Combined decks Flashcards
Start
R19
Mean Variance Optimisation
- AO approach
- Assume investors are risk averse.
- Find the optimal point of the efficient frontier
- Identofies the portfolio that maximise returns for a given level of risk.
- Inputs are returns, risk, and pair-wise correlations.
- Find the certainty equivalent rate of return:
Um = E(Rm) − 0.005λσ2
[input E(Rm) and σ2 in whole numbers if using o.oo5]
λ - risk coefficient 1-10, average 4
- Contraints - budget (utility) contraint - all asset class weights must sum to 1
- Contraint - non-negativity contraint - all weights in asset class must be positive. No shorting,
R19
MVO Issues
- The outputs (asset allocations) are highly sensitive to small changes in the inputs.
- The asset allocations tend to be highly concentrated in a subset of the available asset classes.
- Many investors are concerned about more than the mean and variance of returns, the focus of MVO.
- Although the asset allocations may appear diversified across assets, the sources of risk may not be diversified.
- Most portfolios exist to pay for a liability or consumption series, and MVO allocations are not directly connected to what influences the value of the liability or the consumption series.
- MVO is a single-period framework that does not take account of trading/rebalancing costs and taxes.
R19
Black-Litterman
- Focus on constrained models (no shorting, no negative asset weights)
- Generate well diversifed portfolios and incorporates investors own views and their own confidence in their expectations.
- Use reverse optimisation
- Less likely to have asset class concentrated positions
R19
Reverse Optimisation
- MVO solves for optimal asset weights based on expected returns, covariances, and a risk aversion coefficient. Based on predetermined inputs, an optimizer solves for the optimal asset allocation weights. As the name implies, reverse optimization works in the opposite direction. Reverse optimization takes as its inputs a set of asset allocation weights that are assumed to be optimal and, with the additional inputs of covariances and the risk aversion coefficient, solves for expected returns.
R19
Additional Constraints to use with MVO (5)
- Specify a set allocation to a specific asset—for example, 30% to real estate or 45% to human capital. This kind of constraint is typically used when one wants to include a non-tradable asset in the asset allocation decision and optimize around the non-tradable asset.
- Specify an asset allocation range for an asset—for example, the emerging market allocation must be between 5% and 20%. This specification could be used to accommodate a constraint created by an investment policy, or it might reflect the user’s desire to control the output of the optimization.
- Specify an upper limit, due to liquidity considerations, on an alternative asset class, such as private equity or hedge funds.
- Specify the relative allocation of two or more assets—for example, the allocation to emerging market equities must be less than the allocation to developed equities.
- In a liability-relative (or surplus) optimization setting, one can constrain the optimizer to hold one or more assets representing the systematic characteristics of the liability short.
R19
Resampled Mean–Variance Optimization
- Combines Markowitz’s mean–variance optimization framework with Monte Carlo simulation and, all else equal, leads to more-diversified asset allocations. In contrast to reverse optimization, the Black–Litterman model, and constraints, resampled mean–variance optimization is an attempt to build a better optimizer that recognizes that forward-looking inputs are inherently subject to error.
- Uses an average processes and creates an efficient frontier that is more stable than what is got from traditional MVO
- Better diversification
- Lacks sound theoretical basis
- Inputs still based on historical data, therefore might lack relevence to current period.
R19
Monte Carlo
- Addresses limitations of MVO as a single peroid model
- Can incorpoate taxes and rebalancing
- Can be used to see the probably the client will run out of money (longevity risk)
R19
AA liquidity considerations
- Few indices to track illiquid assets
- If there were accurate indexes, there are no low-cost passive investment vehicles to track them.
- Risk / Return for AI can be very different from traditional assets
- Therefore practical options include the following:
- Exclude less liquid asset classes (direct real estate, infrastructure, and private equity) from the asset allocation decision and then consider real estate funds, infrastructure funds, and private equity funds as potential implementation vehicles when fulfilling the target strategic asset allocation.
