Taxable and Tax-Deferred Investing with the Limited Use of Losses*

1. Introduction

The tax treatment of an individual investor’s trading gains and losses is an important factor influencing household portfolio choice. While trading in conventional taxable accounts can lead to realized taxable gains, trades in tax-deferred accounts are not taxed. As tax laws limit contributions into and early withdrawals out of tax-deferred accounts, individual investors not only have to decide which assets to hold (the asset allocation problem), but also in which account to hold them (the asset location problem). Given tax-deferred accounts are typically retirement savings vehicles, tax considerations can be important drivers of retirement savings decisions.

In early work, Black (1980) and Tepper (1981) show that, with unlimited borrowing, the ability to short sell, and an equal tax treatment of capital gains and losses, defined-benefit pension plans should only hold risk-free assets in their portfolios. By introducing the asset location problem into a household portfolio choice problem, Shoven and Sialm (1998) argue that households should prefer these assets in their tax-deferred accounts. However, many private investors hold substantial amounts of equity in their tax-deferred retirement accounts (Bergstresser and Poterba, 2004). According to the 2010 Survey of Consumer Finances, 85.9% of all families investing in equity have equity holdings in tax-deferred accounts and 42.3% of all equity was held in tax-deferred accounts. This discrepancy between theory and behavior is commonly called the asset location puzzle (Amromin, 2003).

Later research has focused on introducing frictions in the Tepper–Black setting to break the strict preference for risk-free assets in a tax-deferred account. These frictions include the tax-inefficiency of actively managed mutual funds (Shoven and Sialm, 2003), stochastic labor income and/or wealth shocks (Amromin, 2003; Dammon, Spatt, and Zhang, 2004; Garlappi and Huang, 2006; Huang, 2008), trading restrictions such as short-selling and borrowing constraints (Garlappi and Huang, 2006), the Roth-Conversion and Re-characterization option (Dammon, Spatt, and Zhang, 2011), and differential stock market participation costs in taxable and tax-deferred accounts (Zhou, 2012). Our article contributes to this line of research by showing that the tax code itself, namely the different tax treatment of capital gains and losses, can help explain the asset location puzzle.

For investors trading in tax systems with an equal tax treatment of capital gains and losses who face no trading constraints, Huang (2008) generalizes the Tepper–Black results to a dynamic setting and shows that investors prefer risk-free assets in their tax-deferred accounts. However, this result does not generalize to a feature common in most tax systems, namely that capital gains and losses are subject to different tax treatments. The different tax treatment of capital gains and losses causes two additional opposing effects influencing the asset location decision. First, a tax loss is a less attractive compensation than an immediate tax rebate payment since it leaves the investor with the full immediate downside risk, thus making the risk-return profile of equity held in taxable accounts less desirable. Hence, it increases the desirability of holding equity in a tax-deferred account. Second, the opportunity to be compensated with a tax loss carry-forward improves the set of attainable future risk-return profiles in a taxable account. In particular, loss carry-forward from previous trading thus increases the desirability to hold equity in a taxable account.

Our work generalizes Shoven and Sialm (2003) by showing that not only the tax-efficiency of stock portfolios, but also the different tax treatment of capital gains and losses affects the optimal location of assets to taxable and tax-deferred accounts. Specifically, we show that even if equity is taxed at a lower rate than risk-free assets, investors might optimally hold equity mutual funds in tax-deferred accounts when capital gains and losses are subject to different tax treatment.

While the impact of the opportunity to invest in a tax-deferred account has been extensively studied (Shoven and Sialm, 1998, 2003; Dammon, Spatt, and Zhang, 2004; Poterba, Shoven, and Sialm, 2004; Garlappi and Huang, 2006; Huang, 2008; Gomes, Michaelides, and Polkovnichenko, 2009; Zhou, 2009), only limited guidance is available to investors who face tax systems where capital gains and losses are subject to different tax treatments. In a single taxable account setting, Marekwica (2012) and Ehling et al. (2015) argue that a differential tax treatment of capital gains and losses can have a large impact on optimal portfolio choice.

