quant – Some Ben?

Notes on The Man Who Solved The Market (Jim Simons)

Like seemingly everyone who works on the buy side, I have been reading the Zuckerman book about Jim Simons of Renaissance. The book spends a lot of time with the big personalities who have worked at Renaissance over the years. However there are some mathematical and technology hints:

Jim Simons’s academic field is geometric invariants in algebraic geometry.

Renaissance Technology worked with hidden Markov models, fit using the Baum-Welch algorithm. This algorithm has a Bayes update step, and a backward & forward process that feels like backprop. They also used high-dimensional kernel regression.

Henry Laufer worked with (vector) embeddings, very early. He also pushed for a single cross-asset and cross-asset-class model, so they could use all the cleaned “pricing” (market) data. They included assets with known bad data, but assets that nonetheless looked like existing assets in the model. This is maybe what we would call clustering, now-a-days. Everyone had access to the source code, even the administrative staff at first.

They tempted academics by working just one day per week, to see if they found trading interesting. They explicitly avoided trying to find economic sensibility for their strategies, but still followed a “scientific” method.

René Carmona imputed market data, which seems controversial.

Jim Simons invested in private companies alongside the systematic trading, especially in technology companies. This is probably because of the Nasdaq bubble.

They used a simple day-of-week seasonality model, at least for their futures trading.

They provided liquidity when “locals” de-risk, being in the “insurance business”.

They had a betting algorithm around the probability of moves in futures, not used for stocks at first. This was presented as opposed to statistical arbitrage with a factor model.

Their stock transaction cost model was the “secret weapon”. It was self-correcting, by “searching for buy-or-sell orders to nudge the portfolio back”. This increased their holding period to two days, on average. The strategy had very low capacity at first, however. In general they were not the best at trading, but at “estimating the cost of a trade”.

Around the time of the Nasdaq bubble bursting, they were trading 8,000 stocks. However this strategy was only 10% of the business. The futures strategy was still the mainstay, which was probably their chartist model.

Their use of basket options were 1) a tax optimization, but also 2) a way to cap downside, 3) isolate risk, and 4) increase leverage.

The internal Medallion fund is short-term, capped at $5b capital with all external clients eventually bought-out. The maximum capital is difficult to reconcile with Jim Simons’s compensation motivation, so it probably reflects limited capacity of the strategy, which means it trades in less liquid, smaller stocks and futures. In 2002 they were running 12x leverage in Medallion ($5b capital, $60b exposure given options).

They sought out astronomers because of their understanding of low signal-to-noise problems. Their named “Déjà Vu” strategy seems like a pairs or cointegration strategy.

Their strategy gets a 50.75% hit rate.

Why write this book now? Jim Simons is nearing the end of his career. Could also be transparency after the Mercers helped get Trump elected.

They at least use the terminology of risk factors and baskets: “RenTec decrypts them [inefficiencies]. We find them across time, across risk factors, across sectors and industries.”

The author uses strange terminology, suggesting that Zuckerman has actually not talked with many quants. For example, “trenders” for momentum style traders, and “data hunters” instead of “data scientists”.

Also the anecdote about Magerman unleashing “a computer virus that was infecting Renaissance’s computers” is clearly bullshit, and in a way that makes me doubt the author’s understanding of technology in general.

What is a Promise Worth?

How do you prevent hyperinflation without destroying the economy? The answer ain’t Bitcoin.

A virtual currency like Bitcoin uses a decentralized proof-of-work ledger (the block chain) to solve the the double-spending problem. “Satoshi Nakamoto” deserve serious accolades for this clever architecture, but Bitcoin has a few serious problems. The first is its lack of security. The infrastructure around the currency is shoddy and fragile. The website where 80% of Bitcoin trading currently occurs is called the Magic: The Gathering Online Exchange (a.k.a. Mt.Gox). Recently Mt.Gox has crashed and been cracked, and does not support easy shorting. More importantly, the Bitcoin system may never mature without a central authority spending a lot of (traditional) money to build-out the infrastructure, with negligible or negative financial return-on-investment. Without a social program, in other words.

