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Capital gains taxes and optimal trading*

Mattia Landoni

Columbia Business School

[email protected]

December 7, 2013

Abstract

Capital gains taxes are a well known cost of trading. However, the actual “tax cost”

of selling appreciated assets is often negligible and sometimes even negative, because

depreciation or amortization allowances create an offsetting subsidy. No allowance

exists for stocks, making investors reluctant to realize gains (the “lock-in effect”). For

most other assets, however, investors should feel indifferent or even happy about

paying capital gains taxes.

I predict that property and casualty insurers are mildly reluctant to sell appreci-

ated taxable bonds, but very reluctant to sell appreciated tax exempt bonds. Because of

premium amortization, selling appreciated taxable bonds is cheap: one dollar of gain

realized today is matched by a one-dollar reduction in the taxable part of future in-

terest income. Selling appreciated tax-exempt bonds, however, is expensive: capital

gains are taxable, but premium amortization is worthless because interest is already

tax-exempt. I confirmmy prediction using regulatory filings that contain book value,

*PRELIMINARY—PLEASE DO NOT CITE WITHOUT THE AUTHOR’S PERMISSION. COMMENTS ARE WELCOME. ALLAPPENDICES ANDMOST FOOTNOTES NOTMEANT FOR PUBLICATION. Thanks to Charles Jones, my advisor; Dan Amiram,Glenn Hubbard, and Wojciech Kopczuk, my thesis committee; JK Auh, Andrew Ang, Colleen Honigsberg, Gur Huberman, WeiJiang, Tano Santos, Paolo Siconolfi, Morten Sorensen, Suresh Sundaresan, Steve Zeldes, the rest of Columbia Business Schoolfaculty, Rosanne Altshuler, Shmuel Baruch, Daniel Bergstresser, Andrew Ellul, Lorenz Kueng, and Ravi Sastry for free advice andsupport; Michael Graetz, Alex Raskolnikov, Sander Ross, David Wentworth, and Robert Willens for pro bono legal assistance andencouragement; Richard Burness, Paul Clifford, David Cruz, Robert Gordon, Marc Joffe, Andy Kalotay, Matt Kurzweil, John Levin,Rosalie Wolf, and the Wall Street community at large for sharing their real-world wisdom; and Edward Tufte for a personalizedcritique of some of my figures. All remaining mistakes were made, by no one in particular.

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Capital gains taxes and optimal trading

fair value, and transactions for all insurers’ bond positions. Taxes are a first-order

factor in the decision (not) to sell appreciated tax-exempt bonds in the period leading

up to the financial crisis; during the crisis, however, trading motives other than taxes

prevail temporarily.

1 Introduction

The capital market imperfections caused by one of the most important transaction-

based taxes, the capital gains tax, are not well understood. It is widely believed that cap-

ital gains taxesmake investors reluctant to sell appreciated assets—the so-called “lock-in

effect”. The logic in favor of “tax deferral” seems compelling: by deferring the sale of

an appreciated asset, investors get to reinvest their whole pretax gains once more before

paying taxes. For many assets, however, the immediate capital gains tax liability is not

the only consequence of realizing a gain: the sale of an appreciated asset also increases

future depreciation or amortization allowances. This benefit roughly balances the cost

due to the capital gains tax; on occasion, the benefit exceeds the cost, creating a net

incentive to sell. Thus, investors should feel happy or indifferent about paying capital

gains taxes for most assets.

The view that investors should be unconditionally reluctant to pay capital gains taxes

is not just held by a few confused investors. It is held by the very same policy makers

who write the tax code. As recently as 13 December 2012, the U.S. Senate Finance Com-

mittee minutes report ranking minority member Sen. Orrin Hatch as stating:

“There are a number of arguments on behalf of preferential tax treatment for capital

gains. [... I]nvestors can avoid paying the capital gains tax by simply holding on to

their capital assets. As a result, the capital gains tax has a lock-in effect, which reduces

the liquidity of assets and discourages taxpayers from switching from one investment

to another. This impedes capital flows to the most highly valued uses and is, therefore,

a source of economic inefficiency. The higher the rate, the greater the disincentive to

make new investments.”

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Mattia Landoni

In reality, looking at the capital gains tax rate in isolation can be deceptive. For instance,

consider an appreciated short-term bond. Under the current U.S. tax code, individual

investors have an incentive to sell the bond, if it is taxable, and to hold on to it, if it is

tax-exempt; and yet, the tax code applies the same capital gains tax rate in both cases.

The trading incentives created by the taxation of income can only be understood holis-

tically: one must jointly consider the treatment of capital gains, ordinary income, and

depreciation/amortization allowances, while taking the time value of money into ac-

count.

Many rules exist in the U.S. tax code that refer to gains from the sale of capital assets.

Which rules apply to which situation depends on the attributes of the transaction, the

asset, and the parties involved. These rules have been called a “labyrinth” (Burman,

1999). However, most of the labyrinth is designed around the simple principle that one

taxpayer’s income is another taxpayer’s expense.1 In the case of labor income, one dollar

of taxable income for an employee generates one dollar of deductible expense for the

employer. In the case of income from capital assets, one dollar of gains realized today

by the seller is matched by a one-dollar reduction in the taxable part of future cash flow

to the buyer.

For simplicity’s sake and without loss of generality, suppose the seller and the buyer

are the same person (a so-called wash sale). In a wash sale, the investor realizes taxable

capital gains today in exchange for some form of tax benefit tomorrow. If the asset is

a stock, the investor can obtain this benefit only when reselling the stock, and only in

the form of a lower capital gains tax. The tax due today and the future tax savings are

identical; thus, a wash sale has the undesirable effect of causing the investor to pay the

same taxes, but sooner. Therefore, the investor is reluctant to realize capital gains.2

If the asset is not a stock, however, the tax savings begin to accrue immediately and

in the form of lower ordinary income tax, thanks to a depreciation or amortization al-

lowance. The present value of a lower ordinary income tax could easily exceed the

1An early example of a finance paper that applies this principle to exchange-traded options is Con-stantinides and Scholes (1980).

2Even for stocks, this simple and intuitive logic sometimes fails. See, for instance, Dammon and Spatt(1996).

3


capital gains tax paid today; thus, executing a wash sale is profitable. If a wash sale is

profitable, there is no lock-in effect for any sale, even though an investor would appear

to “defer taxes” by selling later.

Section 3 formally develops this intuition into a stylized arbitrage argument that

reduces the complexity of the tax code to three parameters: τ , the ordinary income

tax, τG, the capital gains tax, and T, the time period over which the buyer’s benefit is

realized. The theory developed in Section 3 yields an asset-specific measure of trading

incentives: Θ, the “tax cost of selling”. Θ is defined as the change upon a wash sale in the

expected present value of all taxes paid over the life of the asset.

In order to highlight the utility of this novel “tax cost of selling” measure, I focus on

bonds. Although tax-exempt and taxable bonds have very different tax costs of selling,

they are otherwise very similar assets. I predict (Section 4) and verify (Section 5) that

property and casualty (P&C) insurance companies are very reluctant to realize capital

gains for tax-exempt bonds, but only moderately reluctant to do so for taxable bonds.

P&C insurers are the only category of investors holding hundreds of billions of dollars

in both taxable and tax-exempt bonds at the same time (historically 15-20% of allmunic-

ipal bonds outstanding). Detailed data on these holdings are available from regulatory

filings.

The results of Section 5 are not caused by sample selection, and they do not disap-

pear when comparing similar bonds held by the same insurer at the same time. Before

the 2008 financial crisis, the lock-in effect for tax-exempt bonds was strong; taxes and

transaction costs seemed to be the only two major factors in the decision of what bond

to sell. During the crisis, the coefficient came close to zero, indicating that tax trad-

ing temporarily became a minor concern. In one regression specification, I show that

trading by distressed firms in 2008 and 2009 was still sensitive to tax incentives. This

finding suggests that taxes still mattered for investors that sold to raise cash, though not

for investors that sold bonds perceived to be risky.

Besides the obvious consequences for portfolio optimization, the argument in this

paper indicates where to look for the effects of capital gains taxes on asset prices. The

fact that some investors are “locked in” by capital gains taxes may or may not distort

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Mattia Landoni

equilibrium prices and disrupt the efficient allocation of capital. Nonetheless, where

lock-in does not exist, taxes will certainly not distort asset prices, nor will they explain

anomalies such as momentum and reversal (Klein, 2001; George and Hwang, 2007) or

the January effect (Roll, 1981; Starks et al., 2006). As “big data” on bonds, real estate, and

whole firm acquisitions become available for academic study, it is crucial to knowwhich

investors face which incentives.

