bài giảng kinh tế vi mô tiếng anh ch17 uncertainty

1
Chapter 17
Uncertainty
Main topics
1. degree of risk
2. decision making under uncertainty
3. avoiding risk
4. investing under uncertainty
Degree of risk
• probability: number, 4, between 0 and 1 that
indicates likelihood a particular outcome occur
• frequency: estimate of probability,
4 = n/N, where
n is number of times a particular outcome
occurred during N number of times event occurred
• if we don’t have frequency, may use subjective
probability – informed guess
Probability distribution
• relates probability of occurrence to each
possible outcome
• first of two following examples is less
certain
Probability, %
20
10
40
Days of rain per month
01234
10% 20% 10%
30
(a) Less Certain

20% 40%
Figure 17.1 Probability Distribution
Probability, %
20
10
40
Days of rain per month
01234
30% 40% 30%
Probability
distribution
30
(b) More Certain
Expected value example
• 2 possible outcomes: rains, does not rain
• probabilities are ½ for each outcome
• promoter’s profit is
• $15 with no rain
• -$5 with rain
• promoter’s expected value (“average”)
EV = [Pr(no rain)GValue(no rain)]+[Pr(rain)GValue (rain)]
= [ ½
G $15] + [ ½ G (-$5)] = $5
2
Variance and standard deviation
• variance: measure of risk
• variance = [Pr(no rain)
G (Value(no rain - EV)
2
]

+ [Pr(rain)
G (Value (rain) – EV)
2
]
= [½
G ($15 - $5)
2
] + [½ G (-$5 - $5)
2
]
= [½
G ($10)
2
] + [½ G (-$10)
2
] = $100
• standard deviation = square root of variance
Decision making under
uncertainty
• a rational person might maximize expected
utility: probability-weighted average of
utility from each possible outcome
• promoter’s expected utility from an indoor
concert is
EU = [Pr(no rain) G U(Value(no rain))] + [Pr(rain) G U(Value(rain))]
= [½
G U($15)] + [½ G U(-$5)]
• promoter’s utility increases with wealth
Fair bet
• wager with an expected value of zero

• flip a coin for a dollar:
[½ G (1)] + [½ G (-1)] = 0
Attitudes toward risk
• someone who is risk averse is unwilling to
make a fair bet
• someone who is risk neutral is indifferent
about making a fair bet
• someone who is risk preferring
wants to make a fair bet
Risk aversion
• most people are risk averse: dislike risk
• their utility function is concave to wealth axis: utility
rises with wealth but at a diminishing rate
• they choose the less risky choice if both choices have
the same expected value
• they choose a riskier option only if its expected value is
sufficiently higher than a riskless one
• risk premium: amount that a risk-averse person
would pay to avoid taking a risk
3
Figure 17.2 Risk Aversion
Utility, U
Wealth, $10 26 40 64 70
a
b
d
e
U (W ealth)
U ($70) = 140
0.1U ($10) + 0.9U ($70) = 133

U ($26) = 105
U ($40) = 120
U($10) = 70
0
Risk premium
0.5U ($10) + 0.5U($70) =
c
f
Risk averse decision
• Irma’s initial wealth is $40
• her choice
• she can do nothing: U($40) = 120
• she may buy a risky Ming vase
Expected value of Ming Vase
• worth $10 or $70 with equal probabilities
• expected value (point d):
$40 = [½ G $10] + [½ G $70]
• expected utility (point b):
105 = [½ G U($10)] + [½ G U($70)]
Irma’s risk premium
• amount Irma would pay to avoid this risk
• certain utility from wealth of $26 is U($26) = 105
• Irma is indifferent between
• having the vase
• having $26 with certainty
• thus, Irma’s risk premium is $14 = $40 - $26 to
avoid bearing risk from buying the vase
Figure 17.3a Risk Neutrality
Utility, U
Wealth, $10 40 70

a
b
U (Wealth)
(a) Risk-Neutral Individual
U ($70) = 140
U ($10) = 70
0
U ($40) = 105
0.5U($70) =
0.5U ($10) +
c
Risk-neutral person’s decision
• risk-neutral person chooses option with
highest expected value, because maximizing
expected value maximizes utility
• utility is linear in wealth
105 = [½ G U($10)] + [½ G U($70)]
= [½ G 70] + [½ G 140]
• expected utility = utility with certain wealth
of $40 (point b)
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Figure 17.3b Risk Preference
Utility, U
Wealth, $10 40 58 70
a
b
d
e
c
U (Wealth)

(b) Risk-Preferring Individual
U ($70) = 140
U ($40) = 82
U ($10) = 70
0
0.5U ($70) = 105
0.5U ($10) +
Risk-preferring person’s decision
• utility rises with wealth
• expected utility from buying vase, 105 at b, is
higher than her certain utility if she does not vase,
82 at d
• a risk-preferring person is willing to pay for the
right to make a fair bet (negative risk premium)
• Irma’s expected utility from buying vase is same
as utility from a certain wealth of $58, so she’d
pay $18 for right to “gamble”
Risky jobs
• some occupations have more hazards than
do others
• in 1995, deaths per 100,000 workers was
• 5 across all industries
• 20 for agriculture
(35 in crop production)
• 25 for mining
Risk of workplace homicides per
100,000 workers
1.3Fire fighter
1.5Butcher-meatcutter
2.3Bartender

