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Chapter 05 – Understanding Risk

Chapter 5

Understanding Risk

Chapter Overview

This chapter covers how to measure risk and assess whether it will increase or decrease.

It also develops an understanding of why changes in risk lead to changes in the demand

for particular financial instruments and to corresponding changes in the price of those

instruments.

Learning Objectives: Establish an understanding of

Risk as a measure of uncertainty about payoffs

Statistical measures of risk

Systematic vs. idiosyncratic risk

Risk reduction: hedging and diversification

Important Points of the Chapter

Every day we make decisions involving risk; making any decision that has more than one

possible outcome is similar to gambling in that a sum of money is involved and the

outcomes are uncertain. The tools used to measure risk were originally developed to

analyze games of chance. Applying these rules of probability help us understand the

possibility of various occurrences and allow us to make better choices. While risk cannot

be eliminated, in many cases it can be effectively managed. Risk also creates

opportunities; people are compensated for assuming risk. In order to calculate a fair price

for transferring risk from one person to another requires being able to measure risk.

Application of Core Principles

Principle #2: Risk. People require compensation for taking risks, and without the capacity

to measure risk we could not calculate a fair price for transferring risk from one person to

another, nor could we price stocks, bonds and insurance.

Principle #1: Time. Risk is measured over a time horizon. In most cases, the risk of

holding an investment over a short period is smaller than the risk of holding it over a long

one, but there are important exceptions that will be discussed in a later chapter.

Principle #2: Risk. Adjustable rate mortgages are riskier to the borrower because the rates

on such mortgages go up and down. Lower monthly payments come with added risk,

which is another way to compensate borrowers for taking on the added risk.

Principle #2: Risk. The riskier an investment, the higer the compensation that investors

require for holding it—i.e., the higher the risk premium.

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Teaching Tips/Student Stumbling Blocks

Appendix 5A of the chapter provides a “quick quiz” to help students determine

their risk tolerance. Using and discussing the quiz might be a good way to begin

this material.

If you have not already done so, it will be helpful to find out if the students in

your class have already taken a course in statistics or not. This will help you plan

how you will cover the material in this chapter on the mean, expected value,

variance, and standard deviation.

Point out that we square the differences in calculating the variance because

otherwise negative and positive differences would cancel each other out, giving a

false idea of how much difference there really is.

Here is an analogy that can be used to explain the concept of the standard

deviation. Imagine a floor done in tiles that are 4 inch square. You can measure

the length of something in how many tiles; it would the number of 4-inch blocks.

But the tiles could also be 9 or 12 inches; a different standard size tile. Similarly,

the standard deviation is really the average amount of difference in a data set.

Students may be puzzled by the discussion of the expected value. You should

point out that the average value of a data set might not actually occur. Take, for

example, two people, one of whom has $1 in cash and the other who has $199 in

cash. On average they hold $100 in cash, but that’s far from the amount that

either one actually holds.

You should emphasize that diversification not only depends on owning many

different assets but also requires that their returns move in opposite directions (so

one can hedge) or are independent (so one can spread the risk). For more

advanced students, Appendix 5B illustrates the mathematics of diversification.

Features in this Chapter

Applying the Concept: It’s Not Just Expected Return That Matters

This section describes an individual’s attempt to assess the adequacy of retirement saving

using a software program. The important point made is that the answer returned by the

software depends on whether the assumptions made (about expected rate of return, for

example) actually come to pass. To obtain a higher rate of return the individual will have

to assume more risk. At a lower rate of return the savings may not be enough for the

desired retirement income.

Your Financial World: Choosing the Right Amount of Car Insurance

When it comes to purchasing car insurance consumers have a number of choices to make,

including whether or not to have collision insurance. When you make the decision you

should think about how much your car is worth; buying collision on old cars is rarely

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worth it. For a new car the question is how much of a deductible to have; the higher the

deductible the lower your insurance premium will be.

Tools of the Trade: The Impact of Leverage on Risk

Leverage is the practice of borrowing in order to finance part of an investment.

