Cannot understand workings to a question. Arbitrage-free forward rate.

CFA Level I
#1

Hi I’ve a problem with the question below.

Question: Consider 2 currencies, the WSC and the BDR. The spot WSC/BDR exchange rate is 2.875, the 180 day riskless WSC rate is 1.5% and the 180 day riskless rBDR rate is 3%. The 180 day forward exchange rate that will prevent arbitrage profit is closest to:

ANS given :2.8538 WSC/BDR

WORKING given:

Arbitrage-free forward rate = 2.875WSC/BDR X [(1+0.015/2) / (1 + 0.03/2)] = 2.8538 WSC/BDR.

MY QUESTION:

Why must 0.015 and 0.03 be divided by 2? Isn’t it the 180 day rate already?

Please explain this to me!

Thanks alot!

#2

No. Interest rates are quoted as annual rates.

#3

I doubt he copy the question correctly. His question specify the risks free rate for 180days, in which case disguising by two will not be correct.

#4

If the 180-day risk-free rate is given as 1.5%, that means 1.5% per year, so the rate you will use to discount for 180 days is 1.5% ÷ 2 = 0.75%.

Rates are quoted as annual rates.

#5

I hate to be a stickler for notation but…

When you write WSC/BDR 2.875, that means 1 WSC = 2.875 BDR

using IRP you get 1 / 2.875 * (1.075) / (1.015) = 1 / 2.8964

thus, the no arbitrage forward price is WSC/BDR 2.8964!

Obviously the question writer meant 2.875 WSC = 1 BDR. And, if that’s the case then:

2.875 * (1.075) / (1.015) = 2.8538.

I usually don’t pick on notation but given that the notation WSC/BDR is industry standard, it’s worth being careful about what you write. Occasionally, this is written WSCBDR without the slash, which is slightly less confusing because it doesn’t falsely imply the direction of the ratio.

#6

For whatever the reason, CFA Institute doesn’t use the industry standard notation; they’d write 2.875 WSC/BDR to mean 2.875 WSC = 1 BDR.

People accustomed to the industry standard notation hate this.