Tiêu đề LM4 Principles of Asset Allocation IFT Notes.pdf ✅

LM4 Principles of Asset Allocation 2024 Level III Notes © IFT. All rights reserved 1 LM4 Principles of Asset Allocation 1. Introduction .......................................................................................................................................................3 2. Asset-Only Asset Allocations and Mean-Variance Optimization ...................................................3 Mean-Variance Optimization: Overview................................................................................................3 3. Monte Carlo Simulation .............................................................................................................................. 11 4. Criticisms of Mean-Variance Optimization (MVO)........................................................................... 14 5. Addressing the Criticisms of Mean-Variance Optimization.......................................................... 14 Reverse Optimization ................................................................................................................................. 14 Black–Litterman Model.............................................................................................................................. 15 6. Adding Constraints Beyond Budget Constraints, Resampled Mean-Variance Optimizations and Other Non-Normal Optimization Approaches.................................................. 15 Resampled Mean-Variance Optimization ........................................................................................... 16 Other Non-Normal Optimization Approaches .................................................................................. 17 7. Allocating to Less Liquid Asset Classes................................................................................................. 20 8. Risk Budgeting................................................................................................................................................ 20 9. Factor-Based Asset Allocation.................................................................................................................. 22 10. Developing Liability-Relative Asset Allocations and Characterizing the Liabilities......... 22 Characterizing the Liabilities................................................................................................................... 22 11. Approaches to Liability-Relative Asset Allocation; and Surplus Optimization .................. 24 Surplus Optimization.................................................................................................................................. 24 12. Approaches to Liability-Relative Asset Allocation......................................................................... 28 Hedging/Return-Seeking Portfolio Approach................................................................................... 28 Integrated Asset–Liability Approach.................................................................................................... 30 Comparing the Approaches ...................................................................................................................... 30 13. Examining the Robustness of Asset Allocation Alternatives ..................................................... 31 14. Factor Modeling in Liability-Relative Approaches ........................................................................ 32 15. Developing Goals-Based Asset Allocations....................................................................................... 32 The Goals-Based Asset Allocation Process ......................................................................................... 32 Describing Client Goals .............................................................................................................................. 33 16. Constructing Sub-Portfolios and the Overall Portfolio ................................................................ 35 The Overall Portfolio................................................................................................................................... 38

LM4 Principles of Asset Allocation 2024 Level III Notes © IFT. All rights reserved 3 1. Introduction This reading expands on the previous reading "Introduction to Asset Allocation" by focusing on the fundamental principles of asset allocation. In this reading, we will cover: • Developing asset-only asset allocations • Developing liability-relative asset allocations • Developing goals-based asset allocations • Heuristics and other approaches to asset allocation • Portfolio rebalancing in practice 2. Asset-Only Asset Allocations and Mean-Variance Optimization The goal of the 'asset-only' approach to asset allocation is to create the most efficient combination of asset classes in the absence of any liabilities. The mean-variance optimization technique is commonly used in this approach. Mean-Variance Optimization: Overview Under the mean-variance optimization (MVO) approach, when assets are not perfectly correlated, they can be combined such that the portfolio risk is less than the weighted average risk of assets themselves. In other words, the MVO approach focuses on the impact of an asset on portfolio risk rather than the risk of the asset itself. Mean-variance optimization is based on three sets of inputs: returns, risks (standard deviations), and pair-wise correlations for the assets in the opportunity set. MVO provides a framework for determining how much to allocate to each asset to maximize the portfolio’s expected return at a given level of risk. We can also say that MVO is a risk budgeting tool that helps investors spend their risk budget wisely. Objective Function The MVO approach assumes that the investor’s goal is to maximize his utility function, where the utility is given by the following objective function: Um = E (Rm) − 0.005λσm 2 where: Um = the investor’s utility for asset mix (allocation) m E(Rm) = the expected return for asset mix m λ = the investor’s risk aversion coefficient σ2m = the expected variance of return for asset mix m A few important points to note about the risk aversion coefficient (λ): • λ is investor specific and depends on two things - the willingness to take risk and the ability to take risk.
LM4 Principles of Asset Allocation 2024 Level III Notes © IFT. All rights reserved 4 • The value of λ lies between 1 and 10. The larger the value of λ, the greater the risk- aversion. o λ = 0 means the investor is risk-neutral ➔ implying that utility solely depends on the expected return. o λ = 4, means the investor is moderately risk-averse. o λ = 10, means the investor is extremely risk-averse. • Risk aversion is inversely related to risk tolerance. Instructor’s Note: In the above equation, we use 0.005 when E(Rm) and σm are expressed as percentages rather than as decimals. If those quantities are expressed as decimals, then we use 0.5. Example: The expected return of a given asset mix is 10% and the expected standard deviation is 20%. What is the utility of this asset mix for an investor with a risk aversion coefficient of 2? Solution: Um = E (Rm) − 0.005λσm 2 Um = 10 – 0.005 x 2 x 202 = 6% According to the utility function, utility is enhanced by high expected returns and diminished by high risk. In other words, a risk-averse investor “penalizes” the expected rate of return of a risky portfolio by a certain percentage to account for the risk involved. That is, the greater the risk the investor perceives, the larger the risk aversion co-efficient, the larger the penalization, and consequently, the more conservative asset allocation will be. Under the mean–variance optimization model, we create the minimum variance frontier, which is the set of portfolios with the lowest risk for a given level of return. From this set, the efficient frontier, the portfolio with the highest return for a given level of risk is identified. Once the investor identifies the efficient frontier, the goal is to identify the portfolio with the risk that best fits their preferences. Exhibit 2 given below shows a base case of the efficient frontier. The horizontal axis has standard deviation in % while vertical axis has an expected return in %. • The efficient frontier line gives us the most efficient portfolio for any given level of risk. That portfolio will have a certain weightage of different asset classes that we will have in our opportunity set. • The efficient mix at the far left of the frontier with the lowest risk is referred to as the global minimum variance portfolio, while the portfolio at the far right of the frontier is the maximum expected return portfolio.