ATHK1001 Lecture Notes - Lecture 6: Tail Risk, Predictive Analytics, Frequentist Probability
16 Jun 2018
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Leture 6- Prolems with Proaility
Expected Value
• Is the sum of the different outcomes each weighted by its probability and
payoff
• Playing a game in which rolling a 1=$1, 2= $2 etc.
• Expected value =
• 1/6($1) + 1/6($2) etc. = 21/6= $3.50
Uses
• Law of large numbers: as the number of independent trials increase, the
average of the outcomes will get closer to its expected value
Expected Value
• Expected value is the sum of the different outcomes each weighted by its
probability and payoff
• Playing a game in which rolling a gets you $, gets you $…
• Expected value equals:
- 1/6($1) + 1/6($2) etc.
• Law of large numbers: as the number of independent trials increase, the
average of the outcomes will get closer to its expected value
Predictive Analytics
• Use computer programs to predict likelihood of specific things
• Companies always want to quantify risks, and greater quantities of data
and cheap computing power has yielded new insights
Value at Risk Model (VaR)
• Model assumes range of possible outcome
• The VaR could be calculated over a range of investments and even take
into account correlations between different ones
• A firm could estimate is VaR for 99/100 cases and then safely go ahead
making as much money as it could
• 3 errors of using VaR
1. Confusion with accuracy
2. Underlying probability estimates may have been wrong
3. Neglected the tail risk/ over long run unlikely events are likely
Probabilities
• Allow us to quantify future events and are thus important aids to good
decision making
• Otherwise we are liable to be seduced by stories and anecdotes
• Errors can arise in calculating and interpreting probabilities
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Is the sum of the different outcomes each weighted by its probability and payoff: playing a game in which rolling a 1=, 2= etc, expected value , 1/6() + 1/6() etc. Uses: law of large numbers: as the number of independent trials increase, the average of the outcomes will get closer to its expected value. Expected value: expected value is the sum of the different outcomes each weighted by its probability and payoff, playing a game in which rolling a (cid:883) gets you , (cid:884) gets you , expected value equals: 1/6() + 1/6() etc: law of large numbers: as the number of independent trials increase, the average of the outcomes will get closer to its expected value. Predictive analytics: use computer programs to predict likelihood of specific things, companies always want to quantify risks, and greater quantities of data and cheap computing power has yielded new insights.
