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Alpha, Beta, and Now… Gamma
David Blanchett, CFA, CFP®
Head of Retirement Research, Morningstar Investment Management
Paul D. Kaplan, Ph.D., CFADirector of Research, Morningstar Canada
© 2012 Morningstar. All Rights Reserved. These materials are for information and/or illustrationpurposes only. Morningstar Investment Management is a division of Morningstar which includesMorningstar Associates, LLC, Morningstar Investment Services, Inc., and Ibbotson Associates,Inc., all registered investment advisors and wholly owned subsidiaries of Morningstar, Inc. Allinvestment advisory services described herein are provided by one or more of the registeredinvestment advisor subsidiaries. The Morningstar name and logo are registered marks ofMorningstar. This presentation includes proprietary materials of Morningstar. Reproduction,transcription or other use, by any means, in whole or in part, withoutthe prior, written consent of Morningstar is prohibited.
2 For financial professional use only. See the last slides for important disclosures
Defining Value: Better Outcomes with “Gamma”
Beta
For illustration only.
Alpha
Gammathe additional value achieved from making moreintelligent financial planning decisions.• a non zero-sum game
the market/asset allocation exposures of aportfolio• equity allocation of the portfolio and
underlying asset class exposures
the residual or skill component• a zero sum game in the aggregate (after fees)
3 For financial professional use only. See the last slides for important disclosures
Different Types of Gamma
× Total Wealth Asset Allocation: Using human capital in conjunction with themarket portfolio to determine the optimal equity allocation
× Dynamic Withdrawal Strategy: Updating the annual withdrawal amount annuallybased on the ongoing likelihood of portfolio survivability and mortality experience
× Annuity Allocation: Longevity risk is perhaps the greatest fear among the retirees.Annuities allow a retiree to hedge away this risk and can therefore improve theoverall efficiency of a retiree's portfolio.
× Asset Location and Withdrawal Sourcing: where to place assets and where towithdrawal income in a tax efficient manner.
× Liability Relative Optimization: Asset allocation methodologies commonlyignore the funding risks associated with an investor’s goals, by incorporating theliability into the portfolio optimization process it is possible to build portfolios thatbetter hedge the risks faced by a retiree.
4 For financial professional use only. See the last slides for important disclosures
55+
Human Capital Market Portfolio
Ú
Financial Capital
Total Economic Wealth
?30
7045
Stocks (%)Bonds (%)
Total Wealth Allocation
For illustration only.
5 For financial professional use only. See the last slides for important disclosures
Dynamic Withdrawal Strategy
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
-$1.0 -$0.5 $0.0 $0.5 $1.0 $1.5 $2.0 $2.5
Perc
enta
ge o
f Tot
al D
istr
ibut
ion
Balance at Death
Spent too much money Didn’t spend enough money
For illustration only.
4% Initial Withdrawal Rate
6 For financial professional use only. See the last slides for important disclosures
Annuity Allocation
61%Outliving my
money inretirement
39%Death
Source: https://www.allianzlife.com/content/public/Literature/Documents/ent-1154.pdf
What do youfear most?
7 For financial professional use only. See the last slides for important disclosures
Asset Location and Withdrawal Sourcing
For illustration only.
Taxable AccountFirst
Traditional IRAFirst
Stocks inTaxable Account
Tax EfficientModerately
Efficient
Stocks inTraditional IRA
ModeratelyEfficient
Tax Inefficient
Withdrawal SequencingA
sset
Loc
atio
n
8 For financial professional use only. See the last slides for important disclosures
Liability Relative Optimization
For illustration only.
9 For financial professional use only. See the last slides for important disclosures
More Income with Gamma Optimization
$1.00 $1.00
$0.06$0.04
$0.09$0.02
$0.08
$0.00
$0.20
$0.40
$0.60
$0.80
$1.00
$1.20
$1.40
Asset Location and Withdrawal Sourcing
Liability Relative Optimization
Dynamic Withdrawal Strategy
Annuity Allocation
Total Wealth Asset Allocation
Base Income
Gamma OptimizedPortfolio
4% Withdrawal anda 20/80 Portfolio
$1.29
$1.00
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
10 For financial professional use only. See the last slides for important disclosures
Relationship Between Additional Income and Return Changes
-2.00%
-1.00%
0.00%
1.00%
2.00%
3.00%
-20% -10% 0% 10% 20% 30% 40% 50% 60% 70%
Chan
ge in
Ret
urn
Median Change in Retirement Income
4% Initial Withdrawal 5% Initial Withdrawal 6% Initial Withdrawal
+ 28.8% in retirement income isequivalent to a return increase of+1.82% (i.e., “Gamma-alpha”)
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
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Methodology
12 For financial professional use only. See the last slides for important disclosures
Calculating Gamma
× Gamma is the utility-adjusted income generated by the Gamma-optimized portfolio, which we denote as .
