# random walks, efficient markets & stock prices

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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.TRANSCRIPT

- 1. Random Walks,Efficient Markets &Stock PricesLuigi Cenatti GianniNEO Empresarial
- 2. Why is it so hard to BEAT THE MARKET?
- 3. What should be the STRATEGY of a SMALL INVESTOR?
- 4. How to forecastthe RISK and RETURN of an asset?
- 5. Table of Contents Random Walks Efficient Market Hypothesis Playing with Wolfram Mathematica
- 6. Table of Contents Random Walks Efficient Market Hypothesis Playing with Wolfram Mathematica
- 7. What makes a process random? 1. Sequence of random variables 2. independent from each other 3. and determined by a distributionf(t) outcome time
- 8. Heads or tails? Flip a coin 10 times If heads, +1 If tails, -1
- 9. Heads or tails? Is this a random process?F(t) t -2
- 10. Heads or tails? Whats the expected outcome?F(t) t -2
- 11. Heads or tails? Whats 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? Whats 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 were 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
- 20. Efficient Markets Prices reflect all relevant information
- 21. Efficient Markets Prices reflect all relevant information If information is immediately reflected on stock prices, tomorrows price change will reflect only tomorrows news
- 22. Efficient Markets Prices reflect all relevant information If information is immediately reflected on stock prices, tomorrows price change will reflect only tomorrows news Tomorrows 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, its impossible to consistently beat the market
- 25. Efficient Markets Private investment funds cant beat the market Source: Varga, G., ndice de Sharpe e outros indicadores de performance aplicados a fundos de aes brasileiros
- 26. Efficient Markets Private investment funds cant beat the market Source: Varga, G., ndice de Sharpe e outros indicadores de performance aplicados a fundos de aes 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
- 35. Framework 1. Fit a distribution to past returns
- 36. Framework 1. Fit a distribution to past returns 2. Simulate n random walks
- 37. Framework 1. Fit a distribution to past returns 2. Simulate n random walks 3. Price of stock will be mean of outcomes

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