Session 101 PD, Use of Efficient Frontiers in Strategic Asset Allocation Analysis Moderator: Ken Griffin, ASA, MAAA Presenters: Ken Griffin, ASA, MAAA Sean Kane, CFA
101PD - Use of Efficient Frontiers in Strategic Asset Allocation Analysis Presented to October 28, 2014 Presented by
Efficient frontier (EF) modeling is an intuitive, convenient way to capture the incremental trade-offs between object combinations in the two dimensional space of risk and return. TODAY S DISCUSSION Traditional Mean-Variance EFs and Concepts Other Topical Uses of EFs EF Modeling Input EF Modeling Challenges Practical Limitations and Taming the Optimizer 141028 SOA Use of EF in SAA.ppt 2
EFs are classically used to in a mean-variance context to create optimal portfolios of assets as defined by the highest level of portfolio return at a given level of standard deviation of portfolio return. TRADITIONAL MEAN-VARIANCE EFs We can combine assets together in optimal portfolios using our assumptions for risk, return, and correlation. The Efficient Frontier represents all combinations of assets that maximize return for a given the level of risk (optimal). Portfolio combinations below or to the right of the efficient frontier are dominated by more efficient portfolios along the frontier. 141028 SOA Use of EF in SAA.ppt Source: Investopedia.com, Cardinal Investment Advisors Analysis 3
Annualized Rate of Return Annualized Rate of Return EFs can be very sensitive to the componentry of which they are comprised. EXPANDING/CONTRACTING THE FRONTIER Diversification with new assets can expand the efficient frontier and add value in one of two fashions: 1. Generating incremental return in the portfolio at the same level of risk. 2. Reducing portfolio risk without sacrificing return. Illustrative Return Gain from New Asset Classes Illustrative Risk Reduction from New Asset Classes Return Gain Frontier with existing assets With new asset classes Current allocation With new asset classes Risk Reduction Frontier with existing assets With new asset classes Current allocation With new asset classes Risk % (Standard Deviation of Annual Returns) Risk % (Standard Deviation of Annual Returns) 141028 SOA Use of EF in SAA.ppt Source: Cardinal Investment Advisors Analysis 4
Annualized Return (%) EFs get to the heart of Modern Portfolio theory and the notion of improving efficiency via diversification. HARNESSING DIVERSIFICATION VIA EFs 14% 12% 10% Risk/Return of Efficient Portfolio Combinations Unconstrained Frontier The inverse correlation of the assets creates higher returns at lower risk than a simple linear combination of the assets. 8% Current Target 6% 4% 2% 0% 0% 5% 10% 15% 20% 25% 30% 35% 40% Risk (Annual Standard Deviation - %) Adding new, potential asset classes to the mix will only improve those efficiencies as long as the correlations are less than 1.0. 141028 SOA Use of EF in SAA.ppt Source: Cardinal Investment Advisors, ProVal 5
The opportunity set of objects one can embed in an EF depends on the limits imposed by state, federal, or other regulation. REAL WORLD OF INSURANCE EFs LOCATION, LOCATION, LOCATION! 141028 SOA Use of EF in SAA.ppt Source: State Regulations, Cardinal Investment Advisors analysis 6
