Lecturer: Dr. Hua Deng
ANU Research School of Finance, Actuarial Studies and Statistics
Lecture 4
Asset Allocation:
Asset Assumptions
FINM3008/8016
Applied Portfolio Construction
1

Today’s lecture
What you can expect to learn:
• Issues and methods for forming quantitative
asset assumptions
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Forming asset assumptions: overview
1. Asset Assumptions: return, variance, covariance
2. Start from objectives (ALWAYS!): link client objectives to the
data assumptions, e.g. data interval, sample period, etc.
3. Lots of choices to make:
• parametric / model-based versus non-parametric / data-based
• iid versus conditional (time-varying)
• What data to draw on:
– Measurement interval (unit of time)
– Time period
– Real or nominal?
Most of the time it doesn’t make much difference. We use
nominal.
3
Forming asset assumptions: overview
3. Lots of choices to make (cont.):
• Method of calibrating expected returns
• What about costs, taxes, alpha, etc? (can have a major
impact on actual net return an investor receives so should
not be ignored, eg. imputation credits not available to foreign
investors)
• How to treat assets that lack reliable history?
• new assets, thinly traded assets or assets subject to periodic
appraisal valuations (e.g. private equity, direct property)
• survivorship bias and selection bias can cause return to be
overstated and risk to be understated (e.g. hedge funds)
• asset classes with no good database (e.g. unlisted infrastructure)
• Allow for parameter uncertainty? (it’s only an estimate)
Model uncertainty? (it’s only a model)
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Data-based versus model-based
• Non-parametric / data-based – analysis is performed
by drawing directly on the actual data series:
– Simulation by randomly drawing from the data
– Use historical data series to analyze a ‘hypothetical’
• Parametric / model-based – imposes some structure,
a model to represent the return-generating process
– Simple mean-variance
– More complex distributions, e.g. copulas, mixed
– Factor-based models, e.g. CAPM, Fama-French
– Stochastic asset models
5
Conditional assumptions?
• Billion $ question: Why would you expect conditional
forecasts to outperform an unconditional assumption?
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Conditional vs Unconditional Assumptions
Election Cycle for S&P 500: Log Returns 1926 – 2003
Mean Standard Deviation
First half of presidential
terms 5.45% 20.86%
Second half of
presidential terms 14.38% 16.7%
All years 9.92% 19.42%
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Conditional assumption – mean reversion
Time-variation in interest rates is hard to ignore
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Other conditional models
• Risk measures: ARCH (Autoregressive Conditional
Heteroschedasticity), GARCH (Generalized
Autoregressive Conditional Heteroschedasticity), etc
• Other conditional models: regime-switching, vector
autoregressive model (VAR)
– Note: distinguish from Value at Risk (VaR)
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What data? – ultimately a trade-off
• Data availability may dictate terms
• Measurement interval
– Align with investment horizon if possible (Comment: holding or
investment period versus review period)
– Influence of serial correlation / appraisals / thin trading fades as
measurement interval is lengthened
– Longer intervals = less data points
Note: Geometric & arithmetic means coincide if interval = holding period
• Time period
– Longer = more opportunity to see the entire distribution
– Longer = more exposure to any structure change
• Advice: Scrutinize the data. Draw charts. Run diagnostics.
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Example - Structural Change
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1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019 2021
28%
26%
24%
22%
20%
18%
16%
14%
12%
10%
120-month Rolling Standard Deviation:
Australian Equities
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An anecdote from Merton Miller (2000, page 3) about the
expected market return in the Nobel context:
“I still remember the teasing we financial economists, Harry
Markowitz, William Sharpe, and I, had to put up with from the
physicists and chemists in Stockholm when we conceded that the
basic unit of our research, the expected rate of return, was not
actually observable. I tried to tease back by reminding them of
their neutrino – a particle with no mass whose presence was
inferred only as a missing residual from the interactions of other
particles. But that was eight years ago. In the meantime, the
neutrino has been detected.”
Equity risk premium
– Credit Suisse Global Investment Returns Yearbook 2019
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Methods for calibrating expected returns
1. Use sample means
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The Trouble with Sample Means
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95% Confidence Intervals for Expected Return
Length of Sample
(Years)
Lower Bound Upper Bound
10 0.70 % 19.30 %
25 4.12 % 15.88 %
50 5.84 % 14.16 %
75 6.61 % 13.39 %
100 7.06 % 12.94 %
400 8.53 % 11.47 %
900 9.02 % 10.98 %
True annual mean return is 10%, true annual standard deviation is 15%.
