I had quantified the difference between 30% tax and 12.5% tax—i.e., tax payable for bond fund gains vs tax payable for arbitrage+bond fund gains. The result of that previous analysis tilted in favour of paying less tax. The longer the holding period, the higher the impact of tax.
In a way, that analysis simply quantified what was already obvious. It is a well known fact that the gain (or value appreciation) increases exponentially as the holding period increases. The tax difference is flat 17.5% (30% – 12.5% = 17.5%). A flat percentage on a larger number will of course be larger than the same percentage on a smaller number. There wasn’t anything new to learn there other than quantifying what we can already know intuitively.
Now I want to measure the impact of tax differently, this time controlling for the exponential growth caused by longer holding periods. What if we calculated the CAGR of post-tax returns? That is, use a fixed pre-tax growth rate, compute the final corpus value, deduct estimated tax, and calculate the CAGR from original corpus to post-tax corpus.
When I do this, 2 things become noticeable:
- The difference falls roughly in the 0.5% to 1.5% growth rate.
- The longer the holding period, the lesser the impact on the growth rate. When I ran my previous analysis (i.e., take 2), this is what I expected to see, but I saw the opposite. It’s good to finally see data that validates my intuition.
Each cell in the following tables shows the post-tax growth rate. For example, look at the 6.5% row in the “3 years” table. This row says that if the pre-tax growth is 6.5%, the effective post-tax growth is 5.73% annualised when the tax rate is 12.5% and 4.63% if the tax rate is 30%. By paying higher tax, our investments (effectively) grow 1.1% more slowly each year.
For a holding period of 3 years, the difference in growth rate is 1.1%. If we extend the holding period to 10 years, the difference narrows to 0.96% (per annum). For 20 years, the gap reduces further to 0.78%.
But sensible readers would say that growth rates can go to hell. What really matters is the size of the final corpus, and hence, take 2 is a more useful analysis than this one. They’d be right, except the mutual funds that are taxed at 12.5% come with caveats.
An arbitrage+bond fund behaves differently than a pure bond fund. For some investors, the change in behaviour may not matter. But if the difference matters to you, you shouldn’t feel too bad about paying 30% tax. The impact of tax reduces as you hold the assets for longer and longer.
My conclusion is that long-term investors who plan on holding their investments for 2 or more decades can use this data to rationalise holding pure bond funds. This analysis doesn’t magically reduce the tax we pay, but it changes the narrative to convince oneself to choose a simpler investment asset (pure bond) over a more complex one (arbitrage+bonds).
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