R18 asset allocation

Asset Allocation and the Investor’s Risk and Return Objectives 4.. What is Asset AllocationStrategic Asset Allocation: Investor’s return objectives, risk tolerance, and investment constr

Reading 18

Asset Allocation

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1 Introduction

2 Asset Allocation

3 Asset Allocation and the Investor’s Risk and Return Objectives

4 The Selection of Asset Classes

5 The Steps in Asset Allocation

6 Optimization

7 Implementing the Strategic Asset Allocation

8 Strategic Asset Allocation for Individual Investors

9 Strategic Asset Allocation for Institutional Investors

10 Tactical Asset Allocation

2 What is Asset Allocation

Strategic Asset Allocation: Investor’s return objectives, risk tolerance, and

investment constraints are integrated with long-run capital market expectations to

establish exposures to IPS-permissible asset classes

Read Example 1: Making Asset Allocation a “Horse Race”

Appropriate asset mix under long-term or “normal” conditions

Strategic vs Tactical Asset Allocation

Tactical Asset Allocation: Short-term adjustments to asset class weights based on short-term

expected relative performance among asset classes

TAA creates active risk: variability of active returns

Example 2: Expectations and the Policy Portfolio

Importance of Asset Allocation

Classic empirical study by Brinston, Hood and Beebower:

Asset allocation explained 93.6% of variation of returns

3 Asset Allocation and Investor’s Risk and Return Objectives

3.1 Asset Only and Asset/Liability Management Approaches to Strategic Asset Allocation

3.2 Return Objectives and Strategic Asset Allocation

3.3 Risk Objectives and Strategic Asset Allocation

3.4 Behavioral Influences on Asset Allocation

Asset-Only and Asset/Liability Management Approaches to Strategic Asset Allocation

• AO approach does not explicitly involve modeling liabilities

• ALM approach involves explicitly modeling liabilities

– Cash-flow matching approach

– Immunization approach: assets match weighted average duration of

liabilities

• Dynamic approach: actual returns affect optimal decision for

next period

• Static approach

ALM approach favored when…

• Investor has below average risk tolerance

• Penalties for not meeting liabilities are high

• Market value of liabilities are interest rate sensitive

• Risk taken in the investment portfolio limits the investor’s ability

to profitably take risk in other activities

• Legal and regulatory requirements and incentives favor holding

fixed-income securities

• Tax incentives favor holding fixed-income securities

3.2 Return and Strategic Asset Allocation

exceed rate of inflation in the long term

Qualitative return objectives…

Additive vs multiplicative method for calculating required return

Example 3

Update strategic asset allocation to reflect significant shifts in return and risk requirements

3.3 Risk Objectives and Strategic Asset Allocation

Risk tolerance: below average, above average, average

Risk aversion

Note: return and risk aversion in %

If investor has a numericalrisk aversion of 4, whichallocation will he prefer?

Downside risk: risk related to losses or worse than expected outcomes only

Short-fall risk

Safety first ratio

Example 4: Applying the safety-first criterion

3.4 Behavioral Influences on Asset Allocation

If client displays… Investment advisor should…

Loss aversion  increasingly greater

risk to overcome losses Incorporate appropriate short-fall risk objective

High risk Medium risk Low risk

Sensitivity to regret  holding on to

winners and losers too long

Example 5

4 Selection of Asset Classes

4.1 Criteria for Specifying Asset Classes

4.2 The Inclusion of International Assets

(Developed & Emerging Markets)

4.3 Alternative Investments

4.1 Criteria for Specifying Asset Classes

• Assets within an asset class should be relatively homogeneous

• Asset classes should be mutually exclusive

• Asset classes should be diversifying

• Asset classes as a group should make up a preponderance of world

investable wealth

• Asset class should have capacity to absorb a significant fraction of investor’s portfolio without seriously affecting portfolio’s liquidity

Example 6

4.2 The Inclusion of International Assets

(Developed & Emerging Markets)

Add new asset class if…

Risk, Costs, and Opportunities of International Assets

• Risk of International Assets

Home country bias

• Conditional Return Correlations

 Correlations appear to depend on global volatility which reduces

international diversification benefits

• Investment Characteristics of Emerging Markets

 Higher returns, higher stand-alone risk, lower correlations

 But there are several issues and risks:

 Changes from market integration

Risk, Costs and Opportunities of International Assets

4.3 Alternative Investments

5 The Steps in Asset Allocation

6 Optimization

6.1 The Mean-Variance Approach

6.2 The Resampled Efficient Frontier

6.3 The Black-Litterman Approach

6.4 Monte Carlo Simulation

6.5 Asset Liability Management

6.6 Experience-Based Approaches

6.1 The Mean-Variance Approach

Unconstrained MVF

Sign-Constrained MVF

Corner portfolios define segment where 1) Portfolios hold identical assets 2) Rate of change of asset weights is constant

As MVF passes through a corner portfolio, an asset weight either changes from 0 to + or from + to 0.