Examples include mortgages and buying stock on margin. Leverage increases the

expected return on an investment and also increases the risk. Leverage magnifies the

effect of price changes on an asset. Leverage has at least as big of an impact on value as

risk does because it compounds the worst possible outcome.

Lessons from the Crisis: Systemic Risk

The financial system consists of all the institutions and markets that perform

intermediation. Threats to the system as a whole are known as systemic risks. These

risks arise when a set of vulnerabilities in markets and financial institutions threatens to

disrupt the general function of intermediation. Common exposure to a risk can threaten

many intermediaries at the same time. Connections among financial institutions and

markets may transmit and amplify a shock across the system. The financial system may

have critical parts without which the system cannot function. Some large,

interconnected financial firms are sometimes called “too big to fail” because their failure

might cause a cascade of bankruptcies across the system. One possible source of

systemic risk is liquidity. Obstacles to the flow of liquidity pose a catastrophic threat to

the financial system.

Your Financial World: Your Risk Tolerance

Financial advisors give their clients risk quizzes to help them assess the level of risk with

which they can live. (The appendix to this chapter provides a sample.) But even if you

are willing to take risks it doesn’t mean that you should. For example, as you get older

your investment plan for your savings should have less risk attached simply because you

have less time to recoup any losses.

In the News: Risk-on, risk-off may be ending

After years of markets going up and down in concert, there are signs that assets are

beginning to trade on their own merits. “Risk-on, risk off,” or Ro-Ro, has been the

dominant trade since the beginning of the financial crisis, mostly driven by major

economic news and global events that would affect the investors opinions of risk.

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Additional Teaching Tools

In a May 26, 2010 opinion piece in the Wall Street Journal, John Fund talks about the

possibilities of the market for gold going into a “bubble,” where there is a strong run-up

in prices due to significant demand from investors seeking high returns. Mr. Fund

discusses reasons why the current increases in gold prices might not be a bubble,

including the fact that fourteen years ago when the 400 percent increase in prices began,

gold was significantly undervalued. He compares gold prices to the tech bubble and the

housing bubble and points out that gold prices are following their trends, but not yet

poised to burst, if the trend follows for gold.

A “new twist” on life insurance is discussed in an article by Stephanie Strom in the New

York Times (“Charities Look to Benefit from a New Twist on Life Insurance,” June 5,

2004). The article discusses how wealthy donors are allowing “insurance companies,

hedge funds, and other investors to insure their lives in exchange for a promise that part

of the death benefits will flow to the donor’s favorite charities.” This is not entirely new,

as charities have long insured such donors. What is new is that investors, hoping for

substantial profits, are the ones buying the insurance and paying the premiums. Critics of

the practice point out that it is unclear just how much will end up going to the charities.

Virtual Tools

Here’s an online quiz to test risk tolerance.

http://www.bankrate.com/brm/news/financial-literacy2004/quiz/risk-style.asp

For More Discussion

How risk averse are your students? Use the following scenario for discussion: ask

students to choose between $10 with certainty or $20 with a 50% probability. Point out

that the expected value is the same in either case. Now ask this again with larger sums

involved; this provides a good opportunity to develop students’ intuition about value at

risk.

Appendix 5A to the chapter also provides a “quick quiz” for testing risk tolerance.

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Lessons of the Article: Don’t put all your eggs in one basket: diversify. The less related the

payoffs from different investments, the greater the benefits of diversification. When the

payoffs from different assets move together – that is, their correlation is high – the benefits of

diversification erode. The article highlights the limits of diversification when market

developments are dominated by enormous systematic shocks like the financial crisis of

2007-2009 and the euro-area crisis. The ebb and flow of each crisis resulted in high asset

correlations. Yet, even if diversification doesn’t always help, it’s still the best portfolio

strategy.

Chapter 05 – Understanding Risk

Chapter Outline

I. Defining Risk

A. We need a definition of risk that focuses on the fact that the

outcomes of financial and economic decisions are almost always

unknown at the time the decisions are made.

1. Risk is a measure of uncertainty about the future payoff to an

investment, measured over some time horizon and relative to a

benchmark.