Our contribution to the literature is two-fold. First, to the best of our knowledge, we are the first to study the impact of the differential taxation of capital gains and losses on the asset location decision. Second, we show that with differential tax treatment of capital losses the optimal location of assets depends on the investor’s tax rates on capital gains, dividends, and interest as well as the tax-efficiency of the stock portfolio.

The remainder of this article proceeds as follows. Section 2 introduces our life cycle model and discusses portfolio implications of the different tax treatment of capital gains and losses. Section 3 provides numerical evidence on the impact of the limited use of losses for the optimal location of assets to taxable and tax-deferred accounts. Section 4 demonstrates how tax-timing considerations affect the optimal asset location decision. Section 5 provides international evidence. Section 6 concludes. The technical details on how we solve the optimization problem are provided in the Appendix.

2. The Model

2.1 Asset Returns and Taxation

Since their introduction, equity mutual funds have increased in popularity among private investors as these investment vehicles allow investing in a diversified stock portfolio even when the amount invested is relatively small. We therefore assume that investors in our model hold equity through a well-diversified equity mutual fund.¹ We consider a market in which investors have access to a diversified equity mutual fund and a risk-free money market account. The constant pre-tax risk-free return on the money market account is denoted by r. The return on the equity mutual fund is assumed to be binomially distributed,² serially independent, and is assumed to come with an expected pre-tax capital gain of μ, and a standard deviation of σ. It further distributes a constant pre-tax dividend rate of d. The tax applicable to capital gains in taxable accounts is denoted by τ_g. The tax rate on dividends is denoted by τ_d. Interest and other income is taxed at a rate of τ_i. For early withdrawals from tax-deferred accounts prior to retirement age we follow Dammon, Spatt, and Zhang (2004) and assume that a penalty tax of τ_p applies.

2.2 Full and Limited Use of Losses

Following Ehling et al. (2015), we refer to the tax systems with equal and different tax treatment of capital gains and losses as tax system with full and limited use of losses, respectively, throughout. Definitions 1 and 2 highlight the differences between them: 

A tax system with the full use of losses is widely assumed in the portfolio choice literature in the presence of taxes (Dammon, Spatt, and Zhang, 2001, 2004; Amromin, 2003; Shoven and Sialm, 2003; DeMiguel and Uppal, 2005; Gallmeyer, Kaniel, and Tompaidis, 2006; Garlappi and Huang, 2006; Huang, 2008; Gomes, Michaelides, and Polkovnichenko, 2009; Zhou, 2009). However in reality, realized losses do not result in immediate tax rebate payments in most tax systems around the world.

Definition 2

In contrast to a full use of losses tax system, tax authorities do not share the downside risk resulting from a capital loss with investors under the limited use of losses. Instead, investors receive a tax loss carry-forward (henceforth TLCF) that can be used to offset future capital gains and can be carried forward indefinitely.³ The TLCF is a less attractive compensation than an immediate tax rebate payment for two reasons. First, in contrast to a tax rebate payment, the TLCF cannot be invested and thus does not earn any profits. Second, the TLCF carries the risk of being forfeited if it is not used by the end of the investor’s life. In the following, we describe the tax treatment of capital gains and losses in the tax system with the limited use of losses in more detail.

The limited use of losses carries two important disadvantages relative to the full use of losses. First, the TLCF cannot be consumed or invested. It therefore does not earn any profits. Second, a TLCF which is not used until the end of the investor’s life is forfeited. Both these disadvantages provide incentives for holding equity in tax-deferred accounts. In the next subsection, we argue that it is sufficient to break a replication argument that is often used to argue in favor of a pecking order asset location rule that preferentially locates bonds in tax-deferred accounts. Our numerical analysis in Sections 3 and 4 shows that it is also a sufficient condition for holding stocks in tax-deferred environments for reasonable parameter assumptions.

2.3 The Replication Argument

In the remainder of this section, we show that the different tax treatment of capital gains and losses is sufficient to break the replication argument. The replication argument used by Black (1980), Tepper (1981), and Huang (2008) focuses on a one-period investment horizon and asks how many dollars have to be invested in a taxable account in a given asset to attain the same level of wealth after taxes as investing one dollar in the same asset in a tax-deferred account.

