Timing the Stock Market
Transcript of Timing the Stock Market
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Timing the Stock Market
Richard E. NeapolitanProfessor and Chair of Computer ScienceNortheastern Illinois University
Slides available at:
http://www.neiu.edu/~reneapol/renpag1.htm
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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.
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Stocks are traded on a stock exchange such as the NYSE.
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Stocks go up and down in value throughout the day, week, month, etc.
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Why Do Stock Values Change?
• Growth prospects of the company change.• Macro-economic variables change.
– Inflation– Jobs (Non-farm payroll)
• Momentum?
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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
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Like stocks, indices go up and down.
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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.
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Dow over past 107 years:
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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.
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Invest in Dow now:
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None of this matters if we can ‘time’ the stock market.
• Buy low• Sell high
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During the 1990’s exuberant day traders made big bucks timing the market.
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During the early part of this century day traders lost big bucks timing the market.
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Day Trading
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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.
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Go up one unit after a heads.Go down one unit after a tails.
Eight random walks:
A random walk is the result of a sequence of coin tosses.
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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
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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.
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• 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.
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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.
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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
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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.
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• 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.
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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.
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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)
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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
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Tony’s Variables
3monthavg10T(t)
= [10T(t-3) + 10(t-2) + 10(t-1)] / 3
• 10Ttony(t)
[10T(t) –3monthavg10T(t)] / 3monthavg10T(t)
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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.
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Bayesian Networks
F r a u d
P ( F = y e s ) = . 0 0 0 0 1P ( F = n o ) = . 9 9 9 9 9
G a s
A g e S e x
J e w e l r y
P ( A = < 3 0 ) = . 2 5 P ( A = 3 0 t o 5 0 ) = . 4 0
P ( A = > 5 0 ) = . 3 5P ( S = m a l e ) = . 5
P ( S = f e m a l e ) = . 5
P ( G = y e s | F = y e s ) = . 2P ( G = n o | F = y e s ) = . 8
P ( G = y e s | F = n o ) = . 0 1P ( G = n o | F = n o ) = . 9 9
P ( J = y e s | F = y e s , A = a , S = s ) = . 0 5P ( J = n o | F = y e s , A = a , S = s ) = . 9 5
P ( J = y e s | F = n o , A = < 3 0 , S = m a l e ) = . 0 0 0 1P ( J = n o | F = n o , A = < 3 0 , S = m a l e ) = . 9 9 9 9
P ( J = y e s | F = n o , A = < 3 0 , S = f e m a l e ) = . 0 0 0 5P ( J = n o | F = n o , A = < 3 0 , S = f e m a l e ) = . 9 9 9 5
P ( J = y e s | F = n o , A = 3 0 t o 5 0 , S = m a l e ) = . 0 0 0 4P ( J = n o | F = n o , A = 3 0 t o 5 0 , S = m a l e ) = . 9 9 9 6
P ( J = y e s | F = n o , A = 3 0 t o 5 0 , S = f e m a l e ) = . 0 0 2P ( J = n o | F = n o , A = 3 0 t o 5 0 , S = f e m a l e ) = . 9 9 8
P ( J = y e s | F = n o , A = > 5 0 , S = m a l e ) = . 0 0 0 2P ( J = n o | F = n o , A = > 5 0 , S = m a l e ) = . 9 9 9 8
P ( J = y e s | F = n o , A = > 5 0 , S = f e m a l e ) = . 0 0 1P ( J = n o | F = n o , A = > 5 0 , S = f e m a l e ) = . 9 9 9
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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
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We learned this Bayesian Network:
M a c t
S P F r e t
N F P t o n y
1 0 T t o n y
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.62.21.17220
.48.20.32120
.53.26.20020
.31.30.39210
.63.22.16110
.66.16.17010
.24.3342200
.45.35.20100
.43.35.27000
= 2= 1= 010TtonyNFPtonyMact
P(SPFret)
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.13.54.33212
.34.44.21112
.36.41.22012
.22.29.49202
.28.33.38102
.23.31.45002
= 2= 1= 010TtonyNFPtonyMact
P(SPFret)
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• 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.
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By analyzing many different markets (foreign exchanges, commodities, real estate, etc.), we can always bet only on very promising prospects.
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Cheap Plug:
My new book
Probabilistic Methods for Financial and Marketing informatics
Morgan Kaufmann
is now available.
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