UNSW Business School
School of Banking and Finance
FINS5568 Capstone – Portfolio Management Process
Lecture 3: Asset Allocation
Prepared by Rui Sun (Susan) & Yufeng Yao
Lecture Outline:
• Introduction: asset allocation and its importance in portfolio management process
• The definition of asset classes
• Introduction to optimization techniques
• Implementation issues asset allocation
• Reading:
• Maginn, et Al. chapter 5
Investment
management
process:
Introduction
What is asset allocation
• Select the types of assets for a portfolio and allocating funds among the different asset
classes
• The allocation characteristics should match the investment objectives and circumstances
of the investor - specified in the IPS
• The allocation should be based on the capital market assumptions we have formed
• Combining the two aspects, we first form the strategic asset allocation
Introduction
What is asset allocation
• Strategic asset allocation (SAA):
• A well-defined process to produce a long-term allocation plan
• Depends on investors’ objectives and constraints + long-term capital market
expectations
• The end result of the allocation is a set of portfolio weights for different asset
classes - policy portfolio
• Often the policy portfolio is specified as target percentage for each asset class and
a range of permissible values
Introduction
Introduction
The role and importance of SAA:
• SAA is critical in executing an investment plan – overarching investment plan
• Key economic role of SAA: determine an investor’s desired exposure to systematic risks
• Different asset classes have different systematic risks
• Equity: market risk, value-growth, momentum, volatility
• Fixed income: interest rate, credit risk
• Allocating to different asset classes decides the exposure to different risk factors
• Systematic risks usually account for most of a portfolio’s return and risk
• SAA determines the fundamental risk profile of a portfolio
Introduction
The role and importance of SAA:
• Empirical evidence on the importance of SAA
• Brinson, Hood, and Beebower (1986):
• A time series analysis of how much of the variations in return can be explained by asset allocation
• Between 1974 and 1983, for 91 large U.S. defined benefit pension plans, on average 93.6% of the variation
of returns can be explained by asset allocation
• Timing and security selection can only explain 6.4% return variation
• Ibbotson and Kaplan (2000):
• Cross-sectional study of mutual funds between 1988-1998
• They found asset allocation explains about 40% of the cross-sectional variation in mutual fund returns for
94 large U.S. mutual funds.
Introduction
Tactical asset allocation (TAA):
• SAA sets an investor’s desired long-term exposures to systematic risk: > 5 years
• TAA involves short-term adjustment to asset class weights
• Based on short-term predictions of relative performance among asset classes
• Take advantage of cyclical conditions or perceived mispricing in the market
• Goal is to increase risk-adjusted returns
• Taking policy portfolio as a benchmark, TAA takes on active risk, hoping to generate an active return
– alpha
• Cost of TAA: more trading and monitoring costs, capital gain tax
• Typically there are limits on how much deviation from SAA
Introduction
Tactical asset allocation (TAA):
• Whether TAA successful?
• Sharpe Ratio of TAA > SAA:
=
−
()
and are the returns of the portfolio and risk-free rate of return and () is the standard deviation
of portfolio return
• Information Ratio:
=

( − )
is exceed return of a portfolio.
Introduction
Asset allocation approaches:
• Asset-only approach
• Decisions based solely on the investor’s asset and maximise expected return per unit of risks
• Example: mean-variance optimization based on expected return, volatility and correlation
• Asset/liability approach (liability-relative approach)
• Decisions based on funding liabilities when they are due
• Relevant for institutions with definable liabilities, defined benefit pension funds, insurance company
• Example: surplus optimization – apply mean-variance optimization principle to surplus = assets –
Present Value(future liabilities)
Introduction
Asset allocation approaches:
• Goals-based approach
• Most suitable for individuals and families
• Allocate asset into sub-portfolios, each of which aims to help individuals and families to achieve
particular goals, such as maintain life-style in retirement, accumulate inheritance, down payment for
a home, etc.
• Each sub-portfolio has a unique asset allocation to meet the stated goals
• Higher priority and short-term goals demand lower risks (education fee, retirement funds)
• Combining the asset allocations in the sub-portfolios results in the overall strategic asset allocation
• Also liabilities driven – individual liabilities are diverse and less predictable compared to that of
institutions.
Introduction
Asset allocation needs to meet the return and risk objectives of the investor:
• Return objective:
• Numerical objective is generally required
• Need to consider the effects of compounding as long-term effect can be large:
• Real required rate of return of 6% and inflation of 3%, we then need to have a nominal return of
(1+6%)(1+3%) -1 = 9.18% > 6% + 3% = 9%
• Risk objective:
• Standard deviation
• Downside risk measures
Introduction
Asset allocation needs to meet the return and risk objectives of the investor:
• Risk-adjusted return (utility):
• the utility of the portfolio for a mean-variance investor
• A is the risk aversion of the investor, the larger the A, the higher the penalty for risk. Can range from
1 to 10
• Example 1: what’s the risk-adjusted return of a strategic asset allocation with expected return of 10%
and standard deviation of 15% for an investor with a risk aversion of 4?
