay Area

Our hypothesis for positive real estate beta is easy: those IPO millionaires. But what could cause a real estate market to tank after a good run in the stocks? Perhaps negative real estate betas are in more mobile labor markets, where stock market wealth triggers a move away from home ownership. Or maybe negative real estate betas turn up in markets where the condo stock is higher quality than single-family homes, like in some college towns. Remember the betas mapped above are based on only single-family home prices.

Real estate remains a difficult asset to hedge, an asset almost impossible to short by non-institutions. This is unfortunate, because a short hedge would be a convenient way for people with their wealth tied up in real estate to ride out a depressed market cycle. However like long-only fund managers, real estate investors could benefit from thinking in terms of benchmark sensitivity. If we choose a benchmark that represents the broader real estate market, we could hedge real estate buy purchasing non-property assets that have negative real estate betas. You would want your value-weighted real estate beta to net out to about zero. Now there is a plethora of problems and assumptions around making investment decisions with a crude linear sensitivity number, but at least real estate beta gives us another tool for thinking about housing risk.

(An abbreviated version of this post can found be at http://blog.altosresearch.com/a-different-house-hedge/ on Altos Research’s blog)

Fungal Houses

Ever wondered why your flat’s Zestimate bounces around so much?

In high school economics class you might have learned about fungible goods. This strange word refers to things that could be swapped without the owners especially caring. A dollar is almost perfectly fungible, and so is an ounce of pure silver. Paintings and emotional knick knacks are not at all fungible. Fungible stuff is easy to trade on a centralized market, since a buyer should be happy to deal with any seller. This network effect is so important that markets “push back,” and invent protocols to force fungibility. Two arbitrary flatbeds of lumber at Home Depot are probably not worth the same amount of cash. However the CME’s random length lumber contract puts strict guidelines on how that lumber could be delivered to satisfy the obligation of the future contract’s short trader.

Real estate is seriously non-fungible. Even a sterile McMansion in the suburbs can have a leaky roof, quirky kitchen improvements, or emotional value for the house-hunting recent college grads. If we consider many similar homes as a basket, or a portfolio of the loans secured by the homes, then the idiosyncrasies of each home should net out to zero overall. Across those ten thousand McMansions, there should be a few people willing to pay extra for a man cave, but also a few people who would dock the price. This is the foundation of real estate “structured products,” such as the residential mortgage backed securities (RMBS) of recent infamy. Like flatbed trucks delivering a certain sort of wood for a lumber futures contract, a RMBS makes a non-fungible good more fungible.

The Usual Place
The combined idiosyncrasies of non-fungible things rarely net out to exactly zero, especially during a financial crisis. Nonetheless traders and real estate professionals want to think about a hypothetical, “typical” property. We define a local real estate market by city, neighborhood or even zipcode. How do we decide the value of a typical property? There is an entire industry built around answering this question. One simple, clean approach is to sample a bunch of real estate prices in a local market at a certain point in time, and then average the prices. Or maybe use a more robust descriptive statistic like the median price.

The most readily available residential home prices in the U.S. market are “closed” transactions, the price a home buyer actually paid for their new place. Using a closed transaction price is tricky, because it is published several months after a property is sold. Can a typical home price really be representative if it is so stale?

Even if we ignore the time lag problem, there is another serious challenge in using transactions to calculate a typical home price. Within any local real estate market worth thinking about, there are very few actual transactions compared with overall listing activity and buzz. Your town may have a hundred single-family-homes listed for sale last week, but only four or five closed purchases. A surprise during the buyer’s final walkthrough could wildly swing the average, “typical” home price. For the statistically inclined, this is a classic sample size problem.

There are plenty of ways to address the sample size problem, such as rolling averages and dropping outliers. Or you could just include transactions from a wider area like the county or state. However the wider the net you cast, the less “typical” the price!

Another approach is to sample from the active real estate market, those properties currently listed for sale. You get an order of magnitude more data and the sample size problem goes away. However everyone knows that listing prices do not have a clear cut relationship with closing price. Some sellers are unrealistic and ask too much, and some ask for too little to start a bidding war. What is the premium or discount between listing price and actual value? We spend a lot of time thinking about this question. Even closed transaction prices are not necessarily the perfect measure of typical “value” since taxes and mortgage specifics can distort the final price. Our solution is to assume that proportional changes in listing prices over time will roughly match proportional changes in the value of a typical house, especially given a larger sample from the active market.

A Picture
Below is a chart of Altos Research‘s real estate prices back through 2009, across about 730 zipcodes. For each week on the horizontal axis, and for each zipcode, I calculate the proportional change in listing price (blue) and in sold price (red) since the previous week. Then I average the absolute value of these proportional changes, for a rough estimate of volatility. The volatility of sold prices is extreme.

Price Volatility

Sarah Palin Email Word Cloud

After three years of legal wrangling, the diligent folks at Mother Jones released another set of Sarah Palin’s emails on Friday. There are plenty of subtleties to the story. Should a personal Yahoo! email account be used for government work? And why the frustrating digital / analog loop of printing emails to be scanned at the other end, like a fax machine?

For my own snickering, I spent a couple hours over the weekend downloading the email PDF’s, converting them to text, and then parsing out the choice “holy moly’s” and tender bits about Track in the army. Here is a word cloud of the former governor’s emails, via the amazing Wordle project.

