CFA 2018 r17 principles of asset allocation

Based only on Goddard’s risk-adjusted expected returns for the asset allocations, which asset allocation would she prefer?. Portfolio Number Expected Nominal Returns Standard Deviation

Level III

Principles of Asset Allocation

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Contents and Introduction

1 Introduction

2 Developing Asset-Only Asset Allocations

3 Developing Liability-Relative Asset Allocations

4 Developing Goals-Based Asset Allocations

5 Heuristics and Other Approaches to Asset Allocation

6 Portfolio Rebalancing in Practice

2 Developing Asset-Only Asset Allocations

1 Mean–Variance Optimization: Overview

2 Monte Carlo Simulation

3 Criticisms of Mean–Variance Optimization

4 Addressing the Criticisms of Mean–Variance Optimization

5 Allocating to Less Liquid Asset Classes

6 Risk Budgeting

7 Factor-Based Asset Allocation

2.1 Mean–Variance Optimization: Overview

When assets are not perfectly

correlated they can be combined such

that portfolio risk is less than weighted

average risk of assets themselves

Focus on asset’s impact on portfolio

risk, not the risk of the asset itself

ReturnsRisksCorrelations

Mean-variance optimization (MVO) provides a framework for determining how much to

allocate to each asset in order to maximize portfolio’s expected return at a given level of risk

“MVO is a risk budgeting tool which helps

investors spend their risk budget wisely”

Exhibit 1: Hypothetical UK-Based Investor’s Opportunity Set with Expected Returns, Standard Deviations, and Correlations

Exhibit 3: Efficient Frontier Asset Allocation Area Graph—Base Case

Example 1: Mean–Variance-Efficient Portfolio Choice 1

An investment adviser is counseling Aimée Goddard, a client who recently inherited €1,200,000 and who has

above-average risk tolerance (λ = 2) Because Goddard is young and one of her goals is to fund a comfortable

retirement, she wants to earn returns that will outpace inflation in the long term Goddard expects to liquidate

€60,000 of the inherited portfolio in 12 months to fund the down payment on a house She states that it is

important for her to be able to take out the €60,000 without invading the initial capital of €1,200,000 Exhibit 4 shows three alternative strategic asset allocations.

Asset

Allocation

Expected Return

1 Based only on Goddard’s risk-adjusted expected returns for the

asset allocations, which asset allocation would she prefer?

2 Recommend and justify a strategic asset allocation for Goddard.

Determining Allocation to Cash

• Include cash among assets for which efficient frontier is constructed

• Separate cash from risky assets; define efficient frontier based on ‘risky’ assets

▪ Tangency portfolio

▪ Two fund separation

Example 2: A Strategic Asset Allocation Based on Distinguishing

a Nominal Risk-Free Asset

The Cafastani Foundation for the Fine Arts (CFFA) is a hypothetical charitable organization established to provide funding to Cafastani museums for their art acquisition programs.

CFFA’s overall investment objective is to maintain its portfolio’s real purchasing power after distributions CFFA targets a 4% annual distribution of assets CFFA has the following current specific investment policies.

Return objective

CFFA’s assets shall be invested with the objective of earning an average nominal 6.5% annual return This level

reflects a spending rate of 4%, an expected inflation rate of 2%, and a 40 bp cost of earning investment returns The calculation is (1.04)(1.02)(1.004) – 1 = 0.065, or 6.5%.

Risk considerations

CFFA’s assets shall be invested to minimize the level of standard deviation of return subject to satisfying the

expected return objective.

The investment office of CFFA distinguishes a nominally free asset As of the date of the optimization, the free rate is determined to be 2.2%.

risk-Exhibit 5 gives key outputs from a mean–variance optimization in which asset class weights are constrained to be

Portfolio

Number Expected Nominal Returns

Standard Deviation

Sharpe Ratio

Based only on the facts given, determine the most appropriate strategic asset allocation for CFFA given its stated investment policies.

Asset Allocation and Economic Balance Sheet

Emma Beel is a 45-year-old tenured

university professor in London Capital

market assumptions are as before (see

Exhibit 1) Beel has GBP 1,500,000 in liquid

financial assets, largely due to a

best-selling book Her employment as a tenured

university professor is viewed as very

secure and produces cash flows that

resemble those of a very large,

inflation-adjusted, long-duration bond portfolio The

net present value of her human capital is

estimated at GBP 500,000 Beel inherited

her grandmother’s home on the edge of

the city, valued at GBP 750,000

2.2 Monte Carlo Simulation

• Monte Carlo simulation complements MVO

▪ Handles multiple periods

▪ Realistic picture of potential future outcomes

▪ Impact of trading, rebalancing and tax costs

• Monte Carlo simulation is particularly important when there cash inflows/outflows and returns vary over time

