1.90% of all hedge fund managers are \"normal\", ie, have normal skills. 1% are
ID: 2928061 • Letter: 1
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1.90% of all hedge fund managers are "normal", ie, have normal skills. 1% are "extra- ordinary", e., have extraordinary skills. A normal manager outperforms the market on average, 5 years out of 10. An extraordinary manager outperforms the market, on average, 8 years out of 10. A new hedge fund called "Golden Fleece started up two years ago, and it has outperformed the market in both years. (a) True or false: the probability that Golden Fleeoe's manager is extraordinary is less than 3%. (Explain) (b) Susan is an investor who suffers from base-rate neglect. Specifically, when forming her beliefs she uses Bayes's rule, but she assumes a random fund manager is equally likely to be normal or extraordinary. Show that she thinks there is a greater than 70% chance that Golden Fleece's manager is extraordinary. (e) Susan and her friends invest al money in the Golden Fleece. When they are informed of the answer to part (a), they are astonished-it seems "intuitively obvious" to them that Golden Fleece's manager is highly talented. Angner (Ch 5) and Baron (Ch 6) discuss a number of fallacies and heuristics that influence people's probabilistic judgements Which of the following four fallacies would best explain the mistake made by Susan and her friends conjunction fallacy, confirmation bias, representativeness, or hindsight bias? ExplainExplanation / Answer
Let A represent the outcome of a hedgefund manager being normal (N) or extraordinary (E).
Let B represent the outcome of a hedgefund manager out-performing the market (O) or under-performing the market (U).
a. P(O for 2 years)=P(E) * P(O|E) * P(O|E) + P(N) * P(O|N) * P(O|N) = 0.99*0.5*0.5+0.01*0.8*0.8=0.2539
Required Probability = P(E|O for 2 years)=(0.01*0.8*0.8)/0.2539=0.0252 (<3%, hence the statement is true).
b. If, P(N)=P(E)=0.5,
Required Probability= (0.5*0.8*0.8)/(0.5*0.5*0.5+0.5*0.8*0.8)=0.32/0.445=0.719) (>70% chance of Gloden Fleece manager being extraordinary). Hence Proved.
c. Hindsight Bias as it is the creeping determinism, is the inclination, after an event has occurred, to see the event as having been predictable/
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