× We define as the constant payment amount that a retiree wouldaccept such that his or her utility would equal the utility of the actualincome path realized on a given simulation path
× This is given by = ∑ 1 +∑ 1 += the level of income in year t= the probability of surviving to at least year tT= the last year for which qt>0ρ = the investor’s subjective discount rate (5%)η = the investor’s elasticity of substation (EOS) preference parameter (.5)
13 For financial professional use only. See the last slides for important disclosures
Calculating Gamma
× There are two preference parameters (ρ and η) that describe howthe investor feels about having income to consume at different pointsin time, with no reference to risk.
× Following the approach in Epstein and Zin (1989), we treat theelasticity of substation as a parameter distinct from the risk toleranceparameter. We introduce the risk tolerance parameter (θ) next bytreating the path as unknown and evaluating expected utility.= − 1
Θ = risk tolerance parameter (.333)M= number of pathsi= which ofM paths is being referred topi = the probability of path i occurring which we set to 1/M.
14 For financial professional use only. See the last slides for important disclosures
Calculating Gamma
× We define Y as the constant value for that we yield this level ofexpected utility. This is given by
× We can now formally define the Gamma of a given strategy or set ofdecisions as
== −
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Total Wealth Asset Allocation
16 For financial professional use only. See the last slides for important disclosures
53+
Human Capital Market Portfolio
Ú
Financial Capital
Total Economic Wealth
?30
7047
Stocks (%)Bonds (%)
Targeting the Market Portfolio
For illustration only.
17 For financial professional use only. See the last slides for important disclosures
Financial Capital► Tradable assets such as stocks
and bonds have traditionally beenused when constructing an assetallocation
► Incomplete without consideringHuman Capital
Human Capital► An individuals ability to earn
and save
► Present value of all yourexpected future wagesincluding pension and socialsecurity
+
Individual Portfolio Assignment
For illustration only.
18 For financial professional use only. See the last slides for important disclosures
Life Cycle of Human Capital and Financial Capital
For illustration only.
19 For financial professional use only. See the last slides for important disclosures
Bounded Portfolio Equity Allocation
× Allocations are bounded by Morningstar Aggressive and Conservativeglidepaths
0%
20%
40%
60%
80%
100%
65 70 75 80 85 90 95 100
Equi
ty A
lloca
tion
AgeSource: Morningstar
For illustration only.
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Dynamic Withdrawal Strategy
21 For financial professional use only. See the last slides for important disclosures
Different Ways to Generate Income from a Portfolio
× Constant Dollar: fixed amount, increased annually by inflation, based onthe initial balance
× Endowment Approach: fixed percentage of portfolio value× RMD Method: 1 divided by the remaining retirement duration (life
expectancy)× Dynamically Updated Based on Survivorship Experience: based on
maintaining a constant probability of failure over the estimated remainingretirement duration, based on actual survivorship experience
The strategy tested in most withdrawal research
What financial planners help retirees with andwhat retirees are actually likely to do
22 For financial professional use only. See the last slides for important disclosures
Distribution of Balance at Death with “4% in 30 years”
0.0%
2.0%
4.0%
6.0%
8.0%
10.0%
-$1.0 -$0.5 $0.0 $0.5 $1.0 $1.5 $2.0 $2.5
Perc
enta
ge o
f Tot
al D
istr
ibut
ion
Balance at Death
Spent too much money Didn’t spend enough money
For illustration only.