Even if Bitcoins did have the infrastructure and liquidity of a traditional currency like U.S. dollars or Japanese yen, there is another more fundamental problem with Bitcoin becoming the money of the future. Bitcoins are intrinsically deflationary.

The future will always be in one of two states: Either Bitcoin miners are running up against the limits of Moore’s Law, and are unable to profitably mine new Bitcoins. Or some bullshit singularity has occurred, giving us all access to infinite computational power. In this state, we would run up against the Bitcoin architecture’s hard-coded monetary supply cap of twenty-one million Bitcoins.

If human desire is infinite, then people will always want more money for goods and services. (All else equal, of course!) So we have an intrinsically fixed supply of a fungible good along with increasing demand. Therefore a Bitcoin is guaranteed to increase in value over time. Any fraction of a Bitcoin is guaranteed to increase in value over time. This may sound good if you happen to have a lot of BTC (Bitcoin) in your wallet. However at a macroeconomic level deflation is catastrophic, which I will explain.

A Hamburger on Tuesday
Would you trade something today that is certain to be worth more tomorrow? What about if the “something” is a currency, a good that has no intrinsic value other than it being money? (You cannot heat your house with the digital dollars in your checking account. Gotta pay the utility company first.) In an emergency you might spend your deflating currency, but in general you should hold onto your BTC as long as possible. And since there is uncertainty about the degree to which Bitcoin will deflate, the market will not instantly price BTC correctly. The BTC price of goods and services will not instantly adjust to match the level of computational power available to miners.

Some Bitcoin proponents think we can instantly discount the BTC price of all goods and services to sync-up with systematic BTC deflation, but this would need a seriously high-tech payment infrastructure. Square and Stripe are trying, but does anyone seriously believe the prices of all goods and services can be discounted in real-time by a macroeconomic indicator? We can’t even ditch the wasteful dollar bill!

The Bitcoin bulls also emphasize a currency’s dual role as a means of transaction and a store-of-value, but intrinsic deflation trashes both roles simultaneously. As a means of transaction, deflation makes allocating capital (money) across projects and activities difficult, and again, requires that perfect payment infrastructure. Since systematic deflation destroys every asset’s value and discourages economic activity, deflationary currencies do badly as stores-of-value. Less economic activity means GDP contraction and decreased livelihood. Yes, despite what Professor von Nimby may have spewed in your Postmodern Marxist Studies class, GDP is a very strong indicator for overall human happiness. Perpetual economic contraction makes your savings account irrelevant. You might have a zillion super-valuable BTC in your digital wallet, but you have nothing to spend them on. In other words, if you think (hyper-) inflation is bad, deflation is even worse…

Passing Notes
Let us go back to a few of the original Bitcoin goals. Bitcoin proponents want an efficient, liquid currency immune from the distortion caused by a government or central bank’s monetary policy. This is reasonable since inflationary monetary policy has a sad history of trashing peoples’ savings accounts, in places like the Weimar Republic or more recently in Argentina. So how can we build the decentralized, non-deflationary currency of the future?

Notes are an ancient monetary concept desperate for rethinking in the Internet age. At its most basic level, a note is a promise to exchange money, goods or services at some point in the future. However a note is not quite a futures contract, because the promise need not ever be exercised. And a note is not really an options contract, because a note need not ever expire. The most obvious form of a note is what a U.S. dollar bill used to represent when we were on the gold standard. It was a promise that the holder of the note (dollar bill) could exchange the note for a dollar’s worth of physical gold at any time. Notes are a lot easier to store and deal with than gold, and so they make a lot of sense for getting work done efficiently. We could also talk about the fungibility of notes, but that is less important at this point. And notes are definitely easier to move around than loaves of bread, head of cattle, barrels of oil, or other physical stuff with intrinsic value.

A hoard of notes would also be a decent store-of-value in your savings account, as long as the writer of the notes remains solvent and trusted. For example, a million dollars worth of U.S. gold-convertible notes is a great retirement nest-egg, since most normal people expect the U.S. government to honor its promises for a long time.