Example 3: Monte Carlo Simulation for a Retirement Portfolio

with a Proposed Asset Allocation

Malala Ali, a resident of the hypothetical country of Cafastan, has sought the advice of an investment adviser concerning her retirement portfolio At the end of 2017, she is 65 years old and holds a portfolio valued at CAF$1 million Ali would like to

withdraw CAF$40,000 a year to supplement the corporate pension she has begun to receive Given her health and family history, Ali believes she should plan for a retirement lasting 25 years She is also concerned about passing along a portion of her portfolio

to the families of her three children; she hopes that at least the portfolio’s current real value can go to them Consulting with her adviser, Ali has expressed this desire quantitatively: She wants the median value of her bequest to her children to be no less than her portfolio’s current value of CAF$1 million in real terms The median is the 50th percentile outcome The asset allocation of her retirement portfolio is currently 50/50 Cafastani equities/Cafastani intermediate-term government bonds Ali and her adviser have decided on the following set of capital market expectations

Asset Class Expected Return Standard Deviation of Return

Exhibit 9: Monte Carlo Simulation of Ending Real Wealth with Annual Cash Outflows

2.3 Criticisms of Mean–Variance Optimization

1 The outputs (asset allocations) are highly sensitive to small changes in the inputs

2 The asset allocations tend to be highly concentrated in a subset of the available asset classes

3 Many investors are concerned about more than the mean and variance of returns, the focus of

MVO

4 Although the asset allocations may appear diversified across assets, the sources of risk may not be

diversified

5 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

6 MVO is a single-period framework that does not take account of trading/rebalancing costs and

taxes

Impact on portfolio weights when there is small change in inputs

Expected return of Asia Pacific Ex Japan changed from 8.5% to 9.0% and expected return of Europe ex UK equities changed from 8.6% to 8.1%

2.4 Addressing the Criticisms of Mean–Variance Optimization

Quality of inputs can be improved by using reverse optimization

Asset class returns risks, correlations Mean Variance Optimization

Reverse Optimization

Investment opportunity set

Global market portfolio

Risk aversion

Asset class returns

Asset class risks, correlations and risk tolerance

Investors can provide their views/forecasts as absolute return

Adding Constraints Beyond the Budget Constraint

Standard constraints used in mean-variance optimization

• Budget (unity) constraint: sum of asset class weights = 1

• Non-negativity constraint

Other possible constraints:

1 Specify a set allocation to a specific asset

2 Specify an asset allocation range for an asset

3 Specify an upper limit, due to liquidity considerations

4 Specify the relative allocation of two or more assets

5 Hold one or more assets representing the systematic characteristics of the liability short

Additional constraints used to:

1) Incorporate real-world constraints 2) Overcome shortcomings of MVO

Good constraints:

1) model the actual circumstances

Resampled Mean-Variance Optimization

• Resampled MVO combines MVO

with Monte Carlo simulation

• Leads to more diversified asset

allocation

• Recognizes that forward looking

estimates are inherently subject

Asset allocations (portfolio weights) from simulated frontiers are saved and averaged.

Coupled with starting CME

Resampled Efficient Frontier

Other Non-Normal Optimization Approaches

• MVO focuses on mean and variance while investors might also be concerned about skewness and kurtosis

• Asset returns are not normally distributed

▪ Extreme returns occur 10 times more frequently than what the normal distribution would

suggest

▪ Pain of loss is about twice as significant as joy from equivalent gain

Key Non-Normal Frameworks

Mean–semivariance optimization

Mean–conditional value-at-risk optimization

Mean–variance-skewness optimization

Example 4: Problems in Mean–Variance Optimization (1/3)

In a presentation to US-based investment clients on asset allocation, the results of two asset allocation exercises are shown, as presented in Exhibit 18 There are a total of 9 asset classes

Based on mean–variance analysis, what is the asset allocation that would most likely

be selected by a risk-neutral investor?

Based only on the information that can be inferred from Panel A, discuss the

investment characteristics of non-US developed market equity (NUSD) in efficient portfolios.

Critique the efficient asset mixes represented in Panel A.

