R19 Principles of Asset Allocation

Question 1

R19

Mean Variance Optimisation

Answer 1

• 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} σ^{2 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,

Question 2

R19

MVO Issues

Answer 2

• 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.

Question 3

R19

Black-Litterman

Answer 3

• 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

Question 4

R19

Reverse Optimisation

Answer 4

• 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.

Question 5

R19

Additional Constraints to use with MVO (5)

Answer 5

1. 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.
2. 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.
3. Specify an upper limit, due to liquidity considerations, on an alternative asset class, such as private equity or hedge funds.
4. 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.
5. 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.

Question 6

R19

Resampled Mean–Variance Optimization

Answer 6

• 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.

Question 7

R19

Monte Carlo

Answer 7

• 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)

Question 8

R19

AA liquidity considerations

Answer 8

• 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:

1. 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.
2. 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.
3. 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.

Question 9

R19

Risk Budgeting

Answer 9

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 position_x:

ACTR_x / σ_p

Question 10

R19

MCTR / ACTR

Answer 10

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

Question 11

R19

Factor-Based Asset Allocation

Answer 11

• 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

Question 12

R19

Surplus Optimisation

Answer 12

• 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.

Question 13

R19

Two portfolio approach

Hedging/Return-Seeking Portfolio Approach

Answer 13

• 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

1. If funding ratio is <1 then difficult to hedging
2. Hedging portfolio might not be able to hedge ALL risks

Question 14

R19

Integrated Asset-Liability Approach

Answer 14

• 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.

Question 15

R19

Goals Based Approach

Answer 15

• 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.

Question 16

R19

Heuristics and Other Approaches to Asset Allocation

Answer 16

• 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.