GMV portfolio is a corner portfolio irrespective

What are the asset class weights in an efficient portfolio with an expected return of 7%?

What are the asset class weights in an efficient portfolio with an expected return of 7%?

General points related to Efficient Frontier

• Asset allocations are highly sensitive to small changes in input data… which in turn are hard

to estimate!

– Most important input is expected return which is the most difficult to estimate

• Are T-bills really risk free?

• Tangency point  highest Sharpe ratio

• Capital Allocation Line

• Extensions to the Mean-Variance Approach

– Exhibit 18

• Do Examples 9 and 10

6.2 The Resampled Efficient Frontier

• Efficient frontier is very sensitive to inputs; REF tries to

address this problem

• REF is based on simulation and data set of historical

returns

• Advantages

– Portfolios resulting from REF tend to be more diversified

– Stable relative to portfolios from MVO approach

• Disadvantages

– Lack of theoretical underpinning for the method

– Relevance of historical return data

6.3 Black-Litterman Approach

• Overall objective is to come up with efficient portfolios

– Quantitative approach to deal with the problem of estimation error

– Unconstrained Black Litterman (UBL)

– Black Litterman (BL)

• UBL

– No constraints on assets weights  negative weight (short position) is possible

– Start with market weight of a global index and make adjustments based on

expectations

• BL

– Can not short an asset class

– Curriculum focuses on this approach

Exhibit 21

Exhibit 22: Equity market weights of five major markets across the world

Exhibit 23

Exhibit 24 EfficientFrontier with EquilibriumReturns

Covariance matrix + capitalization weights  Equilibrium expected returns

What is the impact of your view on the relative weights?

Exhibit 28 Efficient PortfolioWeights with BL View-AdjustedReturns

Exhibit 15 Efficient PortfolioWeights Using Raw HistoricalMean Returns

Summarizing BL Benefits…

• Efficient allocations along frontier are more diversified compared with those resulting from MVO using historical mean returns

• Combining investor’s views with equilibrium returns helps

dampen the effect of any extreme views the investor holds

• Anchoring estimates to equilibrium returns ensures greater

consistency across estimates

6.4 Monte Carlo Simulation

Scenarios for investment returns

inflation and other relevant

variables

Monte CarloSimulation

Range of possible investmentresults for given asset allocationover investor’s time horizon

Monte Carlo simulation contrasts and complements MVO

MVO is an analytical, one-period model

Monte Carlo is a statistical method which allows you model real-world constraints (such as

taxes) which are difficult to model analytically

Monte Carlo can help us project portfolio values in a multi-period scenario

Log scale

Refresher on log scale:

Exhibit 29

6.5 Asset Liability Management

• Mean-variance surplus optimization extends traditional MVO to

incorporate investor’s liabilities  surplus efficient frontier

MSV = Minimum Surplus Variance

Review examplespreceding Examples 14and 15; and materialpreceding examplesFunding Ratio = Plan Assets/Plan Liabilities

Exhibit 31

ALM with Simulation

• Determine the surplus efficient frontier and select a limited set of efficient

portfolios, ranging from the MSV portfolio to higher-surplus-risk portfolios,

to examine further.

• Conduct a Monte Carlo simulation for each proposed asset allocation and

evaluate which allocations, if any, satisfy the investor’s return and risk

objectives.

• Choose the most appropriate allocation that satisfies those objectives.

6.6 Experience Based Approaches

• Use tradition, experience and rules of thumb in making SAA

recommendations

1 Use 60/40 as neutral starting point allocation

2 Increase bond allocation with increasing risk aversion

3 High time horizon  increase stock allocation

4 Stock allocation = 100 - Age

Summary of Optimization Models

Mean Variance

Optimization (MVO) Identify portfolios with maximum return for a given level of riskCorner portfolios

Theoretically pleasing (will see this in all books on PM)Major issue: EF is very sensitive to input data

Resampled Efficient

Frontier (REF) Based on simulation and historical returnsREF relatively less sensitive to input data and portfolios more diversified

Not as theoretically elegant as MVOBlack Litterman Aproach

(BL) Start with diversified market portfolio and work backwards do determineexpected returns; incorporate your view; recreate EF

