Being tactical in a vacuum is easy; being tactical in reality with the considerations of trading costs and taxes is far more difficult. We've previously discussed and researched methods to reduce turnover at great length; more recently, we've focused on researching being tactical in the face of taxes.

In the paper, we utilize the framework of *spread options* to develop heuristics around whether a tactical trading signal should be taken or deferred until the position reaches tax maturity. The paper is not ready for publishing yet, but the results are pretty interesting and I wanted to share some general heuristics that are outlined at the end.

As a brief intro, the parameters referenced are:

**µ1, σ1**: The expected annualized return and volatility of the asset we are considering selling

**µ2, σ2:** The expected annualized return and volatility of the asset we are considering buying

**p:** The current unrealized percentage gain in the asset we are holding

**T:** The time until the asset we are holding reaches tax maturity; expressed as a percentage of 1 year

**ρ:** The correlation between the asset we are considering selling and the one we are considering purchasing.

Here is a slightly edited (for clarity) section of the paper:

**Distilling It Down Heuristically**

Another way we can get a more general idea of the functional behavior of the probability is by examining the partial derivatives of the probability function (equivalent to analyzing the Greeks for options). The following heuristics hold for commonly encountered parameter sets (these heuristics are based on parametric runs with ranges µ = [-0.25, 0.25], σ = [0.05, 0.45], p = [0.02, 0.5], T = [0.025, 0.9] and ρ = [-0.9, 0.9]).

**Expected Return** – The probability of a positive spread increases with µ1 and decreases with µ2. This agrees with intuition since higher average returns for the asset we are buying compared to those for the asset we are selling should increase our chances of covering the loss from the higher, short-term tax rate. The effect from µ2 is larger than that from µ1 (absolute value).

**Current Profit** – Increasing the current profit, *p*, decreases the probability because a higher profit increases the strike of the option. Thus, when deciding between selling two very similar assets, the one with the lowest current profit is generally the best option.

**Asset Volatility** – Generally, higher volatility for both assets increase the probability because they widen the final distribution of stock prices. However, there are some instances when it will decrease the probability. The extent of this effect depends on the correlation, but relative to the expected return expectations, the effect of varying volatility is small. Both effects are stronger for higher current profits and shorter time left until the end of the year.

**Time** – Selling sooner generally yields a higher probability of a net profit, especially for higher values of current profit, assuming that µ1 > µ2.

**Correlation** – As the correlation between the assets increases, the probability generally decreases since the assets behave more identically and cannot overcome the required spread. However, this is less pronounced with more time to tax maturity and lower current profits.

We'll hopefully be publishing the paper soon. Stay tuned!

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