However, the replication argument heavily relies on the assumption that the full use of losses applies. With the limited use of losses, the replication argument breaks down. It is no longer possible to replicate the final wealth after taxes from an investment of one tax-deferred dollar in a mutual fund in a taxable account. Whereas for g  ≥  0, the replicating portfolio of holding $11−τg$ dollars in the mutual fund and $−τg(1−τg)(1+(1−τi)r)$ dollars in the risk-free asset still generates a level of total final wealth of 1  +  g; for g  <  0 it leaves the investor with $1+g1−τg$ dollars, reflecting that from Equation (5), capital gains and losses are subject to a different tax treatment.

For g  <  0, the replicating portfolio only consists of one unit of the mutual fund, leaving the investor with 1  +  g dollars in case that it indeed turns out that g  <  0. For g  ≥  0, however, the investor is left with only $1+g(1−τg)$ dollars. In other words, the investor is no longer able to perfectly replicate the outcome of a tax-deferred dollar of wealth invested in the mutual fund in a taxable environment as this would require ex-ante knowledge about whether g  ≥  0 or g  <  0. The replication strategy thus breaks down.

In Sections 3 and 4, we demonstrate that for reasonable parameter assumptions, it can be optimal to preferentially hold equity mutual funds in tax-deferred accounts or to hold mixed portfolios in both accounts under the limited use of losses.

2.4 Optimization Problem

We consider an economy consisting of investors living for at most T years that can only trade at time t  =  0,1,…,T and retire at time J. F(t) denotes the probability that the investor is still alive through period t (t  ≤  T). Investors in that economy derive utility from the consumption of a single good and have CRRA-utility with parameter of risk-aversion $γ∈[0,∞)$⁠.

As shown in Constantinides (1983), investors endowed with unrealized capital losses should realize these losses immediately when trading in a tax system with the full use of losses. Gallmeyer and Srivastava (2011) and Marekwica (2012) show that realizing losses immediately remains optimal in a setting with the limited use of losses. Intuitively, this is because realizing the tax loss makes it more flexible in terms of future use. In particular, a realized tax loss from one share can be used to offset future gains in a different number of shares.

Investors endowed with unrealized gains, however, face a trade-off between postponing the tax payment associated with the realization of their gains and diversifying their portfolios. Following Dammon, Spatt, and Zhang (2001), Dammon, Spatt, and Zhang (2004), Gallmeyer, Kaniel, and Tompaidis (2006), and Ehling et al. (2015), we do not differentiate between long-term and short-term capital gains, and assume that the investor’s tax basis used for computing realized capital gains is the weighted average of her historical purchase prices. Even though under current US tax law investors can choose to sell the shares with the lowest level of unrealized gains first and thereby potentially postpone the taxation of more gains, solving for the optimal consumption–investment strategy over the life cycle in such a setting becomes numerically intractable. Moreover, DeMiguel and Uppal (2005) show that certainty equivalent wealth losses from using the average instead of the exact share identification basis rule are very small.

With $St+$⁠, we denote the number of shares the investor holds in a taxable account from time t to t  +  1. P_t is the price per share at time t. We assume that the equity mutual fund follows the recommendation in Constantinides (1983) and realizes losses immediately. Furthermore, it realizes a fraction $ν∈[0,1]$ of unrealized capital gains to adjust its portfolio to circumstances. ν  =  1 corresponds to a case where the fund realizes all gains periodically, which is equivalent to considering a setting without tax-timing option where all capital gains are subject to mark-to-market taxation. ν  <  1 corresponds to a setting where the mutual fund makes use of the tax-timing option. The case ν  =  0 implies that the mutual fund’s trading strategy never imposes a tax burden on the investor and that the investor can fully exploit the tax-timing option. The parameter ν is determined by the tax-efficiency of the equity mutual fund’s trading strategy. We therefore vary ν throughout Section 4 to demonstrate its impact on optimal asset location decisions.

