Asset Allocation - Part 2

Marginal Contribution to Total Risk - Formula

Asset Beta Relative to Portfolio * Portfolio Standard Deviation

Absolute Contribution to Total Risk - Formula

Asset Class Weight in Portfolio * MCTR

Risk Parity Approach - Asset Weight Equation

Asset Weight * Covariance of Asset with Portfolio = Portfolio Variance / Number of Assets

Surplus Optimization - Utility Function

Expected Utility for Asset Mix = Expected Surplus Return for Asset Mix - (0.005 * Risk Aversion Coefficient * Expected Variance of Asset Mix * Surplus Return)

Liability-Relative Asset Allocation - Best for Risk-Averse Investors

Hedging/Return-Seeking Approach

Liability-Relative Asset Allocation - Best for Changing Liability

Integrated Asset/Liability Approach

Liability-Relative Asset Allocation - Most Complex and Dynamic

Integrated Asset/Liability Approach

Liability Surplus - Formula

MV of Assets - PV of Liabilities

Funding Ratio - Formula

MV of Assets / PV of Liabilities

Markowitz Objective Function - Investor Utility

Percentage Utility for the Asset Mix = Percentage Expected Return - (0.005 * Risk Aversion Coefficient * Percentage Expected Variance)

Liability-Relative Asset Allocation - Best for a Single Period

Surplus Optimization

Liability-Relative Asset Allocation - Best for any Funded Ratio/Risk Level

Surplus Optimization

Liability-Relative Asset Allocation - Most Basic Approach

Surplus Optimization

Re-Sampled Mean-Variance Optimization - Definition

a combination of regular MVO and a Monte Carlo simulation that improves diversification compared to setting lots of constraints on MVO

60/40 Rule

allocation heuristic where you allocate 60% to stocks and 40% to bonds to get a balance of long-term growth and risk reduction that mimics the global investable portfolio

Endowment Model

allocation model for institutional investors with large allocations to alternatives and lots of active management, making it best for investors with a long time horizon with low cash flow needs

Norway Model

allocation model for smaller investors that focuses on passive management and includes almost exclusively public equities and fixed income and often follows the 60/40 rule

Multistage Simulation Analysis

allows you to set rules that guide the asset and liability portfolios along different scenarios instead of changing multiple variables

Minimum Expectations Approach

approach used with goals-based asset allocation where your goal is to achieve the minimum return expected over a given time horizon based on a minimum required probability of success

Risk Parity Approach - Definition

asset allocation approach that focuses on the belief that each asset should contribute equally to the total risk of the portfolio

Integrated Asset/Liability Approach - Definition

asset allocation approach that uses multiperiod models to adjust assets to reflect a better correlation with a changing liability

Hedging/Return-Seeking Approach - Definition

asset allocation approach where you develop one strategy for hedging the liability and then a separate return-seeking strategy for the surplus

5 Criticisms of Mean-Variance Optimization

asset allocations produced are highly sensitive to small changes in inputs, relies on forecasted inputs for estimations, often results in highly concentrated weightings based on the best risk/reward, doesn't consider other investor constraints like liability payments, reliance on normal distribution makes it unable to consider skewness and kurtosis

3 Benefits of Monte Carlo Simulation

can be run over different time periods, helps reveal investor's true risk tolerance by testing many inputs, can account for portfolio withdrawals and big life events

Markowitz Objective Function - Risk Aversion Coefficient

captures the investor's risk-return tradeoff ranging from 0-10, with 0 being completely risk tolerant, 10 being completely risk averse, and 4 being moderately risk-averse

Tangency Theory to Cash Allocation

cash allocation method based on a combination of the risk-free asset and the tangency portfolio, where leverage can be used to increase risk with more investment in the tangency portfolio or risk can be decreased with more cash

Surplus Optimization - Steps

choose asset classes and time horizon, estimate expected returns and volatilities for asset classes and liabilities based on capital market expectations, factor in investor constraints, use capital market expectations and constraints to estimate the correlation mix, create surplus efficient frontier

Reverse Optimization - Process

establish optimal asset allocation weights from the efficient frontier, use CAPM to find the expected return of each asset class, use market cap weights to solve for a weighted average and get total portfolio expected return

Integrated Asset/Liability Approach - Investor Types

good for banks, hedge funds, and certain insurance companies that have changing liabilities

Hedging/Return-Seeking Approach - Investor Types

good for conservative, non-risk seeing investors with a surplus balance and a fixed liability, such as insurance companies

Efficient Frontier

graph representing a set of portfolios that maximizes expected return at each level of portfolio risk

Optimal Asset Allocation - Risk Budgeting POV

happens when the ratio of excess return to MCTR is the same for all asset classes and matches the Sharpe ratio of the tangency portfolio

120 Minus Your Age Rule

heuristic for equity allocation where you take 120 minus your age to solve for the percentage allocation you should have to equities

Re-Sampled Mean-Variance Optimization - Benefit

improves the quality of inputs by replacing forward-looking estimates with averages from hundreds of thousands of simulations

Hedging/Return-Seeking Approach - Important Tool

inflation-linked bonds are important because they move in value as the liability does with inflation, which helps keep the correlation between the liability and the hedging portfolio close to 1

Reverse Optimization - Criticsm

just like MVO, it is very sensitive to changes in specific inputs, such as individual asset class expected return

Risk Parity Approach - Common Asset Class

leads to a focus on fixed income, as the goal of equalizing standard deviations across asset classes leads to the use of fixed income to help balance risk

Risk Parity Approach - Use of Leverage

leads to a higher use of leverage, as the bias towards fixed income means that leverage needs to be used to gain higher returns

Absolute Contribution to Total Risk (ACTR) - Defintion

measures how much the asset class contributes to portfolio return volatility

Integrated Asset/Liability Approach - Risk Measures

measures of tail risk, such as VaR and CVaR

Reverse Optimization - Definition

process of taking efficient asset allocation weights, covariances, and the risk-aversion coefficient and then solving for an expected return

Corner Portfolios

represent points along the efficient frontier at which the weight for constituents goes from positive to zero, or from zero to positive

Bottom-Up Risk Determination

second approach used with goals-based allocation after the minimum expected return is found so that a discount rate can be calculated to solve for the PV of expected cash flows, which is the amount of money needed to fund a goal

Heuristics

simple guidelines that some investors use to direct their asset allocation strategy

Black-Litterman Model

software that takes the returns in excess of the risk-free rate produced from reverse optimization and alters it to incorporate your own personal views on asset returns

3 Approaches for Liability-Relative Asset Allocation

surplus optimization, hedging/return-seeking approach, integrated asset/liability approach

Surplus Optimization - Definition

the adoption of MVO specifically to generate returns on the surplus assets in a liability relative approach, with a penalty for return volatility

Marginal Contribution to Total Risk (MCTR) - Definition

the amount of incremental risk a security or asset class brings to the overall portfolio

Tangency Portfolio

the portfolio on the efficient frontier with the highest Sharpe ratio

Global Minimum Variance Portfolio

the portfolio on the efficient frontier with the least risk

Re-Sampled Mean-Variance Optimization - Process

use Monte Carlo simulations to estimate lots of capital market expectations and then efficient frontiers, and then create asset allocations from averages of these simulated frontiers

Reverse Optimization - Benefit

use of asset class betas applied to each market risk premium captures a more stable expected return by incorporating global (systematic) risk and increasing diversification

Surplus Return - Formula

(Change in Asset Value - Change in Liability Value) / Initial Asset Value

Ratio of Excess Return to MCTR

(Expected Return - Risk-Free Rate) / MCTR