Expected Return (After-Tax) Actual implementable EFs can depart dramatically from conceptual ones. Mundane factors such as taxes leverage constraints/risk controls fundamentally change the shape of EFs. INCLUDING REALISTIC FACTORS IN EFs 12% 10% 8% 30% Trade Finance 14% Small Cap 16% International 14% Private RE 3% Commodities 23% Private Equity 25% HY Bank Loans 75% Private Equity Unconstrained with Taxes Unconstrained 6% 85% Cash 11% TIPS 2% Private Equity 4% 50% Investment Leverage 6% Basket Clause 2% A-Policy Target 0% 0% 5% 10% 15% 20% 25% 30% Risk (After-Tax Standard Deviation) 141028 SOA Use of EF in SAA.ppt Source: Cardinal Investment Advisors 7
Excess Return (Over PBO Liability Return - %) EFs are frequently used to capture other concepts of risk vs. return, or cost vs. benefit tradeoffs. Excess return vs. a liability is one. OTHER TOPICAL EF CONCEPTS Liability Tracking (Excess Return) Frontier 5% 4% The risk-equivalent point on the frontier in this context is a very different allocation than the-risk equivalent from the meanvariance EF 3% 2% 1% 0% -1% -2% Unconstrained Frontier Current Allocation Long Credit 43% Non US Devloped 28% Private Equity 12% US Small 13% PIMCO 4% Total 100% Excess Return 1.4% PBO Liability Tracking Error 12.8% Long Credit 35% Non US Developed 21% US Small 17% Low Volatility Equity 12% Private Real Estate 6% Private Equity 4% PIMCO 4% Commodities 1% Total 100% Compound Return 7.7% Volatility 11.4% -3% 0% 5% 10% 15% 20% 25% 30% 35% Tracking Error (Std Dev. of Excess Return - %) 141028 SOA Use of EF in SAA.ppt Source: Cardinal Investment Advisors, ProVal 8
EF analysis is used to determine the appropriate tradeoff of investment risk as manifest in retirement Income Replacement Ratios in the defined contribution/401k plan space. OTHER TOPICAL EF CONCEPTS (continued) 141028 SOA Use of EF in SAA.ppt Source: Voya 9
An age-old debate Arithmetic means are biased high; Geometric means are biased low. Converting between the two should be thoughtful. INPUTS: ARITHMETIC VS. GEOMETRIC RETURNS Maclaurin series expansion Taylor series expansion 141028 SOA Use of EF in SAA.ppt Source: CDI Advisors 10
Q4 1945 Q4 1947 Q4 1949 Q4 1951 Q4 1953 Q4 1955 Q4 1957 Q4 1959 Q4 1961 Q4 1963 Q4 1965 Q4 1967 Q4 1969 Q4 1971 Q4 1973 Q4 1975 Q4 1977 Q4 1979 Q4 1981 Q4 1983 Q4 1985 Q4 1987 Q4 1989 Q4 1991 Q4 1993 Q4 1995 Q4 1997 Q4 1999 Q4 2001 Q4 2003 Q4 2005 Q4 2007 Q4 2009 Q4 2011 Q4 2013 Annualized Return Intuitive return forecasts based on drivers of value should be favored over historic returns. INPUTS: HISTORIC VS. FORWARD LOOKING RETURNS 25% Using Historic Averages to Forecast Future Returns (10 Yr. Trailing S&P 500 vs. Future 10 Years) 20% 15% 10% 5% 0% RSQ = 0.04-5% -10% Forecast Actual Period Ending 141028 SOA Use of EF in SAA.ppt Source: Cardinal Investment Advisors 11
Building blocks can be used to capture both the current environment and typical mean reverting activity in asset return forecasts. INPUTS: BASIC EQUITY RETURN FORECAST APPROACH 2.70% Current Income Component 4.95% -0.25% 7.40% Large US Growth Valuation + + Component Equity Component = Projection 1.90% +.80% 2.25% Current Dividend Yield Share Repurchase Yield Long-Term Expected Inflation + 2.70% Future Dividend Growth -0.25% Current vs. Long-Term P/E Multiple Speed of Mean Reversion Market Implied Inflation Expert Consensus Forecasts GDP Component Method Real GDP growth rate in US ~ ~ ~ ~ ~ ~ ~ ~ 2.60% 2.00% 2.20% 2.90% 2.65% 2.60% Trailing Historic Averages Expert Consensus Forecasts 0.90% 2.00% Labor Force Growth in the US + Productivity Growth in the US 141028 SOA Use of EF in SAA.ppt Source: Cardinal Investment Advisors 12
