# Riskless rate of return

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The net cost is $548,812, precisely the same as if the liability had been discounted and funded using the 4 percent riskless rate of return. (23)

Since 2003, the riskless rate of return has been abnormally low as central banks kept overnight rates low for a long time after a brief deflation scare in the United States and a prolonged scare in Japan.

Only the relevant economic factors are considered in this analysis: the price of individually purchased goods, product price, warranty expiration, time and a riskless rate of return from an appropriate Treasury security.

Because the real riskless rate of return apparently did not change much during that five-year period, anything short of such an extraordinary permanent increase in the growth of structural productivity, and thus earnings, (4) implies a significant fall in real equity premiums in those years.

The accompanying chart compares at varying loss ratios the present value net ceded premium relative to the present value ceded losses at a riskless rate of return of 6% per annum.

[6] In constructing this estimate, we start with 1977 (premanipulation) market values, subtract dividend payments and add public offerings, assuming that in the absence of manipulation that monthly bank returns would have been equal to the riskless rate of return plus 50% of the industrial shares' excess monthly return.

The Sharpe Utility Measure uses an estimate of the investor's risk tolerance rather than the riskless rate of return as an indicator of the investor's utility function.

where [R.sub.p] is the return on the portfolio, [R.sub.f] the riskless rate of return, [[sigma].sub.p] the standard deviation of the portfolio, and [[beta].sub.p] is the portfolio's beta.

And indeed, if you believe these really quite unbelievable expected earnings-per-share increases over the next three to five years, which have not changed through all of this particular period, then you get a pronounced increase in equity premiums, i.e., the premium in the market for equity issues over the riskless rate of return. And that has risen quite dramatically in the most recent period.

where d = B exp (-rt) / V (a quasi debt-to-asset ratio where the promised payment on debt is valued at the riskless rate of return, r, and P (d) is the per dollar price of risky debt.

The riskless rate of return of the buyer is symbolized by [r.sub.b].

These models derive asset's rates of return relative to a riskless rate of return.(2) Models that derive relatives rates of return cannot answer the question raised by this paper.

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