Asset Allocation

• Asset Risks
  • Three Super-Classes of Risks
  • VaR
    • Advantages of VaR
    • Disadvantages of VaR
  • Optimal Choice Between One Risky Asset and Risk Free Asset
  • Risk Budgeting
• Implementation Choices
• Approaches to Asset Allocation
  • Mean Variance Optimization
    • Utility Function
    • Risk of MVO Portfolio Combined with RF Asset
    • Criticism of MVO
    • Alternative Models
      • Criticisms of resampling
  • Surplus Optimization
  • Hedging/Return-Seeking Portfolio Approach
  • Integrated Asset-Liability Approach
  • Risk Parity
• Tax Consideration
• Strategies to Overcome Behavior Biases in Asset Allocation
  • Loss Aversion
  • Illusion of Control
  • Mental Accounting
  • Representativeness Bias
  • Framing Bias
  • Availability Bias
• Optimal Width of Corridor
• Illiquidity Premium

Asset Risks

Three Super-Classes of Risks

• Capital Assets
• Consumable/transformable Assets
• Store of Value of Assets

VaR

A 100 million portfolio has a 1.37% VaR at the 5% probability over one week means that over one week, the portfolio could lose 1.37% of 100 million or 1.37 million. There is a 5% chance that more than this will be lost and a 95% chance that less than this will be lost.

Advantages of VaR

• It has become the industry standard for risk measurement and is required by many regulators.
• It aggregates all risk into one single, easy to understand number.
• It can be used in capital allocation.

Disadvantages of VaR

• Some of the methods (Monte Carlo) are difficult and expensive.
• The different computation methods can generate different estimates of VaR.
• It can generate a false sense of security. It is only as good as the inputs and estimation process. Even when done correctly it is probabilistic; things can always be worse.
• It is one-sided, focusing on the left tail in the return distribution, and ignores any upside potential.

Optimal Choice Between One Risky Asset and Risk Free Asset

w* =1/λ * (μ−r_f/σ^2) λ: investor’s risk aversion

Risk Budgeting

• Objective: specifies the total amount of risk and how much of risk should be budgeted for each asset class
• Marginal Contribution to Total Risk (MCTR) = beta * portfolio volatility
• Absolute Contribution to Total Risk (ACTR) = weight * MCTR
• An optimal asset allocation is when the ratio of excess return to MCTR is the same for all assets and matches the Sharpe ratio of the tangency portfolio

Implementation Choices

• Whether to allow deviations from the strategic allocation
  • Tactical asset allocation: deliberation short term deviation from the strategic asset allocation
  • Dynamic asset allocation: deliberation long term deviation from the strategic asset allocation
• Invest along the active/passive spectrum

Approaches to Asset Allocation

• Asset-only
  • Mean variance optimization
• Liability-relative
  • Surplus optimization
  • Hedging/Return-Seeking Portfolio Approach
• Goals-based

Mean Variance Optimization

Utility Function

U = E(R) - 0.005 * λ * σ^2 where λ = the investor’s risk aversion coefficient

Risk of MVO Portfolio Combined with RF Asset

Risk of MVO portfolio combined with rf asset = risky asset standard deviation * (1 - rf asset weight)

Criticism of MVO

• Outputs are highly sensitive to small changes in inputs; typically more sensitive to expected return estimates than estimates of volatilities and correlations.
• Investors are concerned more than just mean and variance of return
• Does not take into account of trading costs and taxes
• Efficient portfolios are highly concentrated in a subset of the available asset classes

Alternative Models

• Reverse MVO: can be used to estimate expected returns for use in a forward-looking optimization
• Black-Litterman Model: enables investors to combine their unique forecasts of expected returns with reverse-optimized returns in an elegant manner.
• Constrained asset class weights
• Resampled MVO = MVO + Monte Carlo Simulation

Criticisms of resampling

• Some frontiers have concave “bumps” where expected return decreases as expected risk increases
• The “riskier” asset allocations are over-diversified
• The asset allocations inherit the estimation errors in the original inputs
• The approach lacks a foundation in theory

Surplus Optimization

Use MVO to determine an efficient frontier based on the surplus with its volatility as measure of risk

U = E(R) - 0.005 * λ * σ^2 where E(R) = surplus return = (Δ in asset value - Δ in liability value) / Initial asset value σ^2 = variance of surplus return

Hedging/Return-Seeking Portfolio Approach

• Assumes both linear and nonlinear correlation between assets and liabilities
• Requires positive funded ratio
• Single period model

Integrated Asset-Liability Approach

• Assumes both linear and nonlinear correlation between assets and liabilities
• Can apply to any funded ratio
• Multi period model

Risk Parity

• Each asset (asset class or risk factor) should contribute equally to the total risk of the portfolio
• weight × Cov(ri,rP) = 1/n * σ^2

Tax Consideration

• after-tax standard deviation = pre-tax standard deviation * (1-t)
• Tax Advantage Retirement Account = Investment grade bonds, high yield bond, dividend income stock, total return (capital gain) stock

Strategies to Overcome Behavior Biases in Asset Allocation

Loss Aversion

• Frame risk in terms of shortfall probability
• Fund high-priority goals with low risk assets

Illusion of Control

• Use global market portfolio as the starting point in developing asset allocation
• A formal asset allocation process that employs long-term return and risk forecasts, optimization constraints anchored around asset class weights in the global market portfolio, and strict policy ranges

Mental Accounting

• Goals-based investing by aligning each goal with a discrete sub-portfolio, and the investor can specify the acceptable level of risk for each goal.
• Assign the concentrated stock position to an aspirational goal—one that the client would like to achieve but to which he or she is willing to assign a lower probability of success.

Representativeness Bias

• A formal asset allocation policy with pre-specified allowable ranges
• A strong governance framework with the appropriate level of expertise and well-documented investment beliefs

Framing Bias

• Use alternative risk measurement such as VaR and Conditional VaR
  • VaR: the minimum loss that would be expected a certain percentage of the time over a certain period of time given the assumed market conditions.
  • CVaR: the probability-weighted average of losses when the VaR threshold is breached.
  • Shortfall Proability
• Present the possible asset allocation choices with multiple perspectives on the risk/reward trade-off.

Availability Bias

• A formal asset allocation process using the global market portfolio as the starting point for asset allocation modeling
• A strong governance framework with the appropriate level of expertise and well-documented investment beliefs

Optimal Width of Corridor

Illiquidity Premium

• Expected compensation for the additional risk of tying up capital for a potentially uncertain time period.
• Illiquidity premium equals the value of a put option with an exercise price equal to the hypothetical “marketable price” of the illiquid asset as estimated at the time of purchase.