# Impact of taxes on Investment Risk

p.250 CFAI, we learn that taxes reduce investment risk.

Can you please explain why this is the case? What exactly are we referring to with ‘Investment Risk’ ?

Thanks

Rex

Without taxes you have a mean return of 8% and a standard deviation of returns of 10%.

With taxes at 40% you have (left) a mean return of 4.8% (= 8% × (1 − 40%)) and a standard deviation of returns of 6% (= 10% × (1 − 40%)).

The volatility of the after-tax returns is (40%) less than the volatility of the before-tax returns.

See? The government loves you.

Nicely explained

Thanks.

I try.

S2000,

I actually have a question related to this. So let’s say that we keep the 40% tax rate. If I sell something lower than what I originally bought it at, is that where I get the deferred tax benefit? (assuming this is a capital gains schnario).

Thanks Magician - nicely explained.

My pleasure.

Gentlemen, I have some doubts about such concept.

Suppose, we have the following return distribution:

1st year: -10% before taxes, -10% after taxes.

2nd year: -10% before taxes, -10% after taxes.

3rd year: +10% before taxes, +10% after taxes (we summed up losses from the previous year).

4th year: +10% before taxes, +6% after taxes (again we accounted for losses borne earlier).

5th year: -10% before taxes, -10% after taxes.

6th year: +10% before taxes, +10% after taxes

The expectation is 0% before taxes and 0% after taxes. Standard deviation is 10.95% before taxes and 10.95% after taxes. Why should the SD be less after taxes then?

Your particular scenario assumes that losses can be carried forward, but that really only applies to capital gains… interest income and dividend income are still taxed each year, so the after tax returns on these income are lower than the before tax income, and this will result in lower volatility for the after tax returns…

Hi, will660.

In terms of dividends I agree, as the dividend payments are conventionally subject to fluctuations. On the other hand, coupon & interest payments do not add to return volatility due to their fixed nature.