MISUNDERSTANDING RISK
Don M. Chance, PhD, CFAWilliam H. Wright, Jr. Endowed Chair for Financial Services
Louisiana State University
CFA South Africa Investment Conference 20099 September, 2009
Johannesburg, South Africa
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A Most Difficult Decision
• What would you do if you found a suspicious growth inside a non-vital organ?• The doctor is unable to identify whether the
lump is malignant or not without surgery• The doctor gives you a choice:
• Remove the lump only, examine for the presence of cancer, and return for a second more extensive surgery if cancer is found
• Remove the entire organ, which you can live without, a more drastic surgery
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Making Decisions Under Risk Not just in the financial world, but in life
in general We constantly make decisions under
risk Rarely are we ever presented certainty How we make those decisions tells us a
lot about the human appetite for risk and how we so often make risk mistakes
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What is Risk?
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Elements of the Definition of Risk? Exposure to an event Uncertain outcomes (Usually) undesirability of one or more
outcomes
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Measuring Risk
Measures of riskProbability or oddsStandard deviationWorst case scenarioIn investing
○ Maximum drawdown○ Beta○ Value-at-Risk
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Probability as a Measure of Risk
We do not understand it We misuse it All too often we assume the bell curve
and oftentimes we ignore the tails (the Black Swan effect)
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A Simple (and somewhat silly) Example: The Monty Hall Problem
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Door # 1 Door #2 Door #3
Behind these doors are three prizes: a car and two worthless prizes. A contestant chooses one door.
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The Monty Hall Problem (cont.)
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$0 Door #2 Door #3
Let’s say the contestant chooses Door # 3.
Monty then opens door # 1 to reveal one of the two worthless prizes and offers the contestant the opportunity to switch doors.
(the contestant’s choice)
Should the contestant switch? Most people say it doesn’t matter.
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But it matters a lot!
You double your chance of winning by switching.
Odds of winning by not switching: 1-in-3
Odds of winning by switching: 2-in-3
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A Tougher and More Serious Situation(described by Gerd Gigerenzer in the book Calculated Risks.)
One in every one-hundred 40-year old women has breast cancer
A mammogram detects 90% of all breast cancers and gives a false positive 9% of the time
A 40-year old women gets a positive mammogram. What is the probability she has breast cancer?
A sample of doctors believed it was very high (80-90%)
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10,000 40-year old women
100 with BC 9,900 without BC
90 have + m/m
10 have – m/m
9,909 have – m/m
891 have + m/m
90
Actual Probability = 0.09290 + 891
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Using Misleading Risk Information to Sell a Product
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A pharmaceutical company advertises that a new cholesterol- lowering drug reduces heart attack risk by 22%.
(Also described in Calculated Risks)
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1,000 people with high cholesterol
Receive new drug Receive placebo
32 die of heart attack
968 do not die of heart attack
959 do not die of heart attack
41 die of heart attack
1,000 people with high cholesterol
22% fewer heart attacks
(9/41 = 22%)
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The Correct Interpretation
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9 out of 1,000 people were helped by the drug.
In other words, of every 111 people who took the drug (1,000/9 = 111), one person was helped.
Would you take or recommend a drug in which 111 people have to take it for one person to benefit?
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O. J. Simpson: What He Taught Us About Risk
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The Defense Claim
100,000 battered women in U. S
40 murdered by their batterer
99,960 not murdered by their batterer
Odds that a battering led to a murder = 40/100,000 = 0.04% or 1-in-2,500
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The True Picture
(not argued by the prosecution)
100,000 battered women in U. S
40 murdered by their batterer
5 murdered by someone else
Odds that a battered and murdered woman was killed by her batterer = 40/45 = 89%
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The Weather
We are continuously confronted with risk information about the weatherWhat does x% probability of rain mean?What about hurricane prediction paths?Why is the weather more predictable than
most other uncertainties in life?
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Political Polls
What does it mean to say that 51% favor candidate A and 49% favor candidate B?
What does a sample of 1,000 people out of a population of 100 million registered voters mean?
Why does the public opinion of politicians change so quickly?
