Investment and Portfolio Management. Lecture 1: Managed funds fall into a number of categories that pool investors funds

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1 Lecture 1: Managed funds fall into a number of categories that pool investors funds Types of managed funds: Unit trusts Investors funds are pooled, usually into specific types of assets Investors are assigned units in the fund which are typically traded o Closed in/listed: Sell a fixed number of units to investors o Open ended/unlisted: Can issue new units at any time, the value of which depends on the value of the underlying investments Superannuation funds (pension funds) Accept and manage contributions from employers and/or employees to provide retirement income benefits Superannuation fund structure two types: Defined benefit (employer takes on risk if the fund is not performing well, the employer must still contribute the defined benefit) o The retirement payout is determined based on a formula Defined contribution (employee takes the risk ie whether the fund will pay out well at time of retirement due to stability in markets) o Also termed accumulation funds o Value of retirement payout depends on investments of contributions in the fund Hedge funds Hedge funds seek to hedge against risk price movements via short selling, arbitrage trading, derivatives, distressed securities, low-grade bonds and high leverage portfolios so as to maximize the expected return-risk of the portfolio Access to hedge funds is limited Exchange traded funds Are listed on the stock market Trade as per any stock, throughout the day, unlike other managed funds Are essentially a hybrid between a listed security and an open-ended fund Provide ease of access and low costs of entry and exit Often have explicit objective and benchmark (eg. index tracking) Asset allocation Strategic asset allocation is a benchmark allocation between asset classes (Investment managers will generally have a range of aim portfolio weights for each asset class for the long term) o This allocation depends on the objective of the fund Balanced funds, conservative funds (more fixed income), imputation funds, inflation funds o Asset classes include: Cash Page 1 of 76

2 Fixed interest Property Alternative investments Equity Tactical asset allocation is active between asset classes, when actual portfolio deviates from strategy it takes the actual portfolio holdings away from the strategic asset allocation in the short term o Ie How overweight or underweight a financial manager is in their asset allocation from their benchmarks o Managers attempt to exploit temporary mispricing by adjusting exposure to different asset classes Lecture 2: Choices Risk free assets: o Return is certain across all possible states of the world o Choice is simply between consumption now and later Risky assets o Return is not certain across all possible states of the world o The range of possible future cash flows will impact on wealth Utility analysis Utility functions provide a means to rank alternatives so they can decide o How one chooses the amount to invest in risky assets o How one weights outcomes Investors will choose a combination to maximise expected utility (expected utility theory), based on past performance (among other things) An investor prefers W 1 to W 2 if and only if: E[U(W 1 )] > E[U(W 2 )] o Where U(W i ) is an appropriate individual-specific utility function Axioms of expected utility theory Comparability 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 If an investor prefers A to B and B to C, then the investor prefers A to C Independence An investor is indifferent between two certain outcomes G and H If you introduce something new J where J is uncertain (with probability (1 P)), then an investors preferences will remain indifferent between: o G with probability P and J with probability (1-P) Page 2 of 76

3 o H with probability P and J with probability (1-P) Ie, if something else comes along, it does not change original preferences Certainty equivalent A certain outcome that gives you the same utility as the expected utility of a risky outcome Steps to calculate Expected Utility 1. Determine outcome for each i (W i ) 2. Calculate the function for each i (U(W i )) 3. Multiply by each probability (P = P i ) n 4. Sum together i=1 U(W i )P i 5. Compare to other assets Properties of utility functions More is preferred to less (non-satiated) o This means the first derivative of utility function is positive U W o Additionally, suppose there are two (certain) risk-free investments, one with outcome W 1 dollars, and the other with outcome W 2 dollars. If W 1 >W 2, then U du W dw W U 1 W 2 0 Adding a constant to a utility function or multiplying utility functions by a constant does not change rankings o The same investment is selected Fair gamble A fair gamble is: o A risky investment whose expected return equals the risk-free rate of return o Or, a risky investment which has zero risk premium (makes a return at the risk-free rate) Risk averse investors would hence prefer the non-risky alternative (as it provides the same EV) Types of investors Risk-averse investor Will reject a fair gamble o They require an appropriate risk premium to accept a risky investment o The expected utility of wealth from risky investments must be less than the expected utility of wealth from the risk-free investment E[U(W R )] E[U(W RF )] U(W RF ) U[E(W R )] Page 3 of 76

4 Note: Utility function means that equivalent expected wealth may not produce equivalent utilities: E[U(W)] U[E(W)] Risk-aversion implies second derivative is negative o Utility is concave in wealth Diminishing marginal utility of wealth o Utility from an additional dollar of wealth declines as wealth increases 2 d U W U W 2 dw Certainty equivalent wealth (CEQ) is the indifference point o Ie, how much a risk averse investor values the risky gamble in risk free terms (steps: Calculate utility from risky gamble = A, and then do A = U(W) and then reverse the utility to get to W for certainty equivalent wealth) o Utility of gamble minus CEQ = risk premium required for gamble Note: If risk premium is larger than CEQ risk premium, they will take risk free, if it is smaller, they will take risky 0 Risk-neutral investors Risk-neutral investors will be indifferent to a fair gamble o Indifferent between a fair gamble and a risk-free investment The utility function is linear in wealth The second derivative of the utility function is zero U' '( W ) 0 Page 4 of 76

5 Risk seeking investor Risk seeking investor will select a fair gamble o Prefer the fair gamble over the risk-free investment The utility function is convex in wealth The second derivative is positive U' '( W 0 Risk seeking investors will pay a premium to take risk ) Page 5 of 76

6 Key assumptions for this course Assume investors: Are risk averse Maximise their expected utility of wealth Prefer more wealth to less (U (W)>0) Have diminishing marginal utility of wealth (U (W)<0) Absolute risk aversion Shifts in investor preferences in response to wealth If amount invested in risky assets increases as wealth increases then investor has decreasing absolute risk aversion ARA A(W) -U''(W) U'(W) The derivative of ARA with respect to wealth indicates how absolute risk aversion changes as wealth changes o Decreasing A (W)<0, Constant A (W)=0, Increasing A (W)>0 Generally assumed that investors exhibit decreasing absolute risk aversion Relative risk aversion How the percentage of wealth invested in risky assets change as wealth changes RRA R(W) - WU' '(W) U'(W) RRA R(W) W ARA Derivative of R(W) with respect to wealth indicates how relative risk aversion changes as wealth changes o Decreasing R (W)<0, Constant R (W)=0, Increasing R (W)>0 No consensus on how relative risk aversion changes as wealth changes Page 6 of 76

7 Types of utility functions (typically for risk averse investors) Note: Log utility functions exhibit Decreasing ARA Constant RRA Quadratic utility functions exhibit: Increasing ARA Increasing RRA Exponential utility functions exhibit: Constant ARA Increasing RRA From wealth to mean-variance Investor preferences The use of expected return and standard deviation is appropriate to approximate investor preferences when one of two conditions is satisfied: o If distribution of expected returns is normal Investments can be ranked according to risk and return o When utility functions are quadratic Expected utility is determined by expected wealth and standard deviation of expected wealth Australian data suggests that equity returns are not normal Page 7 of 76