Sarah Palin's Email Word Cloud

Case-Shiller April Forecasts

Another finger in the air, in the beginning of the month lull.

My forecasts for the March, 2011 Case-Shiller index levels were quite rushed. They were released quickly so I could publicly compare the forecasts with the CFE futures contracts about to expire. However, since the statistical models use active market data, there is no mathematical reason to wait on our forecasts until the end of the month. The April, 2011 index levels will be released on June 28th, but here are my forecasts given what the real estate markets were doing a few months ago:

City Confidence Forecast Predicted HPI
Minneapolis, MN +1 -10.52% 94.46
Phoenix, AZ +1 -2.85% 97.42
Las Vegas, NV +3 -1.56% 95.67
Atlanta, GA +2 -1.45% 96.93
Boston, MA 0 -1.32% 145.42
Los Angeles, CA -2 -1.22% 165.73
Seattle, WA +3 -0.46% 132.35
New York, NY -1 -0.21% 163.15
San Francisco, CA -3 -0.20% 129.56
Chicago, IL +2 -0.06% 110.50
San Diego, CA -3 +0.18% 154.16
Detroit, MI 0 +0.41% 67.34
Charlotte, NC 0 +0.50% 107.50
Miami, FL 0 +1.01% 138.66
Dallas, TX +1 +1.62% 114.72
Cleveland, OH +1 +2.12% 98.85
Denver, CO 0 +2.27% 123.29
Tampa, FL +1 +2.28% 129.98
Portland, OR +1 +4.71% 138.92
(The confidence score ranges from negative three for our weakest signals, up to positive three for strength. Unfortunately I am still sorting out a bug in our Washington, DC model.)

Dan Rice on How the Experts May Not Always Be Right: A Story About the Discovery of Preclinical Alzheimer’s Disease in 1991

Machine learning can be a check on conventional thinking, if we let it.

On the new analytics Linkedin group started by Vincent Granville, Dan Rice wrote a personal account of his frustrations with the Alzheimer’s research of 20 years ago, before we understood more about the preclinical period of the disease:

The problem that I have with domain expert knowledge selecting the final variables that determine the model is that it no longer is data mining and it often is no longer even good science. From the time of Galileo, the most exciting and important findings in what we call science are those data-driven findings that prove the experts wrong. The problem is that the prior domain knowledge is usually incomplete or even wrong, which is the reason for research and analytics in the first place. I understand that the experts are helpful to generate a large list of candidate variables, but the experts will often be wrong when it comes to determining how, why and which of these variable combinations is causing the outcome.

I had an experience early in my research career that has made me forever distrustful of the expert. I was doing brain imaging research on the origins of Alzheimer’s disease in the early 1990’s and all the experts at that time said that the cause of Alzheimer’s disease must be happening right when the dementia and serious memory problems are observed which may be at most a year before the ultimate clinical diagnosis of dementia consistent with Alzheimer’s. We took a completely data-driven approach and measured every variable imaginable in both our brain imaging measure and in cognitive/memory testing. From all of these variables, we found one very interesting result. What the experts had referred to as a “silent brain abnormality” that is seen in about 25% of “normal elderly” at age 70 was associated with minor memory loss problems that were similar to but much less severe than in the early dementia in Alzheimer’s disease. We knew that the prevalence of clinically diagnosed dementia consistent with Alzheimer’s disease was 25% in community elderly at age 80. Thus, we had a very simple explanatory model that put the causal disease process of Alzheimer’s disease back 9-10 years earlier than anyone had imagined.

The problem was that all the experts who gave out research funding disagreed and would not even give me another grant from the National Institute on Aging to continue this research. For years, nobody did any of this preclinical Alzheimer’s research until about 10 years ago when people started replicating our very same pattern of results with extensions to other brain imaging measures. What is still controversial is whether you can accurately PET image the beta-amyloid putative causal protein in living patients, but it is no longer controversial that Alzheimer’s has an average preclinical period of at least 10 years. Ironically, one of the experts who sat on the very committee that rejected my grant applications suddenly became an expert in preclinical Alzheimer’s disease over the past 5 years. The experts are very often dead wrong. We allow experts to select variables in the RELR algorithm, but our users tell us that they seldom use this feature because they want the data to tell the story. The data are much more accurate than the experts if you have an accurate modeling algorithm.

(Quoted with permission of the author.)

Housing Finger in the Air

The March, 2011 Case-Shiller numbers will be released this Tuesday, but the CME’s May futures contracts expire tomorrow. Some of the real estate transactions that will be summarized in Tuesday’s numbers are up to five months old, where our data is at most one week old. This is why Altos Research calls its statistics “real time,” since it is an order of magnitude more current than the benchmark in real estate data.

Below is a table of our forecasts for six of the Case-Shiller futures contracts. Check back in a few days, when I will compare with the actual March, 2011 numbers.

Metro Area Feb-2011 CS HPI Forecast Signal
Boston, MA 149.86 -2.33% 111bps below the future’s spot bid price
Chicago, IL 113.26 -1.28% in the spread
Denver, CO 121.26 -3.31% 64bps below the future’s spot bid price
Las Vegas, NV 98.28 -3.26% 96bps below the future’s spot bid price
Los Angeles, CA 168.25 -8.64% 763bps below the future’s spot bid price
San Diego, CA 155.05 +1.66% 209bps above the futures spot ask price
(all spot prices as of 10:30am PST on 26-May-2011)