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 2 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) 4 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 6 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% 7 Conditional assumption – mean reversion Time-variation in interest rates is hard to ignore 8 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) 9 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. 10 Example – Structural Change 11 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 12 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 13 Methods for calibrating expected returns 1. Use sample means 14 The Trouble with Sample Means 15 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%. 16 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 18.4
9 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 17 4-18 Linking returns to the economy tttt MKGDPS **= ( ) ( ) ( ) ( ) ÷÷ è +÷÷ è +÷÷ è =÷÷ è 0000 1111 M M LnTK K LnTGDP GDP LnTS S LnT TTTT 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 19 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 20 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 21 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% 22 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 23 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 ) 24 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 25 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 26 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