Less sensitive to input dataPortfolios more diversified relative to MVOMonte Carlo Simulation

(MLS) Run MLS based on scenarios for investment returns inflation and otherrelevant variables  range of outputs

Complements MVO; determine portfolio values in multi-period environmentAsset Liability

Management (ALM) Explicitly model liabilities

Experience-Based Use tradition, experience and rules of thumb

Passive Investing Active Investing Semi-Active Investing

tracking portfolio of market

securities—whether self-managed, a

separately managed account, an

exchange-traded fund, or a mutual

fund— designed to replicate the

returns to a broad investable index

representing that asset class;

derivatives-based portfolio consisting

of a cash position plus a long

position in a swap in which the

returns to an index representing that

asset class is received;

derivatives-based portfolio consisting

of a cash position plus a long

portfolio of market securities thatreflects the investor’s perceivedspecial insights and skill and that alsomakes no attempt to track any asset-class index’s performance

derivatives-based position (such ascash plus a long swap) to providecommodity-like exposure to theasset class plus a market-neutrallong–short position to reflect activeinvestment ideas

tracking portfolio of marketsecurities that permits some under-

or overweighting of securitiesrelative to the asset-class index butwith controlled tracking risk

derivatives-based position in theasset-class plus controlled active risk

in the cash position (such as activelymanaging its duration)

7 Implementing the Strategic Asset Allocation

7 Implementing the Strategic Asset Allocation

Currency Risk Management Decisions

When investing in non-domestic assets we need to worry about currency risk

To hedge or not to hedge?

Asset allocation and currency hedging jointly optimized or separate?

Rebalancing to the Strategic Asset Allocation

Adjust portfolio because asset price changes have moved portfolio weights away

from target weights

Rebalancing can be done on calendar basis or percentage of portfolio basis

8 Strategic Asset Allocation for Individual Investors

Asset allocation must account for:

the part of wealth flowing from current and future labor income, and the

changing mix of financial and labor-income-related wealth as a person

ages and eventually retires

any correlation of current and future labor income with financial asset

returns

the possibility of outliving one’s resources

tax situation

8.1 Human Capital

• Ability and willingness to bear risk depends on

– Personality makeup

– Current and future needs

– Current and anticipated future financial situation

Investors with safe labor income (thus safe human capital) will invest more of their financial portfoliointo equities A tenured professor is an example of a person with safe labor income; an at-will

employee in a downsizing company is an example of a person with risky labor income

Investors with labor income that is highly positively correlated with stock markets should tend to

choose an asset allocation with less exposure to stocks A stockbroker with commission income is

an example of a person who has that type of labor income

The ability to adjust labor supply (high labor flexibility) tends to increase an investor’s optimal

allocation to equities

Financial Capital andHuman Capital with Age

8.2 Other Considerations in Asset Allocation for Individual Investors

Mortality risk is the risk of loss of human capital if an investor dies prematurely Of

course, it is the investor’s family that bears the effects of mortality risk Life insurance

has long been used to hedge this risk

Longevity risk is the risk that the investor will outlive his or her assets in retirement.

Mitigate using life annuity which guarantees monthly income for life

Fixed annuity

Variable annuity  payments vary depending on underlying investment portfolio

Equity-indexed annuity  fixed return + participation in stock market return

9 Strategic Asset Allocation for Institutional Investors

• Defined Benefit Plans

• Foundations and Endowments

• Insurance Companies

• Banks

9.2 Foundations and Endowments

• High long-term return to spending and inflation

– Recognize appropriate inflation rate

• SAA partly depends on resources available

– Smaller endowments will generally have a constrained opportunity set (long only) and

a relatively low percentage in alternative investments

• Example 18: Constructing an IPS and deciding on an asset allocation

9.3 Insurance Companies

An insurer’s strategic asset allocation must complement and coordinate with the insurer’s

operating policy Investment portfolio policy thus seeks to achieve the most appropriate mix of

assets

1) to counterbalance the risks inherent in the mix of insurance products involved and

2) to achieve the stated return objectives

The insurer must consider numerous factors in arriving at the appropriate mix, the most

important of which are

1) asset/liability management concerns

Advantages of portfolio segmentation

provides a focus for meeting return objectives by product line

provides a simple way to allocate investment income by line of business

provides more-accurate measurement of profitability by line of business For example, the insurer

can judge whether its returns cover the returns it offers on products with investment features such as

annuities and guaranteed investment contracts (GICs)

aids in managing interest rate risk and/or duration mismatch by product line

assists regulators and senior management in assessing the suitability of investments