By $Pt−*$ we denote the investor’s historical purchase price (tax basis) of the equity mutual fund in the taxable account at time t after realization of losses and a fraction ν of the investor’s unrealized gains, but before realization of further gains. $Pt+*$ is the investor’s tax basis after trading at time t. $St−$ is the number of shares the investor holds at time t after realization of losses and a fraction ν of unrealized gains, but prior to realization of further capital gains and purchases of new shares.⁵

Our optimization problem can be simplified by normalizing both the objective function and the constraints by W_t and summarizing information on the level of unrealized gains as a ratio in a single variable. The simplified optimization problem is solved numerically using backward induction. The technical details are outlined in the Appendix.

2.5 The Limited Use of Losses and Asset Location

Garlappi and Huang (2006) show in a stylized two-period model that with portfolio constraints in the taxable account, risk averse investors have an incentive to hold mixed portfolios of the risk-free asset and the risky asset in both accounts to smooth the tax-advantage from the tax-exemption of profits in the tax-deferred account through different states. In this section, we proceed in a manner similar to Garlappi and Huang (2006) and demonstrate that the limited use of losses creates another incentive to hold mixed portfolios in both accounts even when the investor does not face borrowing and short-selling constraints in the taxable account.

Consequently, even if moving some equity holdings from the taxable to the tax-deferred account may increase the investor’s indirect utility, the implied increased marginal utility of a possible future TLCF implies that the investor eventually reaches the point where it is no longer optimal to move more equity from the taxable to the tax-deferred account. Hence, the changing marginal utility of a possible future TLCF can lead to a violation of the pecking order asset location rule.

Whereas in the work of Garlappi and Huang (2006), the desire to smooth the volatility of the tax subsidy resulting from the tax-exemption of profits causes an incentive to hold mixed portfolios in both the taxable and the tax-deferred account, the limited use of losses causes yet another incentive for such mixed portfolios. In Sections 3 and 4, we demonstrate that for reasonable parameter assumptions, these two incentives can cause investors to hold mixed portfolios in both the taxable and the tax-deferred account.

2.6 Base Case Parameters

Throughout, we consider an investor who makes decisions annually starting at age 20 years (t  =  0). The maximum age the investor can attain is set to 100 years (T  =  80). It is assumed that the relative risk-aversion of the investor is γ  =  5, which is in the range of values considered reasonable by Mehra and Prescott (1985). The annual subjective utility discount factor is β  =  0.96. Annual inflation is set to i  =  3.2%. The pre-tax return on the risk-free money market account investment is set to r  =  4.1%. The expected return on the equity mutual fund is μ  =  8.1%, its standard deviation is σ  =  19.6% and the pre-tax dividend rate is d  =  2%. This choice of parameters is in line with historical values as reported in Dimson, Marsh, and Staunton (2002). Estimating the equity premium has been the subject of much theoretical and empirical research (see, e.g., Siegel (2005) for a survey). While the historical US equity premium is around 7.7% (Dimson, Marsh, and Staunton, 2002), economists doubt whether this will be true in future periods. We therefore choose a somewhat lower equity premium that roughly corresponds to that of the world index as reported in Dimson, Marsh, and Staunton (2002). We assume that the tax rate on capital gains is τ_g  =  20%. Dividends as well as interest and other income is taxed at a rate of τ_d  =  τ_i  =  35%.⁹ The penalty tax for early withdrawals from tax-deferred accounts prior to retirement age is set to τ_p  =  10% as under current US tax law.