• Solution:
= 10 − 0.005 ∗ 4 ∗ 15
2 = 5.5%
= − 0.005
2
Introduction
Shortfall risk:
• Roy’s safety-first ratio (SF Ratio)
• The optimal portfolio minimizes the probability of return falling below a required threshold = Maximize
the SF Ratio:
=
() −

is the minimum required return of the investor
Example 2: what’s the SF Ratio of a strategic asset allocation with expected return of 10% and standard
deviation of 15% for an investor with a minimum return requirement of 3%?
=
10 − 3
15
= 0.4667
Asset Classes
• Asset class
• A group of assets with similar investment
characteristics
• Each asset class with their distinct systematic risk
• Criteria for specifying an asset class:
• Assets within an asset class should be relatively
homogeneous
• Asset class should be mutually exclusive
• Asset classes should be diversifying
• The asset classes as a group should contain a
large proportion of world investable wealth
• The asset class should be able to absorb a
significant fraction of investors’ portfolio without
significant liquidity issue
Asset Classes
• Common asset classes
• Domestic equity
• Domestic fixed income
• International equity
• International fixed income
• Real estates: commercial and residential
• Alternative asset classes:
• Private equity: venture capital
• Hedge funds
• Commodity funds
Asset Classes
• The inclusion of international assets
• Can potentially improve the risk and return of a portfolio
• Need to consider:
• Currency risk
• Increased correlation of international and domestic asset returns in times of distress
• Emerging market specific concern: e.g., incomplete market regulation etc.
• For mean-variance investor, one criterion can be:
=
() −

>
() −

,
• Sharpe ratio of the new asset class needs to be higher than the Sharpe ratio of the existing portfolio
multiplied by the correlation between the returns of new asset class and the existing portfolio
Asset Classes
Example 3: suppose the current portfolio of an Australian fund manager has a Sharpe ratio of 0.5
and he is considering whether to add an emerging market (EM) portfolio. The EM portfolio has a
Sharpe ratio of 0.4 and a correlation with the existing portfolio of 0.7.
Solution: as the proposed portfolio has a Sharpe ratio of 0.4 and a correlation with the existing
portfolio of 0.7, the fund manager should add it to the existing portfolio as the proposed portfolio
has a Sharpe ratio of 0.4 > 0.5*0.7=0.35 the Sharpe ratio of the current portfolio multiplied with
the correlation.
Note one assumption of this method is that the return of the proposed asset class is normally
distributed. If the historical record indicates otherwise, this method is not appropriate.
Asset Classes
Allocation by asset class or risk factor:
• Asset classes
• Traditional been used as units in asset allocation
• But there are overlapping risk factors among asset classes:
• Domestic equity and fixed income are both affected by interest rate, foreign exchange rate, market volatility
etc.
• Risk factors
• Volatility, inflation, liquidity, interest rates, etc
• Not necessarily superior but could offer additional insights into the risk and return driver of a portfolio
• Multifactor models can be used to identify risk factors and exposures
• Disadvantage: some of the factors are not directly investable
Optimization for Asset Allocation-MVO
• Mean-variance optimization (MVO)
• Inputs: expected return, variance covariance matrix of the asset returns, constraints
• Maximize the portfolio return for a given level of risk (or minimize the risk for a given
level of return)
• Outputs: optimal portfolio weights
• Efficient frontier, the collection of efficient portfolios
• If assuming risk free rate exists, we can identify the market portfolio (portfolio with the highest
Sharpe ratio)
• Optimal portfolio for an investor depends his risk and return objective
MVO
One example of an efficient frontier and optimal portfolio for a particular investor
Optimization for Asset Allocation - MVO
• Common issues with MVO
• The quality of the outputs heavily depends on the quality of the input data – the “garbage-
in-garbage-out” problem
• Note, the resulting portfolio is very sensitive to the expected returns
• Forecasting return is hard and historical asset return data tend to produce bad predictions for
future asset returns
• Generally need to conduct sensitivity analysis to examine the effects of different expected return
estimates
• Often produce concentrated, large (positive and negative) positions
• Ignore skewness and kurtosis of return distribution – may not account for tail risk
• Single period framework that ignores interim cashflows, return correlation and costs of
portfolio rebalancing
Optimization for Asset Allocation
• Black-Litterman model
• Reverse engineering method to deal with the estimation error problem of the expected
return in MVO
• The process:
• Inputs: an assumed optimal asset allocation and expected variance-covariance matrix of asset
classes
• “Reverse engineer” the expected returns implicit in a diversified market portfolio
• Combine the implied expected returns with an investor’s view in a systematic way taking into
consideration of the investor’s confidence in his views
• The view-adjusted expected return are then used in an MVO
Optimization for Asset Allocation
• Black-Litterman model
• The resulting allocation tends to be well-diversified
• The resulting allocation also incorporates the investor’s views and confidence on asset-
class returns
• Anchoring with market equilibrium return reduces the impact of the extreme views of analysts
