Chapter 5
Understanding Risk
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2008
Understanding Risk:
The Big Questions
1. What is risk?
2. How can we measure risk?
3. What happens when the quantity of
risk changes?
5-2
Understanding Risk:
Roadmap
•
•
•
•
•
Defining Risk
Measuring Risk
The Risk-Return Tradeoff
Sources of Risk
Reducing Risk
5-3
Risk: Definition
Risk is a measure of uncertainty
about the future payoff of an
investment, measured over some
time horizon and relative to a
benchmark.
5-4
Risk:
Elements of the Definition
• Measure: uncertainties that are not
quantifiable can’t be priced
• Uncertainty about the future: future is
one of a series of possible outcomes
•
•
•
•
Payoff: list the possible payoffs
Investment: broadly defined
Time horizon: Longer is usually more risky
Benchmark: Measured relative to risk-free.
5-5
Measuring Risk
1. List of all possible outcomes
2. List the probability of each occurring
5-6
Measuring Risk
Example: Single Coin Toss
Lists all possibilities, one of them must occur.
Probabilities sum to one.
5-7
Measuring Risk:
Case 1
$1000 Investment
1. Rise in value to $1400
2. Fall in value to $700
Two possibilities are equally likely
5-8
Measuring Risk:
Expected Value
Expected Value = ½ ($700) + ½ ($1400) = $1050
5-9
• Are you saving enough for retirement?
• Retirement planners can help figure out
• Be careful
– Investments with high returns are risky
– Risk means you can end up with less than
the expected return
5-10
Measuring Risk:
Case 2
What if $1000 Investment
1. Rise in value to $2000
2. Rise in value to $1400
3. Fall in value to $700
4. Fall in value to $100
5-11
Measuring Risk:
Case 2
Expected Value =
0.1x($100) + 0.4x($700) + 0.4x($1400) +0.1x($2000) = $1050
5-12
Measuring Risk:
Comparing Cases 1 & 2
• Expected value is the same:
$1050, or 5% on a $100 investment
• Is the risk the same?
• Case 2 seems to have more risk
• Why?
5-13
Measuring Risk:
Defining a Risk-Free Asset
A risk-free asset is
an investment whose future value is
known with certainty
and
whose return is the
risk-free rate of return.
5-14
Measuring Risk:
Comparing Cases 1 & 2
• Consider a risk-free investment
$1000 yields $1050 with certainty.
• Compare
Case 1 and the risk-free investment
• As the spread of the potential payoffs
rises, the risk rises.
5-15
Measuring Risk:
Variance & Standard Deviation
• Variance:
Average of squared deviation of the
outcomes from the expected value,
weighted by the probabilities.
• Standard Deviation:
Square root of the variance
(Same units as the payoff)
5-16
Measuring Risk:
Case 1
1. Compute the expected value:
($1400 x ½) + ($700 x ½) = $1050.
2. Subtract this from each of the possible payoffs:
$1400 – $1050= $350
$700 – $1050= –$350
3. Square each of the results:
$3502= 122,500(dollars)2 and
(–$350)2=122,500(dollars)2
4. Multiply each result times its probability and add up the results:
½ [122,500(dollars)2] + ½ [122,500(dollars)2] =122,500(dollars)2
5. Standard deviation = Variance = 122,500dollars 2 =$350
5-17
Measuring Risk:
Case 2
5-18
Measuring Risk:
Comparing Cases 1 & 2
Case 1: Standard Deviation =$350
Case 2: Standard Deviation =$528
The greater the standard deviation,
the higher the risk.
5-19
Measuring Risk:
Comparing Cases 1 & 2
Case 2 has a higher standard deviation because it has a bigger spread
5-20
• Car insurance is especially
expensive for young drivers
• You have to have liability insurance
• What about collision
• See if you should get a high deductible
5-21
• Leverage:
Borrowing to finance part of an investment
• Invest
– $1000 or your own + $1000 borrowed
– Expected return doubles
– Standard Deviation doubles
5-22
Leverage raises the expected value and the standard deviation.
5-23
Measuring Risk:
Value-at-Risk (VaR)
• Sometimes we are less concerned with
spread than with the worst possible
outcome
• Example: We don’t want a bank to fail
• VaR: The worst possible loss over a
specific horizon at a given probability
5-24
• Lotteries are very risky investments
• Why do people play?
• The loss of $1 is inconsequential
compared with the chance to win
millions
5-25
Risk Aversion
• A risk-averse investor:
prefers an investment with a certain
return to one with the same expected
return, but any amount of uncertainty
• A risk-averse person requires compensation
to assume a risk
• A risk-averse person pays to avoid risk
5-26
Risk Premium
The riskier an investment – the higher
the compensation that investors require
for holding it – the higher the risk
premium.
5-27
Risk-Return Tradeoff
More risk  Bigger risk premium  Higher expected return
Risk Requires Compensation
5-28
• How much risk should you tolerate?
• Take a risk quiz (pg. 117):
– What would you do if a month after you
invest the value drops 20%?
• As you get older, your risk tolerance will
probably fall
5-29
Sources of Risk
1. Idiosyncratic or Unique:
Affects a specific a person or business.
2. Systematic or Economy-wide Risk:
Affects everyone
5-30
Idiosyncratic and Systematic Risk
1. Idiosyncratic:
GM loses market
share to another
auto makers
2. Systematic:
The entire auto
market shrinks
5-31
Reducing Risk through
Diversification
1. Hedging Risk:
Make investments with
offsetting payoff patterns
2. Spreading Risk:
Make investments with
independent payoff patterns.
5-32
Reducing Risk:
Hedging
Reduce overall risk by making two
investments with opposing risks.
– When one does poorly, the other does well, and
vice versa
– So while the payoff from each investment is
volatile, together their payoffs are stable
5-33
Reducing Risk:
Hedging
Compare:
1. Invest $100 in GE
2. Invest $100 in Texaco
3. Invest ½ in each:
$50 in GE
+ $50 in Texaco
5-34
Reducing Risk:
Hedging
Hedging has eliminated the risk entirely.
5-35
Reducing Risk:
Spreading
• You can’t always hedge
• The alternative is to spread risk around
• Find investments whose payoffs
are unrelated
5-36
Reducing Risk:
Spreading
Consider three investment strategies:
1. GE only,
2. Microsoft only, and
3. ½ in GE + ½ in Microsoft.
5-37
Reducing Risk:
Spreading
5-38
5-39
Reducing Risk:
Spreading
The more independent sources of risk in
your portfolio, the lower the overall risk
5-40
• Diversification is especially important for you
retirement savings
• Many Enron employees investment their
retirement savings in Enron stock
• If the company you work for goes bankrupt,
you will lose your job. Don’t lose your
savings, too. Diversify.
5-41
Chapter 5
End of Chapter
McGraw-Hill/Irwin
© The McGraw-Hill Companies, Inc., 2008