now that supervised models have been constructed (GBT, RF, Logistic, LogisticNet, LinearReg) with reported PR & ROC-AUC scores implementation of portfolio-level performance metrics are necessary to how these models perform in a real stress test like total tax alpha, opportunity cost, performance against mechanistic oracle.
method of performance testing via backtesting simulation: run the full SimulationEngine on held-out years, use the trained model's scores to make harvest decisions at each timestep, and measure tax-alpha.
Tax alpha: $\alpha = ∑(P_{cost} − P_{harvest}) \times shares \times τ_{marginal}$
where the sum reprsents the total sum of harvested lots.
The importance of these metrics: A model with PR-AUC 0.942 could produce less tax alpha than a model with PR-AUC 0.85 if the former fires on correlated lots simultaneously (spiking $σ_{TE}$) or harvests too aggressively early in the year when $GYTDG_{YTD}$
$GYTD$ is high and misses better opportunities in October-November.
defined basis:
$\beta_{underlying_index}$ - the beta value of the underlying index, referred in context as the market's return beta essentially.
$\beta_{directindexing_portfolio}$ - an estimator (beta hat) of $\beta_{underlying_index}$
A small amount of tracking error risk (the replacement of asset or the removal of one isn't will create deviance from $\beta_{directindexing_portfolio}$)
For an immediate tax benefit (realized losses that can offset gains and sometimes ordinary income up to $3k a year), this is called tax-alpha as $\beta_{directindexing_portfolio}$ will under a very small tracking error still functionally match $\beta_{underlying_index}$.
In the case of $\sigma_{TE}$ even though $\sigma_{TE}$ can be treated as a thing that just increase the variance of $\beta_{directindexing_portfolio}$ has functionally no directional effect on portfolio EV while tax alpha $\alpha$ does havea direct measurable increase in EV, an overall positive EV tradeoff under the condition that tracking error is small enough. However this "functional" assumption breaks down if tracking error becomes too big, thats when the variance/deviance of the high enough tracking error can induce mroe noticable behaviors like bias error as well, $\beta_{directindexing_portfolio}$ an estimator of $\beta_{underlying_index}$ deviates away enough from $\beta_{underlying_index}$ which makes the portfolio less of a tax loss harvest tool for the goal of market-matching tax loss harvesting.
now that supervised models have been constructed (GBT, RF, Logistic, LogisticNet, LinearReg) with reported PR & ROC-AUC scores implementation of portfolio-level performance metrics are necessary to how these models perform in a real stress test like total tax alpha, opportunity cost, performance against mechanistic oracle.
method of performance testing via backtesting simulation: run the full SimulationEngine on held-out years, use the trained model's scores to make harvest decisions at each timestep, and measure tax-alpha.
Tax alpha:$\alpha = ∑(P_{cost} − P_{harvest}) \times shares \times τ_{marginal}$
where the sum reprsents the total sum of harvested lots.
The importance of these metrics: A model with PR-AUC 0.942 could produce less tax alpha than a model with PR-AUC 0.85 if the former fires on correlated lots simultaneously (spiking$σ_{TE}$ ) or harvests too aggressively early in the year when $GYTDG_{YTD}$
$GYTD$ is high and misses better opportunities in October-November.
defined basis:
$\beta_{underlying_index}$ - the beta value of the underlying index, referred in context as the market's return beta essentially.
$\beta_{directindexing_portfolio}$ - an estimator (beta hat) of $\beta_{underlying_index}$
A small amount of tracking error risk (the replacement of asset or the removal of one isn't will create deviance from$\beta_{directindexing_portfolio}$ )$3k a year), this is called tax-alpha as $ \beta_{directindexing_portfolio}$ will under a very small tracking error still functionally match $\beta_{underlying_index}$ .
For an immediate tax benefit (realized losses that can offset gains and sometimes ordinary income up to
In the case of$\sigma_{TE}$ even though $\sigma_{TE}$ can be treated as a thing that just increase the variance of $\beta_{directindexing_portfolio}$ has functionally no directional effect on portfolio EV while tax alpha $\alpha$ does havea direct measurable increase in EV, an overall positive EV tradeoff under the condition that tracking error is small enough. However this "functional" assumption breaks down if tracking error becomes too big, thats when the variance/deviance of the high enough tracking error can induce mroe noticable behaviors like bias error as well, $\beta_{directindexing_portfolio}$ an estimator of $\beta_{underlying_index}$ deviates away enough from $\beta_{underlying_index}$ which makes the portfolio less of a tax loss harvest tool for the goal of market-matching tax loss harvesting.