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Welcome
to our presentation onThe
theory of choice: Utility theory given
uncertainty
on behalf of group :-
FIVE AXIOMS OF CHOICE UNDER UNCERTAINTY
Axiom 1 Comparability (sometimes called completeness).
Axiom 2 Transitivity (sometimes called consistency)
Axiom 3 Strong independence
Axiom 4 Measurability
Axiom 5 Ranking
DEVELOPING UTILITY FUNCTIONS
The utility function will have two properties:
First,
It will be order preserving. In other words, if we measure the utility of x
as greater than the utility of y, U(x) > U(y), it means that x is actually
preferred to y, x >- y.
Second,
Expected utility can be used DEVELOPING UTILITY FUNCTIONS
81 to rank combinations of risky alternatives.
Risk aversion
The subjective tendency of investor to avoid un-necessary risk.
In economy and Finance, risk aversion is the behavior of human when
exposed to uncertainty, in attempting to lower that uncertainty
oEstablishing a definition of risk aversion
oComparison of risk aversion in the small
and the large
oStochastic dominance
o Risk Lover
o Risk neutral
o Risk Averter
o Absolute risk aversion
o Relative risk aversion
o Comparative risk aversion
Utility Function
Measurement of risk aversion
oComparison of risk aversion in the small and the
large
o First Order Stochastic Dominance
o Second Order Stochastic Dominance
Stochastic Dominance
USING MEAN AND VARIANCE AS CHOICE CRITERIA
.
Types of Investors Indifference curves for a risk-averse
investor.
A MEAN-VARIANCE PARADOX
Particulars Horrid Bad Average Good Great
Net operating income $1200 $1600 $2000 $2400 $2800
Probability .20 .20 .20 .20 .20
Firm A
Interest expenses 0 0 0 0 0
EBT $1200 $1600 $2000 $2400 $2800
Tax at 50% -600 -800 -1000 -1200 -1400
Net income $600 $800 $1000 $1200 $1400
EPS $3 $4 $5 $6 $7
Firm B
Net operating income $1200 $1600 $2000 $2400 $2800
Interest expenses -600 -600 -600 -600 -600
EBT $600 $1000 $1400 $1800 $2200
Tax at 50% -300 -500 -700 -900 -1100
Net income $300 $500 $700 $900 $1100
EPS(100 Shares) $3 $5 $7 $9 $11
RECENT THINKING AND EMPIRICAL EVIDENCE
1.Von Neumann and Morgenstern [1947]
2.Kahneman and Tversky [1979, 1986]
Survival Frame
Surgery: Of 100 people having surgery, 90 live through the postoperative period, 68 are alive at
the end of the first year, and 34 are alive at the end of five years.
Radiation Therapy: Of 100 people having radiation therapy, all live through the treatment, 77
are alive at the end of one year, and 22 are alive at the end of five years.
Mortality Frame
Surgery: Of 100 people having surgery, 10 die during surgery or the postoperative period, 32
die by the end of the first year, and 66 die by the end of five years.
Radiation Therapy: Of 100 people having radiation therapy, none die during treatment, 23 die
by the end of one year, and 78 die by the end of five years.
STATE PREFERENCE THEORY
Here we will shift from-
“individual’s choice problem of mutually exclusive investments” to
“Portfolio decision making”
ASSUMPTION
 A perfect capital market with no cost of portfolio construction
Uncertainty And Alternative Future States
Uncertainty
Not knowing what the state of nature will be at some future date
• Once the uncertain state of the world is revealed, the payoff on the security is
determined exactly.
Pure Securities
“Pays $1 if a given state occurs and nothing if any other state occurs”
Every market security may be considered a combination of various
pure securities.
Complete Capital Market
“An efficient market in which the volume and availability of securities ensures that
there are no constraints on investment outcomes and where market values are
determined only by investment decisions”.
Conditions
Negligible transaction costs & perfect information
A price for every asset in every possible state of the world
NO ARBITRAGE PROFIT CONDITION
Capital market equilibrium requires
Supply =Demand
For each individual security
Everyone would want to buy the security or portfolio with the lower price
and to sell the security or portfolio with the higher price. If both the
securities or portfolios are in positive supply, such prices can not represent
an equilibrium.
Single price law of market
Economic Determinants of Security Prices
The prices of pure securities depend on
Time preference of consumption and productivity of capital
Expectations as to the probability that a particular state will
occur
Individuals’attitudes toward risk, given the variability across
states of aggregate end-of-period wealth
Optimal Portfolio
Optimal portfolio theory assumes that investors focus
their efforts on minimizing risk while also striving to
attain the highest possible return.
Optimal Portfolio Decision
Portfolio Optimality Condition and
portfolio separation
Existing Investments
Generate Cash Flows Today
Includes long lived(fixed)
and short lived (working
capital) assets
Expected value that will be
created by future
investments
Firm Valuation: value the entire business
Assets Liabilities
Assets in
place
Growth
Assets
Fixed Claim on cash flows
Little or No role in
management
Fixed Maturity
Tax Deductible
Residual Claim on cash
flows
Significant Role in
management
Perpetual Lives
Debt
Equity
Equity valuation: Value just the
equity claim in the business
The Fisher Separation Principal
The Fisher separation principal States that:
 The firms investment decision is independent of the
consumption preferences of the owner;
 The investment decision is independent of the
financing decision.
 The value of a capital project (investment) is
independent of the mix of methods- equity, debt, and
cash used to finance the project.
