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## Tuesday, September 30, 2008

### CIP illustrated

Jargon: "forward-points" are bid/ask quotes. These are added on top of spot quotes
Sound byte: if my currency "drops", then my interest rate should compensate that.

Q1: Suppose AUD (or USD...) spot interest rate is 200 bps  for a 1-year term. Yen spot rate is 150 bps. Suppose spot USDJPY = 100. What can you say about today's AUDJPY forward rate with far date a year from now?
A1: this is Covered-Interest-Rate-Parity in action. Formula below gives F = 100*1.015/1.02 = 99.5098.

A more basic question is
Q2: will AUDJPY rate rise or fall?

We need to be thoroughly familiar with Q2 -- AUD must WEAKEN (to 99.***) to reduce the high AUD return of 200bps!

 don’t care about Libor or treasury rate. Just consider it a measurable interest-rate

In practice, the 2 IR, the spot and forward fx rates always follow the equation. convert-deposit == deposit-convert. Otherwise, there will be arbitrage. This is described in both my bank online learning and [[complete guide]]

------textbook eg-----
USD 1 mth IR = 418 bps/year
GBP 1 mth IR = 480 bps/year
Spot cable = 1.7249
Number of days in the month = 31
Days basis GBP = 365
Days basis USD = 360

Let's calculate 1-mth GBPUSD forward rate.

418 * 31/360 = 35.99444 bps of interest in USD
480 * 31/365 = 40.76712 bps of interest in GBP

Option A: 1 GBP invested today becomes #1.004076712 in a month
Option B: 1 GBP converted to USD and invested today becomes \$1.7249 * 1.003599444 = \$1.731109. Formula is S*(1+IR)

To make these 2 investments equally appealing to an investor, forward GBPUSD rate must be

1.731109/1.004076712 = 1-mth forward GBP/USD = 1.72408, which represents a depreciation of 8.2 pips.

Intuitively, GBP pays more interest, so GBP must depreciate. If GBP were to appreciate, then it’s too good to be true.

Textbook answer -- Forward points = -0.00082

[ Formula is Spot-GBPUSD * (1 + IR-on-USD) == Forward-GBPUSD * (1 + IR-on-GBP)]
[ GBP convert to USD then deposit =========== GBP deposit then convert to USD ]
[ convert then deposit ==================== deposit then convert ]

----- a similar textbook example -----
AUD 3-mth 550 bps (high-yielder)
USD 3-mth 425 bps
Spot AUD/USD = 0.7326
Days = 92
Days basis AUD = 365
Days basis USD = 360
Forward AUD/USD = 0.7626 * (1 + 425 bps/360*92)/(1 + 550 bps/365*92) = 0.730431
Textbook answer -- Forward points = -0.002169