# Why do we start with a nominal rate and have no idea what the REAL Rate of Return is going to be?

May we discuss starting with a stable/fixed known Real rate of Return and calculate the equivalent nominal units?

Those investors who buy nominal interest rate instruments know the nominal rate of return they will receive. But, they cannot know the real rate of return they will receive because it is a variable to them. That is because they cannot predict the rate of change in the price index, be it CPI+U or GDP as Shiller suggests, which is the usual measure of erosion of purchasing power. Because of this, the realized real rate of return, rn = ((1 + in ) − 1) / (1 + cn )), defined as the quotient less one of one plus the nominal rate over the quantity one plus the index rate, is volatile from period-to-period. The volatility of the index makes it so.

For them to know the realized real rate they must first obtain the realized rate of inflation. There is no avoiding this with a fixed nominal rate of interest.

In contrast, investors who buy fixed real rate of interest instruments do not know, and have no reason to care, what the nominal rate of interest is on them. They know that they will receive a contractually guaranteed, constant rate of real interest. Their expected real return will equal their realized real rate of return.

Nominal Interest Rate = Real Interest Rate + Expected Inflation Rate + Risk Premium

The real interest rate is the true, purchasing power, interest rate.

By going from the real rate to the nominal we have the corresponding calculated nominal rate of interest in = cn + rn + cn× rn where rn is the contractual fixed, real rate. This calculation picks up the cross-product term cn× rn from the calculation rn = (1 + rn)(1 + cn).

Others work in the opposite direction, calculating the real rate as x# = in + cn. This is not precise. It is in error because it ignores the cross-product term. The effect of this can have a significant cumulative effect over the life of a contract.

Allow the borrower and lender to set the Real Rate of Return to be paid or earned. Allow them to agree upon the index to be utilized. Allow them to set the frequency of the update of the index.

What I find happens is:

- A means to shift the efficient frontier to the right and upward.

- A means to increase the credit scores of all participants.

- A means to free up cash flow.

- A means to greatly simplify and to lower the costs of hedging.

- A means to increase the effectiveness of risk management.

- A means to greatly increase the odds of a known life-style to for ourselves and our descendant.

I would like to hear other’s thoughts on structuring an indenture in stable/fixed real terms and not in nominal terms.

Brian Gidley

www.realreturnmethodologies.com