When the entity writing the note is trusted by just about everyone — expected to honor its contract — then the writer can declare the notes to be unconvertible, all at once. The notes become fiat currency, currency that is not explicitly backed by anything but the trust that the note writer will not issue too many notes and inflate away peoples’ savings.

Why does most global economic activity happen using a handful of fiat currencies, like the U.S. dollar or Euro? Nations have traditionally supported their (fiat) currencies through policy and war, because before the Internet trust did not scale. Imagine a small town. Mel and Stannis are neighbors in this town. Mel trusts Stannis to honor his promises, and accepts a note from Stannis in return for mowing Stannis’s lawn for the next year. Stannis’s note he writes for Mel says something like “Stannis promises to give the bearer of this note 100 loaves of bread, anytime.” Mel’s landlord Dave also trusts Stannis, and so he has no problem taking Mel’s note as rent. Stannis has essentially printed his own money that is a lot more convenient that baking 100 loaves of bread. Now in the next town over, no one really knows Stannis. Therefore Dave will have a hard time making use of Stannis’s note when he visits there to spend time with his grandparents. Dave and Mel trust Stannis, but the people living in the next town over do not.

In this parochial example, trust has not scaled across the network of transactions and relationships. The money Stannis created, the note he wrote, is not all that useful to Mel. Instead she could insist on being compensated by a note from an entity more trusted the world over, say the First Bank of Lannister which has a branch in both towns. Mel, Stannis, Dave and his grandparents all probably trust the First Bank of Lannister to pay its debts.

If Dave wants to spend Mel’s note written by Stannis in the next town over, he can ask a third party to guarantee or sign-off on the note. This can be done by exchanging Stannis’s promise for a promise by the First Bank of Lannister, which is more trusted throughout the realm. The First Bank of Lannister would be compensated for extending its trust by taking a cut of the promise from Stannis.

So before he leaves on his trip, Dave takes his rent check (note) from Mel into the First Bank of Lannister. They write a new note saying “The First Bank of Lannister promises to give the bearer of this note 95 loaves of bread, anytime” and gives this note to Dave in exchange for the note written by Stannis. The bank has decided to take responsibility for chasing down Stannis if he turns out to reneg on his promise, and in return they are compensated with the value of five loaves of bread. Here the Bank of Lannister has also issued its own currency, but more as a middle-man than someone doing economic activity like Mel’s lawnmowing or Dave’s landlording.

This middle-man role is very important but also difficult to scale across a physical economy. Eventually someone refuses to trust the First Bank of Lannister, and then the chain of economic activity halts. This is why the world’s global economy has consolidated onto a few currencies, for reasons of both efficiency and trust.

The Internets
In the age of the Internet and pervasive social networks like Facebook and Linkedin, everyone is connected in a global network. This is the famous degrees -of- Kevin Bacon or Erdös Number concept. Any two people are connected by just a few steps along the network. Most of Stannis’s friends on Facebook would be willing to accept a note or promise from Stannis, and the same holds true for Dave, Mel and the First Bank of Lannister’s social networks. Since the whole of humanity is probably connected in a trust network, software can automatically write those middle-man notes along the chain of connections. Therefore any two people can automatically find a chain of trust for spending money.

Back to our example, but in the age of the Internet. Mel, Dave and Stannis all trust each other, since they are Linkedin contacts. Peter reneged on a note a few months ago, so no one really trusts Peter except Stannis. Everyone unfriended Peter but Stannis, so Peter has a very isolated social network. This time around we do not need to care about geography and small towns, since everyone is connected via the Internet and social networks. Let’s say Peter wants to buy an old iPad from Dave, and Dave thinks the iPad is worth about a hundred loaves of bread. Peter could try to write a note promising a hundred loaves of bread, but Dave would not accept this note since he does not trust Peter. Now for the cool part.