- Include less liquid asset classes in the asset allocation decision and attempt to model the inputs to represent the specific risk characteristics associated with the likely implementation vehicles.
- Include less liquid asset classes in the asset allocation decision and attempt to model the inputs to represent the highly diversified characteristics associated with the true asset classes.
R19
Risk Budgeting
Marginal contribution to risk (MCTR):
Asset beta relative to portfolio × Portfolio standard deviation
ACTR:
Asset weight in portfolio × MCTR
Ratio of excess return to MCTR:
(Expected return – Risk-free rate)/MCTR
% of risk contributed by positionx:
ACTRx / σp
R19
MCTR / ACTR
MCTR - the rate at which risk would change with a small (or marginal) change in the current weights of asset
ACTR - for an asset class measures how much it contributes to portfolio return volatility
R19
Factor-Based Asset Allocation
- An alternative approach used by some practitioners is to move away from an opportunity set of asset classes to an opportunity set consisting of investment factors.
- Long the overperforming factor, short the underperforming factor
- Typical factors used in asset allocation include size, valuation, momentum, liquidity, duration (term), credit, and volatility.
- Risk and return possibilities are very similar regardless whether implementing MVO using asset classes or factors
R19
Surplus Optimisation
- Liability Relative approach
- Surplus return defined as:
(Change in asset value – Change in liability value)/(Initial asset value)
- Surplus optimization exploits natural hedges that may exist between assets and liabilities as a result of their systematic risk characteristics.
R19
Two portfolio approach
Hedging/Return-Seeking Portfolio Approach
- Liability Relative approach
- Seperate asset (return-seeking portfolio) portfolio and hedging portfolio
- The hedging portfolio must include assets whose returns are driven by the same factor(s) that drive the returns of the liabilities.
- Often used my insurance companies and pension plans
- Limitations
- If funding ratio is <1 then difficult to hedging
- Hedging portfolio might not be able to hedge ALL risks
R19
Integrated Asset-Liability Approach
- Liability Relative approach
- Significant decisions regarding the composition of liabilities made in conjunction with the asset allocation
- Banks, long–short hedge funds (for which short positions constitute liabilities), insurance companies, and re-insurance companies routinely fall into this situation
- Within this category, the liability-relative approaches have several names, including asset–liability management (ALM) for banks and some other investors and dynamic financial analysis (DFA) for insurance companies.
R19
Goals Based Approach
- More useful for individual investors
- The overall portfolio needs to be divided into sub-portfolios to permit each goal to be addressed individually.
- Both taxable and tax-exempt investments are important.
- Probability- and time horizon-adjusted expectations replace the typical use of mathematically expected average returns in determining the appropriate funding cost for the goal (or “discount rate” for future cash flows).
- Use predetermined sub portfolios
- Ensure that there is no “hidden” goal that should be brought out and that the apparently “single” retirement goal is not in fact an aggregation of several elements with different levels of urgency,
- Higher level of business management complexity. They will naturally expect to have a different policy for each client and potentially more than one policy per client. Thus, managing these portfolios day to day and satisfying the usual regulatory requirement that all clients be treated in an equivalent manner can appear to be a major quandary.
R19
Heuristics and Other Approaches to Asset Allocation
- The “120 minus your age” rule for position in equity
- The 60/40 stock/bond heuristic.
- The endowment model - emphasizes large allocations to non-traditional investments than would be recommended by an MVO approach.
- Risk parity - based on the notion that each asset (asset class or risk factor) should contribute equally to the total risk of the portfolio for a portfolio to be well diversified. Only focuses on risk not return. Critics of these back tests (showing good results from this approach) argue that they suffer from look-back bias and are very dependent on the ability to use extremely large amounts of leverage at low borrow rates (which may not have been feasible)
- The 1/N rule.
R18
Life Cycle Balanced Fund
- A target date retirement fund (life cycle balance fund) incorporates human capital with asset allocation
- Human capital generally 30% equity, 70% Fixed Income
R18
Asset Only
- Does not explicitly model liabilities or goals
- Example Mean Variance Optimisation - best to complement with Monte Carlo analysis.
