04-Stochastic Processes and Market Efficiency

# 04-Stochastic Processes and Market Efficiency - Stochastic...

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Lecture Sponsored by Costa Vida Stochastic Processes and Market Efficiency

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Investing You’re considering whether you should buy a stock for \$10 You know that tomorrow the price will be \$15. What do you do? What happens if other market participants have the same information about Walmart that you do?
What we learn When people know they can make money by taking a simple action, they act quickly. Some people are in a better position to receive/act on the information than others. Some people are willing to pay more costs to act on the information than others. When people act, the profit opportunity goes away very, very fast.

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Predicting Returns The most accurate (unbiased) forecast of any random variable is the probability weighted average of all possible outcomes. We’ve been calling this the expectation E[x] for random variable x Given the PDF we can compute the true E[x].
Example – Discrete PDF Most accurate forecast for returns is But how can this be considered an accurate forecast? Actual return will never be 12.4%: it will be either 18% or -10% How can we measure forecast accuracy? - = = = % 10 for 20 . 0 % 18 for 80 . 0 ) ( r r r P 124 . 0 ) 10 . ( 2 . 0 18 . 0 80 . ] [ = - × + × = r E

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Forecast Accuracy Suppose a coworker proposes that instead of using E[r]=12.4% to forecast the return for the example above, that we just use 18%. He argues that at least that way, we’ll be exactly right 80 percent of the time. In what way is E[r]=12.4% more accurate than 18%? Measure expected deviation of forecast from outcome. E(outcome-forecast) Interpretation: crank out an infinite number of observations from the PDF, subtract your forecast from each outcome, and find the average of this difference across all outcomes. This is called the forecast bias
Forecast Bias Forecast bias of E[r] Forecast bias of 0.18 E[r] looks like a more accurate forecast, since on average, E(r-E[r])=0. Although we’re never exactly right, we can say that we’re right on average. 0.18 allows us to be exactly right 80% of the time, but 20% of the time when the outcome is -10%, this forecast is way, way off.

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