23 For financial professional use only. See the last slides for important disclosures
Better Outcomes
× Dynamically updating the available income can both increase totallifetime income and improve portfolio survivability
× The more frequently a withdrawal strategy is updated/reviewed theeasier it is to make adjustments to help ensure on-going survivabilityand sustainability of the retiree’s portfolio
× Potential “failure”, to some extent, can be inevitable for somescenarios if a retiree wants to maximize lifetime income (i.e.,maximize lifetime happiness)
24 For financial professional use only. See the last slides for important disclosures
“4%” for All Ages
× 4% can be a great starting place for a ~65 year old couple× It is not necessarily valid for older/single retirees
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
20% 30% 40% 50% 60%5 20.0% 19.9% 19.9% 19.8% 19.9%10 10.4% 10.4% 10.5% 10.4% 10.5%15 7.2% 7.3% 7.4% 7.4% 7.5%20 5.7% 5.8% 5.9% 6.0% 6.0%25 4.8% 4.9% 5.0% 5.1% 5.2%30 4.2% 4.4% 4.5% 4.6% 4.7%35 3.8% 3.9% 4.1% 4.2% 4.3%40 3.5% 3.6% 3.8% 3.9% 4.0%
Equity Allocation
Num
ber o
f Yea
rsRe
mai
ning
25 For financial professional use only. See the last slides for important disclosures
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
Gamma of Dynamic Withdrawal Strategy
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Annuities
27 For financial professional use only. See the last slides for important disclosures
Inefficient Retirement Planning
× Defined benefit plans allow forlongevity risk pooling
× DC participants have todeal with longevity risk onan individual basis, whichis inefficient from a lifetime incomemaximization perspective
× Annuities represent one possiblesolution
28 For financial professional use only. See the last slides for important disclosures
Defining the Goal: Which Do You Fear the Most?
61%Outliving my
money inretirement
39%Death
Source: https://www.allianzlife.com/content/public/Literature/Documents/ent-1154.pdf
29 For financial professional use only. See the last slides for important disclosures
Do You Feel Lucky?
30 For financial professional use only. See the last slides for important disclosures
a Morningstar company
Allocation to DeferredVariable Annuities withGMWB for Life
James X. Xiong, Ph.D., CFAThomas Idzorek, CFAPeng Chen, Ph.D.,CFA®
®®
CFA Institute Research Foundationmonograph presenting research onlifetime finance
Award-winning paper on the integrationof human capital and asset allocation
Research paper focused on amethodology reflecting the features ofvariable annuities with GMWB for life
Incorporating Guaranteed Income
31 For financial professional use only. See the last slides for important disclosures
Human Capital
Collect Inputs
Financial Capitaland Current Savings
DetermineProduct Allocations
TraditionalProduct(s)
DetermineAsset Allocations
TraditionalFunds, ETFs
Product
InsLife Insurance
Determining Asset Allocations with Annuities
For illustration only.
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Asset Location and Withdrawal Sourcing
33 For financial professional use only. See the last slides for important disclosures
The Importance of Taxes
$162$222
$304
$171
$255
$388
$0
$100
$200
$300
$400
3% 5% 7%
Grow
th o
f $10
0 A
fter
25
Year
s
Annual Realized Return
Taxable Account Traditional IRAAnalysis assumes a 35% tax rate, where taxes are paid annually in the Taxable Account, but not until the end of the period in the Traditional IRA
34 For financial professional use only. See the last slides for important disclosures
Asset Location and Withdrawal Sourcing
For illustration only.
Taxable AccountFirst
Traditional IRAFirst
Stocks inTaxable Account
Tax EfficientModerately
Efficient
Stocks inTraditional IRA
ModeratelyEfficient
Tax Inefficient
Withdrawal SequencingA
sset
Loc
atio
n
35 For financial professional use only. See the last slides for important disclosures
Impact of Asset Location and Withdrawal Sequencing
Efficient 1/n Inefficient401k First 0.71% -4.06% -10.86%Split 3.83% 0.00% -3.75%Taxable First 8.23% 6.82% 4.95%
Efficient 1/n Inefficient401k First 0.07% -0.24% -0.78%Split 0.21% 0.00% -0.25%Taxable First 0.43% 0.36% 0.25%
Additional Income GeneratedAsset Location Portfolio Efficiency
Inco
me
Orde
r
Equivalent Return ImpactAsset Location Portfolio Efficiency
Inco
me
Orde
r
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
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Liability Relative Optimization
37 For financial professional use only. See the last slides for important disclosures
What is the TRUE risk for a portfolio that exists to fund (pay for) aliability?
× It is NOT the standard deviation of the asset portfolio
× It is NOT the performance of your asset portfolio relative to the assetportfolios of your peers
× The TRUE risk is that it won’t be able to pay for the liability!
What is Portfolio Risk?
38 For financial professional use only. See the last slides for important disclosures
Improving Portfolio Health
For illustration only.
39 For financial professional use only. See the last slides for important disclosures
What is Surplus Optimization?