- Maximize Sharpe ratio for acceptable level of volatility
- Liabilities or goals not defined and/or simplicity is important
- Relevant risk measure is the SD of portfolio returns - taking into account asset class volatilites and correlations
Some foundations, endowments
Sovereign wealth funds
Individual investors
R18
Liability relative
- Models legal and quasi-liabilities
- Example Surplus Optimisation
- Fund liabilities and invest excess assets for growth
- Penalty for not meeting liabilities high
- Based on meeting liabilities - focus on institutions
- Relevant risk - not having enough asset in portfolio to cover liabilities. Measure SD of the surplus could be used as the relevant risk measure.
Banks
Defined benefit pensions
Insurers
R18
Goals based
- Achieve goals with specified required probabilities of success
- Individual investors
- Each sub portfolio has unique asset allocation depending on goal
- Based on meeting liabilities - focus on individual
- Risk - not being able to achieve the stated goals. Probablity of meeting goals.
R18
Asset Class Criteria (5)
- Assets within an asset class should be relatively homogeneous. Assets within an asset class should have similar attributes. In the example just given, defining equities to include both real estate and common stock would result in a non-homogeneous asset class.
- Asset classes should be mutually exclusive. Overlapping asset classes will reduce the effectiveness of strategic asset allocation in controlling risk and could introduce problems in developing asset class return expectations. For example, if one asset class for a US investor is domestic common equities, then world equities ex-US is more appropriate as another asset class rather than global equities, which include US equities.
- Asset classes should be diversifying. For risk control purposes, an included asset class should not have extremely high expected correlations with other asset classes or with a linear combination of other asset classes. Otherwise, the included asset class will be effectively redundant in a portfolio because it will duplicate risk exposures already present. In general, a pairwise correlation above 0.95 is undesirable (given a sufficient number of observations to have confidence in the correlation estimate).
- The asset classes as a group should make up a preponderance of world investable wealth. From the perspective of portfolio theory, selecting an asset allocation from a group of asset classes satisfying this criterion should tend to increase expected return for a given level of risk. Furthermore, the inclusion of more markets expands the opportunities for applying active investment strategies, assuming the decision to invest actively has been made. However, such factors as regulatory restrictions on investments and government-imposed limitations on investment by foreigners may limit the asset classes an investor can invest in.
- Asset classes selected for investment should have the capacity to absorb a meaningful proportion of an investor’s portfolio. Liquidity and transaction costs are both significant considerations. If liquidity and expected transaction costs for an investment of a size meaningful for an investor are unfavorable, an asset class may not be practically suitable for investment.
R18
SAA (9 Steps)
- Determine and quantify the investor’s objectives.
- Determine the investor’s risk tolerance and how risk should be expressed and measured.
- Determine the investment horizon(s).
- Determine other constraints and the requirements they impose on asset allocation choices. What is the tax status of the investor? Should assets be managed with consideration given to ESG issues? Are there any legal and regulatory factors that need to be considered? Are any political sensitivities relevant? Are there any other constraints that the investor has imposed in the IPS and other communications?
- Determine the approach to asset allocation that is most suitable for the investor.
- Specify asset classes, and develop a set of capital market expectations for the specified asset classes.
- Develop a range of potential asset allocation choices for consideration. These choices are often developed through optimization exercises.
- Test the robustness of the potential choices. This testing often involves conducting simulations to evaluate potential results in relation to investment objectives and risk tolerance over appropriate planning horizon(s) for the different asset allocations developed in Step 7. The sensitivity of the outcomes to changes in capital market expectations is also tested.
- Iterate back to Step 7 until an appropriate and agreed-on asset allocation is constructed
R18
Global Market Portfolio
- Global Market Portfolio is tangency portfolio
- The weights of the assets in the Global Market Portfolio can be adjusted up or down.
- Some assets can be difficult to invest in (e.g. residential real estate or private equity) so will use a proxy e.g. ETF’s