2. Risk can be quantified.

3. Risk arises from uncertainty about the future.

4. Risk has to do with the future payoff to an investment, which is

unknown.

5. Our definition of risk refers to an investment or group of

investments.

6. Risk must be measured over some time horizon.

7. Risk must be measured relative to some benchmark, not in

isolation. If you want to know the risk associated with a specific

investment strategy, the most appropriate benchmark would be the

risk associated with other investing strategies.

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II. Measuring Risk

A. Possibilities, Probabilities and Expected Value

1. Probability theory tells us that in considering any uncertainty, the

first thing we must do is list all the possible outcomes and then

figure out the chance of each one occurring.

2. Probability is a measure of the likelihood that an event will occur;

it is always expressed as a number between 0 and 1, such that the

closer to 0 the less likely it is and the closer to 1 the more likely it

is (if it is 0 it is impossible, and if it is 1 it is certain).

3. Probabilities can also be expressed as frequencies.

4. The sum of the probabilities of all the possible outcomes must be

1, since one of the possible outcomes must occur (we just don’t

know which one).

5. To calculate the expected value of an investment, multiply each

possible payoff by its probability and then sum all the results. This

is also known as the mean.

6. Investment payoffs are usually discussed in percentage returns

instead of in dollar amounts; this allows investors to compute the

gain or loss on the investment regardless of its size.

7. A wider payoff range indicates more risk.

8. To compute the real interest rate we need a measure of expected

inflation. One way to calculate expected inflation is to list all the

possible inflation rates, assign each a probability, and then

calculate the expected value of the inflation rate.

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B. Measures of Risk

1. Most of us have an intuitive sense for risk and its measurement; the

wider the range of outcomes the greater the risk.

2. A financial instrument with no risk at all is a risk-free investment

or a risk-free asset; its future value is known with certainty and its

return is the risk-free rate of return.

3. We can measure risk by measuring the spread among an

investment’s possible outcomes. There are two measures that can

be used:

a) Variance and Standard Deviation

(1) The variance is defined as the average of the

squared deviations of the possible outcomes from their

expected value, weighted by their probabilities.

(2) To calculate the variance, first find the expected

value, and then subtract the expected value from each of

the possible payoffs. Then square each of the differences,

multiply them by their associated probabilities, and add up

the results.

(3) Take the square root of the variance to get the

standard deviation, which is more useful because it is

measured in the same units as the payoffs (that is, dollars

and not squared dollars).

(4) The standard deviation can then also be converted

into a percentage of the initial investment, providing a

baseline against which we can measure the risk of

alternative investments.

(5) Given a choice between two investments with the

same expected payoff, most people would choose the one

with the lower standard deviation because it would have

less risk.

b) Value at Risk (VaR)

(1) Sometimes we are less concerned with the spread of

possible outcomes than we are with the value of the worst

outcome. To assess this sort of risk we use a concept called

“value at risk.”

(2) Value at risk measures risk at the maximum

potential loss.

(3) In its formal definition, value at risk is the worst

possible loss over a specific time horizon, at a given

probability.

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III. Risk Aversion, the Risk Premium and the Risk-Return Tradeoff

A. Most people don’t like risk and will pay to avoid it; most of us are risk

averse.

B. A risk-averse investor will always prefer an investment with a certain

return to one with the same expected return but which has any amount of

uncertainty.

C. Buying insurance is paying someone to take our risks, so if someone

wants us to take on risk we must be paid to do so.

D. The riskier an investment—the higher the compensation that investors

require for holding it—the higher the risk premium.

E. Riskier investments must have higher expected returns.

F. There is a trade-off between risk and expected return; you can’t get a high

return without taking considerable risk.

IV. Sources of Risk: Idiosyncratic and Systematic Risk

A. Risk is everywhere. It comes in many forms and from almost every

imaginable place.

B. Regardless of the source, risks can be classified as either idiosyncratic or

systematic.