Example 4: Problems in Mean–Variance Optimization (2/3)

Compare the asset allocations shown in Panel A with the corresponding asset allocations shown in Panel B

Example 4: Problems in Mean–Variance Optimization (3/3)

Identify three techniques that the asset allocations in Panel B might have incorporated to improve the characteristics relative to those of Panel A

2.5 Allocating to Less Liquid Asset Classes

Less liquid asset classes include direct real estate, infrastructure and private equity; offer illiquidity

return premium

Two major problems associated with less liquid asset classes:

• Lack of accurate indexes  challenging to make capital market assumptions

• Difficult to diversity and no low-cost passive investment vehicles

Practical options of investing in less liquid assets:

• Exclude less liquid asset classes; then consider real estate funds, infrastructure funds, and private equity funds

• Include less liquid asset classes in the asset allocation decision and model the specific risk

characteristics associated with the implementation vehicles

• Include less liquid asset classes in the asset allocation decision and model the inputs to represent

2.6 Risk Budgeting

The goal of risk budgeting is to maximize return per unit of risk

Three aspects of risk budgeting:

1 The risk budget identifies the total amount of risk and allocates the risk to a portfolio’s

constituent parts

2 An optimal risk budget allocates risk efficiently

3 The process of finding the optimal risk budget is risk budgeting

Marginal contribution to total risk (MCTR) = rate at which risk changes with a small change in the

current weights = (Beta of asset class i with respect to portfolio) x (Portfolio return volatility)

Absolute contribution to total risk (ACTR) = amount asset class contributes to portfolio return volatility

= (Weighti)(MCTRi)

Asset allocation is optimal from a risk-budgeting perspective when the ratio of excess return (over the risk-free rate) to MCTR is the same for all assets and matches the Sharpe ratio of the tangency portfolio

Marginal contribution to risk (MCTR): Asset beta relative to portfolio × Portfolio standard deviation

For UK large-cap, beta = 1.0289 and portfolio standard deviation = 10.876

Asset Class Weight MCTR ACTR

Percent Contribution to Total Standard Deviation

Ratio of Excess Return to

Example 5: Risk Budgeting in Asset Allocation

1 Describe the objective of risk budgeting in asset allocation.

2 Consider two asset classes, A and B Asset class A has two times the weight of B in

the portfolio Under what condition would B have a larger ACTR than A?

3 When is an asset allocation optimal from a risk-budgeting perspective?

2.7 Factor-Based Asset Allocation

Investment opportunity set can consist of investment factors

• Factors are based on observed market premiums and anomalies

• Factors used in asset allocation include: market exposure, size, valuation, momentum, liquidity,

duration (term), credit, and volatility

Factor/Asset Class Factor Definition

Compound Annual Factor Return

Standard Deviation

Total Return

Standard Deviation

Market Total market return – Cash 7.49% 16.56% 12.97 17.33

Duration Long Treasury bonds – Treasury bills 4.56 11.29 9.91 11.93

…

Asset allocation should be performed in a space (risk factors or asset classes) where one is best

positioned to make capital market assumptions

3 Developing Liability-Relative Asset Allocations

1 Characterizing the Liabilities

2 Approaches to Liability-Relative Asset Allocation

3 Examining the Robustness of Asset Allocation Alternatives

4 Factor Modeling in Liability-Relative Approaches

3.1 Characterizing the Liabilities

Exhibit 23: Characteristics of Liabilities That Can Affect Asset Allocation

1 Fixed versus contingent cash flows

2 Legal versus quasi-liabilities

3 Duration and convexity of liability cash flows

4 Value of liabilities as compared with the size of the sponsoring organization

5 Factors driving future liability cash flows

6 Timing considerations, such as longevity risk

7 Regulations affecting liability cash flow calculations

LOWTECH DB Plan

As of the beginning of 2015, the present value of these liabilities, given a 4% discount rate for

high-quality corporate bonds, is US$2.261 billion The current market value of the assets is assumed to equal US$2.5 billion, for a surplus of US$0.239 billion

The following steps of the valuation exercise for a DB pension plan occur on a fixed annual date:

1 Calculate the market value of assets

2 Project liability cash flows (via actuarial principles and rules)

3 Determine an appropriate discount rate for liability cash flows

4 Compute the present value of liabilities, the surplus value, and the funding ratio

Surplus = Market value (assets) – Present value (liabilities) = 2.500 billion – 2.261 billion = 0.239 billionFunding ratio = US$2.5 billion/US$2.261 billion = 1.1057

If the discount rate is equal to the long-term government bond rate at 2% the surplus becomes a deficit

at $0.539 billion

3.2 Approaches to Liability-Relative Asset Allocation

• Surplus optimization

• Hedging/return-seeking portfolios approach

• Integrated asset–liability approach

Surplus Optimization

Expected surplus return = (Δ asset value – Δ liability value) / Initial asset value

Δ liability value (or liability return) measures time value of money for liabilities plus any

expected changes in the discount rate and future cash flows over the planning horizon

Surplus optimization process:

1 Select asset categories and determine planning horizon

2 Estimate returns and volatilities for assets and liabilities

3 Determine constraints

4 Estimate correlations

5 Compute surplus efficient frontier

6 Select recommended portfolio