tax adjusted portfolio optimization and asset …tax adjusted portfolio optimization and asset...
TRANSCRIPT
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Tax Adjusted Portfolio Optimization and Asset Location
Ashraf Al Zaman
(Co-author: Stephen M. Horan, CFA Institute.)
Northfield’s 22nd Annual Research ConferenceVenice, Italy
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Introduce Concept of Tax-Adjusted Portfolio Optimization (Asset allocation and location)
Outline Two Distinct ApproachesPretax Principal ValuesAfter-Tax Principal Values
Draw ExtensionsMultiple Dimension Taxing SchemeCost BasisTraditional IRA as Distinct from Roth IRA
Compare and Contrast Two Methods
Agenda
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• Asset Allocation: How should investors allocate their investment resources among various risky and risk-free assets?
• Asset Location: Given the availability of both taxable brokerage accounts (TBA) and tax-deferred retirement accounts (TDRA), how should investors locate the risky and risk-free assets in these two accounts?
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Tax EnvironmentTBA:Dividend and interest payments taxed at
individual income tax rateCapital Gains tax payable upon realization
of capital gainsTax-timing optionTDRA:No capital gains tax consequencesNo tax-timing optionTax at the time of withdrawalBasis step-up provision
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Asset allocation and locationEmpirical WorksShovena and Sialm (2003,JPUBE)Bergstresser and Poterba (2004, JPUBE),and Barber and Odean (2004, JPUBE )Dynamic Optimization FrameworkHuang (2008, RFS), Dammon et al. (2004, JF), and Amromin (EFR, 2003)Static Optimization FrameworkWilcox et al. (2006, CFA Ins.),and Reichenstein (2001,JWM, and 2007, FSR)Implementing the model
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• Taxes Affect Return• Taxes Affect Risk• Taxes Affect Asset Allocation• Tax Structures/Locations
–Each possible account-asset combination is a unique after-tax asset
What are the Implications?
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After-Tax Future Value Expressions for Various Tax Structures
nii trFVIF )]1(1[ −+=
cgcgn
cg ttrFVIF +−+= )1()1(
cgn
Taxable tBTTrFVIF )1(**)1(*)1( −−+−+=
)1(* cgcgddii tptptpr −−−=)1/()1(* cgcgddiicgdicg tptptpppptT −−−−−−=
)1()1( nn
TDA trFVIF −+=Tax-Deferred Account
Annual Tax
Deferred Capital Gain
Blended Tax Environment
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After-Tax Return – Tax Deferred Account
Value of a TDA Over Time
466
326
Pretax Value =
After-Tax Value = 70
0
50
100
150
200
250
300
350
400
450
500
0 5 10 15 20
Year
Val
ue
r = 8%
r = 8%
rTE = [(1+r)n(1-tn)]1/n-1 = 6.1%
Value of a tax-deferred account over time assuming an 8% pretax return and a 30% terminal tax rate.
)1()1( nn
TDA trFVIF −+=
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After-Tax Return – Taxable AccountValue of a Taxable Account Over Time
373
323
Pretax Value =
After-Tax Value = 80
0
50
100
150
200
250
300
350
400
0 5 10 15 20
Year
Val
ue
r* = r(1 - pdtd - poitoi - pcgtcg) = 6.8%
rTE = [(1+r*)n(1-T*) + T* - (1-B)tcg]1/n-1 = 6.0%
k = rf + (1 - pdtd - poitoi - pcgtcg)• (Rm - rf) = 7.3%
Value of a taxable account over time assuming an 8% return. The pretax return is 8%. The proportion of return taxed each year as ordinary income, dividends, and capital gains is 25%, 25%, and 0%, respectively. The tax rates on each of these forms of return are assumed to be 30%, 30%, and 25%, respectively. The original cost basis is assumed to be 60% of the initial pretax market value. The risk-free rate is 3%, the beta is one, and the market risk premium is 5%.
cgn
Taxable tBTTrFVIF )1(**)1(*)1( −−+−+=
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Pretax Value vs. After-Tax Value (ATV)
• Taxable Portfolios – A portfolio in a tax-free environment must
worth more than the same portfolio in a taxable environment
• After-Tax Portfolio Value (ATV)– The present value of after-tax cash flows the
portfolio is likely to generate– Incorporates expected tax liability associated
with dividends, taxable income, realized gains, and unrealized gains
– An investor’s economic welfare is determined by ATV
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Simple Example of After-Tax Asset Allocation
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Taxes and Investment Risk
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Tax-Adjusted Discount Rate for ATV• Tax- Adjusted Volatility
• Tax-Adjusted, Risk-Adjusted Discount Rate
• It Does NOT Equal
])([)1( ,, fmiiafiAfterTax rrEtrk −−+≈ β
iiaTaxablepretax t σσ )1( ,, −≈
iBeforeTaxiafmifiaiAfterTax ktrrErtk ,,,, )1(]})([){1( −=−+−= β
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Sample After-Tax Correlation Matrix
Taxable TDA
Equity Bonds Equity Bonds
Taxable Equity 1 0.0 1 0.0
Bonds 0.0 1 0.0 1
TDA Equity 1 0.0 1 0.0
Bonds 0.0 1 0.0 1
• Simple Example–Two uncorrelated asset classes–Two types of accounts
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Summary of Expressions
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Sample Inputs
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Pretax Efficient Frontier
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Tax-Adjusted Efficient Frontier: Pretax Principal Values
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Tax-Adjusted Efficient Frontier: After-Tax Principal Values
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Conclusions
Derivation and implementation of modelsTwo Approaches to After-Tax Portfolio Optimization
– Pretax Principal Values– After-Tax Principal Values
Pretax Principal
After-Tax Principal
AdvantagesFamiliar
Better represents capital at risk
DisadvantagesNegative returns
for short time horizons
Low volatility of non-equity
assets