The positive effect from a guaranteed depreciation allowance can therefore be valued by discounting it at the

riskless rate and adding it to the present value of the other cash flows.

* Julian Kozlowski, New York University and Laura Veldkamp and Venky Venkateswaran, New York University and NBER, "The Tail that Keeps the

Riskless Rate Low" (NBER Working Paper No.

To reiterate, discounting using a

riskless rate is appropriate because we are valuing promised pension payments and can therefore treat them as though they are guaranteed.

Figure 1 shows the effect of the

riskless rate of interest [r.sub.0], the appreciation rate of the risky asset [r.sub.1], the volatility of the insurer's surplus [[sigma].sub.0], and the volatility of the risky asset [[sigma].sub.1] on the optimal investment strategy [[pi].sup.*](t).

However in long periods of history there were no inflation-indexed bonds, so to find a good empirical counterpart for the

riskless rate is not an easy task.

--Pure arbitrage, where, in fact, you risk nothing and earn more than the

riskless rate.

Let us begin with the effect on [P.sub.t] of a permanent change in the

riskless rate r.

In the absence of risk aversion, the yield on cocos should then be equal to the

riskless rate for their remaining term plus a conversion risk premium that compensates for the expected loss conditional on conversion.

Theoretically, the difference between the total rate of return and the safe rate is considered a premium to compensate the investor for risk, the burden of management, and the illiquidity of the capital invested; also called

riskless rate or relatively

riskless rate."

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.

Since the credit risk premium is on top of the interest rate charged for riskless debt, the first step is to understand what moves that

riskless rate around.

Under the risk-neutral probability measure, we can replace the drift coefficient [mu] by the instantaneous

riskless rate r, and hence R([T.sub.j]) is normally distributed with means [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.], variances [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].