week 9

Question 1

 Finance and Probability Theory

Answer 1

o Finance Risk and return
o Return
 Expected value in probability theory
 Higher return the better
o Risk
 Standard deviation in probability theory
 Lower risk the better
o Do we really know/understand the probability of events that are associated with a certain financial product/an information event?
 Are estimations based on the past? Rule of thumb? The law of large numbers?

Question 2

St. Petersburg Paradox

Answer 2

o Using probability theory, the expected payoff is equal to 1 each turn
o Therefore, the rationality is to pay infinity to continue paying
o However, people are only willing to pay a finite amount to get an infinite payoff
o Utility maximizing individuals operating in their own self-interest are expected to buy the stocks they think are likely to produce the best risk-adjusted returns
o By the same token, they sell the others
o But
 All relevant information is priced into the market
 Prices change as new information is introduced
 Investors respond to new information by buying and selling stocks affected by changing circumstances
 In the process stocks are efficiently priced as the new information is discounted

Question 3

 Cognitive and emotional biases

Answer 3

o Cognitive biases arise from faulty reasoning and so can often be addressed through education and better information
o Emotional biases arise through intuition rather than conscious thought
 Even though they are more difficult to cope with and almost impossible to completely eradicate in your own investment and trading
 May be used to spot profitable opportunities if can be recognized from other investors

Question 4

 Think like a finance theorist or a trader

Answer 4

o Almost all investment and trading opportunities will have an element of behavioural finance to them
o Investors and traders tend to not argue this point, we look for opportunities
o A general consensus is that behavioural biases can contribute to market inefficiency in terms of
 Overreaction and/or underreaction to new information

Question 5

o Jegadeesh and Titman

Answer 5

 Overreaction (to good or bad news) can lead to price reversal in the intermediate term
 Underreaction can lead to price momentum

Question 6

 Monty Hall Judgement Error

Answer 6

o The host has to open a door and it has to be no car behind that door
o People refuse to accept the shift from an unconditional probability regime to a less intuitive conditional probability
o Subjects refuse to accept the validity of mathematical proofs offered to demonstrate the wisdom of switching doors
o Most subjects continue to refuse to switch doors

Question 7

 A study on market price

Answer 7

o If investors were rational and understood the nature of the Monty Hall problem, market prices to switch should be twice the levels of prices to retain original selections
o The study finds
 Competition between only two rational investors out of many were necessary for market prices to reflect rational probabilities

Question 8

 Extension from Monty Hall

Answer 8

o Winning Trade
 Stick with choosing Door A = winning trade
 Winning trades are typically dependent on a large number of factors, with luck being the largest component
o Good Trade
 Switch to Door C, still a good trade due to statistics
 Better off with this good trade in the long run

Question 9

 Self- attribution

Answer 9

o A cognitive bias that leads people to attribute successful outcomes to their own skill but blame unsuccessful outcomes on bad luck
o Arises when investors are on a good run
 Attribute profits to skills and edges in information, where it is much more likely that it has been lucky
o Dangerous
 If unable to perceive our errors as errors, we cannot learn from them
 Crediting lucky outcomes to skill leads to overconfidence and undiversified portfolio
o Solid statistical post-trade analysis is the best defense against this bias

Question 10

 Confirmation bias

Answer 10

o Cognitive bias whereby one tends to notice and look for information that confirms one’s existing beliefs, ignoring anything that contradicts those beliefs
o Emphasize confirming evidence and downplay contradictory evidence

Question 11

 Overconfidence

Answer 11

o A cognitive bias that manifests as an unreasonable belief in one’s abilities
o One of the worst biases an investor can have
o Leads to
 Poorly diversified portfolios
 Excessive trading in both position and volume
 Underestimating the risks associated with extreme moves

Question 12

 Disposition effect

Answer 12

o Describes a desire for investors to realize gains by selling stocks that have appreciated, but to delay the realization of losses

Question 13

 Loss aversion and prospect theory

Answer 13

o Loss aversion
 Cognitive bias that people dislike losses and disadvantages more than gains and advantages
 Get-even
• Hold onto bad investments until they get even

Question 14

 Prospect theory

Answer 14

o Inadequacy of utility theory as a description of how people actually make financial decisions
o Find empirically that people underweight outcomes that are merely probability in comparison with outcomes that are obtained with certainty

Question 15

 Endowment effect

Answer 15

o An emotional bias that the value of a good increases when it becomes a part of a person’s endowment
o This effect causes losses or what is given up to weigh more heavily in the decision-making process than gains or what is acquired
o Different from loss aversion
 Endowment effect – ownership creates satisfaction
 Loss aversion – people are more motivated by avoiding a loss than acquiring a similar gain
o May explain
 investors’ reluctance to sell their under-performing stocks to capture tax write-offs
 Underreaction to news
 Exacerbate momentum effects in stock prices

Question 16

 Anchoring

Answer 16

o A cognitive bias that causes people to base estimates and decisions on known anchors, or familiar positions, with a subsequent adjustment relative to this starting point
o We are better at relative thinking than absolute thinking