5.9Gas station worker
6.1Police, detective
10.7Sheriff-bailiff
22.7Taxicab driver
RateOccupation
Risky jobs have small premium
• Kip Viscusi found workers received a risk
premium (extra annual earnings) for job hazards
of $400 on average in 1969
• amount was relatively low because annual risks
incurred by workers were relatively small
• in a moderately risky job,
• danger of dying was about 1 in 10,000
• risk of a nonfatal injury was about 1 in 100
Value of life
• given these probabilities, estimated average
job-hazard premium implies that workers
placed a value on their lives of about $1
million
• and an implicit value on nonfatal injuries of
$10,000
5
Gambling
Why would a risk-averse person gamble
where the bet is unfair?
• enjoys the game
• makes a mistake: can’t calculate odds
correctly
• has Friedman-Savage utility
Application Gambling

Utility, U
WealthW
1
W
2
W
3
W
4
W
5
a
b
b* d *
c
d
e
U (Wealth)
Avoiding risk
• just say no: don’t participate in optional
risky activities
• obtain information
•diversify
• risk pooling
• diversification can eliminate risk if two events
are perfectly negatively correlated
Perfectly negatively correlated
• 2 firms compete for government contract
• each has an equal chance of winning
• events are perfectly negatively correlated:

one firm must win and the other must lose
• winner will be worth $40
• loser will be worth $10
If buy 1 share of each for $40
• value of stock shares after contract is
awarded is $50 with certainty
• totally diversified: no variance; no risk
If buy 2 shares of 1 firm for $40
• after contract is awarded, they’re worth $80 or
$20
• expected value:
$50 = (½
´ $80) + (½ ´ $20)
• variance:
$900 = [½
´ ($80 - $50)
2
] + [½ ´ ($20 - $50)
2
]
• no diversification (same result if buy two stocks
that are perfectly positively correlated)
6
If stocks values are uncorrelated
• each firm has 50% chance of a government
contract
• whether a firm gets a contract doesn’t affect
whether other wins one
• expected value
$50 = (¼

´ $80) + (½ ´ $50) + (¼ ´ $20)
• variance
$450 = [¼
´ ($80 - $50)
2
] + [½ ´ ($50 - $50)
2
]
+ [¼
´ ($20 - $50)
2
]
• buying both results in some diversification
Mutual funds
• provide some diversification
• Standard & Poor’s Composite Index of 500
Stocks (S&P 500)
• Wilshire 5000 Index Portfolio (actually
7,200 stocks)
S&P 500 Funds
• you can get close to rate of return on S&P 500 by
buying a stock fund that tries to duplicate that
index
• deviation is due to management fees (which are
low)
• 1996:
• S&P 500 rose by 7.45%
• Vanguard Index 500’s return was 7.37%
• similar funds’ returns ranged between 7.19 and 7.27%
International risks

• if you invest in only U.S. stocks and bonds,
you bear systematic risk associated with
shifts in the U.S. economy
• holding foreign funds helps diversify: U.S.
returns are not perfectly correlated with
foreign ones
• however, foreign investments may actually
increase your risk
Exchange rate risk
• a foreign investment may increase risk
because of fluctuations in the exchange
rate: how many dollars you must trade to
obtain a unit of another country's currency
• once, a Latin America fund lost 17% of its
value in a month due to exchange rate shifts
Default
• lesser-developed countries may have high risks of
default: failure of a borrower to repay money
owed
• U.S. investors were concerned about threat of
default in Latin America in 1990s
• only held Latin American bond funds that paid a large
premium over safer U.S. Treasury bonds
• at the peak of Latin American debt in March 1995, risk
premium averaged 19 percentage points
• as threat of default eased over the next year, the
differential fell to about 6 percentage points
7
$10,000 certificates of deposit
• in 1995, investing in whichever country had

the highest rate of return on its CDs
produced the largest return
• but that does not happen if rate of change in
exchange rates is negative enough (as
almost happened to the British CD)
Returns on $10,000 1 Year CD
$9,165-10.251.05Japanese yen
$9,617-7.753.63German mark
$10,5250.005.25U.S. $
$10,533-0.646.00British pound
$11,2194.627.00 New Zealand $
$11,6185.3210.00Italian lira
Final
Value
% Change
in $
Return
rate
Diversification traps
• investors less diversified than they think if the
returns on their investments tend to move together
• suppose you decide to invest in a bond fund and in
a stock fund to obtain a diversified portfolio
• during expansions, stock prices rise and bond values
fall
• during contractions, the opposite happens
Trap
• trap: some stock funds hold disproportionate share
of stocks in financial institutions and utilities
• Stratton Monthly Dividend fund had 29% of its

