Finance and the Unexpected

2023 CFMR Keynote

Jessica Wachter

Chief Economist and Director, Division of Economics and Risk Analysis

This speech is provided in the author’s official capacity as the Commission’s Chief Economist and Director of the Division

of Economic and Risk Analysis but does not necessarily reflect the views of the Commission, the Commissioners, or other

members of the staff.
What might one be uncertain about?

1. Outcome of a given FDA trial affecting valuation of a company

2. Whether an executive of a company might be defrauding investors.

3. The return on S&P 500 on any given day? Over the next calendar year? 

4. Whether there will be failure of a major U.S. stock exchange in the next calendar year. 

5. Whether your trading counterparty knows more than you and is thus overcharging.

6. Whether your bank will be forced to close due to withdrawals or loss of funding source

7. What everybody else believes about these questions
What is “the unexpected”?

• Life is full of outcomes that we cannot predict with certainty.

• We can represent the range of outcomes as xx�

• We can form an expectation EE xx�

• Something is unexpected to the degree it is far from EE xx�

• The larger is xx� −EE xx� the more unexpected the event. 
People are risk-averse

• Arises from decreasing marginal utility

• Individuals will not make a risky bet 

without compensation.
The risk averse 

investor requires a 

premium

• The amount you need to 

be compensated for risk 

depends on risk aversion 

and (to a first 

approximation) on the 

volatility of the gamble
Return distribution for a single stock

Mean: 1.11%

Volatility: 13.77%

Skew: 2.96 

Kurtosis 19.22
Return distribution for a portfolio

Mean: 1.11%

Variance: 1.37%

Skewness: 0.30

Kurtosis: 3.17
Some of the unexpected is diversifiable

• The positive skewness of specific returns averages out

• To become an (almost) normal distribution

• With a much smaller variance.

• This is the type of risk associated with the FDA trial. 

• What about moral hazard?
A simple model of moral hazard

HH

LL

ppHH

ppLL

1 − pph

1 − ppLL

RR

RR

+ BB

0

BB
A simple model of moral hazard (cont.)

• Project costs II

• Upper path profitable: II < ppHHRR

• Lower path not profitable: II > ppLLRR.

• Upper path better than lower in total: BB < pphRR

• Entrepreneur only takes upper path if paid at least BB

∆pp

should a positive outcome occur

• Project cannot move forward if ppHH(RR − BB

∆pp ) < I. 
How market regulation can help

• It can reduce private benefits BB

• It can increase the difference in probabilities ∆pp

• This is Pareto-improving: it helps both the entrepreneur and the outside 

investors.
Other events may be subject to moral hazard

• Trading securities involve a commitment to settle at some future date 

• Collateralized borrowing involves commitment to deliver cash

• Securities lending a commitment to deliver securities

• Delegated asset management involves a commitment to fiduciary duty 

• Agency brokerage involves a commitment to best execution
Daily returns on the market portfolio 
Sampling distribution for kurtosis

Mean kurtosis estimate: 15

Population kurtosis: 119
Hidden Kurtosis

• Sample kurtosis is supposed to measure the fat tails of a distribution

• However, true kurtosis may be much larger than any one sample 

indicates.

• The fact that rare events can sometimes surprise is intuitive

• But we cannot take false comfort from a kurtosis statistic

• Kurtosis can reject the normal, not confirm the normal

• For one class of securities, correctly estimating kurtosis matters a 

great deal
Case study: the 

options market

• Payoffs to a long and a short options position • Exercise price XX • Price of underlying SS1
Black-Scholes-Merton model

• Their continuous-time model is a limiting case of a binomial tree

SS0

pp

1 − pp

uu 0

dd 0

uu2SS0

uu 0

dd2SS0

uu3SS0

uu2dd 0

uudd2SS0

dd3SS0
Implied volatility

• Under Black-Scholes-Merton, the price of an option depends on the price of the underlying, the exercise price, the interest rate, the time to maturity, and the 

volatility

• All are known, except the volatility.

