Tax efficiency

I have just spent a couple of days entering data for some mutual funds I own into my new Quicken program . I had been vaguely aware that index funds have tax advantages over actively managed mutual funds but a concrete example was still startling. I owned $X of index fund A and $Y of actively managed fund B on 12/31/1986. In both cases I have reinvested all distributions and paid the taxes with other income. As of 10/28/2009, A was worth 7.21*X and B was worth 6.69*Y. So ignoring taxes the annual rates of return for A and B are about 9.04% and 8.69% respectively. The higher fees of active management don't seem to be adding value. However the after tax picture is even worse. Over the years the index fund has distributed 2.28*X while the actively managed fund has distributed 8.01*Y. So the tax cost of B has been much higher than A. This probably has increased the after tax difference in annual return by 1% or so.

Now much of this tax advantage would disappear if I sold both funds as the distributions have increased the basis so selling A would produce a substantial capital gain and selling B would produce a substantial capital loss. However under current law if I hold until death the basis will step up preserving the tax advantage.

Another way of looking at this is to assume annual returns of 9% consisting of 3% in dividends and 6% in capital appreciation. Suppose the index fund just distributes the dividends while the actively managed fund distributes the dividends and the capital gains. Then if you assume a tax rate of 20% and that you pay the taxes from the distributions and reinvest the remainder, the index fund will grow at an annual rate of 8.4% while the annual rate of growth for the actively managed fund will be 7.2%.

To substantially benefit from tax free compounding rather long holding periods are required. Suppose we ignore dividends and assume capital appreciation of 6% a year. Assume we hold for n years, then sell and pay 20% capital gains tax and reinvest. Then as n goes to infinity the effective annual yield rises from 4.8% (n=1) to 6% but rather slowly. It is an interesting exercise to determine how big n is required to be to get half the benefit (ie an annual yield of 5.4%).