Finally, the arbitrage argument presented in this paper has important implications

for tax policy. Section 6 concludes with an examination of these implications. Though

Sen. Hatch’s desire for a “trading-neutral” tax code is almost universally shared by tax

policymakers, it appears that the actual U.S. tax code is already informed by a principle

of neutrality. I demonstrate this neutrality with a back-of-the-envelope calculation: us-

ing statutory tax rates and a range of reasonable discount rates, I show that capital gains

taxes should not create meaningful trading incentives for most assets, including taxable

bonds, noncorporate firms, and depreciable real estate. Thus, lock-in is limited to assets

with “special” tax regimes, such as corporate stocks and tax-exempt bonds. Regardless,

the policy implications of this paper do not depend on one’s view of whether the tax

code should or should not create trading incentives. For instance, a policy maker who

thinks that the tax code should encourage entrepreneurs to sell their firms still needs to

know which policies create which incentives.

2 Capital gains taxes: the literature as a teaching tool

This paper fills an important gap in the literature on optimal trading and optimal port-

folio, as well as in the public finance literature on capital gains taxes.3 The two literatures

are intimately connected. The point that a lock-in effect should exist for some assets

but not others is implied by Constantinides and Ingersoll (1984) in their analysis of opti-

mal bond trading with taxes, specifically for tax-exempt versus taxable bonds. A similar

3The term “lock-in” seems to have been used for the first time in a finance paper by Holt and Shelton(1961). However, investors’ reluctance to realize gains because of taxes is described already in a famousWall Street Journal article by Haig (1937). Haig describes the main implications for optimal trading andequilibrium prices, later formally modeled by Constantinides (1983); Seltzer (1951) recounts that capitalgains taxes were blamed for exacerbating the 1929 boom and bust.

5


understanding is implicit in the argument that few firm acquisitions are tax-motivated,

made by Gilson et al. (1988). However, the difference in tax treatment across assets con-

tinues to be the source of some confusion.

Of course, the theory literature on lock-in does not contain any statements that cap-

ital gains taxes lock in the owners of every appreciated asset, and that deferring tax

is always advantageous; neither does it contain any statements to the opposite effect,

unfortunately. A clueless graduate student who holds this incorrect belief could read

through every major work on the topic without ever changing his mind. In both Auer-

bach (1991) and Klein (2001), deferring a sale is always advantageous, because they only

consider stock-like assets; a working paper by Chari et al. (2005) assumes that all startup

firms are corporate entities.

Further, the empirical literature on optimal portfoliowith taxeswill not challenge the

student’s view, because it focuses almost entirely on stocks. Several recent papers show

evidence that taxable investors defer gains or take losses (Barber and Odean (2004) and

Ivković et al. (2005) for individual investors, Sialm and Starks (2012) for mutual funds).

Poterba and Bergstresser (2002) show that investors are reluctant to buy into funds that

have large unrealized capital gains. All these authors focus on stocks, and none of these

authors happen to discuss the difference between stocks and bonds.4

The empirical public finance literature on capital gains taxes also focuses on stocks, as

one can infer from statements like “if realizations of capital gains are responsive enough

[to a drop in tax rates], the tax rate on capital gains could be cut at no cost to the Trea-

sury” (Burman and Randolph, 1994). The reader should be convinced by now that in-

creasing capital gains tax revenue need not increase overall tax revenue: more capital

gains realized today means less ordinary income realized tomorrow for many assets.

In general, there is plenty of empirical evidence that investors trade stocks consis-

tently with tax incentives. I add to the scarce andmostly indirect evidence that investors

4Other papers are more focused on the pricing, as opposed to portfolio, implications of capital gainstaxes, but nonetheless focus on stocks: Dai et al. (2008) show that stock prices are at times pushed upbecause of lock-in, and at times depressed by the capitalization of future taxes (an effect also found byLang and Shackelford, 2000). Jin (2006) shows direct evidence that tax-sensitive institutional investorsare reluctant to sell appreciated stocks, sometimes preventing public information from being incorpo-rated into prices. Landsman and Shackelford (1995) show that individuals with higher unrealized capitalgains tendered their shares at a higher price in a leveraged buyout.

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Mattia Landoni

follow optimal bond trading policies. Constantinides and Ingersoll (1984) discuss opti-

mal trading of bonds with taxes; they conclude that, unlike in the case of taxable bonds,

realizing gains on tax-exempt bonds is never advantageous. To the best of my knowl-

edge, Section 5 presents the first-ever direct empirical evidence that any investors trade

bonds consistently with this advice.5,6

Finally, this paper contributes to the understanding of “how corporate capital gains

taxes influence firm behavior”, in the words of Desai and Gentry (2004), through the

use of the tax arbitrage approach. Arbitrage arguments are not foreign to tax planning

literature on mergers and acquisitions: similar arguments are used in multiple places

in Scholes et al. (2009), as well as in the above mentioned Gilson et al. (1988).7 This

paper demonstrates the wide applicability of the arbitrage method by providing new

evidence on the interaction between taxes and the bond trading of insurance compa-

nies, the largest category of taxable institutional investors in the United States.

3 Calculating the tax cost of selling

Upon a sale of an appreciated asset, the seller pays capital gains tax. The purpose of this

section is to propose a tax arbitrage argument to quantify Θ, the tax cost of selling. Θ is

defined as the change upon a wash sale in the expected present value of all taxes paid over the life

5Perhaps the reason why this very important finding has not been understoodmore widely is that (i) itis buried in Section 8 of the paper, and (ii) it is stated in a slightly indirect manner: “The main differencebetween the optimal trading policies for municipal and taxable bonds is that no trades are ever made at aprice above par since there is no advantage in establishing an amortizeable basis.” Strictly speaking, thisstatement is correct only because the authors assume the bond is issued at par. In reality,many tax exemptbonds are issued at a premium, as shown by Landoni (2013b), and therefore trades do happen—becauseit is possible to have unrealized losses, yet have a price above par.

6The closest to direct evidence is the finding by Starks et al. (2006) that individual investors in mu-nicipal bond closed-end funds engage in end-of-year tax loss selling. However, they do not discuss thedifference between taxable and tax-exempt bonds. Also focusing on end-of-year trading, Chang andPinegar (1986) explicitly look for evidence of tax-loss selling of taxable bonds, even though sometimes itcan be profitable to do tax-gain selling.Some indirect evidence was produced shortly after the publication of Constantinides and Ingersoll

(1984): Litzenberger and Rolfo (1984) suggest that the value of tax-timing options is included in the priceof Treasury bonds (which implies that taxable investors must be trading optimally, or else they wouldn’tvalue the opportunity to do so). However, Jordan and Jordan (1991) reexamine the same evidence andconclude it is less strong than initially thought. Green and Ødegaard (1997) and Elton and Green (1998)find evidence that tax-timing options have little or no effect on U.S. government bonds after 1986.

7For more on taxes and mergers see Scholes and Wolfson (1990, 1991); Erickson and Wang (2000);and Erickson and Wang (2007)’s finding that there are tax premia on the acquisitions of passthroughcorporations.

7


of the asset per dollar of capital gain realized. Upon realizing one dollar of capital gains, a

tax τG is paid; however, the actual tax cost of selling is almost always less than the tax paid

upon selling (Θ ≤ τG) because of future offsetting tax benefits. If Θ is negative, realizing

gains is advantageous in spite of having to pay a tax, and there is no lock-in effect.

Focusing on a wash sale is without loss of generality. In a “good faith sale” of an ap-

preciated asset, a taxable investor (1) realizes taxable gain and (2) gives up ownership. In

a “wash sale”, the investor realizes taxable gain only, by selling the asset and buying it

back immediately at the same price. Because a wash sale resets the unrealized gain to

zero (i.e., the asset is not “appreciated” any longer), after a wash sale an investor can ex-

ecute a good faith sale with no tax consequences. In other words, any sale from investor

A to investor B has the same tax and ownership consequences as a wash sale from A to

A, followed by a good faith sale from A to B. The wash sale carries only the tax conse-

quences, and the good faith sale carries only the ownership consequences. Because of

this “separability” result, we can focus on a wash sale and study the tax consequences of

selling in isolation.8

Θ is calculated assuming the following hypothetical scenario. An investor holding an

appreciated, income-producing asset is considering a wash sale. The economy is static

and the risk free interest rate is r > 0. The yield curve is flat: one dollar received t years

from now is worth (1+ r)−t dollars today. The tax code never changes. All ordinary

income from the asset is taxed at a flat rate τ , and all capital gains/losses at a flat rate τG.