portfolio in financial stocks and 71% in utilities
• Weitz Value fund had 56% in financial institutions and
14% in utilities
• you are less diversified if you pair bond fund with
stock fund that concentrates on financial
institutions and utilities - so the price of the funds
are positively correlated - than if you use other
types of stock funds
3 common measures of risk
• standard deviation
• Morningstar measure of risk of loss
•beta
Morningstar, Inc.
• Chicago funds rating company
• looks at a fund's monthly returns and
determines how many times it has failed to
match the results of risk-free investments
like Treasury bills
• then compares that figure to those of similar
funds and sets the risk at 1 for the average
• higher the number indicates riskier fund
8
Beta (+)
• shows whether a fund's return moves with
that of the market as a whole
• beta = 1 means fund's return moves with
S&P 500
• beta = 1.5 means,
• if S&P goes up 10%, fund rose 15%
• if S&P went down 10%, it fell 15%

Reasonableness of beta
• beta is a reasonable way to assess risk of stocks
• can be misleading for non-stock investments
• example
• price of gold and foreign funds do not move closely
with the U. S. stock market, so they have very low
betas
• such investments tend to be very risky in terms of
standard deviations
Vanguard 500 fund
• weighted average of the S&P 500 stocks
• standard deviation for 3 years
• Vanguard 500 was 8.1
• highest observed was on Lexington Strategic
investment, 49.3
• lowest was on T. Rowe Price Spectrum Income
fund, 3.8
3-year Morningstar measure
• Vanguard 500 was 0.7
• Lexington Strategic Investments was 3.8
• Merger fund was 0.2
3-year beta
• Vanguard 500 is 1.0
• Smith Barney Special Equities B fund was
1.6
• Merger fund was 0.1
Insurance
• risk-averse people will pay money – risk
premium – to avoid risk
• world-wide insurance premiums in 1998:

$2.2 trillion
9
House insurance
• Scott is risk averse
• wants to insure his $80 (thousand) house
• 25% chance of fire next year
• if fire occurs, house worth $40
With no insurance
• expected value of house is
$70 = (¼
´ $40) + (¾ ´ $80)
• variance
$300 = [¼
´ ($40 - $70)
2
] + [¾ ´ ($80 - $70)
2
]
With insurance
• suppose insurance company offers fair insurance
• lets Scott trade $1 if no fire for $3 if fire
• insurance is fair bet because expected value is
$0 = (¼ ´ [-$3]) + (¾ ´ $1)
• Scott fully insurances: eliminates all risk
• pays $10 if no fire
• receives $30 if fire
• net wealth in both states of nature is $70
Commercial insurance
• is not fair
• available only for diversifiable risks

Investing under uncertainty
• monopoly’s owner has an uncertain payoff
this year
• if risk neutral, owner maximizes expected value
of return
• otherwise, owner maximizes his or her
expected utility
• summarize analysis in decision tree
Figure 17.04 Investment Decision Tree with Risk Aversion
Low demand
High demand
$200
80%
20%
–$100
$0
EV
=
$140
EV
=
$140
Invest
(a) Risk-Neutral Owner
Do not invest
Low demand
High demand
U($200) = 40
80%
20%

U
(–
$100) = 0
U($0) = 35
EU =35
EU
=
32
Invest
(b) Risk-Averse Owner
Do not invest
10
Investing under uncertainty and
discounting
• problem is more complicated if future
returns are uncertain
• need to calculate expected utility (or value)
and then discount
Figure 17.5 Investment Decision Tree with Uncertainty and
Discounting
Low demand
High demand
R = $125
C = $25
80%
20%
R = $50
$0
ENVP
=

$75
EV
=
$110
EPV = $100
Invest
This year
Next year
Do not invest
Investing with advertising
• future demand is uncertain
• advertising affects demand
• suppose risk neutral owner
Figure 17.6 Investment Decision Tree with Advertising
EV
=
$10
Invest
Do not invest
Low demand
High demand
$100
80%
20%
–
$100
Low demand
High demand
$100
40%

60%
–
$100
EV
=
$10
$0
EV =
$60
EV
=
–$20
Advertise
– $50
Do not
advertise
1. Degree of risk
• probability: likelihood that a particular state of
nature occurs
• expected value: probability-weighted average of
the values in each state of nature
•variance
• commonly used measure of risk
• weighted average of the squared difference of the value
in each state of nature and the expected value
2. Decision making under
uncertainty
• most people are risk averse
• people choose the option that provides the
highest expected utility

• expected utility is the probability-weighted
average of the utility from the outcomes in
the various states of nature
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3. Avoiding risk
people reduce risk they face by
• avoiding optional risks
• take actions that lower probabilities of bad
events or reduce harms from those events
• collect information before acting
•diversify
• insure
4.Investing under uncertainty
investment depends on
• uncertainty of payoff
• attitudes toward risk
• expected return
• interest rate
• cost of altering the likelihood of a good
outcome