Spot Rates Across the Yield Curve and Forward Rates

# Spot rate investment horizon


# Spot rate investment horizon












I'm learning about spot rates from Financial Mathematics for Actuaries and something about the definition is confusing me.

Spot rates are used (in the textbook) to specify the interest rate on a payment made at time 0, for some fixed but arbitrary period into the future. But elsewhere, like on Wikipedia, spot rates are said to apply only to very short term investments, as in those due to mature a few days from now. Assuming the term has an unambiguous meaning in finance, is it that, theoretically, spot rates can be defined for arbitrary periods into the future but in practice that never happens? Or is it something else?

Thanks

## Answer by demully (score 1)

https://quant.stackexchange.com/a/54337

The confusion arises because “spot” is variousLy used in FX, equities and commodities to refer to the immediate/very-short-term price (before any forward adjustments for interest rates, dividends, contract rolls etc).

The same is sort-of the same with interest rates. If the spot 2 year rate is say 10% for a zero-coupon loan, then you would receive 1.21x back in two years time. Or a spot 10 year rate close to 7% would double your capital.

This is consistent because these rates might not be 10%, but be 9% or 11% tomorrow. So it’s an immediate rate to cover a future period. In a sense, it’s today’s average for a future period. Or you could think of it, if you had a variable rate mortgage, as the rate you’d get locking into a fixed rate.

This is obviously very different from saying something like “(short-term) rates will be 10% in 2 years time, or 7% in a decade’s time”. With a granular yield curve, one can infer what these forward rates should be (to prevent arbitrage); and these forward rates can be and are traded (on swap) today.

The most famous of these for economists is the “5y5y inflation breakeven” that the Fed used to talk about, Ie the take the spot 5y breakeven and the spot 10y breakeven, and work out what the breakeven in 5 years time for the next 5 years is (ie for years 5-9 from now).

But these are just derivatives of spot interest rates - what is the rate today covering the next T years. There being obviously multiple spots covering different values of T across the yield curve.

In fact “the yield curve is spot” is probably the simplest and shortest explanation possible :-) Given this, one can then slice-and-dice to deduce “expected” (that is, arb-free) forward interest rates for any period one might be Interested in.

## Answer by John (score 0)

https://quant.stackexchange.com/a/54328

there are plenty of different situations where we consider the contract signing date, or the settlement date, depending on the product, see https://www.investopedia.com/terms/s/spot_rate.asp

The rule of thumb is: spot rate means now, at the present time, or at time t=0 by default when considering a fixed income pricing formula for instance

the rate at any time t between 0 and T is not spot rate, but forward rate, and should not be confused