• Ensure greater consistency across estimates
Optimization for Asset Allocation
• To reduce concentrated positions from MVO
• Adding constraints to the optimization:
• Budget constraint (sum of weights = 100), non-negative weights (no short positions), allocation
range for each asset class (or deviation range from benchmark), industry, factor exposure
constraints
• Adding too many constraints might limit the resulting portfolio to be what is expected rather
than optimized
Implementation issues in asset allocation
• Portfolio rebalancing
• Currency risk management
• Behavioural issues in asset allocation
Implementation Issues
• Rebalancing
• Adjust portfolio weight to the strategic asset allocation - asset price changes can move
portfolio weights away from the target weight outside the permissible range
• Maintain investor’s desired exposure to systematic risk factors
• Impose discipline - buy low and sell high to take advantage of the time-varying risk
premium
• Let’s assume a portfolio with 50/50 in equity and fixed income
• Equity has performed well recently and fixed income under-performed – 70/30 now
• Sell equity and buy fixed income - sell higher-priced securities and buy lower-priced
• Inverse relationship between price and discount rates (expected return) of future cash flows –
buy lower-priced security will generate a higher expected return
Implementation Issues
• Rebalancing
• Approaches:
• Calendar rebalancing: rebalance on a pre-determined and regular basis and provide discipline
without the need for constant monitoring
• Ignore deviations from target weights between rebalancing dates – could have large deviations but less
frequent monitoring and trading
• Percent-range rebalancing: rebalance if the change in value is beyond the permissible range
(tolerance bands or corridors) that are considered optimal for each asset class
• The target allocation is 50% for equity with a corridor of [45%, 55%]
• Weights closer to the target but more monitoring and trading
Implementation Issues
• Rebalancing strategic considerations:
• Transaction costs: the higher the transactions costs, the less frequent trading, the wider the
corridor
• Risk tolerance: the more risk averse the tighter rebalance corridor
• Correlations of movements of asset classes: the higher the correlation, the wider the
corridor
• Taxes: taxable portfolios will typically have wider rebalancing corridors than tax-exempt
portfolios
• Tax can reduce the return volatility: 10% gain become 7% for a 30% tax rate
• Setting a 10% limit for a taxable portfolio will have the same effect of setting a 7% limit for a
tax-exempt portfolio after tax
Implementation Issues
• Currency risk management
• If allocation includes nondomestic asset classes, the investor’s portfolio can be exposed to
currency risk
• Manager needs to decide whether to hedge and how to hedge
• Hedge strategy can be passive or active:
• Passive: not taking views on currency return
• Active: forecast currency return and actively manage the positions to provide excess return
• Currency management function can be delegated to a currency overlay manager, a currency risk
management specialized mainly operating in currency forward and other derivatives markets
Implementation Issues
• Currency risk management
• Often subordinated to asset allocation decision – currency management is undertaken after
the asset allocation decision
• IPS should include instruction on currency hedging strategy
Implementation Issues
• Behavioural issues in asset allocation
• Loss aversion: dislike loss more than like gains and tend to lose discipline when facing loss
• Difficult for investors to maintain discipline when facing loss
• Can use a goal-based investing where higher priority goals are funded with less risky
investments – less likely to suffer loss and easier to maintain the strategy
• Overconfidence or illusion of control: tendency to overestimate the ability to control events
• Fail to diversify (concentrated positions), trade too frequently and aggressive use of leverage or
short selling
• Assistance from professionals and formal review of the investment process
Implementation Issues
• Behavioural issues in asset allocation
• Mental accounting: separate assets and liabilities into different accounts based on
subjective criteria
• Have large cash savings while maintain high-interest debt, spend tax refund on luxury good
with inadequate savings
• Goal-based investing can help as saving/spending and investment decision can be disciplined by
specific goals.
• Note goal-based investing is a rational effort to prioritize goals based on objective criteria
(required return, savings etc) and build sub-portfolios, therefore not mental accounting.
Implementation Issues
• Behavioural issues in asset allocation
• Availability bias: personally experienced, more recent and familiar events can influence
decisions disproportionally.
• Familiarity bias: only invest in what is familiar, such as employer company stocks
• Home bias: over-weight in domestic securities
• Starting with a global market portfolio can help mitigate the bias
Summary
After this lecture, you should understand
• What is asset allocation, the role and importance of
asset allocation, and common approaches
• What defines an asset class and the benefit of
international investment
• The rational of common optimization approaches
• MVO
• Black-Litterman
• The important issues associated with implement asset
allocation:
• Rebalancing
• Currency risk management
• The behavioural issues in asset allocation