Modern portfolio theory is clear. A diversified portfolio is preferable to a risky one. When the decision to diversify requires selling equities and paying taxes, however, the solution may not be as clear. Consider this case: if your capital gain is large and you must pay taxes when you sell, should you pay up now or later? How much of your portfolio should you sell in order to diversify?*
To sort through the taxable investor’s diversification dilemma, consider a very simplified case in which there are two assets: an initial risky portfolio and a diversified benchmark portfolio. Our analysis contrasts the probable returns, after taxes, for these two holdings.
Consider Portfolio 1 (see page 97), which consists of $1 million worth of a single risky stock that the investor acquired with a zero cost basis. It has a volatility (the standard deviation of the annual rate of return), or risk, of 40%.The 40% number corresponds to the risk of a medium- to large-sized, but not too risky, company. Microsoft, Intel, and AT&T all have volatilities around 40%.
Compare this with Portfolio 2 (see page 99), which starts with $1 million as well, but the investor decides to diversify. He sells his risky $1 million portfolio and sets aside 20%, $200,000, to pay his long-term capital gains tax. He reinvests the balance, $800,000, in a portfolio of diversified equities. This new portfolio has a volatility of 15%, the average volatility lately of a diversified, indexed portfolio.
In our study, both portfolios share a set of benefits and costs:
o They appreciate (i.e., yield total return) at an average rate of 10% per year.
o They pay 3% in dividends; the investor pays dividend taxes at a 39.6% rate.
o The investor pays a 20% capital gains tax.
o The investment horizon is 20 years. At the end of this period, both portfolios are sold and unrealized capital gains are taxed.
If the return is known to be 10% per year, Portfolio 1 will appreciate to $4.5 million after taxes by the end of the period. Portfolio 2 will appreciate to $3.8 million. It would appear that the investor would do better to hold off paying taxes rather than to diversify. He gains a benefit from having his unpaid taxes appreciate in his favor.
However, we cannot be sure what the stocks will return. And we know that the concentrated investment is more risky. How does this change the decision?
The Concept of Risk
While we cannot be certain which portfolio will have more wealth at the end of the term, we know the risk of each, and we have the mathematical tools to determine the probability of outcomes. Our analysis derives the probable results using Monte Carlo simulation.
Portfolio 1, with 40% volatility, can be expected to grow from $1 million to $4.5 million after taxes. However, there is a 50% probability that this portfolio will grow to only $1.3 million after taxes (the median value). That’s less than 20 years worth of inflation at 3.5%. Six out of 10 times, the portfolio will grow to less than $2 million. The risky portfolio has a sizable probability–43%–that it will shrink in value.