The Term Structure of Harvestable Losses: Why a Direct-Indexing SMA Ages, and When to Reset

Summary

Anyone who has watched a direct-indexing separate account for a few years has seen the pattern. Year one produces a large pile of realized losses, year two less, and by year five the harvest has thinned; by year ten the account is mostly a book of appreciated positions with little left to harvest. Practitioners call this the account aging. We have given it a formula. Our working paper then asks the question the qualitative story leaves open: when, if ever, does a refresh of the account's basis pay, and by which route?

Why the harvest decays

Positive drift acting on a population of tax lots is the mechanism. A lot is harvestable only while it trades below the price at which it was bought, and under a positive expected return the odds that a given lot does so fall as the lot ages. The winners that never dip run away from their basis and leave the harvestable pool for good. What remains is a small churning set of names near their cost, alongside a growing block of appreciated holdings that the account will carry to its exit. Figure 2 shows the two series moving in opposite directions as the account ages: the share trading below basis falls while the embedded gain rises.

We write each name's log-moneyness, the log of price over current basis, as a Brownian motion with drift, and read the harvesting policy as a lower barrier: a lot is harvested when its moneyness falls to the threshold, and its basis resets at that moment. That makes the probability that a fresh lot is ever harvested a first-passage probability, p = exp(-2mh/sigma^2). Everything follows from that one number. Per name, the lifetime number of harvests is p/(1-p), a finite budget the account spends down. A density recursion for the cross-section of moneyness integrates the full curve. Alongside it, a fixed-seed Monte Carlo of the same account traces the same curve name by name.

At the base calibration the year-one harvest yield is 20.3% of NAV from the formula against 19.5% from the simulation, and by year ten it is 2.8% against 2.7%. Nearly a quarter of the twenty-year harvest is realized in year one. Figure 3 overlays the analytic curve on the 40-trial Monte Carlo; Table 1 gives the full term structure. The level has an outside check. Our twenty-year cumulative harvest at the base calibration lands within a few points of the long-only average that Goldberg, Cai and Schneider report over 1995 to 2023.

The reset as impulse control

Refreshing basis costs something now and restores the steep early part of the harvest curve. There are three routes. Selling appreciated lots and repurchasing them is one, and it costs more with age because the embedded gain that must be realized grows with age; donating the lowest-basis lots to charity and rebuying the exposure is another; retiring the aged account into a diversified vehicle under section 351 and redeploying is the third.

A cap determines most of the answer: the value of a harvested loss is limited by how much outside gain the investor can shelter in a given year. The model resets once the decayed yield of the account falls below a threshold, which depends on the cost of the reset, on the discount rate, and on what a harvested loss is worth to the investor. Figure 4 plots lifetime value, as a present value in percent of NAV, against the reset period for the two interior cases. Each curve is humped. Its optimum is marked.

Table 2 puts figures on this. With a loss value of 40.8% and capacity of 5% of NAV a year, the optimal reset arrives at 6.7 yr, when the yield has decayed to 3.59%, and the uplift over never resetting is 639 bps of NAV. Raise capacity to 8% and the reset comes at 2.9 yr with an uplift of 1527 bps. At 2% the answer is never within 30 years. Where the account will end in a step-up in basis, the model usually prefers leaving it alone, even at a low yield.

Moving the reset date

Figure 5 draws the comparative statics.

Higher single-name volatility delays the reset, because more volatility means a higher hit probability and a larger lifetime budget. Table 3 shows that at 18% volatility the hit probability is 0.847 and the reset comes at 1.9 yr, while at 26% the hit probability rises to 0.948 and the reset moves out to 4.7 yr, with the year-one yield rising from 9.4% to 16.5%.

Contribution flow pushes in the same direction. New capital brings fresh lots. Those lots raise the floor the yield decays toward. Table 4 shows that with no contributions the yield floor in years 26 to 30 is 1.28% and the reset is at 6.7 yr, whereas with contributions of 3% of NAV a year the floor rises to 2.85% and the reset moves to 14.5 yr. At 6% the floor is 4.09% and the model never resets.

Outside-gain capacity has the largest effect, and it pulls the other way. In Table 5 the reset arrives at 18.8 yr when capacity is 3% of NAV a year, at 10.3 yr when it is 4%, and never at 2%.

So the rule the paper arrives at reduces to a comparison. The signal is the account's harvest yield set against the outside-gain capacity of the investor. When the yield falls through that line, the model refreshes basis through the cheapest available route, taking the charitable flush before the taxable partial liquidation.

Who this is for: CPAs and tax professionals, researchers and quants, and journalists covering direct indexing will find the aging formula and the reset rule useful.