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95% Confidence Intervals for the Sample Standard Deviation
Sample Period (Yrs) Frequency Lower Bound Upper Bound
3 Quarterly 8.83 21.17
3 Monthly 11.50 18.49
3 Weekly 13.33 16.67
3 Daily 14.24 15.76
5 Quarterly 10.27 19.72
5 Monthly 12.30 17.70
5 Weekly 13.71 16.29
5 Daily 14.41 15.59
10 Quarterly 11.68 18.31
10 Monthly 13.10 16.90
10 Weekly 14.09 15.91
10 Daily 14.79 15.42
Methods for calibrating expected returns
2. Impose expected returns. Could be based on:
a) Linking to economy
b) Asset pricing model, e.g. cross-sectional risk (i.e.
factor) model
c) Investor’s forecasts
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4-18
Linking returns to the economy
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Decompose stock market level (S) into product of GDP, share of earnings in
GDP (K), and PE multiple (M).
Continuously compounded annual PRICE return over T years
“K” & “M” are bounded by economic forces. So
these terms must be “small” for large T.
Price Return  Nominal GDP Growth Rate
Decomposition of S&P500 Return
Log Returns 1945 - 2007
Annual Return/Growth
Rate
Standard Deviation
S&P500 Return 10.82 % 15.31 %
Real GDP Growth 3.01 2.97
Inflation 3.94 3.29
EPS/GDP - 0.12 17.62
PE ratio 0.32 23.80
Dividend Yield 3.67 1.49
Total 10.82
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Methods for calibrating expected returns
3. Implied views
– ‘equilibrium’ expected returns for a particular portfolio
of assets and covariance matrix
– let the model determine expected returns conditional
on the variance-covariance metrics so that a user-
specified portfolio (the benchmark) is on the efficient
frontier
– mitigates the hypersensitivity problem of M-V model
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Methods for calibrating expected returns
4. Bayesian techniques, e.g. James Stein
- combine prior information with new information to
generate a more refined estimate
- “shrinking” the individual sample means toward a
common value referred to as the grand mean
5. Mixed estimation, e.g. Black-Litterman:
- combine implied views with specific investor forecasts
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Annualized Sample
Moments
James-Stein
Estimate
Implied Views Estimate
Std Dev Mean (Estimate(Estimate (
Target Portfolio
Weight
Russell 1000 Value 14.67% 10.03% 8.22% 7.62% 20%
Russell 1000 Growth 18.21% 8.42% 8.22% 8.22% 20%
Russell 2000 Value 17.15% 10.10% 8.22% 7.48% 4%
Russell 2000 Growth 23.89% 5.81% 8.22% 8.06% 4%
MSCI EAFE 17.63% 8.91% 8.22% 7.12% 12%
Barclays High Yield 8.61% 7.39% 8.22% 5.73% 5%
Barclays Aggregate Bond 4.34% 7.83% 7.93% 4.50% 27%
Citi Hedged Non-US Govt 3.25% 7.27% 7.41% 4.29% 8%
Grand Mean
Std Dev of Sample Means
8.22%
1.46%
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Costs and alpha
• Asset returns comprise much more than just the reported
returns for the asset class index
• Costs of investing
– Transaction costs, management fees, taxes, admin
– May seem obvious, but . . .
– What costs are priced by market? What are investor-specific?
Should the latter be analyzed and managed separately?
– Capital gains tax (CGT) is problematic
• Alpha (discussed further week 5)
– Industry approach is try to separate asset class (beta) decision
from active (alpha) return decision
– Many alternatives bundle market and skill-based returns
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Lack of reliable data history
• Likely problem areas:
a) New assets
b) Illiquid assets, especially where appraisal-based
c) Structural change
d) Latent, unobserved risks (e.g. liquidity back holes, peso problem)
e) Large outliers in the data (think twice before removing!)
• Some responses:
– Interpolate from like assets given fundamental nature, e.g. is the
asset equity or bond-like?; exposure to factors or fundamental risk
– Draw on other representative data, e.g. a close proxy asset
– Adjust the available data series, e.g. ‘de-smooth’ illiquid asset
returns, shorten the estimation period, review effect of outliers
– Ad-hoc adjustments (are they better than nothing?)
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Dealing with uncertainty
• Parameter uncertainty
– Incorporate into the analysis if practical
– Appreciate the implications, e.g. sensitivity to assumptions
• Model uncertainty
– Always be aware: “it’s only a model”
– Avoid relying on a single model
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Some advice
• First ask which approach best suits your objectives
• Scrutinize both the inputs and the output
• If something looks wrong, it most probably is
• Keep your wits about you, and think
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Wrap-up
• Final messages
• Comments on tutorial
– Appreciate how return and risk measures change due to change
in data interval and holding period
– Filling in all of the formulas is NOT the purpose
• Comments on readings
– supplementary reading “Expected returns on major asset
classes”, over 100 pages, very well-structured, for your reference
if time allows. It provides a background understanding of the
fundamental drivers of returns in various asset classes.
– “Capital market assumptions Q1 2022 AQR”, real world example
of forming asset assumptions, focus on the framework and
discussions on how forecasts are used (not simply feeding a
model)
• Announcements 27