Chapter 7

Question 1

Describing Risk

To measure risk we must know:

Interpreting Probability

• –*
• –*
• *

Answer 1

Describing Risk

To measure risk we must know:

1. All of the possible outcomes
2. The probability or likelihood that a given outcome will occur

Interpreting Probability

• – Objective probability*
• Observed frequency of past events
• – Subjective probability*
• Perception that an outcome will occur
• Influenced by different information or different abilities to process the
  same information – based on judgment or experience

Question 2

2 measures to help describe and compare risky choices

1. • • measures the
   • Example: Investment in offshore drilling exploration: 2 possible outcomes
     
     • Success – the stock price increases from $30 to $40/share
     • Failure – the stock price falls from $30 to $20/share
     • Objective Probability
       
       • 100 explorations: 25 successes and 75 failures
       • Probability of success = and probability of failure =
       • EV = formula = + =

Variability

• Extent to which
• How much
  
  • Example: Suppose you are choosing between two part-time sales jobs that have the same expected income ($1,500) (table image)
  • Greater variability from expected values signals
  • Variability comes from
  • Difference between
  • Calculating Deviation in example
  • take
  • and then to calculate
    
    • σ =
  • σ1= =

Answer 2

2 measures to help describe and compare risky choices

1. Expected value
   
   • ​Probability-weighted average of the payoffs or values associated with all
     possible outcomes
     
     • measures the central tendency; the payoff or value expected on average
   • Example: Investment in offshore drilling exploration: 2 possible outcomes
     
     • Success – the stock price increases from $30 to $40/share
     • Failure – the stock price falls from $30 to $20/share
     • Objective Probability
       
       • 100 explorations: 25 successes and 75 failures
       • Probability of success = 0.25 and probability of failure = 0.75
       • EV = Pr(success)(value of success) + Pr(failure)(value of failure)= 0.25($40/share) + 0.75($20/share) = $25/share

Variability

• Extent to which possible outcomes of an uncertain event differ
• How much variation exists in the possible choices
  
  • Example: Suppose you are choosing between two part-time sales jobs that have the same expected income ($1,500) (table image)
  • Greater variability from expected values signals greater risk
  • Variability comes from deviations in payoffs
  • Difference between expected payoff and actual payoff
  • Calculating Deviation in example
  • take expected payoff: 2000 for job 1outcome 1 and substract actual payoff E(x1) 1500 so deviation = 1500
  • and then to calculate σ(standard deviation) you take those deviations for each job , square them and multiply by theres probabilities
    
    • σ = racine(Pr (X − E(X ))^2 + Pr (X − E(X ))^2)
  • σ1= racine((5. 250,000) +(5. 250,000) =500

Question 3

Preferences toward risk

• Utility function:
• Marginal utility:
• Expected utility:
• Expected utility(Image):where, i

Answer 3

Preferences toward risk

• Utility function: Assigns a level of utility to each possible market basket.
• Marginal utility: the additional satisfaction obtained by consuming an additional amount of a good.
• Expected utility: Sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur.
• Expected utility(Image):where, u(Xi) is the utility one obtains with outcome Xi

Question 4

Different preferences towards risk:

• Risk-averse:
• Risk neutral:
• Risk loving:

Answer 4

Different preferences towards risk:

• Risk-averse:Condition of preferring a certain income to a risky income with the same expected value.
• Risk neutral: Condition of being indifferent between a certain income and an uncertain income with the same expected value.
• Risk loving: Condition of preferring a risky income to a certain income with the same expected value.

Question 5

Risk Premium

Risk Premium:

Answer 5

Risk Premium

Risk Premium: The risk premium is the maximum amount of money that a risk-averse person will pay to avoid taking a risk.

Question 6

For a risk-averse person:

• The steeper the indifference curve,
• Each individual has

Answer 6

For a risk-averse person:

• The steeper the indifference curve, the more risk-averse this person is, vice versa.
• Each individual have infinite number of indifference curves, and each indifference curve represents at a given utility U, the combination between risk of the income and expected income.

Question 7

Reducing risk

1. : practice of
   
   • Negatively correlated variables:
   • Positively correlated variables:
2. …:…
   
   • The law of large number:
   • Actuarial fairness:
3. The value of information:

Answer 7

Reducing risk

1. Diversification: practice of reducing risk by allocating resources to a variety of activities whose outcomes are not closely related. One can reduce risk through diversification. (e.g. mutual fund: an organization that pools funds of individual investors to buy a large number of different stocks or other financial assets.)
   
   • Negatively correlated variables: Variables having a tendency to move in opposite directions.
   • Positively correlated variables: variables having a tendency to move in the same direction.
2. Insurance: Buying insurance assures a person of having the same income whether or not there is a loss. For a risk-averse consumer, the guarantee of the same income regardless of the outcome generates more utility than would be the case if that person had a high income when there was no loss and a low income when a loss occurred.
   
   • The law of large number: Although single events may be random and largely unpredictable, the average outcome of many similar events can be predicted. (e.g. tossing a coin 100 times)
   • Actuarial fairness: A situation in which an insurance premium is equal to the expected payout
3. The value of information: Difference between the expected value of a choice when there is complete information and the expected value when information is incomplete.

Question 8

The Demand for risky Assets

1. Asset: something that
   
   • Risky asset:
   • Riskless (risk-free) asset:
2. Asset Returns:
   
   • Real return:
   • Expected return:
   • Actual return:

Answer 8

The Demand for risky Assets

1. Asset: something that provides a flow of money or services to its owner.​
   
   • Risky asset: Asset that provides an uncertain flow of money or services to its owner
   • Riskless (risk-free) asset: Asset that provides a flow of money or services that is known with certainty
2. Asset Returns: total monetary flow of an asset as a fraction of its price; asset return can be positive or negative
   
   • Real return: nominal return less the rate of inflation.
   • Expected return: return that an asset should earn on average;
   • Actual return: return that an asset actually earns.

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11