Lesson 15 of 25 · 7 min

Real and nominal, and why the distinction reaches collateral

Two routes to the same quoted rate leave your interest bill identical and your collateral value thirty-five percent apart.

A nominal rate is the number you are charged. A real rate is that number less expected inflation. Because interest is computed on the nominal figure, the distinction looks like an economist's footnote. It is not, because your collateral is valued on the other one.

An asset's value is a stream of future cash flows divided by the gap between the required return and the growth of those cash flows. Both of those contain inflation. If inflation expectations rise, both rise together, and the gap that actually sets the value can be entirely unchanged.

value = cash flow ÷ (required return − growth rate)

value: What the asset is worth today, given the stream it produces.
cash flow: The amount the asset produces in the coming year.
required return: The nominal return demanded to hold the asset. Contains expected inflation.
growth rate: The nominal rate at which the cash flow grows. Also contains expected inflation.

Start with a required return of 6.20 percent and growth of 2.10, a gap of 4.10, giving a value of 100 ÷ 0.0410 = $2,439.02 per unit of cash flow. Now raise the nominal rate by 2.20 points, twice, by different routes. If the rise is entirely inflation expectations, the required return becomes 8.40 and growth becomes 4.30: the gap is still 4.10 and the value is still $2,439.02. If the rise is entirely a higher real rate, the required return becomes 8.40 while growth stays at 2.10: the gap is 6.30 and the value is $1,587.30, a fall of 34.92 percent.

In both cases your nominal rate rose the same 2.20 points and cost the same money — $19,580 a year on an $890,000 balance. Identical interest, and a collateral outcome more than a third apart. Which case you are in is not on your statement and cannot be read off the rate, which is the attribution problem of lesson 5 restated one level further out.

Key terms

Nominal rate: The rate as quoted and as charged. Contains expected inflation without saying how much.
Real rate: The nominal rate less expected inflation. Not charged to anyone directly, and the one that governs asset values.
Inflation expectation: The rate of price increase the market is pricing in. It sits inside both the discount rate and the growth rate, which is why it can cancel.

Worked example

One rate rise, two worlds

A stream of $100 next year. Required return 6.20 percent, growth 2.10 percent. The nominal rate then rises 2.20 points by two different routes. Balance $890,000.

Starting value: $2,439.02
Route A: inflation expectations up 2.20: Required return 8.40, growth 4.30
Value under route A: $2,439.02
Route B: real rate up 2.20: Required return 8.40, growth 2.10
Value under route B: $1,587.30
Extra interest, either route: $19,580 a year

Same quoted rate, same interest, same statement. One route left the collateral untouched and the other removed a third of it.

Check yourself

A nominal rate rises 1.60 points entirely because inflation expectations rose, taking a required return from 7.10 to 8.70 and cash flow growth from 2.60 to 4.20. What happens to the asset's value and to the interest on a $1,275,000 balance?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.