Yield to Worst (%) Long-term EFs should not be predicated on untenable short-term assumptions. INPUTS: LOW YIELD ENVIRONMENT NEEDS TO BE ADDRESSED Barclays Capital Agg and Long Credit Yield to Worst and Subsequent 10-Year Returns (Since Inception 1973-2013) 18 16 14 12 10 8 6 4 R² = 0.8156 Cardinal s fixed income asset class return projections are based on current market yields as an unbiased consensus indicator of anticipated bond pricing. However 2 0 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% Subsequent 10-Year Return 141028 SOA Use of EF in SAA.ppt Source: Barclays, Cardinal Investment Advisors 13
Yield (%) Forecasting bond returns may require a two-stage or reversion approach. INPUTS: SECULAR TREND IN YIELDS OVER LONG-TERM US Treasury Yield Curve Domestic Core Fixed Income (Two-Stage) 8.0 2.60% 7.0 6.0 Core Bond Return Projection 5.0 4.0 Long-term downward trend 2.30% 3.30% 3.0 2.0 1.0 Recent stabilization in rates Current Aggregate YTM ~ Aggregate Reinvestment Yield 0.0.5 1 2 5 10 Term (Years) Ave Last 10 Years Ave. Last 30 Years 6/30/2013 6/30/2014 30 141028 SOA Use of EF in SAA.ppt Source: Federal Reserve, Cardinal Investment Advisors 14
Time series can experience regime changes or persistent shifts. If these can be linked to underlying drivers that are persistent, the future may be very different and adjustment should be made. INPUTS: RISK REGIME CHANGES Intermediate Bonds Volatility Regime Change Barclays Aggregate St Dev 1970 to 2013 6.96 1980 to 1990 8.93 1990 to 2013 4.99 141028 SOA Use of EF in SAA.ppt 15
Q1 1982 Q4 1982 Q3 1983 Q2 1984 Q1 1985 Q4 1985 Q3 1986 Q2 1987 Q1 1988 Q4 1988 Q3 1989 Q2 1990 Q1 1991 Q4 1991 Q3 1992 Q2 1993 Q1 1994 Q4 1994 Q3 1995 Q2 1996 Q1 1997 Q4 1997 Q3 1998 Q2 1999 Q1 2000 Q4 2000 Q3 2001 Q2 2002 Q1 2003 Q4 2003 Q3 2004 Q2 2005 Q1 2006 Q4 2006 Q3 2007 Q2 2008 Q1 2009 Q4 2009 Q3 2010 Q2 2011 Q1 2012 Q4 2012 Return (%) Illiquid, private asset classes suffer from pricing biases that require unsmoothing. INPUTS: ALTERNATIVE ASSET CLASSES UNDERSTATE RISK 15.00 Reported Real Estate Returns vs. Unsmoothed 10.00 5.00 0.00-5.00-10.00-15.00-20.00 St Dev Return Reported 2.2 2.0 Unsmoothed 4.5 1.9-25.00-30.00 Unsmoothed Reported 141028 SOA Use of EF in SAA.ppt Source: NCREIF, Cardinal Investment Advisors 16
3-Year Centered Correlation Coefficient Correlations often converge during periods of market stress. INPUTS: CORRELATIONS ARE NOT ALWAYS STABLE Historic Correlations to Investment Allocations 1.00 0.80 0.60 0.40 0.20 0.00-0.20-0.40-0.60-0.80-1.00 1 High Convergence Convergence Bull Mkt. Bull Mkt. Bear Mkt. 4 2 5 3 EFs require a covariance structure. Using a single point static value can hide the impact of real world convergences. Shock testing is important. Asset Rolling Asset Ave. 141028 SOA Use of EF in SAA.ppt Source: Cardinal Investment Advisors 17
Return (Annualized) - % Artificial constraints can be very costly and should be quantified. ACKNOWLEDGING THE COST OF CONSTRAINTS Comparative Frontiers - Typical Assets vs. Impairment Sensitive 10 9 8 7 6 5 4 3 2 Typical Pension Asset Frontier Cost of constraints Impairment Sensitive Frontier Imprudent levels of asset concentration Any constraint will, by definition, reduce and shift the EF. Operating constraints related to accounting, audit complexity etc. can be quantified and a business case made. 1 0 0 2 4 6 8 10 12 14 16 18 20 Risk (Annual Standard Deviation) - % 141028 SOA Use of EF in SAA.ppt 18
