# Annualizing FRA that's already annualized?

Spots:

90 days - .05%

180 days - .10%

270 days - .15%

360 days - .25%

Determine that the annualized equilibrium fixed swap rate for Japanese yen:

The equilibrium swap fixed rate for yen is calculated as

‸rFIX,JPY=1−PV0,t4,JPY(1)4∑i=1PV0,t4,JPY(1)

The yen present value factors are calculated as

90-day PV factor = 1/[1 + 0.0005(90/360)] = 0.999875.

180-day PV factor = 1/[1 + 0.0010(180/360)] = 0.999500.

270-day PV factor = 1/[1 + 0.0015(270/360)] = 0.998876.

360-day PV factor = 1/[1 + 0.0025(360/360)] = 0.997506.

Sum of present value factors = 3.995757.

Therefore, the yen periodic rate is calculated as

‸rFIX,JPY=1−0.997506/3.995757=0.000624 or 0.0624%

The annualized rate is (360/90) times the periodic rate of 0.0624%, or 0.2496%.

Why are we annualizing the result if we already used an annualized PV factor (360/360)?

in the question she mentions that the swap has quarterly resets so the swap rate result is the quarterly rate and you just x4

The process to calcuate the fixed rate swap is

SFR = (1 − zn) / Σ_zi_

Where Zi is the PV factor

Because you broke down (not sure if that’s the right word) the annualized rates in calculating each PV factor, you have to re-annualize it at the end.

That makes sense, the rates are quoted on annual basis, we deannualized them and had to annualize back the result.

Thank you guys.