i] can be expressed as a function of

expected return, r, and standard devition, [sigma]:

where V(t) is the cumulative value at t, [mu] the

expected return, [sigma] the underlying volatility of the return and B(t) is a standard Wiener process.

The

expected return is determined by multiplying the $550 monthly payment by 12 to arrive at the yearly payment of $6,600, and then multiplying this amount by the contract holder's life expectancy (25.

Consequently,

expected return (the average cost of capital), [omega](Y), exceeds the growth boundary (the marginal cost of capital), [omega](Y) [greater than or equal to] [[xi].

Moreover, as the level of debt is always proportional to the value of the unlevered firm, the

expected return on the tax shield is the same as the cost of capital of the unlevered firm ([r.

Thus, any

expected return variation that is both real and novel must correspond to a new "factor.

Figure 1 uses a stylized example to illustrate the concept of tax risk: The two tax positions have the same

expected return but different levels of risk.

GE's pension expense for fiscal 2001, however, included the

expected return on pension plans assets of $4,327,000,000, based on a long-run expected rate of return of 9.

If the

expected return in these industries also is negative, then the lottery explanation acquires some plausibility.

It is arguable that risk minimization with no regard to the effect on

expected return cannot be optimal.

If a manager's or a fund's

expected return potential is significantly greater than the competition but suffers from a low tax-efficiency ratio, consider using this manager or fund inside the tax-deferred portion of the portfolio.

The discount rate is commonly called the

expected return because it is the return the investor earns if the income stream is realized as expected.