(all content here are for academic and self-entertaining purpose, check the facts with authority before you can believe it is true and the authors claims no responsibility for misusage or misinterpretation)

One can make money or lose money by investing in stocks. Stock price usually goes up and down, people usually lose money by selling their stocks out of panic during a market downturn which also means missing out following up-turn (aka. mean reversion). There is a saying “it is not a loss until you sell” which tend to urge people don’t sell in the scenarios like this.

However, there is a technique in investments called tax loss harvesting. This technique is meant to take tax into consideration and demonstrated under certain/most scenarios, it is a better decision to realize the loss, and used the tax saved to reinvest to achieve superior performance than “being passive”. This post is meant to go through an example, explain how tax loss harvesting works and highlights some of the underlying assumptions.

If I have a portfolio which is a mixture of company stocks with the total value of $100K at the beginning of 2020. By the end of 2020, we have recognized a $10K gain by trading. Of course, some stocks went up and some went down, assuming that some of the stocks literally dropped the value $10K or even more. And the tax rate is at 20%.

The question is what difference will it make if I sell those “losers” and replace with more promising ones.

The baseline scenario is that if we don’t sell those losers. We will need to pay 20% on those realized gains which is $10K * 20% = $2K taxes.

If we sell those losers with a realized loss of $10K. That completely cancel out the gain so far and the net gain will be 0. No tax for you this year or the tax saving from the baseline is $2K.

Free money?! No.

As one can tell, just by realizing the loss, you immediately eliminate your tax this year but taxes are NOT gone. You are postponing by reducing the cost base for your newly invested replacements for those losers. For example, if those $10K losses were from a $50K initial investment, after you realized the losses and reinvested the $40K left buying new stocks. If in the future, the price goes up and you try to harvest the gain then. You will need to use the $40K as the cost basis rather than $50K if you did not sell it. So basically you still have to pay the tax for the “losses” then. Hence, tax loss harvesting in nature is a type of tax deferral.

Let’s go through an example, if those securities or replacement securities have its value rise to $100K, and we will sell it one way or another by end of next year. In the baseline scenario where we don’t realize the loss at end of year 1, at that time, our gain will be ($100K – $50K) = $50K. And we will need to pay 20% of those gains as taxes which equates to $10K. And if we realized the loss, our gain will be instead be ($100K – $40K) = $60K. And our taxes next year will be $12K.

Tax	Baseline	Realize Loss
Year1	$2K	N/A
Year2	$10K	$12K
Total	$12K	$12K

As you can tell, no difference. Let’s parameterize it.

Tax	Baseline	Realize Loss
Year1	T1	T1 – L * T
Year2	G * T	(L + G) * T
Total	T1 + G*T	T1 – LT + (L+G)*T = T1+G*T

As you can see, the realized loss item will be cancelled out in the future by the time you sell it anyway so there are only two scenarios that this “extra work” worth doing, a different and lower tax rate in the future, or reinvest from deferred tax.

If you understand the time value of money, a dollar today is not the same as a dollar tomorrow, or a dollar next year. By defering any type of cash outflow in the future will reduce the net present value of the cash outflow. Minimally speaking, it will be the inflation rate but in the investment cases. If there are better ways of leveraging those cashes to reinvest (buying new promising stocks), the difference can be substantial.

So basically, in this very example, you have $2K at your leisure to invest. Any return on those $2K will be net gains. Or in more general, L * T amount of money that you can use. Almost, like the higher amount, the better it is if and only if you can realize extra gains from those.

In the grand scheme, this whole tax loss harvesting might not be substantial. Why? The tax alpha (abnormal return) is basically how much money you can gain out realized tax loss, tax rate and the return out of that. We say L * T * r.

For example, if the loss rate is r_l and the positive is r_g. The total is r_l * T * r_g. This thing can only be substantial under the premises that your loss was somehow huge and then all of a sudden you have a promising investment. In regular days, this rarely happens but at big market downturns, this return can be substantial. r_l being -50% and r_g be +50%. That is 25% with a tax rate 40%. You got 10% return rate just out of tax harvesting loss.

Also, if you do this on a consistent basic, little things add up and you also gain a compounding effect of wealth accumulation by deferring tax payments on a consistent basis (how long it got deferred is now up to how soon you sell it, if you realized the gain this year, reinvest and sold it far far in the future, theoretically, you deferred it for a very long time).

In the end, to summarize, tax loss harvesting is one way to take advantage of the two-sided tax regimes in both most countries to passively allow gains to grow unharvested, but actively realizing losses. Again, this by no means to encourage purse losses, nor even give any level of comfort that loss is good, it is just another way to get some value out of a shitty situation. Just like not to intentionally make make your food go bad, but if it did, why not a make a banana bread out it.