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retaker
10-08-2002, 07:03 PM
1) 1993 course 220 #9 AKA CSM #D6 in Wachtel I:

Calculate the forward exchange rate of dollars to pounds that results in no arbitrage opportunity:

1 -year US Treasury bill rate 6%

1 -year UK government bill rate 7%

initial exchange rate \$1.75 to 1 UK pound

Assuming "forward" means real and initial "nominal":

the formula is: e_real = e_nom (P/P_foreign)

Since in this case we are dealing with UK pounds, the rate is measured WRT UK pounds (a kick back to when the UK use to be the dominant oppressor of the world, a title recently taken over by yours truly :D )
Hence the "foreign" in this case is the US dollar.

So: e_real = 1.75 ( 1.07/1.06) = 1.767

2) 1997 Course 220 #14 AKA CSM, Watchel I, #D10

You are given the following:
i) A U.S. Treasury Bill with a 182-day maturity and a bank discount yield of 7.91%.

ii) A UK government 182-day maturity and a bank discount yield of 9.89%.

iii) The exchange rate at maturity is: \$1.93 = 1 pound (I'm sorry, but I can't resist with all this talk about the UK... isn't it funny how the UK is kissing our butt's now. Blair is like a little puppet ... :D .. dance Blair, dance)

e_real = e_nom (P_foreign/P) ???

= 1.93 (1.0989/1.0791) ??

It seems like they are considering the UK as the foreign currency again, and also got the formula mixed up???

Seems like it should be: e_real = e_nom (P/P_foreign)

= 1.93 (1.0989/1.0791) Same answer but with two less mistakes.

FIOB
10-08-2002, 07:19 PM
1) You can either have \$1.75 and earn 6%, or you can convert to 1 pound and earn 7%. At the end of the year you will either have \$1.855 or 1.07 pounds. They are worth the same (today), so \$1.733645 = 1 pound 1 year in the future.

retaker
10-08-2002, 07:32 PM
So you can't use that formula for "forward" exchange rates?

Wait a minute! This is an Interest Rate Parity question, isn't it?

e_expected = e_nom ((1+i_f)/(1+i))

What is it doing in this section?

retaker
10-08-2002, 07:45 PM
Actually can't D10 also be viewed as an interest rate parity question where they give you the future rate and ask for the initial?

So:
e_initial = (1.93/1.0791)/(1/1.0989) = 1.93 (1.0989/1.0791) = 1.9654

Note: CSM has /\ above but
says it equals 1.95?

PsychMajor
10-09-2002, 10:04 AM
I believe that in this problem you will have to note that they give you a discounted annual interest rate. You will need to change that to the effective interest rate for the 180 day period. So for US currency {the square root of [1/(1-.0791)] = 1.04206249}; for the pound {the square root of [1/(1-.0989)] = 1.053448976}.

So 180 days ago at beginning of period values were:
1.93(US)/1.04206249=1(pound)/1.053448976

(1.93(US)/1.04206249)*1.053448976=1(pound)

1.9510888868(US)=1(pound)

Hope this helps.

retaker
10-09-2002, 10:21 AM
Yeah, I was wondering about that, but I didn't try it to see if came out to 1.95 since they wrote for the solution in the CSM manual exactly what I had above and set it equal to 1.95?

Thanks. These are "interest rate parity" questions, right?