Chapter 5: Asset Allocation

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Chapter 5 Asset Allocation
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What is Strategic Asset Allocation?

• Strategic asset allocation
• Combines an investors objectives and constraints
  with long-term capital market expectations
• In other words, how the pie (i.e. portfolio)
  should be divided for a specific investor, given
  forecasted market conditions, and the investors
  objectives and constraints
• Process leads to a set of portfolio weights
  called the policy portfolio

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Policy PortfolioHarvard Management
Company(Endowment Fund)
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Policy Portfolio (Harvard)

• The Policy Portfolio is a theoretical portfolio
  allocated among asset classes in a mix that is
  judged to be most appropriate for Harvard
  University from both the perspective of potential
  return and risk over the long term.
• review ... for continued fit with the
  Universitys risk profile and our projections of
  long-term market returns, volatility and
  correlations.
• The Policy Portfolio (is) a guide...to the
  actual allocation in the investment portfolio and
  also serves as a measuring stick against which we
  judge the success of our active investment
  management activities.

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Performance History
Overall impact of alternative investments? Impact
of alternative investments in the last 5
years? Impact of active management? Note BIG
Broad Investment Grade
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Strategic versus Tactical Asset Allocation

• Strategic allocation sets investors long-term
  exposure to systematic risk, caters to investors
  risk and return objectives and constraints
• Tactical asset allocation (TAA) involves
  short-term adjustments to asset weights based on
  short-term predictions of relative performance
  across asset classes
• TAA is an active and ongoing investment
  discipline, whereas strategic asset allocations
  are revisited only periodically, or when the
  investors circumstances change

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Example 5-2

• John Stevenson is an analyst for an endowment
  fund. His recent research strongly suggests that
  domestic equities will underperform international
  equities in the next 6 months. He asks the CIO
  for a special meeting with the Board of Trustees
  to review the funds strategic asset allocation
  policy (to reduce the weight of domestic equities
  in the policy portfolio).
• Is such a meeting appropriate?

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Asset Allocation and Portfolio Performance

• Suppose portfolio returns can be attributed to
  the following three elements
• Asset allocation
• Market timing (tactical)
• Security selection (e.g., stock picking)
• How important is the asset allocation decision,
  out of the three?

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Asset Allocation and Portfolio Performance

• Empirical findings
• Time-series studies (same pension fund over time)
  suggest that asset allocation explains 90 of
  the variations in portfolio returns on average
• Brinson, Hood and Beebower (1986), Brinson,
  Singer and Beebower (1991), and Blake, Lehmann,
  and Timmermann (1999)
• Interpretation funds with similar asset
  allocation have similar returns.
• Financial Crisis of 2008 Canadian pension plans
  had returns ranging from -25 to 6 (average
  -18)

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Asset Allocation and Portfolio Performance

• Cross-sectional studies (different balanced
  mutual funds within the same period) show that
  asset allocation explains 40 of the variations
  in portfolio returns
• Ibbotson and Kaplan (2000)
• Overall, asset allocation is the most important
  factor in determining portfolio returns the
  other factors (tactical and security selection)
  are secondary.

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Asset-Only versus Asset/Liability Management (ALM)

• Asset-only approach does not explicitly model
  liabilities, though they are indirectly
  considered via investor objectives and
  constraints (e.g., to achieve a target return)
• Asset/Liability Management (ALM) explicitly
  models future liabilities and adopts an asset
  allocation best suited to funding those
  liabilities (e.g., inflation protection, manage
  interest rate risk)
• Particularly important if investor is averse to
  loss managing shortfall risk becomes more
  important

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Dynamic versus Static Approaches to Asset
Allocation

• Dynamic Approach
• Asset allocation, actual returns and liabilities
  in one period directly affect the optimal
  decision for the following period
• Example If mean reversion exists in stock
  returns, then stocks are less risky if horizon is
  long, and optimal allocation to stocks should be
  higher
• Static Approach
• Does not consider links across time periods
• Less costly and less complex to model and
  implement

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Risk and Return in Strategic Asset Allocation

• Risk objective
• General description can be qualitative Below
  average or above average risk tolerance
• But in conducting strategic asset allocation,
  need to quantify risk attitude
• Individuals Numerical risk aversion score,
  measured through interview, questionnaire (see TD
  Mutual Funds example)
• Recall the utility function U E(R)-0.005A?2
• Translate/map risk aversion score to an A for
  your client, and compare the utility derived from
  different investments

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Risk Objective in Asset Allocation

• Example if A 4
• Portfolio P E(R) 9.7, ? 15
• Portfolio Q E(R) 7, ? 10
• UP 5.2
• UQ 5
• Another way to quantify risk tolerance Specify
  an acceptable level of volatility (e.g., ? 10,
  thereby eliminating portfolio P above)
• Downside risk If investor is averse to loss
  (LPSD instead of ?)
• Or if there is a target, then can consider
  shortfall risk. For example, risk that return
  will fall below a certain percentage

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Risk Objective in Asset Allocation

• Roys safety-first criterion
• A simple shortfall risk criterion
• Where RP is the portfolio return, RL is the
  threshold level of return, and ?P is the std.
  dev. of RP

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Example 5-4

• Inheritance of 1,200,000. Expects to withdraw
  60,000 in 12 months from the investment income
  without having to invade the initial principal
• Three portfolios to choose from

Managers forecasts Managers forecasts
Asset Allocation Expected Return () Std. Deviation ()
A 10 20
B 7 10
C 5.25 5
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Example 5-4 (Contd)