× Surplus optimization is a special case (or extension) of traditional mean-varianceoptimization in which the optimizer is constrained to hold a combination of assetsrepresenting the liability short
× Surplus optimization is one element of a broader approach called liability-relativeinvesting or asset-liability management (ALM), which can include 1) durationmatching (a.k.a. immunization), 2) convexity matching, and 3) cash flow matching
× Surplus optimization focuses on the entire portfolio – assets and liabilities – not justthe assets of a portfolio
40 For financial professional use only. See the last slides for important disclosures
Surplus Frontier
Surplus Optimization
Standard Deviation
Expe
cted
retu
rn
Liability
Minimum Surplus Variance Portfolio
Asset Allocation decision insurplus optimization
MV frontier
Surplus optimization considers both the amount and the investment characteristics of theliability (funding ratio).
For illustration only.
41 For financial professional use only. See the last slides for important disclosures
Different Portfolios
For illustration only.
42 For financial professional use only. See the last slides for important disclosures
Return and Risk Impact
Liability-Relative
OptimizationAsset-Only
OptimizationGeometric Return 6.00% 6.00%Standard Deviation 7.45% 6.71%
Surplus Geometric Return 3.74% 3.66%Surplus Standard Deviation 6.79% 7.38%
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
43 For financial professional use only. See the last slides for important disclosures
Average Annual Returns for the Inflation Quintiles
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
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Conclusions
45 For financial professional use only. See the last slides for important disclosures
More Income with Gamma Optimization
$1.00 $1.00
$0.06$0.04
$0.09$0.02
$0.08
$0.00
$0.20
$0.40
$0.60
$0.80
$1.00
$1.20
$1.40
Asset Location and Withdrawal Sourcing
Liability Relative Optimization
Dynamic Withdrawal Strategy
Annuity Allocation
Total Wealth Asset Allocation
Base Income
Gamma OptimizedPortfolio
4% Withdrawal anda 20/80 Portfolio
$1.29
$1.00
For illustration only. Source: “Alpha, Beta, … and Now Gamma” by David Blanchett and Paul D. Kaplan, Morningstar White Paper
46 For financial professional use only. See the last slides for important disclosures
Relationship Between Additional Income and Return Changes
-2.00%
-1.00%
0.00%
1.00%
2.00%
3.00%
-20% -10% 0% 10% 20% 30% 40% 50% 60% 70%
Chan
ge in
Ret
urn
Median Change in Retirement Income
4% Initial Withdrawal 5% Initial Withdrawal 6% Initial Withdrawal
+ 28.8% in retirement income isequivalent to a return increase of+1.82% (i.e., “Gamma-alpha”)
For illustration only. Source: “Generating More Retirement Income with “Gamma” Portfolio Optimization” by David Blanchett, Morningstar White Paper
47 For financial professional use only. See the last slides for important disclosures
Conclusions
× Creating retirement income from a portfolio is complicated× There are a number different risks that need to be considered when
building an “optimal” retirement income portfolio× An optimized retirement income plan (i.e., Gamma optimized) can
generate 29% more retirement income than a naïve approach
48 For financial professional use only. See the last slides for important disclosures
× The information, data, analyses, and opinions presented herein do not constitute investment advice; areprovided as of the date written and solely for informational purposes only and therefore are not an offerto buy or sell a security; and are not warranted to be correct, complete or accurate. Past performance isnot indicative and not a guarantee of future results.
× Some of the author's calculations are based upon Monte Carlo simulations. Monte Carlo is an analyticalmethod used to simulate random returns of uncertain variables to obtain a range of possible outcomes.Such probabilistic simulation does not analyze specific security holdings, but instead analyzes theidentified asset classes. The simulation generated is not a guarantee or projection of future results, butrather, a tool to identify a range of potential outcomes that could potentially be realized. The Monte Carlosimulation is hypothetical in nature and for illustrative purposes only. Results noted may vary with eachuse and over time.
× Indexes shown are unmanaged and not available for direct investment. Although index performance datais gathered from reliable sources, Ibbotson Associates cannot guarantee its accuracy, completeness orreliability. Except as otherwise required by law.
Important Disclosures
49 For financial professional use only. See the last slides for important disclosures
For Information and/or illustrative purposes only. Not for public distribution.©2012 Morningstar. All rights reserved. Morningstar Investment Management isa division of Morningstar. Morningstar Investment Management includesMorningstar Associates, Ibbotson Associates, and Morningstar InvestmentServices; all registered investment advisors and wholly owned subsidiaries ofMorningstar, Inc. The information contained in this presentation is the proprietarymaterial of Ibbotson Associates. Reproduction, transcription or other use by anymeans, in whole or in part, without the prior written consent of IbbotsonAssociates, is prohibited.
The Morningstar name and logo are registered marks of Morningstar, Inc. TheIbbotson name and logo are registered marks of Ibbotson Associates, Inc.
50 For financial professional use only. See the last slides for important disclosures 50
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