(This implies that the government sends a check for τG to an investor who has realized

a one-dollar capital loss). Capital gains are defined as the difference between sale price

and tax basis, where tax basis is the book value of the asset for tax purposes.

3.1 Warm-up: a stock

The case of a stock should be familiar to every reader. For every dollar of capital gains

realized, there is an immediate tax liability τG. The tax basis is correspondingly in-

8The U.S. tax code contains rules voiding the tax consequences of certain wash sales. However, theserules apply only to realizing losses. Moreover, these rules do not affect the separability of the tax andownership consequences from an actual sale.

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Mattia Landoni

creased by one dollar, reducing the tax liability upon a future sale by the same amount

τG. Every year, the stock has a constant given probability λ of being sold. The tax cost

of selling incurred upon a wash sale is then9

Θ = τG

[1−

(λ

(1+ r)1+

λ (1− λ)1

(1+ r)2+ . . .

)]= τG

rλ+ r

> 0 (1)

Unsurprisingly, this quantity is always positive: for stocks there is a tax cost of realizing

gains, and a tax benefit of realizing losses. Equation (1) already makes clear that only if

one plans never to sell the stock again (λ = 0), is the tax cost of selling equal to the tax

paid.

3.2 General case: bonds and other assets

Stocks are unlike most assets when it comes to taxation. The tax regime of many assets

(bonds, noncorporate firms, non-owner-occupied real estate) includes a “depreciation”

or “amortization” benefit. Roughly speaking, for every dollar of capital gains income

realized now, the tax basis is increased by one dollar.10 Then, in each of the next T

years, both ordinary income and tax basis are reduced by an amount 1/T. Therefore,

in each year t ∈ {1, 2, . . .T}, the tax basis will be T−tT higher than it would have been

without the sale; if a sale occurs t < T years in the future, the future capital gains will

be correspondingly reduced by an amount T−tT . Because a tax rate τ applies to ordinary

9The probability that the position will be sold after exactly t years is

Pr(Sale at t

)· Pr(No sale at t− 1) · Pr(No sale at t− 2) · · · = λ (1− λ)t−1 .

The present value of expected tax savings in year t is therefore τGλ (1− λ)t−1

(1+ r)−t. Equation (1) is thesum of this term over all future years t = {1,2, ...∞}.10The mechanism described here is called “straight line amortization”. In fact, the amortization rules

vary by asset, and they are particularly complex for bonds. However, a more “realistic” model wouldyield only minor gains in accuracy.

9


income and a tax rate τG applies to capital gains, the tax cost of selling is

Θ = τG︸︷︷︸ − τ(

1

(1+ r)1· 1T

+(1− λ)1

(1+ r)2· 1T

+ . . .

)︸︷︷︸ +

Paid Expected benefit

today from amortization

− τG

(λ

(1+ r)1· T− 1

T+

λ (1− λ)1

(1+ r)2· T− 2

T+ . . .

)︸︷︷︸

Expected benefit from

lower future gains

Rearranging to highlight the differences between a stock and a general asset:11

Θ = τGr

λ+ r︸︷︷︸ − τG rλ+ r(1− λ)

(1−

(1−λ1+r

)T)T (λ+ r)︸︷︷︸ − (τ − τG)

1−(1−λ1+r

)TT (λ+ r)︸︷︷︸

Same as Benefit is Benefit is at

stock realized sooner different tax rate

(2)

The third term indicates that if τ is high enough compared to τG, tax cost can be negative,

i.e. realizing gains (instead of losses) can be profitable. Equation (1) is a special case of

(2) for T→ ∞.

3.3 Endogeneity of λ

Up to this point I have assumed that the probability of selling, λ, is a fixed, exogenous

quantity. However, the statement that capital gains taxes “lock in” the owners of appreci-

ated assets is actually a statement about the effect of tax cost of selling on the probability

of selling itself. Thus, today’s λt is a function of today’s Θt, and in turn Θt is a function

of all future λt+1, λt+2,... λT−1. This problem quickly becomes intractable. Still, Θ can

be a good approximation of the true cost of selling when investors trade optimally, if

its magnitude does not depend greatly on future λ’s. This is the case with infrequently

11See Appendix B for a detailed derivation.

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Mattia Landoni

.

.

.

.

.

.

.

.

QT

ax C

ost

Per

$ o

f G

ain

Rea

lize

d

T Maturity in Years

Taxable bonds r = %

λ = %

λ = %

λ = %

λ = %

λ = %

.

.

.

.

.

.

.

.

QT

ax C

ost

Per

$ o

f G

ain

Rea

lize

d

T Maturity in Years

Tax-exempt bonds r = %

λ = %

λ = %

λ = %

λ = %

λ = %

Figure 1: Θ (the tax cost of selling per dollar of gain realized) for taxable and tax-exemptbonds is plotted over T (bond maturity), assuming five different values for λ (one-yearprobability of selling). Θ is calculated as in Equation (2), assuming that the investor is aproperty and casualty insurer (interest and gains are taxed at 35%, tax-exempt interestat 5.25%). Especially at short maturities, ignoring the endogeneity of λ introduces onlya small bias in the estimated Θ.

11


f Logisticdistribution

.

.

.

.

.

- Shock to private valuation

Sale probability

Taxes

Figure 2: Reduced form model of trading. An investor holding an asset receives a ran-dom valuation shock ϵ, distributed according to the logistic distribution. If the tax costof selling is zero, the investor wants to sell the asset when ϵ is negative; the probabilityof selling is the entire shaded area to the left of zero. If the tax cost of selling is Θ > 0,however, only ϵ < −Θ is negative enough to cause the investor to sell the asset, reducingthe probability of selling to the darker-shaded area only.

traded assets such as bonds. Figure 1 compares the tax cost of selling for taxable and

tax-exempt bonds held by a property and casualty insurer. For all values of λ and T, the

tax cost of selling taxable bonds is always low; and it is always lower than the tax cost

of selling tax-exempt bonds. Thus, the sensitivity of Θ to the choice of a λ is negligi-

ble at short maturities of zero to ten years, at least for reasonable values of λ (0 to 10%

probability of selling per year).

Other potential objections to this simplified setup are discussed in Appendix (D).

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Mattia Landoni

4 Measuring the lock-in effect empirically

Suppose that an investor holding asset position i at time t observesmarket price Pi,t. The

investor’s private valuation is Vi,t = Pi,t + ϵi,t, where ϵi,t ∼ F (μ, σ) is a “private valuation

shock” term referring to the cumulative effect of private information, cost of trading,

and any other variable that would make the value of holding different from the value

of selling.12

Upon a sale, the investor also incurs a tax cost Θi · CGi,t where Θi is, as always, the tax

cost per dollar of capital gains realized on position i, and CGi,t is the unrealized capital

gains per dollar of asset value for position i at time t. The investor will sell whenever

selling is more advantageous than holding, as depicted in Figure 2:

Pr(Sale

)= Pr

(Vi,t < Pi,t −Θi · CGi,t

)= Pr

(ϵi,t < −Θi · CGi,t

)= F

(−Θi · CGi,t − μ

σ

)(3)

With appropriate assumptions on the shape of F (·), this equation describes a discrete

choice model and can be estimated. For instance, if F (·) is assumed to be the logistic

distribution, (3) describes a common logit model. In this section I describe how best to

estimate the model, and then I derive hypotheses about the coefficients. In Section 5 I

present the estimation results.

4.1 Specification

Equation (3) says that the coefficient on capital gains estimated by a discrete choice

regression (i.e., the effect of capital gains on propensity to sell) is equal to −Θi/σ. The

lock-in effect increases inΘi, the tax cost of selling, and decreases in σ, the cross-sectional

dispersion in selling motives across bonds (ϵ). For instance, think of two bonds, A and

B, each with one dollar of unrealized capital gains. The bonds’ tax cost of selling is re-

spectively ΘA = 0.1 and ΘB = 0.2. If the bonds are risk-free and identical, there is no

cross-sectional dispersion in selling motives (i.e., σ = 0). Only taxes matter, and the in-

12ϵi,t need not have zero mean; for instance, constant transaction costs would be included in μ. More-over, for the purposes of the current argument it does not matter whether the investor is “marginal” inthe sense of Dybvig and Ross (1986), i.e. indifferent to whether or not they hold the asset.

13


vestor will always sell bond A before bond B due to the lower tax cost. However, suppose

that the bonds are risky and the investor has private information indicating that bond

B will default (i.e., σ is very large). In this case, the tax cost becomes a minor concern.

