- The 1st portfolio will have a 4% per year guaranteed return.
- The 2nd portfolio will have either a 50% or -25% annual return for each of the 10 years. The returns for each year are completely random and independent.
Well, that depends. At the end of 10 years, portfolio 1 will have increased 48% (with compounding). Portfolio 2 will have a return somewhere between -95% and 5,500% and the expected (geometric mean) return is 80%. 80% is a lot better than 40%, but only about 13 out of 20 people would end up doing better with portfolio 2 than with portfolio 1, the rest would've been better off sticking with portfolio 1.
In my experience, about half (maybe somewhat more than half) would choose portfolio 1 and the others would choose portfolio 2. Those who are more risk-adverse would go with portfolio 1 and those who have a higher tolerance for risk would go with portfolio 2. There is nothing wrong with either choice. It's completely subjective.
However, the rich generally can be more risk-seeking. If you lose 95% of $1 billion, you still have $50 million left, which is a bummer, but no threat to survival or even comfort. If you lose 95% of your $200,000 of retirement savings, you're in serious, serious trouble.
Now let's consider what happens when taxes are added to the equation. Let's use the nice round number of 50% as the tax rate. For a rich investor in California if Obama increases taxes on assets for the rich as he said he would while campaigning, 50% is a pretty realistic number.
Portfolio 1's after tax return is 2% per year which would compound to 22% for the 10 year period.
Portfolio 2 is more interesting. The results depend not only on chance, but also on order. If the early returns are good, they're heavily taxed, and later losses will badly hurt the overall return. If the early returns are losses, then later profits go tax-free until you make the losses up (assuming that losses can be carried forward). Indeed, the calculation is complicated enough that I had to write a short matlab program to calculate the results.
The bottom line is that the expected 10 year return for portfolio 2 is now negative (between -3% and -4%). As a result, except for very risk-seeking individuals, portfolio 1 is now much better.
The point: Taxes on capital punish risk. This isn't an opinion, it is a mathematical certainty. While the above example was specifically picked to help illustrate this point, under a high-tax regime, higher risk investments are negatively impacted more than lower risk investments, and therefore, investors will have a greater incentive to avoid higher risk investments.
In a future post, I'll look at the ramifications of discouraging risk-taking.