FINC3017
FINC3017 Investments and Portfolio Management (Exam Notes)
FINC3017 Exam Notes
2 Week 1: Introduction
The Investment Funds Industry ! Managed funds fall into a number of categories that pool investor’s funds Unit Trusts
! Investor’s funds are pooled, usually into specific types of assets ! Investors are assigned units in the fund which are typically traded ! Invest in tradeable units, e.g. listed property trusts o Sell a fixed number of units to investors (closed funds) ! An unlisted trust however can issue new units at any time o Value of each unit depends of the value of the underlying investments, open-ended fund (mutual funds)
Superannuation Funds
! Accept and manage contributions from employers and/or employees to provide retirement and income benefits o Globally known as ‘pension funds’ o Managed by life insurance companies, fund administrators, master trusts and pooled trusts (wholesale vehicle) ! Superannuation fund structure: o Defined benefit – the retirement payout is determined based on a formula (risk on fund) o Defined contribution/accumulation fund – value of retirement payout depends on investment contributions in the fund (risk on investor)
Hedge Funds
! Seek to hedge against risky price movements via short selling, arbitrage trading, derivatives, distressed securities, low grade bonds and high leverage portfolios ! Maximise expected return-risk of the portfolio ! Access to hedge funds (as a retail investor) is limited
Exchange Traded Funds (ETFs)
! Listed on the stock market and trade as per any stock unlike other managed funds ! Essentially a hybrid between a listed security and an open-ended fund ! Provide ease of access and the low costs of entry/exit ! Often have an explicit objective/benchmark (e.g. index tracking)
Asset Allocation ! Strategic asset allocation is a benchmark allocation between asset classes (cash, fixed interest, equities, property, alternative investments) ! Investment managers will generally have a range of portfolio weights for each asset class and this allocation depends on the objective of the fund (balanced fund, conservative fund, imputation fund, inflation fund) (a) -
Tactical Asset Allocation Active between asset classes (takes the actual portfolio holdings away from the strategic asset allocation) Managers attempt to exploit temporary mispricing by adjusting exposure to different asset classes Then tactical asset allocation will move between a minimum and maximum bounds on the amounts invested in each asset class
(b) Strategic Asset Allocation - Describes the philosophy underlying the allocation of the portfolio between asset classes to reflect the fund’s objectives - Commit to maintaining the weights to reflect these objectives
FINC3017 Exam Notes
3 Week 2: Investment Decisions under Uncertainty
Choices ! Risk-free assets o Return is certain across all possible states of the world, choice is simply between consumption now/later ! Risky assets o Return is not certain across all possible states, the range of future cash flows will impact on wealth Utility Analysis ! Utility functions provide a means to rank alternatives, to weigh outcomes and their value ! It weighs all outcomes using the expected utility theorem
E[U(W)] = ∑U(W)P(W) W
Comparability
o
An investor is able to state whether they prefer A to B, B to A or if they are indifferent between A and B
Transitivity
o
If an investor prefers A to B and B to C, then the investor must prefer A to C
Independence
! An investor is indifferent between two certain outcomes G and H ! If J is uncertain then they will be indifferent between: o G with probability P and J with probability (1 – P) o H with probability P and J with probability (1 – P)
Certainty Equivalent
! For every gamble there is a value such that the investor will be indifferent between the gamble and a ‘certainty equivalent’
According to theory, an investor prefers W1 to W2 if and only if:
E[U(W1)] > E[U(W2 )] Properties of Utility Functions ! More is preferred to less (non-satiation), first derivative of utility function is positive, U’(W) > 0 ! Adding a constant to a utility function/multiplying utility functions by a constant does not change rankings ! A fair gamble is defined as one where the expected value of the gamble is equal to its cost (risk premium on the risky investment is zero) " a fair gamble is thus a risky investment whose risk premium equals the risk free rate of return/has a zero risk premium (a) Risk Averse Investors o Will reject a fair gamble (they require an appropriate risk premium to accept a risky investment) o Negative second derivative and display a diminishing marginal utility of wealth, U’’(W) < 0 o The expected utility of wealth from the risky investment must be less than the expected utility of wealth from the risk-free investment
E[U(WR )] ≤ E[U(WRF )] = U(WRF ) = U[E(WR )]
E[U(W)] ≠ U[E(W)] E[U(W)] ≤ U[E(W)]
FINC3017 Exam Notes (b) Risk-Neutral Investors o Will be indifferent to a fair gamble and a risk-free investment o The utility function is linear in wealth, the second derivative U’’(W) = 0 o E[U(W)] = U[E(W)]
(c) Risk-Seeking Investors o Will always select a fair gamble, prefer the fair gamble over riskfree investment o Utility function is convex in wealth and the second derivative is positive, U’’(W) > 0 o Risk seekers will pay a premium to take risk Assumption on Investors ! Investors are risk-averse ! Investors maximise their utility of wealth ! Investors prefer more wealth to less wealth ! Investors have diminishing marginal utility of wealth How do we categorise risk aversion? 1. Absolute risk aversion: if amount invested in risky assets increases as wealth increases then investor has decreasing absolute risk aversion (shift in investor preferences in response to wealth) a. Generally assumed that investors exhibit decreasing absolute risk aversion
ARA = A(W) =
- U' ' (W) U' (W)
! The derivative of A(W) indicates how ARA changes as wealth changes 2. Relative risk aversion: how the percentage of wealth invested in risky assets changes as wealth changes a. However, there is no consensus as to how relative risk aversion changes as wealth changes (inconsistent)
RRA = R(W) =
- WU' ' (W) U' (W)
RRA = R(W) = W × ARR Various types of utility functions: log, quadratic, exponential, power (A restricted to be greater than zero)