Unobserved variation in selling motives can shrink the magnitude of the estimated

coefficient in the manner just described. Unobserved variation can also bias the value

of the coefficient if such variation is not independent of unrealized capital gains. Thus,

the main identifying assumption I need in order to estimate equation (3) is that any

unobserved variation is negligible, i.e., σ is small, and it is not correlated with unrealized

capital gains.

To minimize σ, I estimate equation (3) as a conditional logit model with fixed effects

for each unique combination of year, owner, tax treatment, andmaturity. For instance,

suppose that in year 2009 (year t), owner GEICO decided to sell a taxable bond in the 0

to 5 year maturity class (portfolio Bt). Which bond b ∈ Bt did GEICO sell? The equation

I estimate is

Pr(SaleBt,b,t

)=

expVBt,b,t∑i∈Bt expVBt,i,t

VBt,b,t = βTaxableCG CGBt,b,t + β

ExemptCG Exemptb × CGBt,b,t (4)

βTaxableCG = −ΘTaxable

σ; βTaxableCG + β

ExemptCG = −

ΘExempt

σ.

where Exemptb is 1, if bond b is exempt from U.S. federal taxes, and 0 otherwise.13 This

specification is meant to emulate the actual set of options available to a portfolio man-

ager who needs to sell a bond and must decide which. In particular, what matters is not

the absolute tax cost of selling, but the cost compared to the available alternatives.14

To further reduce σ, I use only bonds that are very safe (A-rated or better) and short-

13In this paper, I ignore state-level taxes. State taxes are a source of valuable identification, but alsocomplexity. The state where the insurer is chartered determines (a) whether bonds issued in the samestate are tax exempt; (b) whether out-of-state bonds are tax exempt; (c) which legal forms of organization(e.g. mutual or stock) are taxed; and (d) whether taxed insurers are taxed based on income, revenue, orother. Luckily, state-level taxes are “small” compared to federal taxes.

14Another apparently attractive specification uses fixed effects for each unique combination of bondand year. This specification would compare the same bond, at the same time, in two different portfolios,but only at the cost of ignoring heterogeneity in available options. Moreover, much welcome between-bond variation goes to waste, because unrealized capital gains for the same bond are highly correlatedacross portfolios at the same time.

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Mattia Landoni

Tax rates for property and casualty insurersOrdinary interest (τTaxable) 35%Tax-exempt interest (τExempt) 5.25%Capital gains (τG) 35%

Table 1: Statutory tax rates for property and casualty insurance companies (top bracket).P&C insurers are taxed similarly to ordinary corporations, but 15% of their tax-exemptinterest income is included in ordinary income, creating an effective tax rate of 5.25%.

or medium-term (0-5 or 6-10 years to maturity). Finally, I remove from the sample the

bonds with extreme gains or losses, defined as the top and bottom 1% of the distribu-

tion of unrealized capital gains for a given maturity class. I discuss potential leftover

weaknesses later in Section 5.2 (“Robustness”).

4.2 The tax regime of P&C insurers

Θ depends on the tax rates faced by the taxpayer; in order to form hypotheses on Θ, it is

necessary to focus on a specific case. A particularly interesting case is that of the bond

holdings of property and casualty (P&C) insurance companies. P&C companies have a

special tax regime, the main features of which are summarized in Table 1.

P&C companies are taxed as corporations, with a statutory rate of 35% for both in-

terest income and capital gains. However, 15% of tax-exempt income is included in

ordinary income. The effective statutory tax rate for tax-exempt income is therefore

15%× 35% = 5.25%. Capital gains on tax-exempt bonds enjoy no special treatment, and

thus capital gains on tax-exempt bonds held by P&C insurers are taxed at a rate that is

30 percentage points higher than the corresponding interest income rate. Usually cap-

ital gains are taxed at a lower rate than income (i.e. usually the third term of Equation

(2) is negative). Because of this, the tax-exempt bondholdings of P&C insurers might be

considered the most extreme case of lock-in in the entire tax code.15,16

15Because of other tax rules, P&Ccompanies are the only example of corporations holding ameaningfulamount of tax-exempt bonds. Moreover, tax-exempt bonds are the only asset subject to a large lock-ineffect that is nonetheless held almost exclusively by taxable investors. For this latter observation, I thankCharles Calomiris.16A potential confounding factor is the corporate alternative minimum tax (AMT). The “AMT income”

includes 70% of the income that escapes ordinary taxation, such as tax-exempt income. The corporateAMT rules apply to all tax-exempt income, unlike the more familiar individual AMT rules, which affectonly the income from certain well-specified tax-exempt bonds. AMT income is then taxed at a flat overallrate of 20% and the insurer must pay the higher of “traditional” tax and AMT. In practice, under the AMT

15


4.3 Hypotheses

I combine equations (3) and (2) with the information on tax rates, and state three main

hypotheses on the estimated coefficients on capital gains β̂iCG (i ∈ {Taxable, Exempt}).

1. For all i, τG ≥ τ i, hence Θi ≥ 0. There is lock-in for both taxable and tax-exempt

bonds:

E[β̂iCG

]= −Θ

i

σ< 0 (5)

2. τExempt ≪ τTaxable, hence ΘExempt > ΘTaxable. Lock-in is worse for tax-exempt bonds:

E[β̂ExemptCG − β̂

TaxableCG

]= − 1

σ

(ΘExempt −ΘTaxable

)< 0

3. β̂iCG should be consistent with “realistic” values of σ. For the logistic distribution,

σ = π√3StDev(ϵi,t).

4.4 Data

My main data source is the National Association of Insurance Commissioners (NAIC).

All U.S. insurers submit to the NAIC a quarter-by-quarter history of all bond positions

and transactions as part of their mandatory regulatory filings. I focus on the top 2,100

property and casualty insurers, corresponding to about 99.5% of all bond holdings by

dollar value of positions. Positions data provide very rich information, such as book

value, mark-to-market value, purchase date, and bond characteristics (coupon, matu-

rity, call features, coarse rating). Transactions data provide, among other things, transac-

tion date, consideration, and a description (“Maturity”, or “Call @ 100.00”, or “JP Mor-

rules, interest income and capital gains are taxed at a statutory rate of 20% while tax-exempt interestincome is taxed at a rate of 14.9% (=

(15%+ 85%× 70%

)× 20%). Thus, when the AMT rules apply, or are

expected to apply frequently in the future, the estimated Θmay shrink substantially.How often are P&C companies subject to the AMT, and does it matter? In theory, to maximize the

tax benefit from holding tax-exempt bonds, a P&C company should increase its holdings of tax-exemptbonds until the AMT and traditional tax liabilities are expected to be equal; such a policy may frequentlycause AMT income to be higher than “traditional” taxable income. In practice, however, the tax-exemptbond holdings of most P&C companies are substantially below the amount necessary to trigger the AMTrules. A casual observation of the actual average rates paid by P&C companies confirms that many ofthem are rarely subject to the AMT. Moreover, because of the “credit” feature of the AMT rules, a firmwill effectively pay the AMT in the long run only if the AMT income is higher, on average, in the longrun. Thus, for all these reasons, I believe that the AMT should not be an important factor in tax trading.

16

Mattia Landoni

One-quarter sale frequency Taxable Tax-exemptAt gain 4.8% 2.5%At loss 5.4% 3.7%

Table 2: Raw frequency of sales, broken down by gain/loss and taxable status. Eachnumber is significantly different from every other number at the 1% significance levelor better. Losses aremore likely to be realized than gains, but the spread is twice as largefor tax-exempt bonds, which are less likely to be traded in the first place.

gan Chase Securities”). Finally, the regulatory filings also provide firm-level financial

statement information, such as total capital gains realized, total assets, and capital and

surplus.

Additionally, Bloomberg provides information about the 206,389 distinct bond is-

sues that is not available from insurance company disclosures (i.e., tax status, issue price,

and other security-specific information). Finally, to estimate a time series of yields

and transaction costs, I use data on individual transactions from TRACE (for corporate

bonds) and the Municipal Securities Rulemaking Board (for municipal bonds).

NAIC data are quarterly and span from 2004q1 to 2013q2 (the latest available at the

time of writing). However, most variables are reported on a yearly basis and interpo-

lated. To use the freshest data, I match every year’s December 31 position information

to transaction information in the subsequent quarter. In order to establish whether

a transaction constitutes a sale, or something else, I manually classify 38,491 unique

transaction descriptions into a few categories (“Sale”, “Maturity”, “Call”, etc.). For 89,791

transactions out of a total of 5,780,764 I was not able to identify the type of transaction

to my satisfaction, and made an educated guess.

Many observations are excluded, as detailed in Appendix E. The remaining sample

has a total of 2,095,297 observations, each corresponding to a unique year-insurer-bond

combination, and 102,669 of which result in a sale. The sample includes stocks and U.S.

