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Imagine a world where, for a given time period, the expected inflation rate is 10%, but the nominal risk free interest rate over the same period is 5%.

Should my starting point - from a discounted valuation perspective - use 10% or 5% as the discount rate?

All in nominal terms.

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    $\begingroup$ What security are you valuing? $\endgroup$
    – Mild_Thornberry
    Jan 5, 2022 at 19:55
  • $\begingroup$ No particular security. $\endgroup$
    – Bryan Franco
    Jan 6, 2022 at 20:32

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To avoid arbitrage opportunities in your valuation model, you have to use the nominal risk-free interest rate as a discount rate:

Let us consider a Zero Coupon Bond (ZCB) expiring in one year with a (nominal) payoff of 1. If we discount with 10% then this ZCB would cost approximately 0.9.

Let us assume that we buy the ZCB for 0.9 using money borrowed in the bank at the risk-free rate of 5%. This would be an initially costless strategy. After one year we would have to pay the loan back and this would cost us approximately 0.95. We receive 1 from the ZCB meaning that we can pocket approximately 0.05 by putting up no money and taking no risk. This is thus an arbitrage opportunity. To avoid arbitrage opportunities in the model we must use a the nominal risk-free rate to value nominal cash flows.

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