C. Idiosyncratic, or unique, risks affect only a small number of people.

D. Systematic risks affect everyone.

1. A good way to think of this is that while idiosyncratic risk

represents a change in the share of a pie (for an industry, for

example), systematic risk is a change in the size of the entire pie.

E. Idiosyncratic risks come in two types; in the first, some firms are affected

one way and others are affected in the opposite way, and in the second

risks are completely independent.

F. In the context of the entire economy, higher oil prices would be an

idiosyncratic risk (and is an example of a risk that can affect different

firms in opposing ways) and changes in general economic conditions

would be systematic risk.

V. Reducing Risk through Diversification

A. Risk can be reduced through diversification, the principle of holding more

than one risk at a time.

B. Holding several different investments reduces the overall risk that an

investor bears.

C. A combination of risky investments is often less risky than any one

individual investment.

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D. There are two ways to diversify your investments: you can hedge risks or

you can spread them among the many investments.

E. Hedging Risk

1. Hedging is the strategy of reducing overall risk by making two

investments with opposing risks so that when one does poorly the

other does well and vice versa.

F.Spreading Risk

1. Investments don’t always move predictably in opposite directions,

so you can’t always reduce risk through hedging.

2. You can lower risk by simply spreading it around and finding

investments whose payoffs are completely unrelated.

3. The more independent sources of risk you hold the lower your

overall risk.

4. Adding more and more independent sources of risk reduces the

standard deviation until it becomes negligible.

5. Spreading the risk is a fundamental strategy.

6. Diversification and the spreading of risk is the basis for the

insurance business.

Appendix: A Quick Test of Your Risk Tolerance

This is a short (5 questions) quiz to assess risk tolerance. Students can compare

their scores to the analyses provided to see if they are conservative or not.

Appendix: The Mathematics of Diversification

This appendix provides the mathematical analysis of how diversification reduces

risk. Students will need an understanding of the variance (covered in the chapter)

and the covariance. Both hedging and spreading risk are analyzed.

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Using FRED: Codes for Data in This Chapter

Data Series FRED Data Code

S&P 500 stock price index SP500

30‐year conventional mortgage rate MORTG

1‐year adjustable rate mortgage MORTGAGE1US

Moody’s Aaa corporate bond yield AAA

Moody’s Baa corporate bond yield BAA

BofA Merrill US CCC or below effective yield BAMLH0A3HYCEY

CBOE VIX Volatility Index VIXCLS

CBOE DJIA Volatility Index VXDCLS

Terms Introduced in Chapter 5

average

benchmark

diversification

expected return

expected value

hedging

idiosyncratic risk

leverage

mean

payoff

probability

risk

risk-free asset

risk-free rate of return

risk premium

spreading risk

standard deviation

systematic risk

value at risk (VaR)

variance

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Lessons of Chapter 5

1. Risk is a measure of uncertainty about the possible future payoffs of an investment. It

is measured over some time horizon, relative to a benchmark.

2. Measuring risk is crucial to understanding the financial system.

a. To study random future events, start by listing all the possibilities and assign a

probability to each. Be sure the probabilities add to one.

b. The expected value is the probability-weighted sum of all possible future

outcomes.

c. A risk-free asset is an investment whose future value, or payoff, is known with

certainty.

d. Risk increases when the spread (or range) of possible outcomes widens, but the

expected value stays the same.

e. One measure of risk is the standard deviation of the possible payoffs.

f. A second measure of risk is value at risk, the worst possible loss over a specific

time horizon, at a given probability.

3. A risk-averse investor

a. Always prefers a certain return to an uncertain one with the same expected return.

b. Requires compensation in the form of a risk premium in order to take risk.

c. Trades off between risk and expected return: the higher the risk, the higher the

expected return risk-averse investors will require for holding an investment.

4. Risk can be divided into idiosyncratic risk, which is specific to a particular business

or circumstance, and systematic risk, which is common to everyone.

5. There are two types of diversification:

a. Hedging, in which investors reduce idiosyncratic risk by making investments with

offsetting payoff patterns.

b. Spreading, in which investors reduce idiosyncratic risk by making investments

with payoff patterns that are not perfectly correlated.

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