Nominal Return Two, apparently, near-identical EFs appear below. OPTIMIZERS ARE FICKLE TESTING SENSITIVITY Identical Frontiers? 10.0% 9.0% Efficient Frontier #2 8.0% 7.0% Efficient Frontier #1 6.0% 5.0% 4.0% 3.0% 2.0% 1.0% 0.0% 0% 5% 10% 15% 20% 25% 30% Standard Deviation of Nominal Return 141028 SOA Use of EF in SAA.ppt 19
Asset class return/risk assumptions only flexed +/- <20 bps. Can result in +/- 10% allocation changes. MINOR INPUT CHANGES CAN BE SIGNIFICANT Efficient Frontier #1 Efficient Frontier #2 100% 100% 90% 90% 80% 80% 70% 70% 60% 60% 50% 50% 40% 40% 30% 30% 20% 20% 10% 10% 0% 0% 141028 SOA Use of EF in SAA.ppt 20
Objects flow in and out of the EF depending on constraints and relative efficiency. DETERMINING WHAT IS BINDING 100% 90% 4 5 Commodities Private Equity FOF 80% 2 3 Hedge FOF Non US Emerging Equity 70% Non US Developed Equity 60% 50% 40% 6 US Small Cap Equity US Large Cap Equity Private Real Estate LC Emerging Mkts Debt 30% 1 High Yield Bonds Long Gov/Credit 20% TIPS 10% Core Bonds Cash 0% 1 2 3 High Yield Bonds current yields are sufficiently high to maintain a presence throughout most of the frontier. TIPS enter immediately due low correlations. The 10% max binds initially with allocations declining as correlation is offset by low returns. Real estate is prominent along the frontier as a high income diversifier. 4 5 6 Domestic and non-us equity s low correlation to core bonds pulls the asset into the frontier almost immediately. Commodities high expected returns drive it to the max limit as it quickly dominates hedge funds, REITs etc. The incremental yield pickup of Long Gov/Credit drive a max allocation early in the frontier. 141028 SOA Use of EF in SAA.ppt 21
Annualized Return (%) ADDING AN OVERLAY Projected Asset Class Risk/Return Active Management 14% Alpha TE Cash 0.1% 0.2% Domestic Bonds 0.2% 0.5% 12% Long Government 0.1% 0.5% Non-US Emerging Long Credit 0.3% 0.5% US Small Cap All Private Equity Equity TIPS - - 10% Equity US Mid Cap Equity Non-US Developed High Yield 0.8% 3.5% Equity Hedge Funds - - US Large Cap 8% Equity Private Real Estate - - Low Volatility REITs (Public Real Estate) 0.5% 2.0% Equities Non-US Emerging US Large Cap Equity 0.5% 2.5% Bonds 6% Hedge Funds Commodities US Large Cap (Passive) - - Private Real Estate High Yield REITs (Public Real US Mid Cap Equity 0.8% 3.8% Long Credit Estate) US Small Cap Equity 1.0% 5.0% 4% Non-US Developed Equity 1.5% 5.0% Domestic Bonds Long Government Market Return Commodities - - TIPS 2% Cash Active Mgmt Return All Private Equity - - Emerging Market Equity 1.5% 5.0% Emerging Market Bonds 0.4% 1.5% 0% Low Volatility Equities - - 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% Risk (Annual Standard Deviation of Returns - %) 141028 SOA Use of EF in SAA.ppt 22
ALPHA OVERLAY ASSUMPTIONS 141028 SOA Use of EF in SAA.ppt 23
OTHER CONSIDERATIONS Non-normality Fat-tails (leptokurtosis) Correlation Convergences Shock-testing Historic Scenarios/Crisis 141028 SOA Use of EF in SAA.ppt 24
CONCLUSIONS EFs can be simple / intuitive EFs can capture trade-offs EFs are conducive to what-if analysis EFs can be very sensitive EFs are classic GIGO EFs include some simplifying assumptions 141028 SOA Use of EF in SAA.ppt 25