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Jury Duty
The American judicial system is terribly flawed in that it prohibits use of all information related to the risk
“Innocent until proven guilty”
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Voting Voting is an amazingly low-risk situation, yet we
often act like it is a high-risk one Elected officials are typically elected by a fairly
uninformed populace They constantly clamor for an even more
uninformed populace to vote Which is better? Large turnout of uninformed
voters or small turnout of informed voters Ballot measures
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Mental Health and Emotional Instability Identifying serial killers in advance Examples, true and false
Virginia Tech shootingImams on a planeSuspicious people
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Predictors Predictors are notoriously pessimistic
AirlinesRestaurantsHospitalsWhy?
And what about the weather forecaster? What about economists?
Granville, Kaufman, Roubini Politicians running for office against an incumbent Predictors are almost useless, not because they
cannot predict but because they engage in self-protecting bias
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Evaluating Predictors
We too often succumb to the small sample fallacy
It takes an incredibly large sample to adequately evaluate predictive ability
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What does it Mean to Make a Mistake in Making a Decision Under Risk?
Given the choices A and B, you choose A
Assume that A works out poorly and it is apparent that B would have worked out better
Was that a mistake?MaybeMaybe not, but perhaps a lesson can be
learned (e.g., WMD in Iraq)
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Common Risk Mistakes Confusing ex post with ex ante Inability to distinguish luck from skill or lack
of it Fearing risk less the further back bad
outcomes occur Overweighting highly improbable events and
underweighting highly probable events
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Common Risk Mistakes(continued)
Trusting government for risk information Being irrational about risk Assuming that if a “bad” outcome occurs, it
would have been better to have made a different decision
Does the reward justify the risk? Is the cost of risk reduction worth it?
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Common Risk Mistakes(continued)
Expecting some decision makers to be 100% correct
Paying too much attention to predictions
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The Loneliness of the Decision Maker Sports Killing a product: the Coca-Cola case Decisions made by doctors Presidents and leaders of countries In understanding the decision maker, we
need to appreciate the Heisenberg Uncertainty Principal (of social science)Obama: “I was right about the war”McCain: “I was right about the surge”
Changing one’s mind (flip-flopping)
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Risk Information – So Misleading
Violence in Iraq? Violence in the U. S. A new source of energy School violence Which is riskier?
a house with a gun or a house with a swimming pool
Lawn mowers or beds
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How We (All too Often) Cope with Risk Litigation (mostly in the U. S.) Making someone else take the risk (as
in sports) Taking the safe route Relying too much on others, such as the
government, to make our decisions Overstating the amount of information
you have
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Using Risk Ignorance to our Advantage A personal story from my teen years D-Day: 6 June, 1944
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Viewing the Risk as Though it were Someone Else’s
Torture
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Making a Tough Decision Under Risk: The Prisoner’s Dilemma
Two people are arrested and charged with the same crime
The suspects are put into different rooms and separately interrogated
Each is given an offerTestify against the other and receive
immunity (cooperate) If only one cooperates, that person is free and the
other is punished If both cooperate, each is given a lighter sentence If neither cooperates, both will be punished
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The Prisoner’s Dilemma
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Prisoner B
Cooperate Do not Cooperate
Prisoner A
Cooperate A: light punishmentB: light punishment
A: freedomB: severe punishment
Do not Cooperate A: severe punishmentB: freedom
A: punishmentB: punishment
Assuming that each prisoner has no idea what the other will do, each should independently decide to cooperate. Why?
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How do We Manage Risk? Panic Forecast Decide on how much risk we want, how
much risk we have, the cost of changing the level of risk, and whether an adjustment is economically justified
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Making Good Decisions under Risk Some times we have too many choices Get as much information as possible Decide which risks are worth taking and
which are not For risks not worth taking, evaluate the
cost of eliminating the risk and do so if supported by cost-benefit analysis
Be moderately pessimistic
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What Should We do After the Fact? Do not assume that a decision that
turned out adversely was a bad risk management decision
A correct risk management decision was one that would be made again if the circumstances were identical
Do not evaluate the decisions of others without putting ourselves in their position
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What Does This Mean for Investment Managers Use probability and risk quantification
but be sure you use it carefully Respect the past but don’t obsess over
it The financial media knows no more than
anyone else (and oftentimes a lot less) Investment decisions that look bad after
the fact can actually be good decisions
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Risk is Good
Do you really want to know the future? What would a financial world be like if
there were no risk?
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Thank you for having me here to speak.
If you have any questions later:
Feel free to email me for a copy of this presentation.