• The volatility that equates the theoretical price of the option with its data value is 

called implied volatility

• Lognormal model → implied volatility = actual volatility at all levels of moneyness
Implied volatilities
Case study: the options market (cont.)

• However, daily return on October 19, 1987 implied a 20 standard deviation 

event, essentially impossible. 

• That day proved that the model for returns used to price options was wrong.
Two types of uncertainty

The uncertainty within the model, e.g. the 

binomial tree

The uncertainty outside the model, e.g. an 

event outside the binomial tree
Two types of uncertainty

• Why did market participants fail to take into account non-normality in returns in pricing 

options?

• Even if events do lie outside models, why not use a model that better explains the data?

• Especially when the difference is important?

Perhaps 80s were the beginning of quantitative modeling in industry. Perhaps downward 

bias and small sample
Bertrand Russell’s chicken:

• “The man who has fed the chicken every day throughout its life at last wrings its neck 

instead, showing that more refined views as to the uniformity of nature would have been 

useful to the chicken.” – Bertrand Russell

• Some types of uncertainty seem destined to fool us, like the short put strategy.

• Some distributions seem destined to fool us, like those with fat tails
Distribution 

of returns 

to putwrite

index
Outliers
The chicken problem

• Writing an option illustrates the chicken problem in two ways:

1. Their day-to-day payoffs represent the chicken before its neck is wrung

2. Option traders were like the thoughtful chicken: they had the wrong 

model
CDX spreads 

– supersenior 

tranche
Put options everywhere

• Short-put payoffs prone to the chicken problem. 

• The super-senior tranche on the CDX is an out-of-the-money put 

option on the overall economy

• Equity = call option written on the value of the firm

• Debt = Riskless bond + short put

• Run dynamics associated with short-term debt can make this problem 

worse.
How do 

individuals 

think about 

the 

unexpected?

Do people make explicit probability 

calculations in decision-problems? 

The evidence suggests not. Even 

colloquially: expected means “what comes 

to mind,” not a probabilistic statement

Recent research turns to evidence on 

memory to understand expectations 
Core 

principles 

of memory

Our 

memories, 

and thus 

our 

thoughts 

and beliefs 

are driven 

by:

Recency

Similarity

Temporal Contiguity

Recency 

effect 

exacerbates 

the chicken 

problem
Evidence of recency in expectations of returns

• Gallup investor survey (700 respondents, 1996—2012)

• Graham-Harvey CFO survey (200 respondents 1998– present)

• Many others

• Survey expectations are well-explained (e.g., RR2= 61% for Gallup) by 

returns over the past 12 months
Recency in 

expectations 

of stock 

returns
Older cohorts of asset managers rely less on 

recent experience
Explaining why some individuals invest

• How to invest and how much are some of the most important decisions an 

individual can make

• A 90th to 10th percentile difference in stock market performance over the 

lifetime implies an average difference in participation of 10 percentage 

points

• This effect is of comparable size to anything else known to influence 

household participation (for example, income and education).
Early-life stock returns are not forgotten
Context model

• Individuals’ thoughts and beliefs governed by an internal context

• Information from the environment retrieves a context.

• Retrieved context depends on the features filtered through past memories: the 

individual retrieves past contexts in which similar features were experienced.

• Retrieved context averages with past context to form current context

• Current context determines what pops to mind.

• The current features – either real or imagined -- are encoded into memory
Evidence from experiments and surveys

• Professional traders required a higher premium to take the same bet 

after the financial crisis as compared with before.

• Professional traders who are presented with crash risk scenarios 

require a greater premium to take a bet

• Subjects who watch a scene from a horror movie require a greater 

premium to take a bet as compared with those that don’t. 
Summary

• Individual stocks exhibit positive skewness; 

• This skewness is diversifiable; requires equity issuance and hence 

amelioration of moral hazard through regulation.

• Aggregate market exhibits excess kurtosis; measurement problems 

mean we don’t know how much.

• Put option pricing subject to “the chicken problem”

• Recency bias makes the chicken problem worse

• Lifetime experience, associations, and context matter
Closing thoughts