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Simulation Modeling Approach Economic Scenario Generator (ESG) Company Model - Projects Future States of the Company Scenario 1 Q 1 Q 2 Q3 Q 4 Models Future States of the Economy & Financial Markets Company Data Input Start of Simulation Scenario 2 Scenario 3 Scenario 4 Scenario n Whole- Company Outputs Accounting Regulatory Financials Tax Current Business State Current Financials Business Plans Actuarial Models Input from ERM... High Performance Business Computing
Economic Value (EV) Efficient Frontier Integrated ALM Identify investment strategy to meet specific risk/reward profile Maximize economic value - not just investment returns - for various levels of risk Provides a platform for aggregating enterprise risks Source: Conning ADVISE 28
Economic Value (EV) Efficient Frontier Transition The efficient frontier does not reflect the deduction of estimated investment management and transaction fees that the client may incur. * All dividends and other earnings are assumed to be reinvested semi-annually. Source: Conning analysis 29
Economic Value (EV) Efficient Frontier Current Benchmark A B C D E F G H I J K Cash and Gov't 5% 4% 36% 16% 8% 6% 1% - - - - - - Corporate 65% 40% 21% 40% 32% 31% 54% 52% 41% 35% 39% 50% 59% Structured 16% 29% 43% 43% 44% 33% 14% 17% 26% 32% 28% 20% 19% CML/Private Placement 11% 20% - 1% 15% 29% 30% 30% 30% 30% 30% 26% 15% High Yield 3% 3% - - - - - - - - - - - US Equity - 1% - - - - - - - - - 1% 4% Alternative Assets - 3% - - 1% 1% 1% 1% 3% 3% 3% 3% 3% Total 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% Overall Duration 7.1 8.1 6.7 6.8 6.5 6.6 6.8 7.4 7.7 8.5 9.7 11.0 12.2 Economic Value ($MM) 1,617 1,654 1,577 1,590 1,603 1,616 1,629 1,642 1,656 1,669 1,681 1,694 1,709 Risk ($MM) 154 167 122 122 124 128 136 146 158 171 185 204 228 The efficient frontier does not reflects the deduction of estimated investment management and transaction fees that the client may incur. All dividends and other earnings are assumed to be reinvested semi-annually. Source: Conning Analysis 30
Economic Value (EV) Duration Targeting Market Value Balance Sheet Assets : Modeled Assets and Liabilities (Amount in $ millions) Immunized Book Market Effective Effective Value Value Duration Duration US Corp 6,000 6,000 9.0 8.4 US Structured Securities 3,000 3,000 4.5 4.5 Other Invested Assets 1,000 1,000 3.0 3.0 Total Invested Assets 10,000 10,000 7.1 6.7 Liabilities : Liabilities 8,000 8,000 8.2 8.2 Other 500 500 2.0 2.0 Total Liabilities 8,500 8,500 7.9 7.9 Surplus : Total Surplus 1,500 1,500 2.4 0.0 MV Surplus % of MV Assets = 15% 31
Economic Value (EV) Duration Targeting 32
Economic Value (EV) Efficient Frontier Not preferred from an SAA standpoint! The efficient frontier does not reflects the deduction of estimated investment management and transaction fees that the client may incur. All dividends and other earnings are assumed to be reinvested semi-annually. Source: Conning Analysis 33
Economic Value (EV) Efficient Frontier Integrated ALM Identify investment strategy to meet specific risk/reward profile Maximize economic value - not just investment returns - for various levels of risk Provides a platform for aggregating enterprise risks Source: Conning ADVISE 34
Economic Value (EV) Efficient Frontier 35
Economic Value (EV) Efficient Frontier Minimum 4% High Yield 36