Mandatory retirement age is J  =  65. To keep our model numerically tractable, we follow Dammon, Spatt, and Zhang (2004) and assume that nonfinancial labor income N_t is a constant multiple of wealth. Labor income is typically a regular stream of positive cash flows and can be viewed as a coupon-bearing bond with stochastic coupon payments. Labor income therefore has an effect on the asset allocation decision (Cocco, Gomes, and Maenhout, 2005). More generally, the asset allocation decision heavily reflects an individual’s desired risk versus return trade-off. For that purpose, potentially preexisting risk factors, such as labor income risk, are important. The asset location decision on the other hand, is primarily driven by the goal of tax-optimizing an investment strategy. For tax-optimizing purposes, however, the exact modeling of an individual’s labor income stream should not have a first-order effect. We assume that nonfinancial labor income is n  =  15% of effective wealth $WtE$⁠, which we define as wealth that effectively belongs to the investor and on which fiscal authorities do not have a claim: $WtE=Wt−τgmax(St−(Pt−−Pt−*)−Lt−,0)$⁠. That is, $Nt=0.15·WtE$⁠. We adjust for potential unrealized gains to avoid an economically implausible link between nonfinancial income and the realization of capital gains. During retirement we assume that nonfinancial income drops to 10.5% of her effective wealth, corresponding to a replacement ratio of λ  =  70%, which is in the range of replacement ratios empirically estimated by Cocco, Gomes, and Maenhout (2005). During the accumulation phase until retirement age J, the employer contribution is set to k  =  10% of the investor’s labor income, roughly corresponding to the average contribution reported in Huberman, Iyengar, and Jiang (2007). Survival probabilities are set to the survival probabilities for female investors according to the 2001 Commissioners Standard Ordinary Mortality Table. Table I summarizes our choice of base case parameters.

3. Numerical Results with Mark-to-Market Taxation

3.1 Structure of Optimal Portfolios

We begin our numerical analysis by studying the structure of optimal portfolios. Specifically, our goal is to illustrate how the limited use of losses impacts optimal asset location decisions. We begin the discussion of our results in a setting with mark-to-market taxation, that is a setting where ν  =  100%. Throughout, we report the optimal equity exposures $αT,t*=St+PtSt+Pt+Mt$ and α_D,t as fractions of taxable and tax-deferred wealth invested.

Figure 1 depicts the optimal taxable (left graphs) and taxable equity exposures (right graphs) for an investor who trades in a tax system with the full use of losses (Panel A) or the limited use of losses (Panel B) as a function of the investor’s age and the fraction of wealth held in a tax-deferred account. For the setting with the limited use of losses, we consider an investor who is not endowed with a tax loss from previous trading. The top panel of Figure 1 confirms the classical finding of Black (1980), Tepper (1981), Dammon, Spatt, and Zhang (2004) and Huang (2008) and documents that an investor trading in a tax system with the full use of losses optimally follows a strict pecking order asset location rule and prefers holding equity in taxable and money market mutual funds in tax-deferred accounts. With the full use of losses, the investor prefers holding the asset that is subject to the highest tax rate in the tax-deferred account. In general, such an asset location strategy maximizes the investor’s expected benefits resulting from the tax exemption of profits in tax-deferred accounts. Investors trading under the full use of losses prefer holding even the most tax-inefficient mutual funds in taxable accounts.

The bottom panel demonstrates that explicitly acknowledging the limited use of losses found in many tax laws around the world has an overwhelming impact on the optimal location of assets to taxable and tax-deferred accounts. In fact, the optimal location is reversed. Whereas with the full use of losses the investor follows a pecking order asset location rule that preferentially locates equity mutual funds in taxable accounts, with the limited use of losses the investor preferentially holds equity in tax-deferred accounts.

This rather extreme result is entirely driven by the change in the taxable treatment of realized losses in assets held in taxable accounts. Whereas with the full use of losses, the investor gets an immediate tax rebate payment of τ_g times the realized loss, with the limited use of losses the investor is not compensated in cash, but only receives a tax loss carry-forward that can be used to offset future realized gains. As already mentioned above, a tax loss is a less attractive compensation than an immediate tax rebate payment because it cannot be consumed or invested. Furthermore, it carries a risk of never being used and thus being forfeited. In particular, our risk averse investor gets the tax rebate payment when it is most valuable to her, that is in situations where she faces a loss on her equity investments. That is, with the full use of losses, capital gain taxation does not only reduce the mutual fund’s expected return but also its after-tax downside risks in that fiscal authorities share these risks with the investor.¹⁰