Treasury and Agency bonds; however, I do not use these in the subsequent analysis in

order to make the sample more homogeneous. Table 2 shows the raw frequency of

sales: for both taxable and tax-exempt bonds, losses are more likely to be realized than

gains, but the spread is twice as large for tax-exempt bonds, which are less likely to be

traded in the first place.

17


A. Base Logit B. Fixed Effects C. SampleSelection

D. Pre-Crisis

Capital Gains -0.04 -0.06 -0.05 -0.03[0.002]*** [0.000]*** [0.000]*** [0.000]***

Exempt x -0.03 -0.02 -0.02 -0.20Capital Gains [0.063]* [0.017]** [0.019]** [0.000]***

N. Obs. 1,004,074 491,845 491,845 177,704N. Clusters 9 7,262 7,262 2,541Cluster by Year (Year, Owner, Tax treatment, Maturity)

Table 3: Logit regressions of bond sale on unrealized capital gains (p-values in brackets).Capital gains have a significantly negative effect on the probability of sale (first row),but the effect is significantly more negative for tax-exempt bonds (second row). Thisresult is a robust feature of the data (column A) which holds after adding fixed effectsfor each unique combination of year, owner, tax treatment, andmaturity (columns B, C,D). The result is not caused by sample selection because it persists when adding indicatorvariables for how many years the position has been held (column C). Before the 2008crisis the effect is much larger for tax-exempt bonds (column D), and its magnitude isconsistent with theory. All regressions use 0-10 year maturity bonds.

Finally, about 87% of the sample consists of high quality bonds (rated A or better). I

use only these in the subsequent analysis unless otherwise specified. Another 11% of the

sample consists of lower investment-grade bonds. The balance consists of junk bonds

and stocks.

5 Results

5.1 Basic Results

Table 3 shows the results of logit regressions of bond sale on unrealized capital gains. All

regressions use 0-10 year maturity bonds, but results are similar for 0-5 and 5-10 year

bonds. Capital gains have a significantly negative effect on the probability of sale (first

row), but the effect is significantly more negative for tax-exempt bonds (second row).

This result confirms Hypotheses 1 and 2, and it is a robust feature of the data (column

A) which holds after adding fixed effects for each unique combination of year, owner,

tax treatment, and maturity (column B and Figure 3), as described in equation (4).

18

Mattia Landoni

Tax-exempt

Taxable

Unrealized Capital Gain as Percent of Market Value

0

2%

4%

6%

-5% 0% 5% 10% 15% 20%

1-Quarter Sale Frequency (Raw Data)

Tax-exempt

Taxable

Unrealized Capital Gain as Percent of Market Value

0

2%

4%

6%

-5% 0% 5% 10% 15% 20%

1-Quarter Sale Frequency (Fitted)

Figure 3: Sale frequency of taxable and tax-exempt bonds as a function of unrealizedcapital gains. These graphs represent the conditional logit specificationwith fixed effectsfor each unique combination of year, owner, tax treatment, and maturity.

5.2 Robustness

This subsection reports some interesting robustness checks. More can be found in Ap-

pendix A.

5.2.1 Sample selection

Sample selection may cause a violation of the identifying assumption that unobserved

variation in selling motives is not correlated with unrealized capital gains. Old bonds

are likely to have unrealized capital gains, especially when the yield curve is upward

sloping. At the same time, old positions may have survived in a portfolio because of

unobserved characteristics that make them less likely to be sold. One might then ob-

serve a negative correlation between capital gains and likelihood of selling, but for the

wrong reason. Sample selection subsumes several stories; for instance, suppose that

some bonds are bought as buy-and-hold investments and some others are earmarked

to provide liquidity. Liquidity bonds are likely to be traded often and to have a book

value closer to the actual price, because they are traded often and their book value is

updated often.

To address sample selection concerns, I add indicator variables for how many years

the position has been held (1 if the position is t years old, and 0 otherwise, for t =

19


β Exempt Year

Maturity 9 Average

- y Bonds - . - . - . - . - . 9 . - . 9 - . 9 - . - .

- y Bonds - . 9 - . 9 - . - . . - . - . - . - . - .

- y Bonds - . 9 - . - . - . 9 . - . - . - . - . - .

- y Bonds - . 9 - . - . - . 9 . - . - . - . - . - . 9

- y Bonds - . 9 - . - . - . . . - . - . - . 99 - .

Average - . - . - . - . . . - . - . - . - .

β Taxable Year

Maturity 9 Average

- y Bonds - . - . - . - . 9 - . - . - . - . 9 - . - . 9

- y Bonds - . 9 - . . - . . 9 - . - . 9 - . 9 - . 9 - .

- y Bonds - . 9 - . . - . . 9 . . - . - . - . 9

- y Bonds . - . . - . 99 . - . - . . - . .

- y Bonds - . 9 - . - . - . . 9 - . . - . . - .

Average - . - . . - . . - . 9 - . - . 9 - . - .

Table 4: The crisis brought about massive disruptions to trading. Before the crisis, thecoefficient is large and significant for every year and every maturity class. The coeffi-cient magnitude for tax-exempt bonds is consistent with random variation in tradingcosts, as explained in Section 5.2.3. In 2008, insurers engage in some gains trading butthey appear to prefer to realize gains on taxable bonds. After 2009, the coefficientsseem to slowly return to normal. As in Table 3, the column for year t uses position in-formation as of 31 December of that year to predict trading executed in the first quarterof year t+ 1.

{1, 2, 3, 4, 5}).17 The result is robust to this adjustment, as can be seen in column C

of Table 3.

5.2.2 The financial crisis and credit risk

The 2008 financial crisis brought aboutmassive disruptions to the financialmarketplace

that have not completely disappeared at the time of writing. Investors are said to have

traded for all kinds of nontax reasons, such as acting upon perceived private informa-

tion (“information trading”), raising cash (“liquidity trading”), or realizing gains in order

to report higher profits or capital (“gains trading”). Column D of Table 3 shows that the

coefficient is much larger (in absolute value) before the crisis. Table 4 shows that the

pattern predicted by tax trading appears in every period and everymaturity class in the

pre-crisis period, suddenly disappears in 2008, and only gradually reappears thereafter.

17Few bonds have been in the portfolio for more than five years, and adding more indicator variablesdoes not improve the regression fit, so these bonds are lumped into the “5” category for parsimony; theeffect on the main coefficient is negligible

20

Mattia Landoni

During the crisis, information trading may have dominated tax trading. As investors

rushed to differentiate good credits from bad ones, newly uncovered information and

irrational fear alike could have created meaningful variation in the ϵi,t term from equa-

tion (3), increasing σ in the denominator of the estimated coefficient. On the other

hand, before the crisis, tax considerations could have been important in the choice of

what bonds to sell. Bonds are relatively easy to value, and the bonds used in this study

are very safe. Default rates for A- or better-rated bonds are essentially zero, and this is

confirmed by the extremely low number of downgrades observed in the sample. Most

of the time, there would have been little private information to speak about.18

Other kinds of trading also appear to interfere with the measurement of tax trading.

The 2008 and 2009 columns of Table 4 show that P&C companies did show a mild

preference for realizing gains in these years—especially gains on taxable bonds. This

pattern could be explained by several mechanisms.

First, insurance companies have been known to engage in gains trading, i.e. realizing

gains on purpose to boost their regulatory capital. An insurer wishing to realize gains

would still prefer to realize them with the lowest tax cost possible, i.e. by selling taxable

bonds. However, Ellul et al. (2012, p.1) explain that “[f]or the most part, P&C insurers

do not engage in gains trading”, because their benefit in terms of regulatory constraints

is dubious.

Second, in the presence of temporarymispricings, investors trading on liquidity and

information alike would rather sell “good” assets and keep the ones that look unreason-

ably cheap, producing once again a pattern similar to that observed in the data.

In order to show that there is some merit to liquidity and information explanations,

I create a special variable corresponding to the empirical cumulative distribution func-

tion of shocks to capital and surplus in 2008 and 2009. I define a “shock” as net pretax

operating income (including underwriting gains or losses, changes in reserves, and net

investment income) divided by capital and surplus. For a considerable number of firms,

18Unobservable public information about credit quality would shrink the measured coefficient towardzero, but it would not bias the coefficients in one or the other direction: as long as all market participantsagree on a bond’s credit risk, the bond’s price will reflect this risk, and there would be no motive fortrading.