Expected Results and Range of Results Return Return Efficient Frontier Probability Distribution + 90-95% 75-90% 50-75% 25-50% 10-25% 5-10% + mean Risk Each point on the efficient frontier, defined by a single risk and a single reward measure, is based on the results of 1,000s of scenarios We usually want the investment strategy that on average gives the "best" reward for a given level of risk However, we also want to know the downside risk - how bad could results be? We evaluate this risk by looking at the range of potential results; for example, how bad is the 5% probability level (1 year in twenty), and can we accept that much risk? Source: Conning Analysis 37
Expected Results and Range of Results Observations Benchmark economic value is improved over the Current allocation at nearly every percentile Extreme tail events are similar between the Benchmark and Current allocations Tail risk exceeds the Current allocation in the longest duration and riskiest portfolios J and K *The efficient frontier does not reflects the deduction of estimated investment management and transaction fees that the client may incur. All dividends and other earnings Source: Conning Analytics BM* means Benchmark Strategy 38
Investment Optimization Tool (IO) - Risk Measures Additional Risk Measures Pull down menu selection Standard deviation Coefficient of variation Minimum Semi-standard deviation Conditional standard deviation Average Percentiles Conditional Tail Expectation (CTE) Source: Conning Analytics 39
Economic Efficient Frontier 40
Initial-to-Initial vs. Initial-to-Normative 6.00% Average of 10-Yr Rates over 1,000 Scenarios 5.00% 4.00% 3.00% 2.00% Initial to Initial Initial to Normative 1.00% 0.00% 0 2 4 6 8 10 12 14 16 18 20 Projection (Years) Source: Conning Analysis 41
Example - Asset Model Calibration Parameters Source: Conning Analysis 42
Example - Asset Model Calibration Parameters Source: Conning Analysis 43
The question to extend or not extend? Economic Value ($millions) 8,500 8,000 7,500 7,000 6,500 6,000 5,500 Life Insurance Efficient Frontier Example 1 2 3 4 5 6 7 8 9 10 11 C D E F B A 5,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 Risk G K J I H Initial to Initial Asset Allocation: A B C D E F G H I J K Overall Duration 3.6 4.5 5.9 6.5 7.1 7.7 8.3 8.9 9.5 10.1 10.7 Initial to Normative Asset Allocation 1 2 3 4 5 6 7 8 9 10 11 Overall Duration 2.7 3.3 3.6 4.7 5.3 5.9 6.5 7.7 8.3 9.5 10.7 Source: Conning analysis 44
The question to extend or not extend? Even Our Former Fed Chair Can t Refi Source: U.S. Federal Reserve History. http://www.federalreservehistory.org/people/detailview/12 Accessed on 10/23/2014 45
The Efficient Frontier Progressive Analysis Asset Only Efficient Frontier Examine Projection Biases Standalone Asset Performance Optimization on Total Return EV Efficient Frontier MV of Assets minus PV of Liabilities Incorporate Liabilities and Liability Constraints Asset classes include Government Bonds, Corporate Bonds and Equity PVDE Efficient Frontier Profit based Efficient Frontier Incorporates Liabilities and Solvency Constraints Asset classes include Government Bonds, Corporate Bonds and Equity ALM Efficient Frontier Source: Conning Analysis C11:2173029 46
Efficient Frontier Analysis Optimization Metrics Source: Conning Analysis
Reward Reward PVDE vs Economic Value (EV) Efficient Frontiers EV Regime PVDE Regime 250 80 60 200 40 20 150 0 100-20 -40 50-60 -80 0 0 100 200 300 400 500 Risk -100 0 10 20 30 40 50 60 Risk EV under EV PVDE under PVDE PVDE under EV EV under PVDE Source: Conning Analytics 48
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