## Equation (3.3)shows...

Equation (3.3) shows the after-tax return for an individual with a stock portfolio comprising 90 percent of the investment assets and a hedge fund with the remaining 10 percent of the assets.

In this scenario, the hedge fund return lowers the aggregate after-tax return because the higher tax rate on the hedge fund's pretax return lowers the after-tax return below the stock after-tax return. Assume that the stocks and the hedge fund in the preceding example have standard deviation of return (also called volatility) of 20 percent annualized. However, the returns have a correlation of only 25 percent.

Relying on the formula for portfolio volatility presented in answer 2.13,
the standard deviation of return on the portfolio is given by equation
(3.4):

formula for portfolio volatility presented

where A = Standard deviation on stock portfolio = 20%

B = Standard deviation on hedge fund = 20%

A,B = Correlation between the stock portfolio and the hedge fund.

The hedge fund provides a lower after-tax return but also a lower level of volatility in the combined portfolio. Clearly, if the individual investor can locate a hedge fund with returns higher than the investment alternatives, this comparison looks more favorable still.

It is also clear that individual investors would prefer hedge funds that:
**(1)** have higher expected return; **(2)** have lower volatility; and **(3)** have
lower correlation to assets already in the portfolio. Similarly, if a hedge
fund could deliver some portion of its return as long-term capital gain, it
could create higher after-tax portfolio returns than hedge funds that provide
a return taxed as ordinary income.