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## Timing the Stock Market

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**Timing the Stock Market**Richard E. Neapolitan Professor and Chair of Computer Science Northeastern Illinois University Slides available at: http://www.neiu.edu/~reneapol/renpag1.htm**Stock Market Review**• Corporations sell shares of the company to the public. • These shares are called the stock in company. • Each share of stock represents one vote on matters of corporate governance.**Stocks go up and down in value throughout the day, week,**month, etc.**Why Do Stock Values Change?**• Growth prospects of the company change. • Macro-economic variables change. • Inflation • Jobs (Non-farm payroll) • Momentum?**Stock Indices**• A stockmarket index is an indicator that keeps track of the performance of some subset of stocks. • Dow Jones Industrial Average • 30 blue chip companies • Currently around 12000 • S&P 500 • 500 large U.S. companies • Currently around 1400**Common maxim:**• Own stocks (Dow) if you have a long-term time horizon. • The stock market has averaged 10% yearly over the past 100 years. • So if you own stocks, in the long run you will average 10% on your investment. • Instead of the 5% or so a CD or the bank will pay.**What will market do in next 20 years?**• Harvard Economist John Chapman noted the following: • Price/Earnings (PE) Ratios are way out of wack compared to historical norms. • Previously PE ratios have always returned to norms by prices going down.**None of this matters if we can ‘time’ the stock market.**• Buy low • Sell high**During the 1990’s exuberant day traders made big bucks**timing the market.**During the early part of this century day traders lost big**bucks timing the market.**In the short term (several years) the daily values of the**market seem to follow a random walk. • A number of researchers have shown this. • I ran my own ‘runs’ test indicating it.**A random walk is the result of a sequence of coin tosses.**Go up one unit after a heads. Go down one unit after a tails. Eight random walks:**Fooled by Randomness**• Book by Nassim Nicholas Taleb. • He argues people constantly delude themselves because they do not understand probability and are programmed to find reasons where none exist. • People end up believing in magic. • Astrology • Hot dice or coins • Hot stock markets**However,**• As noted earlier, the market’s value is related to macroeconomic variables. • Perhaps we can predict the market’s performance for the coming month from information about these variables today.**We want to predict the market’s return at end of the month**from information at beginning of the month. • The fact that the market’s return follows a random walk does not pre-empt that we could do this. • Suppose I toss a coin at the beginning of each month, and the market goes up or down each month based on the outcome of the toss. • The market’s return would follow a random walk even though we could predict it.**Factor Models**Factor models give the value of a stock at the end of a month as a function of the values of macroeconomic variables at the end of the month.**Edwin Burmeister’s factors:**• f1: Business Cycle • Monthly change in a business index • f2: Inflation • Monthly change in investment • f3: Investor Confidence • Monthly change in difference between returns on risky corporate bonds and gvmt. bonds • f4: Time Horizon • Monthly change in difference between returns on 20-year gvmt. bonds and 30-day T-bills • f5: Market Timing**We then have:**ri(t) = ři(t) + bi1f1(t) + bi2f2(t) + bi3f3(t) + bi4f4(t) + bi5fk(t) + εi(t) ri(t) is the monthly return of asset i at the end of month t. ři(t) is the expected return of asset i at the end of month t. bik is the risk exposure of asset i to factor k.**Burmeister has shown that his factor model is accurate.**• This shows that the market’s performance is indeed related to macroeconomic factors. • However, it does not help with timing the market since all values are at month’s end. • We want the return at the end of the month in terms of macroeconomic variable information at the beginning of the month.**Market Timing with Tony Volpon**• Tony Volpon is an ex-mutual fund manager, who now spends his days, relaxing on the beach in Brazil, trying to figure out how to time the market. • He identified around 30 variables as possibly having predictive value for the S&P 500 return.**Tony’s Variables**• SPFret(t) (This is what we want to predict.) [S&P(t+1) – S&P(t)] / S&P(t) • SPret(t) [S&P(t) – S&P(t-1)] / S&P(t-1) • 10Tret(t) (change in 10 year treasury bonds) [10T(t) – 10T(t-1)] / 10T(t)**Tony’s Variables**• NFPret(t) (change in non-farm payroll) [NFP(t) – NFP(t-1)] / NFP(t-1) • Fedret(t) (change in federal funds) [Fed(t) – Fed(t-1)] / Fed(t -1) • Mact A complex momentum indicator**Tony’s Variables**3monthavg10T(t) = [10T(t-3) + 10(t-2) + 10(t-1)] / 3 • 10Ttony(t) [10T(t) –3monthavg10T(t)] / 3monthavg10T(t)**Regression with Tony’s Variables**• We looked at about 220 months of data. • Regression for SPFret in terms of the other variables did not yield meaningful results. • Over-fitting. • In similar cases the following has sometimes worked: • Discretizing the variables. • Learning a Bayesian network from the data.**Our Study (Tony and I)**• We discretized each variable into 3 ranges so as to have the same number of data items in each range. • 0 (low) • 1 (medium) • 2 high) • Example: SPFret (annualized) • 0 : < - .075 • 1 : - .075 to .294 • 2 : > .294**These results make economic sense.**• We can use them to make buying rules: • If Mact = 0 and NFPTony = 1 and 10Ttony = 0 go long. • If Mact = 2 and NFPTony = 0 and 10Tony = 0 go short.**By analyzing many different markets (foreign exchanges,**commodities, real estate, etc.), we can always bet only on very promising prospects.**Cheap Plug:**My new book Probabilistic Methods for Financial and Marketing informatics Morgan Kaufmann is now available.