21


2008 Shock 2009 Shock

Capital Gains 0.0238 -0.002[0.2196] [0.4668]

Exempt x -0.2112 -0.1504Capital Gains [0.0015]*** [0.0165]**

N. Obs. 16,295 20,627

Table 5: In 2008 and 2009, tax trading is still important for those firms who are sellingbecause of large negative shocks to their surplus and capital, rather than because ofinformation about the bonds. Coefficients are interacted with the empirical cumulativedistribution function of shocks to capital and surplus. Thus, the coefficients reportedhere essentially describe the behavior of the worst-hit firms. The magnitude of thecoefficients is similar to that of the pre-crisis period in Table 3.

2008 operating results erased 20% or more of capital and surplus, likely causing a con-

siderable strain to liquidity. I then rank theN firms within a year, assigning rank i to the

one which received the i-th worst shock, and N to the one that received the most posi-

tive shock. The empirical cdf is then calculated as i/N, so that the estimated coefficient

can now be interpreted as the tax trading of the hardest-hit firm.

The “shock” variable contains useful information about trading motives because it

predicts sales at a high level of significance (hardest-hit firms will sell more). By looking

at the trading of the worst-hit firm, I should be able to isolate trading that happens

because of liquidity concerns rather than unobservable information about the bond.

Indeed, the results in Table 5 show that once again the coefficient on tax-exempt bonds

is large and significant.

5.2.3 Hypothesis 3: a calibration exercise

The magnitude of the coefficient is as important as its sign. To verify hypothesis 3, I

focus on the point estimates of the coefficients for tax-exempt bonds, and in particular,

those from the pre-crisis period. These coefficients should be consistent with mean-

ingful estimates of σ.

As in Table 4, I calculate the logit regression coefficient for every year and maturity

class, and take the average over the years from2004 to 2007 (“pre-crisis”) and 2008-2012

22

Mattia Landoni

Pre-crisis (2004-2007) Post-crisis (2008-2012)

−̂Θ/σStDev(ϵi,t) −̂Θ/σ

StDev(ϵi,t)Bond maturity Implied Observed Implied Observed0-5 years -0.27 0.61% 0.43% -0.06 2.65% 0.42%6-10 years -0.21 0.80% 0.61% -0.04 3.88% 0.61%11-15 years -0.18 0.92% 0.74% -0.02 9.87% 0.74%16-20 years -0.18 0.91% 0.85% -0.03 6.18% 0.84%21-30 years -0.14 1.18% 0.89% -0.01 23.57% 0.91%

Table 6: For tax-exempt bonds, themagnitude of the coefficient on capital gains −̂Θ/σ =β̂TaxableCG + β̂

ExemptCG implies a certain cross-sectional dispersion for the ϵi,t term of equation

(3). Before the crisis, “Implied” dispersion is consistent with the only realistic source ofcross-sectional dispersion in selling motives: transaction costs, directly and indepen-dently “Observed” using raw bond transaction data from the MSRB. With the onset ofthe crisis, “Observed” dispersion remains roughly constant while “Implied” becomesmuch larger, indicating other motives for trading. The coefficients are row averagesfrom Table 4. Details of the calculation are in the text. Units are percentage points oftrade par value.

(“post-crisis”). These coefficients, when combined with a rough estimate of Θ , give an

estimate for σ:19

E[β̂CG

]= −Θ

σ=⇒ σ̂ = − Θ̂

β̂CG≈ −(35%− 5.25%)

β̂CG

In turn, σ can be transformed into an estimate for the standard deviation of ϵ, because

we assumed ϵ is distributed according to the logistic distribution:

StDev(ϵi,t) =

√3π

σ̂

Howdoes one estimate the “true” standard deviation of ϵ in a way that is independent

of the regression results? At least before the crisis, the only meaningful source of cross-

sectional variation in selling motives across high quality bonds (especially short term

ones) was transaction costs. To independently estimate these costs, I use MSRB data on

individual transactions.20 I identify a “full trip” when I observe a customer buy trade

together with a customer sell trade of the same par amount for the sameCUSIP number

19Θ is simply estimated as the tax rate difference between capital gains (35%) and interest income (5.25%).This approximation ignores the different timing of cash flows and the probability of selling in the future(i.e., r = 0 and λ = 0). Calibrating the inputs more realistically would produce a less incorrect estimate.However, as shown in Figure 1, only a minor improvement would be gained. To avoid conveying a senseof false precision, I choose to use this simpler estimate.20I thank Andrew Ang for kindly sharing these data.

23


on the same day. For each full trip, the estimated cost of trading is equal to half of the

spread between the buy price and the sell price. The spread is measured in percentage

points: transaction costs of 0.54means 0.54% of trade size. Table 6 shows that in the pre-

crisis period, the magnitude and sign of the estimates are roughly consistent across the

two unrelated estimation methods; this provides further verification of the tax trading

hypothesis. With the onset of the crisis, dispersion in transaction costs remains roughly

constant and is dwarfed by other factors.

6 Conclusion

In this paper I make a simple tax arbitrage argument that identifies when capital gains

taxes are likely to create a “lock-in effect”, i.e., to make investors reluctant to sell appre-

ciated assets. The argument shows lock-in should only exist for “special” assets such as

stocks and tax-exempt bonds. For taxable bonds, and for many assets, future deprecia-

tion benefits roughly balance out the immediate cost of paying capital gains taxes.

In addition to the optimal portfolio implications demonstrated by this paper, this

insight has important policy consequences. For instance, assume without loss of gen-

erality that a “trading-neutral” tax code is optimal. Then, a policy maker would wish to

set the capital gains tax rate to a “neutral” level that creates exactly zero incentives. To

find this rate, we can set Θ = 0 in equation (2) and solve for τG:

τ ∗G = τ

/λ 1+ rr+ λ

+Tr

1−(1−λ1+r

)T (6)

Which, in the special case of a buy-and-hold investor (λ = 0), becomes

τ ∗G|λ=0 = τ1− (1+ r)−T

rT≡ τA

T(7)

where A ≡ 1r(1−

(11+r

)T)is the usual annuity formula for the present value of T annual

unit payments. Because A ≤ T (holding with equality only when the discount rate r is

zero), the “neutral” capital gains tax rate can never be larger than the ordinary income

24

Mattia Landoni

Individualtaxpayers,currentrates

“Neutral”τ∗ G

Tλ

ττ G

r=2%

r=5%

r=15%

10-yeartaxablebond

1015%

39.6%

20%

35%

29%

18%

2-yeartaxablebond

215%

39.6%

20%

38%

37%

32%

Tax-exem

ptbond(anymaturity)

1010%

0%

20%

0%

0%

0%

Noncorporatestock

155%

39.6%

20%

33%

27%

15%

Smallbusinesscorporatestock

∞5%

20%

0%

0%

0%

0%

Corporatestock

∞30%

20%

20%

0%

0%

0%

Rentalproperty(actualrentalincome)

30

5%39.6%

20%

28%

19%

8%Owner-occupiedhome(implied

rentalincome)

∞2%

0%

0%

0%

0%

0%

Land

∞2%

39.6%

20%

0%

0%

0%

Table7:Formanyassets(taxablebonds,noncorporateequity,depreciablerealestate)lock-inisnegligible(exceptions

aremarkedin

boldredfont).Theactualcapitalgainstaxrate

τ Gisoften

closetoits“neutral”counterpartτ∗ G(afunction

ofdiscountrate

r,one-yearsellingprobability

λ,depreciationhorizonT,andordinaryincometaxrate

τ).Some

non-obviousexam

plesof(rough)neutralityare:theexem

ptiononthefirsthalfmilliondollarsofcapitalgainson

one’sfirsthome,consistentwiththefactthat“income”from

livinginone’shomeisnottaxed(IRC§121sets

τ G=

τ∗ G=0consistentwith

τ=0);theam

ortizationofgoodwillandotherintangiblescreateduponthegainfulsaleof

noncorporatebusinesses(IRC§197setsT

=15);andtheexem

ptiononthefirsttenmilliondollarsofcapitalgainson

thesaleofsm

allcorporatestock(IRC§1202sets

τ G=

τ∗ G=0consistentw

ithT

=∞).Equation(6)alsohelpsmakesense

offeaturesoftaxcodesinotherplacesandtimes,such

asreducedorabsentdepreciation/amortizationbenefitsin

countriesthatlevy

notaxoncapitalgains(Oliver,2001,forthecaseofNew

Zealand)andtheso-calledGeneralUtilities

regimethatapplied

towholefirm

salesintheU.S.priortothe1986

taxreform

(ScholesandWolfson,1990).

