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Chicago Booth BUSF 35150 - Detailed notes on predictability.

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3 Week 1 Detailed notes on predictability.This week we’re going to study how returns behave over time. If you see a good return today, doesthat mean it will continue with some “momentum” tomorrow, or will it “mean-revert” in a wave of“profit-taking?” Are there other signals that can tell you whether returns will be better or worsethan average going ahead?We’ll also study two questions that seem to be different, but turn out to be the same: Is theresuch a thing as a “bubble,” and hence its opposite, a great buying opportunity? And why do pricesseem to vary so much?Both issues come down to the question, can you forecast returns ahead of time? “Forecast” or“predict” does not mean with certainty, of course. But is there a way to know that the odds are inyour favor on some days and against you on others?Recent research has really changed how we think about this question.3.1 MethodTo find out if returns are (a bit) predictable, we can simply run a regression+1=  + + +1We run regressions of tomorrow’s return +1on any variable we can see today .Ifwefind a“big” ,oralarge2, you might be able to make money, buying when is high and vice versa. Ifyou find a small ,andlow2, returns are not predictable, and you can’t make much money thisway. Thus, the regression measures the question “are returns (somewhat) predictable?”• We use forecasting regressions such as+1=  + + +1to see if returns are (a bit) predictable.Equivalently, this regression model implies that the expected return at time  is(+1)= + This statement is a bit subtle. The “expected return” can vary over time, being higher when thesignal is higher and vice versa. We can state the point of the regression equivalently as• The return-prediction regression measures whether expected returns (risk premiums) vary overtime.“Expected returns” generates a common confusion, which we need to address right now. A coinflip, or a sequence of unpredictable returns, has the property that the expe cted return is constantover time. That does not mean that the return is constant over time, just that at each point,looking forward, you don’t know which way it will go, and the probabilities of each outcome arealways the same.31On the other hand, it’s possible for expected returns or other quantities to move over time.For example, the expected temperature one week ahead mo ves steadily over the season, (+7)c hanges as  moves, lower in the winter and higher in the summer. T he actual temperature ofcourse moves even more.This is a good time to remind yourself about conditional expectations and what (+1)means. The unconditionally expected temperature tomorrow in Chicago is about 60,theoverallaverage. If it’s July, or if you know that today’s temperature is 90 degrees, the conditionally expectedtemperature tomorrow is high, maybe 85 degrees. The actual, or ex-post temperature tomorrowwill vary beyond this expectation.The question for us is whether stock returns are a bit lik e this; whether there are times, measuredby the variable , when the coin is 51/49 and other times when it’s 49/51. We’re asking if thereare “seasons” in stock returns, not whether anyone knows exactly what the return (temperature)will be tomorrow.• “Predictable” doesn’t mean perfectly. “Expected” means conditional mean but there is a lot ofvariance. “Risk” includes unexpected positive returns.Be aware that these terms, like many you will run across, have different meanings in financeand statistics than in c olloquial usage.Most people you will talk to don’t really understand this. They think “predict” or “forecast”means a soothsayer, who can tell which way the market is going. The idea that a good “prediction”is just someone who can get 55/45 odds rather than 50/50 is not what they have in mind whenthey hear the word “predict.” Someone may say “you predicted the market to rise but it wentdown. You don’t know anything.”The idea that “predict” is the same as “conditional mean moves over time” is even more difficult.Make sure you understand it.At an ev en more basic level, “expected” to us means “conditional mean,” while most peopleuse it to mean “best case.” To them, “risk” is all “downside risk. To us, “risk” includes the 50%probability that you could make more money than you “expect,” hardly conventional u sage3.2 Classic efficien t markets viewNow, what result do we expect for this regression +1=  + + +1? In the classic “efficient-markets” view, stock prices are not predictable, (loosely, the “random walk” view) so we shouldsee  =0,2= 0, for any variable .Its worth remembering the logic behind this classic view. If you could predict good/bad daysin the stock market, what would you do? On days when a signal predicts good returns, you buy,and vice versa, of course.But, we can’t all do this. If everyone sees a high , they also try to buy, driving prices up untiltoday’s price is the same as the price we expect tomorrow. Competition in stock markets shoulddrive out any predictable movement in stock prices. Competition means that the information inthe signal will quickly be impounded in toda y’s price. Thus, “informational efficiency” — theproposition that information is already impounded in today’s price — is really nothing more thanthe predicted effect of competition and free entry.32Efficiency seems so easy, but it’s so easy to slip in to classic fallacies. See if you can debunkthese:1. “The market declined temporarily because of profit-taking. It will bounce back next week.”2. “The stock price rises slo wly after an announcement, as new information diffuses through themarket.”3. “The internet is the wave of the future. You should put your money in in t ernet stoc ks.”4. “Buy stocks of strong companies, with good earnings and good earnings growth. They willbe more profitable and give better returns to stockholders.”5. “The demand curve slopes down;” “Big trades hav e a lot of price impact.” “Stock prices felltoday under a lot of temporary selling pressure,” “Some stocks fell too far in the crash becausemutual funds and hedge funds had to unload them to meet redemptions” “Small losers


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