Optimal Investment Decision
The theory of choice: Utility theory given uncertainty & State preference theory

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The theory of choice: Utility theory given uncertainty & State preference theory

  • 1. Welcome to our presentation onThe theory of choice: Utility theory given uncertainty on behalf of group :-
  • 2. FIVE AXIOMS OF CHOICE UNDER UNCERTAINTY Axiom 1 Comparability (sometimes called completeness). Axiom 2 Transitivity (sometimes called consistency) Axiom 3 Strong independence Axiom 4 Measurability Axiom 5 Ranking
  • 3. DEVELOPING UTILITY FUNCTIONS The utility function will have two properties: First, It will be order preserving. In other words, if we measure the utility of x as greater than the utility of y, U(x) > U(y), it means that x is actually preferred to y, x >- y. Second, Expected utility can be used DEVELOPING UTILITY FUNCTIONS 81 to rank combinations of risky alternatives.
  • 4. Risk aversion The subjective tendency of investor to avoid un-necessary risk. In economy and Finance, risk aversion is the behavior of human when exposed to uncertainty, in attempting to lower that uncertainty oEstablishing a definition of risk aversion oComparison of risk aversion in the small and the large oStochastic dominance
  • 5. o Risk Lover o Risk neutral o Risk Averter o Absolute risk aversion o Relative risk aversion o Comparative risk aversion Utility Function Measurement of risk aversion
  • 6. oComparison of risk aversion in the small and the large o First Order Stochastic Dominance o Second Order Stochastic Dominance Stochastic Dominance
  • 7. USING MEAN AND VARIANCE AS CHOICE CRITERIA . Types of Investors Indifference curves for a risk-averse investor.
  • 8. A MEAN-VARIANCE PARADOX Particulars Horrid Bad Average Good Great Net operating income $1200 $1600 $2000 $2400 $2800 Probability .20 .20 .20 .20 .20 Firm A Interest expenses 0 0 0 0 0 EBT $1200 $1600 $2000 $2400 $2800 Tax at 50% -600 -800 -1000 -1200 -1400 Net income $600 $800 $1000 $1200 $1400 EPS $3 $4 $5 $6 $7 Firm B Net operating income $1200 $1600 $2000 $2400 $2800 Interest expenses -600 -600 -600 -600 -600 EBT $600 $1000 $1400 $1800 $2200 Tax at 50% -300 -500 -700 -900 -1100 Net income $300 $500 $700 $900 $1100 EPS(100 Shares) $3 $5 $7 $9 $11
  • 9. RECENT THINKING AND EMPIRICAL EVIDENCE 1.Von Neumann and Morgenstern [1947] 2.Kahneman and Tversky [1979, 1986] Survival Frame Surgery: Of 100 people having surgery, 90 live through the postoperative period, 68 are alive at the end of the first year, and 34 are alive at the end of five years. Radiation Therapy: Of 100 people having radiation therapy, all live through the treatment, 77 are alive at the end of one year, and 22 are alive at the end of five years. Mortality Frame Surgery: Of 100 people having surgery, 10 die during surgery or the postoperative period, 32 die by the end of the first year, and 66 die by the end of five years. Radiation Therapy: Of 100 people having radiation therapy, none die during treatment, 23 die by the end of one year, and 78 die by the end of five years.
  • 10. STATE PREFERENCE THEORY Here we will shift from- “individual’s choice problem of mutually exclusive investments” to “Portfolio decision making” ASSUMPTION  A perfect capital market with no cost of portfolio construction
  • 11. Uncertainty And Alternative Future States Uncertainty Not knowing what the state of nature will be at some future date • Once the uncertain state of the world is revealed, the payoff on the security is determined exactly.
  • 12. Pure Securities “Pays $1 if a given state occurs and nothing if any other state occurs” Every market security may be considered a combination of various pure securities.
  • 13. Complete Capital Market “An efficient market in which the volume and availability of securities ensures that there are no constraints on investment outcomes and where market values are determined only by investment decisions”. Conditions Negligible transaction costs & perfect information A price for every asset in every possible state of the world
  • 14. NO ARBITRAGE PROFIT CONDITION Capital market equilibrium requires Supply =Demand For each individual security Everyone would want to buy the security or portfolio with the lower price and to sell the security or portfolio with the higher price. If both the securities or portfolios are in positive supply, such prices can not represent an equilibrium. Single price law of market
  • 15. Economic Determinants of Security Prices The prices of pure securities depend on Time preference of consumption and productivity of capital Expectations as to the probability that a particular state will occur Individuals’attitudes toward risk, given the variability across states of aggregate end-of-period wealth
  • 16. Optimal Portfolio Optimal portfolio theory assumes that investors focus their efforts on minimizing risk while also striving to attain the highest possible return.
  • 18. Portfolio Optimality Condition and portfolio separation
  • 19. Existing Investments Generate Cash Flows Today Includes long lived(fixed) and short lived (working capital) assets Expected value that will be created by future investments Firm Valuation: value the entire business Assets Liabilities Assets in place Growth Assets Fixed Claim on cash flows Little or No role in management Fixed Maturity Tax Deductible Residual Claim on cash flows Significant Role in management Perpetual Lives Debt Equity Equity valuation: Value just the equity claim in the business
  • 20. The Fisher Separation Principal The Fisher separation principal States that:  The firms investment decision is independent of the consumption preferences of the owner;  The investment decision is independent of the financing decision.  The value of a capital project (investment) is independent of the mix of methods- equity, debt, and cash used to finance the project.