Annualizing FRA that's already annualized?

CFA Level II Derivatives
#1

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

PV0,ti(1)=11+rSpoti(NADiNTD)

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)?

#2

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

#3

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.

#4

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

Thank you guys.