risk

Riskjuliohuato@gmail.com

Goals: To learn about… The effect of uncertainty in our

economic life Ways in which risk can be estimated Our attitudes towards risk The different sources of risk The ways in which manage our

economic risk

Uncertainty Kenneth J Arrow: “Uncertainty is our relative

ignorance about the future effects of our current choices -- the more so, the further removed the effects are from these choices.”

We are ignorant about how the world and our society functions (economics barely makes a dent), ultimately because our productive powers are finite

On top of our regular ignorance vis-à-vis the rest of nature, uncertainty about our own social life is self-referential – it depends on how we deal with our own uncertainty (chicken-and-egg).

Risk In economics and finance, we usually

think of risk as: The economic effect (benefits/costs) of

our uncertainty One usual way in which risk is quantified

in economics and finance is as the variability in payoffs

Probability & Statistics Probability is a mathematical theory

about our cognitive behavior in the face of uncertainty

Statistics is a set of techniques that use probability theory (and other assumptions) to extract knowledge from data (observations)

Possibilities, Probabilities, and Expected Value We can construct a table of all outcomes

and probabilities for an event, like tossing a fair coin.

Lottery AFlip a ‘fair’ coin:

If heads, you receive $1: If tails, you receive $1: The expectation (or expected value or

mean or average) payoff of this lottery is:

In general:

Lottery BFlip the same ‘fair’ coin:

If heads, you receive $0: If tails, you receive $2: The expectation (or expected value or

mean or average) payoff of this lottery is:

Lottery CFlip the coin again:

If heads, you give $1: If tails, you receive $3: The expectation (or expected value or

mean or average) payoff of this lottery is:

The 3 lotteriesLotto x bar Range:

max(x)-min(x)

A $1 $0

B $1 $2

C $1 $4

With which lottery do the effects of your uncertainty feel more painful?

Risk aversionPeople prefer a certain payoff to an uncertain one

In a market system, people trade off risk for reward

Statistics Let be the “payoff,” i.e. the economic costs of

benefits of a choice, e.g. acquiring an asset). We already know how to compute the expectation: Range of payoff: Variance of payoff:

+…+ Standard deviation of payoff: Coefficient of variation of payoff:

Exercise Calculate the variance, standard deviation, and

coefficient of variation of the lotteries above.

Exercise Calculate the variance, standard deviation, and

coefficient of variation of the lotteries above. A)

.

Exercise Calculate the variance, standard deviation, and

coefficient of variation of the lotteries above. A)

. B)

.

Exercise Calculate the variance, standard deviation, and

coefficient of variation of the lotteries above. A)

. B)

. C)

.

Risk in economics & finance Usually, we think of risk as a measure of

uncertainty about the future payoff to a bond over a time period and compared to a benchmark

The benchmark is usually a hypothetical risk-free bond

Again, in a market system with prevailing risk aversion, there is a tradeoff between risk and reward

The use of probability theory requires that we envision all possible scenarios (“states of the world”) and their likelihood

Sources of RiskAll risks can be classified into two groups:1. Those affecting a small number of

people but no one else:idiosyncratic or unique risks

2. Those affecting everyone:systemic, systematic, economy-wide, or

macro risks

Sources of RiskIdiosyncratic risks can be classified into two extreme types:

1. A risk is bad for one sector of the economy but good for another.

2. Unique risks specific to one person or company and unrelated to others.

Dealing with riskRisk can be reduced through: Hedging: building a portfolio with assets

that have offsetting payoffs Diversification: randomly adding more

assets to one’s portfolio, since the additional assets are unlikely to have payoffs that move exactly like those already in the portfolio

Hedging Risk• Hedging is the strategy of reducing

idiosyncratic risk by making two investments with opposing risks.• If one industry is volatile, the payoffs are

stable.• Let’s compare three strategies for

investing $100:• Invest $100 in GE.• Invest $100 in Texaco.• Invest half in each company.

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Spreading Risk You can’t always hedge as investments

don’t always move in a predictable fashion.

The alternative is to spread risk around. Find investments whose payoffs are

unrelated. We need to look at the possibilities,

probabilities and associated payoffs of different investments.

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Spreading Risk The more independent sources of risk

you hold in your portfolio, the lower your overall risk.

As we add more and more independent sources of risk, the standard deviation becomes negligible.

Diversification through the spreading of risk is the basis for the insurance business.

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We learned about… Uncertainty and its economic effect: risk Estimating risk by measuring the variation of payoffs

to our assets Risk aversion and the tradeoff between risk and

reward in a market system Idiosyncratic (unique) risk and systemic (macro) risk How hedging (if there are assets with contrarian

payoffs) and diversification (spreading risk around) lowered idiosyncratic risk

In our next session, we will study how the risk premium on bonds can be estimated (under certain assumptions)