25


tax rate:21

τ ∗G ≤ τ (8)

Table 7 reports a back-of-the-envelope calculation: reasonable discount rates r, sale

probabilities λ, and time horizons T are plugged into (6), and the resulting “neutral”

capital gains tax rate τ ∗G is compared with the actual tax rate τG. It is apparent that for

many assets the actual τG is not very far from τ ∗G, and is sometimes meaningfully lower;

hence, the lock-in effect should be weak and sometimes negative. The absence of lock-

in became directly observable for a short time in 2007, when several large private equity

partnerships went public. The partners sold a stake in the firm and paid capital gains

taxes, but theymaintained explicit ownership of the future amortization benefit created

by the transaction.22 Erickson andWang (2007) analyze a larger sample of noncorporate

firm sales, finding that such amortization benefits are valued by buyers. Other examples

of “neutrality” of the U.S. tax code are discussed in the caption of Table 7.

Inequality (8), combined with a widespread desire for a “neutral” tax code, might be

behind the worldwide custom of imposing low capital gains taxes (regardless of whether

a “neutral” tax code is optimal in a macroeconomic sense). Capital gains taxes are of-

ten prepaid taxes—not deferred as it is commonly said—and the preferential rate is

essentially a prepayment discount. In this sense, many income-based tax codes are not

too far from an “ideal” realization-based tax code similar to the ones proposed in Vick-

rey (1939), Auerbach (1991) or Auerbach and Bradford (2004). Many departures from

the “ideal” are deliberate and motivated by mundane tax administration issues, such as

fighting tax avoidance (Stiglitz, 1985) or reducing compliance cost for individuals (Str-

nad, 1995, on the market discount rules for bonds). In many cases, however, the tax

code seems to be designed to minimize trading distortions.

21This inequality holds for every λ. See Appendix B for a detailed derivation.22This unusual arrangement is called “tax receivable agreement” (TRA). This paper originated frommy

attempt to comprehend a New York Times article by Pulitzer prize-winning reporter David Cay Johnston(2007), “Tax loopholes sweeten a deal for Blackstone”.

26

Mattia Landoni

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31


Specification CG CG×Exempt N.Obs. CG CG×Exempt N.Obs.

1. Subsamples1.1 Only 0-5 year bonds -0.07 -0.02 217,830 -0.04 -0.23 69,5541.2 Only 6-10 year bonds -0.04 -0.03 182,028 -0.03 -0.18 77,6961.3 Only callable bonds -0.06 0.00 244,097 -0.03 -0.16 82,0891.4 Only noncallable bonds -0.05 -0.05 162,899 -0.04 -0.20 64,457

2. Alternative "Sale" variables2.1 Δ(Face Value of Position) -0.05 -0.07 502,640 -0.03 -0.15 183,9962.2 All year trading* . . . -0.03 -0.15 187,9582.3 Q4 trading -0.01 -0.04 173,731 0.05 -0.05 29,403

3. Potential omitted variables3.1 Bonds that never did, will downgrade -0.05 -0.04 284,602 -0.03 -0.23 114,1213.2 At-loss sales 0.04 -0.04 63,276 0.03 -0.06 44,2703.3 "Adding Controls" -0.05 -0.02 487,159 -0.02 -0.18 175,400

Not significant at the 5% levelPositive and significant

Full Sample Pre-crisis sample

Table 8: Robustness checks

A Some robustness checks

Table 8 reports some robustness checks. All regressions use the main specification

with portfolio-period fixed effects. The original sale variable is 1 if sale is recorded

in the first quarter of year immediately following balance sheet snapshot and 0 oth-

erwise; in “All year trading”, it is 1 if the bond is traded at any point in the next 12

months. In “Q4”, only the trading from the last quarter of the following year is used.

The “∆(Face value of Position

)” specification aims to capture sales that may have gone

unrecorded as transactions, but still reflected in next year balance sheet. “Downgrades”

and “At-loss” specifications indicate that the effect is not due to the fact that downgraded

bonds are likely to be sold, and to be sold at a loss. ”Controls” is a kitchen sink regression

that contains time to maturity, time from issuance, log issue size and number of insur-

ers holding the same bond at the same time (both measures of liquidity), and a dummy

variable for whether the bond is callable or not. The ”All year” regression for the full

sample caused Stata’s “clogit” procedure to go in overflow because of toomany positives

over too many observations in a cluster. If a reader is bothered, I will personally find a

way to make it work and report the results in an email.

32

Mattia Landoni

B Derivation of Θ, τ ∗G, and Equation (8)

B.1 Derivation of Θ

The tax cost of selling Θ is derived as follows. For simplicity, it is assumed that the yield

curve is flat, i.e. the value of 1 dollar in t periods is just (1+ r)t. Moreover, this is a partial

equilibrium argument and r is exogenous.23 Assume without loss of generality that an

investor is holding an asset with 1 dollar of unrealized capital gains. The asset is sold

with exogenous probability λ at every period.

For assets with a depreciation or amortization benefit, a wash sale has the following

consequences:

• Cost: pay capital gains tax τG today.

• Benefit: receive τ 1T amortization benefit every period until timeT, or until the asset

is sold.

• Upon a sale at time t < T, capital gains tax is reduced by τGT−tT .

The present value of cost net of benefits is:

Θ = τG︸︷︷︸ − τ(

1

(1+ r)1· 1T

+(1− λ)1

(1+ r)2· 1T

+ . . .

)︸︷︷︸ +

Paid Expected benefit

today from amortization

− τG

(λ

(1+ r)1· T− 1

T+

λ (1− λ)1

(1+ r)2· T− 2

T+ . . .

)︸︷︷︸

Expected benefit from

lower future gains

23In principle, this argument can affect the equilibrium rate r. In a world where government tax rev-enues are dumped in the ocean, executing this arbitrage increases the demand for real resources todaybecause more tax will be paid today, and viceversa reduces the demand for resources tomorrow. Even insuch a world, in most cases, r cannot adjust until there are no arbitrage opportunities because one price (r)cannot equalize bothmarginal utilities of consumption across time periods andmarginal tax rates acrosstrading strategies.

33


The “amortization” part simplifies as follows:

τ

(1

(1+ r)1· 1T

+(1− λ)1

(1+ r)2· 1T

+ . . .

)=

= τ · 1T

· 11+ r

·T−1∑t=0

(1− λ1+ r

)t=

= τ · 1T

· 11+ r

·1−

(1−λ1+r

)T1− 1−λ1+r

=

= τ1−

(1−λ1+r

)TT (r+ λ)

.

The “lower future gains” part on the other hand can be rewritten as

τG

(λ

(1+ r)1· T− 1

T+

λ (1− λ)1

(1+ r)2· T− 2

T+ . . .

)=

= τGλ

T (1+ r)

((T− 1) +

(1− λ1+ r

)1· (T− 2) + . . .

)=

= τGλ

T (1+ r)

T−1∑t=0

(1− λ1+ r

)t(T− 1− t) = . . .

and you have to trust me that this simplifies to24

· · · = τGλ

T (1+ r)

T1− 1−λ1+r

−1−

(1−λ1+r

)T(1− 1−λ1+r

)2 =

= τG

λr+ λ

− λ (1+ r)(r+ λ)

1−(1−λ1+r

)TT (r+ λ)

.

24Typing sum (T-1-t)*deltaˆt, t=0..(T-1) into Wolfram Alpha, one obtains

T−1∑t=0

δt (T− 1− t) = δT − δT+T− 1

(1− δ)2=

T1− δ

− 1− δT

(1− δ)2.

34

http://www.wolframalpha.com/input/?i=sum+%28T-1-t%29*delta^t%2C+t%3D0..%28T-1%29

Mattia Landoni

Putting everything together,

Θ = τG − τG

λr+ λ

− λ (1+ r)(r+ λ)

1−(1−λ1+r

)TT (r+ λ)

− τ 1− ( 1−λ1+r )TT (r+ λ)

(9)

Θ = τG

[1− λ

r+ λ

]+ τG

λ (1+ r)(r+ λ)

1−(1−λ1+r

)TT (r+ λ)

− τG 1− ( 1−λ1+r )TT (r+ λ) − (τ − τG) 1−(1−λ1+r

)TT (r+ λ)

Θ = τGr

λ+ r︸︷︷︸ − τG rλ+ r (1− λ)1−

(1−λ1+r

)TT (λ+ r)︸︷︷︸ − (τ − τG)

1−(1−λ1+r

)TT (λ+ r)︸︷︷︸

Same as Benefit is Benefit is at

stock realized sooner different tax rate

(10)

B.2 Derivation of τ ∗G

To derive τ ∗G, set (9) equal to zero and solve for τG:

0 = τG − τG

λr+ λ

− λ (1+ r)(r+ λ)

1−(1−λ1+r

)TT (r+ λ)

− τ 1− ( 1−λ1+r )TT (r+ λ)

τ1−

(1−λ1+r

)TT (r+ λ)

= τG

1− λr+ λ

+λ (1+ r)(r+ λ)

1−(1−λ1+r

)TT (r+ λ)

τ ∗G = τ

1−( 1−λ1+r )T

T(r+λ)

1− λr+λ +λ(1+r)(r+λ)

1−( 1−λ1+r )T

T(r+λ)

τ ∗G = τ1−

(1−λ1+r

)TTr+ λ 1+rr+λ

(1−

(1−λ1+r

)T)τ ∗G =

τ

λ 1+rr+λ +Tr(1−

(1−λ1+r

)T)−1τ ∗G = τ

/λ 1+ rr+ λ

+Tr

1−(1−λ1+r

)T (11)

35


If λ = 0, this becomes

τ ∗G|λ=0 = τ1− (1+ r)−T

rT≡ τA

T≤ τ

where A is the classic formula for the present value of an annuity of T unit payments.