Peter goes to a notes exchange website (NoteEx), and asks for a hundred-loaf note that Dave will trust. The website knows that Stannis trusts Peter, and that Dave trusts Stannis. (See the triangle?) Through the website, Stannis writes Peter a note for one hundred loaves of bread that Peter gives to Dave in exchange for the iPad. Dave has a note he trusts in exchange for his good, at the price he wanted. Similarly Stannis receives a note written by Peter, whom he trusts. This note might be for 105 loaves of bread, giving Stannis a little cut in exchange for trusting the dodgy Peter. This five loaf interest, cut or edge is Stannis’s compensation as a middle-man.

This can all be done automatically by the NoteEx server with a list of middle-men volunteers. People volunteer to be middle-men up to a maximum amount of exposure or risk (i.e. one thousand loaves of bread total). Or middle-men could even offer to guarantee up to two degrees of Kevin Bacon away, for a much higher cut. After a bunch of people volunteer to be middle-men in the NoteEx process, all economic activity could be subsumed, with social networks ensuring that you only ever receive payment (promises) from people you trust. A NoteEx transaction could have more than one middle-man, up to the six degrees of Kevin Bacon maximum that we assume connects all people.

Ironically, the good or service underlying the notes is not all that important, since notes are very rarely redeemed. In the same way that powerful governments can support fiat currencies backed by nothing, fiat notes backed by loaves of bread will not actually turn everyone into a baker. Usually notes are exchanged with their value being the trusted promise, but not necessarily the realization. Heavy stuff here.

Decentralized Bakery
The NoteEx website would be built atop an open and standard protocol, and competing notes exchanges could borrow from the Bitcoin architecture to be decentralized (i.e. the shared ledger). More importantly, there would be a natural level of inflation in the system as the cuts or interest that middle-men demand increase the total value of all promises across the economy. And of course, notes are an excellent store-of-value because who would you trust more to support you in an emergency or retirement than your tightest friends & family?

So! We have a theoretical monetary system free from government interference, and one that encourages economic activity through modest and natural inflation.

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.

Fundamentalism

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.

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)

Fighting the Last War: Shiller Paper

A new type of mortgage gets a price that means you never have to walk away.

Last month Robert J. Shiller, Rafal M. Wojakowski, Muhammed Shahid Ebrahim and Mark B. Shackleton published a paper with the financial engineering to price “continuous workout mortgages.” This is the Shiller of Irrational Exuberance and housing index fame.

A continuous workout mortgage leaves some of the risk of house price deprecation with the mortgage lender, since the mortgage balance automatically adjusts if the market tanks. The authors model an interest-only continuous workout mortgage as a loan bundled with a put option on the value of the home and a floor on interest rates. By design, the option to abandon the mortgage is always out of the money, so the borrower has little incentive to strategically default or walk away.

Pricing a continuous workout mortgage uses a standardized housing index. Perversely, this prevents a borrowers from trashing their own homes in order to reduce payments. So the bundled put option is on a housing index and not on the exact home. Others have written about the political and class bias encouraged when your savings are connected so directly to the neighborhood. Standard & Poor’s conveniently sells metropolitan housing indices. These S&P Case-Shiller housing indices have serious problems, including methodology transparency and data lag — no one can replicate and therefore validate the Case-Shiller numbers, the indices are published several months late, and they ignore the prices of homes pulled off the market without a sale.

Like proper quants, Shiller and colleagues push hard for a closed-form pricing formula. The party line is that clean formulas make for better markets, but computer simulation is easy enough now-a-days and far more accurate. Ahh, job security! To get a formula for the interest rate a lender should charge for a continuous workout mortgage, they make the heroic Black-Scholes universe assumptions, including:

The housing index can be traded, and traded without any brokerage fees. Also the index can be sold or bought for the same price.
Cash can be borrowed or lent at the exact same interest rate.
No one pays taxes.
The variance (jitter) in the housing index is independent of how much a trader expects to earn from investing in the housing index. This one is rarely mentioned, but not so obscure once you drop the “risk neutral” jargon.

And so also like proper quants, Shiller and his colleagues assume the frictionless, massless pulley from a high school physics class.