Most asset allocation studies are framed in a tax-free context. The authors
examine the return–risk ratio as defined by the Sharpe ratio to determine
how asset allocations and their probability of achieving a desired rate of
return differ under various taxable assumptions. The authors acknowledge that
taxes detract from investment returns but find that taxable investors can accept
a higher return−risk ratio than their tax-free counterparts because
current U.S. tax structures for long-term capital gains differ from those for
income received on cash. The authors also find that the ability to use losses to
offset gains alters the return−risk ratio in favor of the taxable
investor.
The authors use the Sharpe ratio (SR) to examine allocations between cash and equities
and the return characteristics on these allocations under taxable and tax-free
scenarios. They start with a simple two-asset model allocation composed of cash and a
single equity asset. The equity is assumed to be subject to an advantageous capital
gains tax rate. The authors find that most U.S. portfolios, from both individual (taxed)
portfolios to highly diversified institutional (tax-free) funds, have nearly the same
level of equity risk at a 60 percent allocation to equities. The authors interpret this
result as representing both the maximum amount of volatility that investors are prepared
to accept as well as the minimum risk required to achieve an acceptable return over
cash. They assume that the base expected return for the equity investment will be 7
percent pretax, which represents a 4 percent rate for cash plus a 3 percent equity risk
premium. The pretax assumption for the volatility of an all-equity portfolio is set at
16.5 percent. The authors also assume that interest on cash will be taxed at 40 percent
and that all equity returns will be taxed at the long-term capital gains tax rate of 20
percent. Any losses to a taxable investor will be used to offset immediate or future
gains.
The return−risk ratio measures the return that investors receive for moving toward
different risk allocations; the more risk an investor is willing to assume, the more
return the investor should expect. To translate a tax-free return−risk ratio into
its taxable counterpart, both the return premium in the numerator and the volatility in
the denominator must be restated in after-tax terms. Once these calculations are made,
the authors find the slope of the return−risk ratio for the taxable investor to be
greater than that for the tax-free investor. So, for a given increase in risk, the
taxable investor is compensated more than the tax-free investor is. The main factors are
the lower taxation of long-term capital gains versus that of cash and the benefit of tax
loss offsets.
The authors also consider the probability of achieving a return that is higher than cash
with different equity/cash allocations. A tax-free investor can always achieve a
risk-free rate of 4 percent with 100 percent cash. Once equity is added to a portfolio,
however, the probability of beating the 4 percent rate drops to less than 100 percent.
They find that with an SR of 0.18, the probability of beating the 4 percent rate drops
to 57 percent regardless of whether the equity exposure is 20 percent or 60 percent. The
authors then show the probability of achieving a 1 percent and 2 percent net spread over
the cash rate. To achieve a spread of 1 percent over the risk-free rate with an SR of
0.18, an investor would need 20 percent in equities for a 45 percent chance and 60
percent in equities for a 53 percent chance. These probabilities are applied to one-year
returns. When the authors look at longer-term horizons, such as five years, the odds of
achieving a positive spread over cash improve. The odds of achieving a 1 percent spread
over cash, if one assumes a 7 percent risk premium, grows from 63 percent in one year to
77 percent in five years. Additionally, five-year after-tax portfolios have a 79 percent
probability of achieving the spread because of the aforementioned tax loss offsets and
lower taxation on capital gains compared with taxation on cash.
The authors conclude that although taxes lower prospective returns, the return−risk
ratio and the net equity premium may actually increase. They find that, as a result, the
incentive for risk taking is somewhat greater for taxed investors than for their
tax-free counterparts.