Under what conditions will a discount bond have a negative nominal interest rate? Is it possible

Under what conditions will a discount bond have a negative...

Key Concepts

Perpetuity

A perpetuity is a type of financial instrument that provides unending periodic payments—usually fixed in amount—with no maturity date. Its yield is often derived simply as the ratio of the periodic payment (or coupon) to its current price. In a standard case with positive periodic payments, the yield remains positive; however, if the market structure were to force the price extremely high or the payments were somehow negative, a negative nominal yield might ensue, though such scenarios are atypical for perpetuities.

Discount Bond

A discount bond is a debt instrument that is typically issued below its face (or redemption) value and does not make periodic interest payments. The nominal interest rate (or yield) on a discount bond is determined by the difference between the redemption value and the purchase price relative to the purchase price. When a discount bond is purchased at a price that exceeds its redemption value, the yield becomes negative, meaning the investor effectively loses money even if there are no interim cash flows.

Nominal Interest Rate

The nominal interest rate is the annualized rate of return on an investment, computed using the difference between cash flows such as the purchase price and the repayment at maturity without adjusting for inflation or compounding effects. It directly reflects the return based on the contractual cash flows from a financial instrument, and a negative nominal interest rate signals that the cash flows received are insufficient to cover the initial outlay.

Coupon Bond

A coupon bond is a debt security that pays regular interest (coupon payments) throughout its life and returns the principal at maturity. The yield on a coupon bond is calculated by finding the discount rate that equates the present value of all future coupon payments and the principal to the bond's purchase price. While it is possible for a coupon bond to exhibit a negative nominal yield if its market price is sufficiently above the sum of its future cash flows, such scenarios are less typical and occur under conditions of strong demand or safety concerns.

Transcript

00:01 Here we're taking a look at nominal interest rates, specifically when they're negative in discount bonds, coupon bonds, and in perpetuity.

00:07 So we'd like to first examine the discount bond.

00:11 So let's try to determine when that nominal interest rate may be negative.

00:16 And to do that, we can look at this fishery equation where we have nominal interest rate is equal to the real interest rate plus expected inflation.

00:24 But now let's suppose that expected inflation were actually negative, in which case we're experiencing deflation.

00:30 So in that case, we would have our expected inflation.

00:33 It would be negative.

00:34 So let's suppose it's negative 3, all right, just for easy to work with numbers.

00:39 And let's also suppose that our real interest rate is equal to 1.

00:43 Now, in this case, if we wanted to calculate that nominal interest rate, it would be equal to 1 plus a negative 3.

00:51 Okay, and that ends up giving us negative 2 for a real interest rate.

00:54 So from this basic algebraic example, what we can see is that a discount bond may experience a negative non -3.

01:00 Interest rate when that expected inflation in absolute value terms is greater than r.

01:09 Right? so if that were negative, and that's exactly the example we just showed.

01:14 We just showed for three in absolute value terms, it is three and that is greater than one.

01:20 But it must be for deflation because obviously it has to be negative.

01:23 We're subtracting from that real interest rate...

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