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FINC3017 Exam Notes
2 Week 1: Introduction
The Investment Funds Industry ! Managed funds fall into a number of categories that pool investor’s funds Unit Trusts
! Investor’s funds are pooled, usually into specific types of assets ! Investors are assigned units in the fund which are typically traded ! Invest in tradeable units, e.g. listed property trusts o Sell a fixed number of units to investors (closed funds) ! An unlisted trust however can issue new units at any time o Value of each unit depends of the value of the underlying investments, open-ended fund (mutual funds)
Superannuation Funds
! Accept and manage contributions from employers and/or employees to provide retirement and income benefits o Globally known as ‘pension funds’ o Managed by life insurance companies, fund administrators, master trusts and pooled trusts (wholesale vehicle) ! Superannuation fund structure: o Defined benefit – the retirement payout is determined based on a formula (risk on fund) o Defined contribution/accumulation fund – value of retirement payout depends on investment contributions in the fund (risk on investor)
Hedge Funds
! Seek to hedge against risky price movements via short selling, arbitrage trading, derivatives, distressed securities, low grade bonds and high leverage portfolios ! Maximise expected return-risk of the portfolio ! Access to hedge funds (as a retail investor) is limited
Exchange Traded Funds (ETFs)
! Listed on the stock market and trade as per any stock unlike other managed funds ! Essentially a hybrid between a listed security and an open-ended fund ! Provide ease of access and the low costs of entry/exit ! Often have an explicit objective/benchmark (e.g. index tracking)
Asset Allocation ! Strategic asset allocation is a benchmark allocation between asset classes (cash, fixed interest, equities, property, alternative investments) ! Investment managers will generally have a range of portfolio weights for each asset class and this allocation depends on the objective of the fund (balanced fund, conservative fund, imputation fund, inflation fund) (a) -
Tactical Asset Allocation Active between asset classes (takes the actual portfolio holdings away from the strategic asset allocation) Managers attempt to exploit temporary mispricing by adjusting exposure to different asset classes Then tactical asset allocation will move between a minimum and maximum bounds on the amounts invested in each asset class
(b) Strategic Asset Allocation - Describes the philosophy underlying the allocation of the portfolio between asset classes to reflect the fund’s objectives - Commit to maintaining the weights to reflect these objectives
FINC3017 Exam Notes
3 Week 2: Investment Decisions under Uncertainty
Choices ! Risk-free assets o Return is certain across all possible states of the world, choice is simply between consumption now/later ! Risky assets o Return is not certain across all possible states, the range of future cash flows will impact on wealth Utility Analysis ! Utility functions provide a means to rank alternatives, to weigh outcomes and their value ! It weighs all outcomes using the expected utility theorem
E[U(W)] = ∑U(W)P(W) W
Comparability
o
An investor is able to state whether they prefer A to B, B to A or if they are indifferent between A and B
Transitivity
o
If an investor prefers A to B and B to C, then the investor must prefer A to C
Independence
! An investor is indifferent between two certain outcomes G and H ! If J is uncertain then they will be indifferent between: o G with probability P and J with probability (1 – P) o H with probability P and J with probability (1 – P)
Certainty Equivalent
! For every gamble there is a value such that the investor will be indifferent between the gamble and a ‘certainty equivalent’
According to theory, an investor prefers W1 to W2 if and only if:
E[U(W1)] > E[U(W2 )] Properties of Utility Functions ! More is preferred to less (non-satiation), first derivative of utility function is positive, U’(W) > 0 ! Adding a constant to a utility function/multiplying utility functions by a constant does not change rankings ! A fair gamble is defined as one where the expected value of the gamble is equal to its cost (risk premium on the risky investment is zero) " a fair gamble is thus a risky investment whose risk premium equals the risk free rate of return/has a zero risk premium (a) Risk Averse Investors o Will reject a fair gamble (they require an appropriate risk premium to accept a risky investment) o Negative second derivative and display a diminishing marginal utility of wealth, U’’(W) < 0 o The expected utility of wealth from the risky investment must be less than the expected utility of wealth from the risk-free investment
E[U(WR )] ≤ E[U(WRF )] = U(WRF ) = U[E(WR )]
E[U(W)] ≠ U[E(W)] E[U(W)] ≤ U[E(W)]
FINC3017 Exam Notes (b) Risk-Neutral Investors o Will be indifferent to a fair gamble and a risk-free investment o The utility function is linear in wealth, the second derivative U’’(W) = 0 o E[U(W)] = U[E(W)]
(c) Risk-Seeking Investors o Will always select a fair gamble, prefer the fair gamble over riskfree investment o Utility function is convex in wealth and the second derivative is positive, U’’(W) > 0 o Risk seekers will pay a premium to take risk Assumption on Investors ! Investors are risk-averse ! Investors maximise their utility of wealth ! Investors prefer more wealth to less wealth ! Investors have diminishing marginal utility of wealth How do we categorise risk aversion? 1. Absolute risk aversion: if amount invested in risky assets increases as wealth increases then investor has decreasing absolute risk aversion (shift in investor preferences in response to wealth) a. Generally assumed that investors exhibit decreasing absolute risk aversion
ARA = A(W) =
- U' ' (W) U' (W)
! The derivative of A(W) indicates how ARA changes as wealth changes 2. Relative risk aversion: how the percentage of wealth invested in risky assets changes as wealth changes a. However, there is no consensus as to how relative risk aversion changes as wealth changes (inconsistent)
RRA = R(W) =
- WU' ' (W) U' (W)
RRA = R(W) = W × ARR Various types of utility functions: log, quadratic, exponential, power (A restricted to be greater than zero)
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