• If the investor has an above-average risk
  tolerance (A2), which portfolio would she
  prefer?
• What is the shortfall level of return given that
  the investor does not want to dip into the
  principal for the 60,000 expenditure?
• According to Roys criterion, which portfolio is
  best?
• Recommend a portfolio to the investor, taking
  into account all of the above

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Sortino Ratio

• Similar to Roys Safety First Ratio, but uses
  downside risk instead in the denominator
• where DDP is downside deviation (standard
  deviation calculated using only returns below the
  target, RL)

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Return Objective in Strategic Asset Allocation

• Return objective
• Quantitative return objectives are easier to
  define Specify return needed to achieve goals
• If a compound growth rate is used in the
  calculations for long-term investors, then report
  geometric mean returns, rather than arithmetic
  mean returns
• Example 10 return in first year, 8 in second
  year
• If arithmetic mean ?
• If geometric mean v(10.1)(10.8) 1
• 0.08995
• One approximate of the relationship if
  distribution is normal
• Geometric arithmetic
  0.5?2

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Selection of Asset Classes

• Criteria for specifying asset classes
• What constitute an asset class?
• Popular choices, in addition to domestic stocks
  and bonds
• International assets
• Inflation-sensitive assets
• Alternative investments

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Criteria for specifying asset classes

• Assets within a class should be relatively
  homogeneous
• Have similar attributes/features
• Asset classes should be mutually exclusive
• Global equities and U.S. equities
• Asset classes should be diversifying
• Correlation?
• Asset classes as a group should comprise the
  majority of world investable wealth
• Asset class should not compromise the investors
  desired liquidity
• When there is a need to rebalance to the
  strategic asset allocation, should not be moving
  asset prices or incurring high transaction costs

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A Simple Rule-of-Thumb

• An asset class should be considered in a
  portfolio if it improves the portfolios
  mean-variance efficient frontier
• This occurs if its Sharpe ratio exceeds the
  product of the existing portfolios Sharpe ratio
  and the correlation between the asset class and
  the portfolio
• E.g., an asset class with a Sharpe ratio of 0.2
  and a correlation of 0.9 to the return of a
  portfolio with a Sharpe ratio of 0.15. It should
  be added, because 0.2 gt 0.15(0.9) 0.135
• Correlation matters a great deal if the asset
  class has a lower Sharpe Ratio (e.g., same Sharpe
  Ratio as the existing portfolio)

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International Assets

• When investing in international assets, investors
  should consider the following special issues
• Currency risk affects both return and volatility,
  and investors must decide whether to hedge
• Increased correlations in times of stress
• Emerging markets are less liquid, less
  transparent and more likely to exhibit non-normal
  return distributions (but if markets are
  efficient, investors will receive compensation
  for bearing these risks)

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Inflation-Sensitive Assets

• Assets that provide a good hedge against
  inflation
• Gold, on average, maintains its value over time.
  If bought a dollar's worth of gold 200 years ago,
  after adjusting for inflation, it would be worth
  1.07 in the fall of 2010
• CPPIB In addition to real return bonds, also
  Infrastructure, real estate
• OTPP Also includes commodities
• We invest in commodities, which typically mirror
  short-term changes in inflation, as a hedge
  against the cost of paying inflation-protected
  pensions.

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Inflation Protected Bonds

• Bonds with an inflation hedge
• Principal/par value is indexed to the Consumer
  Price Index (CPI)
• Fixed coupon rate (e.g., 4) is applied to the
  inflation-indexed principal
• Hence, cash flow is fixed in real terms
• Low correlation with other assets improves
  diversification
• Particularly suitable for managing liabilities
  that are also affected by inflation

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Cash Flow (4 coupon)
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Inflation Protected Bonds

• Product developed in the 1980s
• Treasury Inflation-Protected Securities (TIPS) in
  U.S., Real-Return Bonds (RRB) in Canada
• Also available in many countries, e.g., Sweden,
  Australia, the U.K., France.
• Small investors can participate through a
  real-return bond mutual fund, or through an ETF

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Inflation Protected Bonds

• For each inflation-indexed bond, a real yield
  plus an inflation protection are quoted. The real
  yield is a proxy for the real rate of interest
• Hence, (nominal yield real yield) is a proxy
  for the markets inflation expectation
• E.g. U.S. 10-year Treasury yield minus 10-year
  TIPs yield 1.92 - 0.17 1.75

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Alternative Investments

• Label of convenience for a diverse set of assets
  including real estate, hedge funds,
  infrastructure, and private equity
• Resources necessary to research such investments
  not available to all investors
• Liquidity an issue
• Correlations between various alternative assets
  and traditional assets require separate
  consideration
• For example, lack of benchmark for alternative
  assets

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Recap Asset Allocation Process

• Investor Specific
• Consider investors net worth and risk attitudes
• Determine the investors risk tolerance
• Capital Market Opportunities
• Identify capital market conditions
• Implement a prediction procedure
• Generate expected returns, risks and correlations
• Combined Investor-Market Information
• Determine allocations to different assets given
  investors risk tolerance, e.g., use an optimizer
  to determine optimal asset mix
• Actual returns determine feedback for process

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Mean-Variance Optimization

• Investors should choose from efficient portfolios
  consistent with the investors risk tolerance
• Unconstrained asset class weights must sum to
  one
• Sign-constrained no short sales (negative
  weights)

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Efficient Frontier (Excel)
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Efficient Frontier (Excel)