This value can be at most T and is equal to T only in the case of no discounting, yielding

the last inequality. This inequality can be shown to hold for every value of λ ∈ [0, 1] by

showing that the denominator of (11) is always larger than one.

λ1+ rr+ λ

+Tr

1−(1−λ1+r

)T ≥ 1Tr

1−(1−λ1+r

)T ≥ r1− λr+ λUse the fact that

r+ λ1− λ

=r+ λ1+ r

· 1+ r1− λ

=

(1− 1− λ

1+ r

)· 1+ r1− λ

and simplify r on both sides:

T

1−(1−λ1+r

)T ≥ 11− 1−λ1+r · 1− λ1+ rAlso use the fact that

(1− xT

)= (1− x)

(1+ x+ · · ·+ xT−1

)= (1− x)

T∑t=1

xt−1.

to decompose the denominator on the left. Then,

T(1− 1−λ1+r

)∑Tt=1

(1−λ1+r

)t−1 ≥ 11− 1−λ1+r · 1− λ1+ rT∑T

t=1

(1−λ1+r

)t−1 ≥ 1− λ1+ rwhich is obviously always true, because the left hand side is equal to one when r = 0

and λ = 0, and greater than one otherwise; and conversely the right hand side is equal

36

Mattia Landoni

to one when r = 0 and λ = 0, and less than one otherwise. Thus, finally, the great truth

can be stated—a truth as simple and elegant as E = m · c2:25

τ ∗G ≤ τ

i.e., the neutral capital gains tax rate is at most as large as the ordinary income tax rate,

with equality holding only in the case of a perfect buy-and-hold investor with a discount

rate of zero.

C Econometric modeling choices

C.1 On the choice of a logit model compared to a linear specification

and other non-linear specifications

The model of Section 4 is cast as a discrete choice model. The choice is very natural

since the problem is, indeed, one of discrete choice. However, one may wonder if the

findings of this paper are robust to using a linear (OLS) specification. They are not, and

for a good reason. As it is clear by looking at the pattern in Figure 3, the difference in

slope between taxable and tax-exempt bonds is negligible, and turns out to be statisti-

cally insignificant (while both slopes are still negative and significantly different from

zero).

This discrepancy between specifications is not a problem in terms of the interpreta-

tion of the results, and in fact further strengthens the interpretation given in the text.

Figure 3 shows that within 25 percentage points (unrealized capital gains going from

-5% of asset value to +20%) the probability of sale drops rougly from 5% to 2% (taxables)

and from 4% to 1% (tax-exempts). While the drop is similar, the second drop is much

more dramatic if one considers that the probability cannot go below zero. The statisti-

cally significant difference between taxable and tax-exempt bonds is essentially driven

by the different level of the observed sale frequency between taxable and tax-exempt

25LOL, I didn’t think anybody would ever read this.

37


bonds.

A least squares linear specification measures the “average treatment effect” (see, e.g.

Angrist and Pischke, 2008). “Treatment” is a term borrowed from the medical science

to indicate a positive value of the explanatory variable, i.e. in this case the presence of

unrealized capital gains. The coefficient on capital gains should then be interpreted as

the effect of one unit of unrealized capital gains on the probability of a sale happening.

On the other hand, a choice model like the one of Section 4 measures the effect of

unrealized capital gains on an unobservable variable, the investor’s incentive to sell (Vb,

in the notation of Equation 4). In turn, the incentive to sell affects the probability of a

sale happening. This incentive is measured in percent of the asset’s monetary value and

is therefore the relevant variable for utilitymaximization. In this case, the coefficient on

capital gains should then be interpreted as the effect of one unit of unrealized capital gains

on the happiness to sell.

It is useful tomake a thought experiment to understand the practical meaning of this

difference. In the limit, if there were a law that prohibits people from trading bonds,

least squares would correctly measure no effect. However, the effect of capital gains on

the happiness to sell would be unidentified.

Which effect is the “right” effect to measure depends on one’s purpose. An econo-

metrician trying to see whether investors behave rationally would be interested in the

discrete choice effect. Similarly, a policy maker intent on creating a trading-neutral

tax code would be interested in the discrete choice effect. A market regulator intent on

explaining to the Senate Finance Committee the liquidity effects of capital gains taxes

would want to quantify the number of transactions that did not happen because of lock-

in, and may be interested in some transformation of the linear least squares effect. The

objective of this paper is closest to the first case (the econometrician) and the second

(the policy maker) and thus I chose to show the discrete choice estimates.

Finally, the estimates are not the product of specific assumptions on the functional

form. Similar estimates would have been obtained using other functional forms, such

as a Probit model instead of Logit. I chose Logit for tractability and because it allows

me to add a great number of fixed effects in a painless way.

38

Mattia Landoni

C.2 Law of one price

Each issuer reports an independent end-of-quarter value for each bond in their port-

folio. These values are not always the same. Because of this, a choice has to be made

whether to impose the law of one price, and use a common market price for every-

one, or to assume that everyone’s fair value estimate is the best estimate of the price they

can actually get if they were to sell the bond. In the opaque bond market (especially for

municipal bonds), there is no obvious choice. The results in the paper use the “subjec-

tive” price, but the results do not change by imposing the law of one price and using

instead the average of all prices reported for the same bond in the same period by all

institutions that own it.

D Discussion of simplifying assumptions

The arbitrage argument of Section 3 rests on several key simplifications, but is quite

robust.

Investors do not understand these things This is true, but the arbitrage argument

works even if investors do not understand it, as long as every agent trades to maxi-

mize their after-tax wealth. If markets are efficient, all the relevant tax information will

be reflected in prices, and investors will sometimes feel that they just can’t fetch a rea-

sonable price for their bondholdings in the current market, or that their holdings are

now overvalued by the market.

Will this hold in equilibrium? r is not exogenous This arguments is examined in

Landoni (2013a). The fact that an investor is (or isn’t) selling a bond may affect r (i.e.

the interest rate process is not exogenous). The main result in that paper is that tax

trading will in fact affect the equilibrium interest rate, but typically by not enough to

make the arbitrage argument invalid. The reason is that the amount of tax trading that

it is possible to do given the asset positions and tax bases inherited from the previous

period is limited. This limited amount is not guaranteed to move the price enough

39


to re-establish an unconstrained equilibrium. In other words, one price can adjust to

equalize marginal utilities across two states, or marginal tax rates across two trading

strategies, but not both.

Who is the marginal investor? Equilibrium results in Landoni (2013a) show that, as

long as there is a representative agent with well-defined tax rates, these results hold. In

other cases there may be no single price that makes each agents’ demand for each asset

finite, like in Dybvig and Ross (1986). Even in these cases, the argument is valid, but

lock-in may have little consequences on the efficiency of the allocation of capital in the

first place.

Risk Because of risk, it is not clear which discount rate applies to future changes in tax

liability. On the one hand, one could argue that the asset’s own discount rate includes

a risk premium, and under a symmetric tax code (where the government reimburses

taxpayers for a proportion τG of their losses), risk premia earned essentially go untaxed,

because both risk and return are reduced by a proportion τG. Thus, changes in future

tax liabilities should be discounted to present value using some tax-exempt, risk-free

spot rate curve. This is the stance chosen in this paper.

On the other hand, it is unclear whether all cross-sectional variation in expected

returns is due to risk premia, and it seems natural to apply the same discount rate to all

of the asset’s cash flows, including the change in after-tax cash flows upon a transaction.

It’s hard in theory tomotivate this choicewithout resorting to very detailed assumptions

about, say, the probability of actually being able to deduct losses from taxable income

in the future and obtain a benefit. Fortunately, Table

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