taxes and private wealth management

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Taxes and Private Wealth Management: After-tax Asset Allocation

March 24, 2007William Reichenstein, PhD, CFA

Tom Powers Professor of Investments

Baylor University

Texas Investment Texas Investment Portfolio SymposiumPortfolio Symposium

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Outline:

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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Should taxes matter in asset allocation?

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Assumptions

For simplicity, let’s assume the ordinary income tax bracket during retirement is 28%, tn = 0.28, --Ordinary income tax bracket before retirement is 28%, t = 0.28, and --Capital gain tax bracket before and during retirement, tc = 0.15.

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TDA versus Roth IRA Joe has $100 of pretax funds in a tax-

deferred account (TDA) and $72 of after-tax funds in a Roth IRA invested in the same asset.

They will buy the same amount of goods and services in retirement.

The $100 of pretax funds in TDA can be separated into $72 of 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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What is the Asset Allocation? $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.By failing to distinguish between pretax funds and after-tax funds, the traditional approach mixes apples and oranges. You can convert pretax dollars in TDAs to after-tax dollars by multiplying by (1 – tn), where tn is the tax rate at withdrawal in retirement

Lessons

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How do we calculate an after-tax asset

allocation?

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What is Jan’s Asset Allocation?

$500,000 Stocks held in TDA $500,000 Bonds held in taxable account

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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What is Jan’s Asset Allocation?

--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 tax-deferred accounts.

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How does the choice of savings vehicles affect the

portion of principal effectively owned by, return received by, and risk borne

by individual investors?

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After-tax Ending Wealth Models for Bonds and Stocks in Roth IRA, TDA, and Taxable Account

Beginning investment value: $1Bonds Stocks

Roth IRA (1+r)n (1+r)n

TDA e.g.,(401(k) (1+r)n (1-.28) (1+r)n (1-.28) Taxable Account (1+r(1-.28))n 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 yearsFor 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

Principal Returns RiskRoth IRA, bonds and stocks 100% 100% 100%TDA, bonds and stocks 72% 100% 100%Taxable Account bonds 100% 72% 72%

stocks, day trader 100% 72% 72%stocks, active investor 100% 85%85%stocks, passive investor 100% >85%>85%stocks, exempt investor 100% 100%100%

TDA denotes tax-deferred account such as 401(k)

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Risk Sharing for Active Stock Investor

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

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% 8% 16%Bonds 50% 5% 10%

Maximize Utility = E(return)-StDev/RiskTol = .0650 - .1024/2.53 = .0245

Constraints: S ≥ 0, B ≥ 0, S + B = 1.0Correlation between stocks and bonds = 0.2

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Jan’s Portfolio: Tax Oblivious

Market SavingsValue Vehicle

Stocks $500,000 TDABonds $500,000 Taxable acctTotal $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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Tax-Aware Optimization

Portfolio Expected Standard Weights Returns Deviation

Stocks TDA 0% 8% 16%Bonds TDA 42% 5% 10%Stocks Taxable 58% 6.8% 13.6%Bonds Taxable 0% 3.6% 7.2%

Active stock investorMaximize Utility = E(return)-Stdev/RiskTol = .0604 - .0965/2.53 = .0223Constraints: 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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Jan’s Portfolio: Tax Aware

After-Tax Market SavingsValue Value Vehicle

Bonds$360,000 $500,000 TDAStocks $500,000 $500,000

Taxable acctTotal $860,000After-tax Allocation: 58% stocksAsset Location: stocks in taxable accounts

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Other Target Asset Allocations

After-Tax Values 50% Stocks 70% Stocks

Bonds TDA $360,000 $258,000 Stocks TDA $0 $102,000Bonds Tax Acct $70,000 $0Stocks Tax Acct $430,000 $500,000Total $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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Logic of Asset Location

Stock management style

Asset Location Active Investor

1. Stocks in taxable accountsBonds in TDA (or Roth IRA)

15% tax rate

Tax exempt

2. Bonds in taxable accountsStocks in TDA (or Roth IRA)

28% tax rate

Tax exempt

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Generalized Advice on Asset Location

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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References

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.tiaa-crefinstitute.org/research/trends/tr020106b.html

Waltenberger et al, “The Expanding Roth IRA,” www.tiaa-crefinstitute.org/research/trends/tr030106.html

Reichenstein, “Tax-Efficient Sequencing of Accounts to Tap in Retirement,” See www.tiaa-crefinstitute.org/research/trends/tr100106.html

Jennings & Reichenstein, “The Literature of Private Wealth Management,” Research Foundation of CFA Institute, forthcoming.