In 1956, John Kelly introduced his “Kelly criteria” betting strategy: bet on each possible outcome in proportion to (your estimate of) that outcome’s chances of winning, regardless of the betting odds offered. More generally, a Kelly rule invests in each possible asset in proportion to its expected future payout, regardless of current asset prices. For example, if you estimate land will be worth 30% of world wealth in the distant future, you put 30% of your investments into land today, regardless of today’s land prices.
It turns out that the Kelly rule is close to the optimal long run investment plan, i.e., the one that would win an evolutionary competition. The exact best strategy would consider current prices and expected future price trajectories and carefully choose investments to max expected growth, i.e., the expected log of a distant future portfolio. But Kelly’s rule is far simpler, gets better than average growth regardless of state, time, or prices, and approaches the exact best strategy as good strategies come to dominate prices. In fact:
A stock market is evolutionary stable if and only if stocks are [price] evaluated by [Kelly rule] expected relative dividends. Any other market can be invaded in the sense that there is a portfolio rule that, when introduced on the market with arbitrarily small initial wealth, increases its market share at the incumbent’s expense. (more)
(More on evolutionary finance here, here, here, here; see especially this review.) We’ve had big financial markets for at least a century. Has that been long enough for near-optimal strategies to dominate? Not remotely. John Cochrane explains just how bad things are:
We thought returns were uncorrelated over time, so variation in price-dividend ratios was due to variation in expected cash flows. Now it seems all price-dividend variation corresponds to discount-rate variation. We thought that the cross-section of expected returns came from the CAPM. Now we have a zoo of new factors. … For stocks, bonds, credit spreads, foreign exchange, sovereign debt and houses, a yield or valuation ratio translates one-for-one to expected excess returns, and does not forecast the cash flow or price change we may have expected. In each case our view of the facts have changed 100% since the 1970s. …
All of these facts and theories are really about discount rates … and risk premiums. None are fundamentally about slow or imperfect diffusion of cash-flow information, i.e. informational “inefficiency.” Informational efficiency isn’t wrong or disproved. Efficiency basically won, and we moved on. When we see information, it is quickly incorporated in asset prices. … Informational efficiency is much easier for markets and models to obtain than wide risk sharing or desegmentation, which is perhaps why it holds more broadly. (more)
Got that? Finance prices today do a great job of aggregating info – relative prices between similar assets are great predictors of relative payouts. But when it comes to broad price aggregates, such as stocks in general or land in general, price changes basically reflect crazily-changing values. While in markets dominated by near-optimal traders, prices would only change when expected future payouts changed, in fact aggregate prices changes have almost no relation to matching future payouts changes. For example, land prices change plenty (as in the recent real estate bubble), but aggregate land price changes say almost nothing about future land rents.
I’ve talked before about how our era is a rare extreme “dreamtime,” with fast change and behavior quite out of equilibrium with evolutionary selection pressures. We not only have dreamtime fertility, i.e., far fewer kids per couple than selection would favor, we also have crazy-price dreamtime finance. This allows a relatively clear prediction of the future: finance will eventually “equilibrate.” Either the world will coordinate to block the creation of investment funds following near Kelly rules that reinvest most gains, or financial prices will eventually come to be dominated by such near-Kelly funds.
Once dominated by near-Kelly funds, finance prices will no longer suffer huge crazy booms and busts, like the recent dotcom boom or real-estate crash. Furthermore, interest rates should fall dramatically — future returns will no longer be discounted intrinsically, but only for opportunity cost reasons.
Apparently many funds today do now follow near Kelly rules:
The claim has been made that well-known successful investors including Warren Buffett and Bill Gross use Kelly methods. (more)
So the main barrier seems to be fund ability and inclination to reinvest most gains. As I wrote a year ago:
Many folks would be willing to create trusts that accumulated funds long after their death and then paid distant descendants (perhaps indirectly) to do things like remember their ancestor’s name, pray to his gods, etc. Unless stolen, such funds would eventually come to dominate the world economy and dramatically lower interest rates. With lower interest rates … businesses and governments would have far stronger incentives to attend to the interests of distant future folks, such as via global warming policies. But we in fact refuse to enforce a great many such long term deals. (more)
In a large decentralized world, however, I doubt this barrier will stand. Nor can I see why it should. I for one welcome our new financial overlords. Seriously.
I wonder if anyone could estimate how long it should take Buffett/Gross size Kelly funds to dominate finance prices. More Kelly rule details from that review: Continue reading "Dreamtime Finance" »
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