The famous financial theory of Efficient Markets is associated with the idea of a Random Walk. If the theory holds true, that makes prices unpredictable, and therefore it'd be impossible to consistently beat the market.
The seminar discusses the mathematical idea of a random walk, then moves on to understand what makes a market efficient.
Finally, we conduct a Monte Carlo Simulation on Wolfram Mathematica, to forecast the behaviour of Google's stock price one year from now.
11. Heads or tails?
What’s the expected outcome?
We have a feeling that, if we play it
many times, in most of them we will
end up with 0
12. Heads or tails?
What’s the expected outcome?
We have a feeling that, if we play it
many times, in most of them we will
end up with 0
And we’re right
13. Heads or tails?
But what if the distribution looks like this?
14. Heads or tails?
But what if the distribution looks like this?
What is the expected outcome?
15. Heads or tails?
If we know the distribution, we can
simulate the process
16. Heads or tails?
If we know the distribution, we can
simulate the process
17. Heads or tails?
If we know the distribution, we can
simulate the process
18. Heads or tails?
This is commonly referred to as a
Monte Carlo Simulation
19. Table of Contents
Random Walks
» Efficient Market Hypothesis
Playing with Wolfram Mathematica
21. Efficient Markets
Prices reflect all relevant information
If information is immediately reflected on
stock prices, tomorrow’s price change will
reflect only tomorrow’s news
22. Efficient Markets
Prices reflect all relevant information
If information is immediately reflected on
stock prices, tomorrow’s price change will
reflect only tomorrow’s news
Tomorrow’s price change is independent
of the price changes today
23. Efficient Markets
The Efficient Market hypothesis is
associated with the idea of a “random
walk”
24. Efficient Markets
The Efficient Market hypothesis is
associated with the idea of a “random
walk”
Therefore, it’s impossible to consistently
beat the market
25. Efficient Markets
Private investment funds can’t beat the
market
Source: Varga, G., Índice de Sharpe e outros indicadores de performance aplicados a fundos de ações brasileiros
26. Efficient Markets
Private investment funds can’t beat the
market
Source: Varga, G., Índice de Sharpe e outros indicadores de performance aplicados a fundos de ações brasileiros
27. Efficient Markets
According to Bloomberg:
BOVA11 beat 60% of active funds and
100% of passive funds, prior to 2009
28. Efficient Markets
According to Bloomberg:
BOVA11 beat 60% of active funds and
100% of passive funds, prior to 2009
With lower volatility (risk) than 78% of
active funds and 100% of passive
29. Non-Efficient Markets?
Behavioral Finances: imperfections in financial
markets due to overconfidence, overreaction, and
other biases
30. Non-Efficient Markets?
Behavioral Finances: imperfections in financial
markets due to overconfidence, overreaction, and
other biases
Economic Bubbles
31. Non-Efficient Markets?
Behavioral Finances: imperfections in financial
markets due to overconfidence, overreaction, and
other biases
Economic Bubbles
Markets are efficient for small investors
32. Table of Contents
Random Walks
Efficient Market Hypothesis
» Playing with Wolfram Mathematica
33. Problem
Today is January 1st, 2011. We want to
figure out the price of GOOG in one year
$ 593.97
34. Assumptions
1. Markets are efficient, so daily returns
are random variables, independent from
each other
2. Daily returns follow a determined
probability distribution
43. Fitting data to a distribution
The stable distribution allows us to solve
this problem, because of two additional
parameters (alpha & beta)
44. Fitting data to a distribution
𝐆𝐎𝐎𝐆𝐒𝐭𝐛𝐃𝐢𝐬𝐭
= 𝐄𝐬𝐭𝐢𝐦𝐚𝐭𝐞𝐝𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧[𝐆𝐎𝐎𝐆𝐑𝐞𝐭𝟐𝟎𝟎𝟔, 𝐒𝐭𝐚𝐛𝐥𝐞𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧[𝟏, 𝛂, 𝛃, 𝛍, 𝛔
StableDistribution[1, 1.5313, −0.0097, 0.0004, 0.0110
45. Fitting data to a distribution
𝐆𝐎𝐎𝐆𝐒𝐭𝐛𝐃𝐢𝐬𝐭
= 𝐄𝐬𝐭𝐢𝐦𝐚𝐭𝐞𝐝𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧[𝐆𝐎𝐎𝐆𝐑𝐞𝐭𝟐𝟎𝟎𝟔, 𝐒𝐭𝐚𝐛𝐥𝐞𝐃𝐢𝐬𝐭𝐫𝐢𝐛𝐮𝐭𝐢𝐨𝐧[𝟏, 𝛂, 𝛃, 𝛍, 𝛔
StableDistribution[1, 1.5313, −0.0097, 0.0004, 0.0110
𝓗 = DistributionFitTest[GOOGRet2006, GOOGStbDist, "HypothesisTestData"]
46. Fitting data to a distribution
The stable distribution is a better fit.
59. An idea of risk & return
GOOG traded at $ 727.44 on
September 20, 2012
60. An idea of risk & return
GOOG traded at $ 727.44 on
September 20, 2012
In one year, there’s a 95% chance its
price is going to be between $ 454.11
and $ 1294.98
61. An idea of risk & return
Would you buy it today?
66. References
Random Walks and Finance:
http://sas.uwaterloo.ca/~dlmcleis/s906/chapt1-6.pdf
http://www.norstad.org/finance/ranwalk.pdf
Random Walks and Efficient Markets:
http://www.duke.edu/~rnau/411georw.htm
http://www.amazon.com/Random-Walk-Down-Wall-Street/dp/0393325350
Wolfram Mathematica:
http://reference.wolfram.com/mathematica/howto/PerformAMonteCarloSimulation.html