With the limited use of losses, however, the investor bears the entire immediate downside risk and because optimal portfolios are not changing dramatically over time, realized losses are typically not used for an extended period of time. As a consequence, the risk-return profile of equity mutual funds held in taxable accounts gets substantially less attractive. Specifically, tax authorities still put a tax burden on capital gains held in taxable accounts where they do not grant tax rebate payments on capital losses, but instead only provide the investor with a less desirable tax loss carry-forward. Our results show that this less attractive tax treatment causes the investor to optimally shift the preferred location of the equity mutual fund to the tax-deferred account where she still faces the full downside risk, but at the same time does not have to share capital gains with tax authorities. If, however, investors are endowed with a TLCF from previous periods, the ability to take advantage of the TLCF increases the incentive to hold equity in the taxable account.

3.2 Optimal Consumption–Investment Strategies over the Life Cycle

Examining optimal state-dependent portfolio decisions is useful in understanding the conditional differences between optimal asset location strategies for an investor trading in a tax system with full and limited use of losses. However, such an analysis does not indicate how likely it is that the investor ends up in a specific state. In this section, we therefore study the impact of the limited versus the full use of losses over the life cycle by performing Monte Carlo simulations on our numerically optimized grid. More specifically, we perform 10,000 simulations over the life cycle. We assume that the investor is neither endowed with unrealized capital gains nor with a tax loss from previous trading at the age of 20 years. We report optimal consumption, equity exposures in taxable and tax-deferred accounts, tax losses and the fraction of wealth held in a tax-deferred account conditional on survival.

Confirming the intuition from Figure 1, Table II shows that an investor trading in a tax system with the limited use of losses follow asset location strategies that are diametrically opposed to those of an investor trading in a tax system with the full use of losses. With the limited use of losses, the preferred location for equity mutual funds is the tax-deferred account, whereas with the full use of losses they are preferentially held in taxable environments.

Whereas the optimal consumption policy is hardly influenced by the limited use of losses, Table II shows that the allocation of wealth to taxable and tax-deferred accounts is essentially reversed. With the full use of losses the investor prefers holding equity mutual funds in taxable accounts, with the limited use of losses, the equity mutual fund is preferentially held in the tax-deferred account. The preference for equity in tax-deferred environments in tax systems with the limited use of losses implies that tax-deferred wealth on average grows at a stronger rate due to the equity premium the investor on average earns.

In total, our results presented in this section can help understanding why many private investors hold equity in their tax-deferred accounts. However, assuming mark-to-market taxation ignores the tax-timing option and thus potentially overestimates the impact of the limited use of losses. Furthermore, our results cannot explain why some investors prefer equity in taxable environments, whereas others hold mixed portfolios in both taxable and tax-deferred accounts. In Section 4 we therefore demonstrate that the optimal location of equity mutual funds to taxable and tax-deferred accounts heavily depends on the tax-efficiency, ν, of the mutual fund’s trading strategy. In particular, an investor trading a tax-efficient mutual fund should preferentially hold it in a taxable account, whereas an investor trading a tax-inefficient mutual fund should prefer holding it in a tax-deferred account. For intermediate levels of a mutual fund’s tax-efficiency, we confirm the intuition from Section 2.5 that it can be rational to hold mixed portfolios in both accounts.

4. Numerical Results with a Tax-Timing Option

Our results in Section 3 show that with the full use of losses, the investor should follow a strict pecking order asset location rule and preferentially hold equity mutual funds in taxable accounts. With the limited use of losses and mark-to-market taxation, equity mutual funds are preferentially held in tax-deferred environments. However, many tax codes around the world first tax capital gains when they are realized, thus providing investors with a tax-timing option. In particular, this option makes holding equity mutual funds in taxable environments more attractive as it essentially reduces the effective capital gains rate.

We next turn to the case where ν  =  0, that is, where investors can fully exploit the tax-timing option. From Table III, the tax-timing option does not affect optimal asset location decisions with the full use of losses. With the limited use of losses, however, the optimal asset location decision is heavily altered. With mark-to-market taxation (ν  =  1), investors prefer holding the mutual fund in the tax-deferred account. While when able to fully exploit the tax-timing option (ν = 0), they prefer holding equity mutual funds in taxable environments.