Taxes and Private Wealth Management:
After-tax Asset Allocation
March 24, 2007
William Reichenstein, PhD, CFA
Tom Powers Professor of Investments
Baylor University
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Should taxes matter in asset allocation?
How do we calculate an after-tax asset allocation?
How does the choice of savings vehicles affect the portion of principal effectively owned by, return received by, and risk borne by individual investors?
How should taxes affect asset location?
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For simplicity, let’s assume the ordinary income tax bracket during retirement is 28%, t n
= 0.28,
--Ordinary income tax bracket before retirement is 28%, t = 0.28, and
--Capital gain tax bracket before and during retirement, t c
= 0.15.
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Joe has $100 of
The $100 of pretax deferred account (TDA) and $72 of funds in a Roth IRA invested in the same asset.
They will buy the same amount of goods and services in retirement. pretax separated into $72 of funds in a taxafter-tax funds in TDA can be after-tax funds plus
$28, the government’s share of the current principal.
TDAs include 401(k), 403(b), traditional IRA,
Keogh, etc.
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$100K in stocks held in TDA and
$72K in bonds held in Roth IRA
What is Joe’s asset allocation?
According to the traditional approach to calculating an asset allocation, it is 58% stocks and 42% bonds.
According to the after-tax approach, it is 50% stocks and 50% bonds.
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 The traditional approach is wrong, because it considers the TDA to be worth 39% more than the Roth IRA.
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By failing to distinguish between and after-tax pretax funds funds, the traditional approach mixes apples and oranges.
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You can convert pretax dollars in TDAs to after-tax dollars by multiplying by (1 – t where t n is the tax rate at withdrawal in retirement n
),
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$500,000 Stocks held in TDA
$500,000 Bonds held in taxable account
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For simplicity, assume cost bases equal market values of assets held in taxable accounts.
See Reichenstein (2006) and references therein for treatment of unrealized gains and losses.
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-According to the traditional approach, she has a 50% stocks-50% bonds allocation.
--According to after-tax asset allocation, she has $360,000 after taxes in stocks and
$500,000 in bonds for a 42% stocks-58% bonds allocation.
-The traditional approach exaggerates the allocation to the dominant asset held in taxdeferred accounts.
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After-tax Ending Wealth Models for Bonds and
Stocks in Roth IRA, TDA, and Taxable Account
Beginning investment value: $1
Bonds
Roth IRA
TDA e.g.,(401(k)
Taxable Account
(1+r) n
(1+r) n (1-.28)
(1+r(1-.28)) n
Stocks
(1+r) n
(1+r) n (1-.28)
Day Trader: (1+r(1-.28)) n
Active Investor : (1+r(1-.15)) n
Passive Investor: (1+r) n (1-.15)+.15
Exempt Investor: (1+r) n r=pretax return, n = investment horizon in years
For simplicity assume all stock returns are capital gains
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Principal Owned, Returns Received, and Risk Borne by
Individual Investors in Roth IRA, TDA, and Taxable Account
Roth IRA
TDA
, bonds and stocks
, bonds and stocks
Taxable Account bonds stocks, day trader stocks, active investor stocks, passive investor stocks, exempt investor
Principal
100%
72%
100%
100%
100%
100%
100%
TDA denotes tax-deferred account such as 401(k)
Returns
100%
100%
72%
72%
85%
>85%
100%
Risk
100%
100%
72%
72%
85%
>85%
100%
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Risk Sharing for Active Stock Investor
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Suppose pretax returns are -8%, 8%, and
24% in three years.
Mean = 8%, standard deviation = 16%
After-tax returns: -6.8%, 6.8%, and 20.4%.
Mean = 6.8% or 8%(1-.15) standard deviation = 13.6% or 16%(1-.15)
The individual receives 85% of returns and bears 85% of risk
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Risk Sharing for Bond Investor
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Suppose pretax returns are -5%, 5%, and
15% in three years.
Mean = 5%, standard deviation = 10%
After-tax returns: -3.6%, 3.6%, and 10.8%.
Mean = 3.6% or 5%(1-.28) standard deviation = 7.2% or 10%(1-.28)
The individual receives 72% of returns and bears 72% of risk
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How should taxes affect asset location?
Asset Location: Should bonds be held in retirement accounts and stocks in taxable accounts or vice versa?
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Tax-Oblivious Traditional
Optimization: Jan’s Portfolio
Pretax Pretax
Portfolio Expected Standard
Weights Returns Deviation
Stocks 50%
Bonds 50%
8%
5%
16%
10%
Maximize Utility = E(return)-StDev/RiskTol = .0650 -
.1024/2.53 = .0245
Constraints: S ≥ 0, B ≥ 0, S + B = 1.0
Correlation between stocks and bonds = 0.2
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Market Savings
Value Vehicle
Stocks
Bonds
$500,000 TDA
$500,000 Taxable acct
Total $1,000,000
Stock Allocation: traditional 50% (after-tax 42%)
Asset Location: silent; assumed stocks in TDA
Most people have primarily stocks in retirement accounts
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Stocks TDA
Bonds TDA
Stocks Taxable
Bonds Taxable
Portfolio Expected Standard
Weights Returns Deviation
0%
42%
58%
0%
8%
5%
6.8%
3.6%
16%
10%
13.6%
7.2%
Active stock investor
Maximize Utility = E(return)-Stdev/RiskTol = .0604 - .0965/2.53 = .0223
Constraints: S(TDA), B(TDA), S(t), B(t) ≥ 0,
S(TDA) + B(TDA) = 0.42,
S(TDA) + B(TDA) + S(t) + B(t) = 1
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After-Tax Market Savings
Value Value Vehicle
Bonds $360,000 $500,000 TDA
Stocks $500,000 $500,000 Taxable acct
Total $860,000
After-tax Allocation: 58% stocks
Asset Location: stocks in taxable accounts
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Other Target Asset Allocations
After-Tax Values
Bonds TDA
50% Stocks
$360,000
Stocks TDA $0
Bonds Tax Acct $70,000
Stocks Tax Acct $430,000
70% Stocks
$258,000
$102,000
$0
$500,000
Total
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$860,000 $860,000
Bonds and stocks should not be held in both retirement and taxable accounts …
… except liquidity reserves must be in taxable acct
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Asset Location
1.
2.
Stocks in taxable accounts
Bonds in TDA (or
Roth IRA)
Bonds in taxable accounts
Stocks in TDA (or
Roth IRA)
Stock management style
Active Investor
15% tax rate
Tax exempt
28% tax rate
Tax exempt
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Place bonds, REITs, hedge funds and other assets with returns subject to ordinary income tax rate in TDAs and
Roth IRAs.
Place stocks, especially passively held stocks, in taxable accounts.
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Reichenstein & Jennings,
Integrating Investments and the Tax Code, Wiley, 2003.
Reichenstein, “After-tax Asset Allocation,” Financial Analysts
Journal, July/August, 2006 .
Reichenstein, “Tax-Efficient Saving and Investing,” www.tiaacrefinstitute.org/research/trends /tr020106b.html
Waltenberger et al, “The Expanding Roth IRA,” www.tiaacrefinstitute.org/research/trends/tr030106.html
Reichenstein, “Tax-Efficient Sequencing of Accounts to Tap in
Retirement,” See www.tiaacrefinstitute.org/research/trends/tr100106.html
Jennings & Reichenstein, “The Literature of Private Wealth
Management,” forthcoming.
Research Foundation of CFA Institute ,
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