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Monday, January 19, 2009

Risk and Taxes

Consider the following two portfolios over a ten year period.
  1. The 1st portfolio will have a 4% per year guaranteed return.
  2. 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.
Which is better?

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.


David said...

Well, not exactly or, at least, not necessarily. Taxation requires a taxable event, either the investment being sold or it throwing off income. If the investment simply accrues value but the value is unrealized, there is no tax until the end, at which point capital gains rates won't effect the relative returns.

Bret said...

My example assumes realized gains and losses, of course.

Considering higher risk investments, the VC/Angel model is to sell off winners and losers alike and move on to the next investment so the gains and losses are realized in a moderately short term.

Susan's Husband said...

Being personally involved in precisely this sort of thing, let me re-iterate Bret's point by stating that the only VC model I have ever seen, after many many VC presentations and workshops, is the "sell as soon as we can get our money" model.

David said...

Except that you figured out your return with compounding, which implies that the investment is not throwing off a realized income stream.

David said...

Plus, you're ignoring diversification. So long as the investments are independent, if you make enough of them you're more or less certain to get the 80% return. That's actually relevant to the current economic crisis, which was caused in part by banks, etc., assuming that their investments and loans were independent and not figuring in (and then charging for) the likelihood of a systemic crash.

Bret said...


Are your comments just nitpicks with the example or are you claiming that the impact of taxes is essentially identical on low and high risk portfolios?

Bret said...

Since David didn't respond, we'll need to assume that his comments are regarding the details rather than the conclusion. A higher risk portfolio is certainly going to have more volatile returns and chances are the realized returns are going to be more volatile which will be harder hit by taxes per my example. Also, keep in mind that entrepreneurs and small businesspersons are also investors in that they often work for extended periods with no salary or below market salaries in order to reap future benefits, which is also a huge income volatility and punished by high taxes.

David said...

I'm sorry, I thought I did respond, but I must not have hit "publish."

I think that you're presenting a false choice. There's no investment like your second investment in which you have "compounding," an annual recognized profit or loss and get the capital gains rate. And you certainly can't compare it to a 4% compounded guaranteed rate that's taxed at the end of the period. Also, random variable dichotomous interest rates don't exist in real life. If the two investments are held for their lifetime, the capital gains tax rate doesn't effect their relative returns.

David said...

OK, I ran your theoretical investment through a 10000 iteration Monte Carlo simulation. I used a $100,000 initial investment and a random interest rate, normally distributed, with a mean of 12.5% and a sd of 12.5, so that 95% of the returns will be between -12.5% and 37.5%.

Without tax, after 10 years I ended up with a mean value of $288,777, with a 95% confidence interval of $137,919 and $519,829. That's an average annual return of about 19%. With tax at 50% every year and assuming all losses could be used to offset gains, I got a mean of $183,269 (8% per year) and a CI of $124,450 to $258,715. The tax reduced the return but also substantially reduced the variance.

Bret said...


False choice? It's a hypothetical choice to make a point, which your simulation confirms (as do my simulations). Taxes hurt a higher risk/higher volatility portfolio more than a lower risk/lower volatility portfolio.

Hey Skipper said...

Bret -- please send your email address to

Harry Eagar said...

Before I read this, I had already posted at Restating the Obvious the obvious point that if you don't tax capital gains, the rich will not pay any tax at all.

This is Louis XVI-conomics.

I am not as surprised that it still has its defenders as I ought to be, but let's call it what it is.

Susan's Husband said...

" if you don't tax capital gains, the rich will not pay any tax at all."

And that's bad because ...?

P.S. I am looking for something functional or economic, rather than spiteful or envious.

Harry Eagar said...

Uh. Because we're a society and not just a gang?

Because we saw how Louis XVI-conomics worked?

Because if the rich don't pay taxes they will end up swinging from lampposts?

Susan's Husband said...

1) The essence of a gang is using its combined might to take money from other people. That would seem to be far more like taxation than its opposite. Therefore, if we are not "just a gang" we should avoid taxation as much as feasible.

2) Yes, but that's completely irrelevant since tax rates on the "rich" were at best a tertiary level feature of those economics. Louis-XIV economics also featured grocers selling food — should we therefore avoid that as well?

3) With regard to lampposts, I couldn't have asked for a better demonstration of point (1).

Harry Eagar said...

Well, that's the way the world works. You're big on realism.

Be realistic.

Harry Eagar said...
This comment has been removed by the author.
Susan's Husband said...

How I am not being realistic? I was asking a question, not proposing policy.

Harry Eagar said...

Because, the way I see things, it is unrealistic, in any kind of modern social setup, to expect the masses to exempt a class from paying taxes.

With the exception, in the USA, of religion. a special case.

If the names of 251,000 rich tax cheats really are turned over the by Swiss banks to the IRS, don't expect too many tears from the other 299,749,000 of us.

Susan's Husband said...

But I didn't ask why it was politically infeasible, I asked why you think, as you claimed, it would be a bad thing.

I think this is just an unexaming catch phrase and you might find it interesting to consider why you believe that. If it's just spite and a gang attitude, OK, at least you'd know.

P.S. I was also unaware that the rich were exempt from sales taxes and property tax.

P.P.S. If you really wanted to rich to pay taxes, I would think you would support a flat tax, as it is the complex tax code that is the primary enabler of tax avoidance by people who can afford fancy tax lawyers. Yet I seem to recall you being on the record as mocking the very idea. Why is that?

Harry Eagar said...

I've been wavering a bit on the flat tax.

Didn't trust the messenger.

Still don't.

At heart, I'm a Single Taxer. That's a kind of flat tax.

The rich should pay taxes because, if they didn't support a just society, they would be either A) immoral or B) dead.