Risk and uncertainty

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Lecture 8

• Risk and uncertainty

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Uncertainty is Pervasive

• What is uncertain in economic systems?
• tomorrows prices
• future wealth
• future availability of commodities
• present and future actions of other people.

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Characteristics of risky activities

• 2 characteristics of risky activities
• - likely outcome
• - degree of variability of possible outcomes
• Examples fair game 50-50 chance of making or
  losing 100 unfair game 70-30 chance of winning
  or losing 100
• - Compare this to a 50-50 chance of making or
  losing 500

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Individual tastes classification

• Risk averse may not be prepared to take a gamble
  even if the odds are favourable
• Risk loving prepared to take a gamble even if
  the odds are unfavourable
• Risk neutral will take a gamble if the odds are
  favourable not take a gamble if the odds are
  unfavourable and be indifferent if the odds are
  fair

5
Individual tastes and insurance

• - Suppose you have a 100,000 apartment 10 of
  burning down and 90 of continuing to have
  100,000
• - This gives on average 90,000
  (90100,000100)
• - An insurance company offers to pay back the
  whole 100,000 for a premium of 15,000, thus
  leaving you with 85,000 for sure. What will you
  do?

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Diminishing marginal utility and risk aversion

• Think of a lottery You have 10 and there is a
  50-50 chance of either winning or losing 5
• Expected utility (EU) 1/2U(5)1/2U(15)
• 1/2(2)1/2(12)7
• The expected money value is 10

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Diminishing marginal utility and risk aversion

• EU 7 and EM 10.
• U(10) gt 7 ? 10 for sure is preferred to the
  lottery ? risk aversion
• U(10) lt 7 ? the lottery is preferred to 10 for
  sure ? risk loving
• U(10) 7 ? the lottery is preferred equally to
  10 for sure ? risk neutrality

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Diminishing marginal utility and risk aversion
U(10) gt EU ? risk-aversion.
12
MU declines as wealth rises.
U(10)
EU7
2
Wealth
5
15
10
9
Diminishing marginal utility and risk aversion
U(10) lt EU ? risk-loving.
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MU rises as wealth rises.
EU7
U(10)
2
Wealth
5
15
10
10
Diminishing marginal utility and risk aversion
U(10) EU ? risk-neutrality.
12
MU constant as wealth rises.
U(10)EU7
2
Wealth
5
15
10
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Diversification and insurance

• Risk-pooling works by aggregating independent
  risks to make the aggregate more certain.
• Does not work if everyone faces the same risk.
  Acts of God risk- sharing more appropriate

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Diversification and insurance
Individual 1
Individual 2
Individual 3
Individual 1,000,000
Risk pooling
Insurance market
Insurance Co. 1
Insurance Co. 2
Insurance Co. 3
Insurance Co. 25
Risk sharing
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Moral hazard and adverse selection

• Moral hazard
• is the exploiting of inside information to take
  advantage of the other party to a contract
• e.g. if you take less care of your property
  because you know it is insured.
• Adverse selection
• occurs when individuals use their inside
  information to accept or reject a contract, so
  that those who accept are not an average sample
  of the population
• e.g. smokers taking out life insurance.

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Diversification and portfolio selection

• The risk-averse consumer prefers a higher average
  return on a portfolio of assets but dislikes
  risk.
• Return (Dividend Capital Gain)/Initial
  Purchase Price
• Risk volatility OR beta
• Diversification
• is a strategy of reducing risk by risk-pooling
  across several assets whose individual returns
  behave differently from one another.
• negative correlation in returns

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Diversification and portfolio selection

• Two firms, A and B. Shares cost 10.
• With prob. 1/2 As profit is 100 and Bs profit
  is 20.
• With prob. 1/2 As profit is 20 and Bs profit
  is 100.
• You have 100 to invest. How?

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Diversification and portfolio selection

• Two firms, A and B. Shares cost 10.
• With prob. 1/2 As profit is 100 and Bs profit
  is 20.
• With prob. 1/2 As profit is 20 and Bs profit
  is 100.
• You have 100 to invest. How?
• Buy only firm As stock?
• 100/10 10 shares.
• You earn 1000 with prob. 1/2 and 200 with prob.
  1/2. Expected earning 500 100 600
• Buy 5 shares in each firm? You earn 600 for sure

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A less negatively correlated example
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Efficient asset markets

• The theory of efficient markets
• says that the stock market is a sensitive
  processor of information
• quickly responding to new information to adjust
  share prices correctly.
• An efficient asset market already incorporates
  existing information properly in asset prices.
• It is not possible to systematically beat markets.

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Forward Market Transaction

• Commodity
• Copper
• Hedger
• Expected spot price after 12 months 880
• 12-month forward price 860
• Plan to sell (go short) at 860 to avoid risk
• Speculator
• Plan to buy (go long) at 860 and take risk
• Expected gain 20