Question

Exercise 6: The current exchange rate is 0.9 USD for 1 AUD. Each year the value of the USD relative to the AUD can either go up by 25% with probability 25% stay constant with probability 50% go down by 20% with probability 25% a) Fill out the following table for the exchange rates and the corresponding probabilities. Year Exchange rate Probability t= 1 t= 2 t= 3 b) We obtain 100 USD in one year from now. Calculate the AUD value in one year from now of the 100 USD payment (without discounting). Year Exchange rate Value of 100 USD in AUD t= 1 c) Calculate the variance of the AUD value in one year from now of the 100 USD payment (without discounting). d) We obtain 100 USD in three years from now. Calculate the AUD value in three years from now of the 100 USD payment (without discounting). Year Exchange rate Value of 100 USD in AUD t=3 e) Calculate the variance of the AUD value in three years from now of the 100 USD payment (without discounting). f) What can we conclude for the relationship between maturity and exchange rate risk?

can you please help out with part a - f thank you

what additional info do you need?

Answer 1

Part a:

Current exchange Rate =USD 0.9/AUD

Exchange Rate at t=1

Probability :0.25: Rate =0.9*1.25=1.125USD/AUD

Probability : 0.50 Rate =0.9USD/AUD

Probabilty :0.25 Rate =0.9*(1-0.2)=0.72USD/AUD

Exchange Rate at t=2

If it goes up:

Probability 0,25*0.25=0.0625 Rate =1.125*1.25=1.40625 USD/AUD

Probability 0.50*0.25=0.125 Rate =0.9*1.25=1.125USD/AUD

Probability 0.25*0.25=0.0625 Rate =0.72*1.25=0.9USD/AUD

If it remains the same:

Probability 0,25*0.50=0.125 Rate =1.125 USD/AUD

Probability 0.50*0.50=0.25 Rate =0.9 USD/AUD

Probability 0.25*0.5=0.125 Rate =0.72 USD/AUD

If it goes DOWN:

Probability 0,25*0.25=0.0625 Rate =1.125*0.8=0.9 USD/AUD

Probability 0.50*0.25=0.125 Rate =0.9*0.8=0.72USD/AUD

Probability 0.25*0.25=0.0625 Rate =0.72*0.8=0.576USD/AUD

			Multipliying Factor
		Probability	Amount
	Going Up	0.25	1.25
	Remaining the same	0.5	1
	Going Down	0.25	0.8
	At t=1
	Exchabge Rate at t=0(USD/AUD)	Exchange Rate USD/AUD)	Probability
	0.9	1.125	0.25
		0.9	0.5
		0.72	0.25
		TOTAL	1.0000
	At t=2
	Exchange Rate at t=1(USD/AUD)	Exchange Rate USD/AUD)	Probability
	1.125	1.40625	0.0625
	0.9	1.125	0.125
	0.72	0.9	0.0625
		1.125	0.125
		0.9	0.25
		0.72	0.125
		0.9	0.0625
		0.72	0.125
		0.576	0.0625
		TOTAL	1.0000
	At t=3
	Exchange Rate at t=2 (USD/AUD)	Exchange Rate USD/AUD)	Probability
	1.40625	1.7578125	0.015625
	1.125	1.40625	0.03125
	0.9	1.125	0.015625
	1.125	1.40625	0.03125
	0.9	1.125	0.0625
	0.72	0.9	0.03125
	0.9	1.125	0.015625
	0.72	0.9	0.03125
	0.576	0.72	0.015625
		1.40625	0.03125
		1.125	0.0625
		0.9	0.03125
		1.125	0.0625
		0.9	0.125
		0.72	0.0625
		0.9	0.03125
		0.72	0.0625
		0.576	0.03125
		1.125	0.015625
		0.9	0.03125
		0.72	0.015625
		0.9	0.03125
		0.72	0.0625
		0.576	0.03125
		0.72	0.015625
		0.576	0.03125
		0.4608	0.015625
		TOTAL	1.0000000

AUD value of 100 dollar one year from now At t=1 VB C=V*B D=V-91.125 E=D^2 FEE*B Value of 100 dollar at the Deviation Deviatio Deviation Exchange exchange Value *Probabil from Squared* Prob Rate rate Probability ity expected Squared ability 1.125 112.5 0.25 28.125 21.375 456.8906 114.2226563 0.9 90 0.5 45 - 1.125 1.265625 0.6328125 0.72 72 0.25 18 - 19.125 365.7656 91.44140625 SUM 91.125 SUM 206.296875 91.125 AUD 206.296875 AUD Value one year from now (USD/AUD) Variance of AUD value one year from now Standard Deviation =Square Root(Variance) Standard Deviation of AUD value one year from now 14.3630385 AUD SQRT(206.296875)

d) AUD value of 100 dollar Three years from now At t=3 BC=VB D=V-91.125 E=D^2 FEB Value of 100 dollar at the Deviation Deviatio Deviation Exchange exchange Value *Probabi from n Squared Pro Rate rate Probability lity expected Squared bability 1.7578125 175.78125 0.015625 2.746582031 82.3638867 6783.81 105.9970287 1.40625 140.625 0.03125 4.39453125 47.2076367 2228.561 69.64253015 1.125 112.5 0.015625 1.7578125 19.0826367 364.147 5.689797253 1.40625' 140.625 0.03125 4.39453125 47.2076367 2228.561 69.64253015 1.125 112.5 0.0625 7.03125 19.0826367 364.147 22.75918901 0. 9 90 0.03125 2.8125 -3.4173633 11.67837 0.364949118 1.125 112.5 0.015625 1.7578125 19.0826367 364.147 5.689797253 0. 9 90 0.03125 2.8125 -3.4173633 11.67837 0.364949118 0.72 72 0.015625 1.125 -21.417363 458.7034 7.167241404 1.40625 140.625 0.03125 4.39453125 47.2076367 2228.561 69.64253015 1.125 112.5 0.0625 7.03125 19.0826367 364.147 22.75918901 90 0.03125 2.8125 -3.4173633 11.67837 0.364949118 1.125 112.5 0.0625 7.03125 19.0826367 364.147 22.75918901 90 0.125 11.25 -3.4173633 11.67837 1.459796473 0.72 72 0.0625 4.5 -21.417363 458.7034 28.66896562 0.9 90 0.03125 2.8125 -3.4173633 11.67837 0.364949118 72 0.0625 4.5 -21.417363 458.7034 28.66896562 0.9 0.9" 0.72

༧ 4 0.s་ 30 09 057དུ་ 1.2དྲ་ 0.72 72 0.015525 1.40525 140.6250.03125 1.125 112. 5 0.0525 0.g 900.03125 1125 112. 5 0 .0525 0.125 0.72 720.0525 900.03125 0.72 72 0.0625 57. 6 0.03125 112.5 0.015525 900.03125 0.72 72 0.015625 D. 900.03125 0.72 720.0525 0.57657. 5 0.03125 0.72 72 0.015525 0.576 57. 6 0.03125 0.450g་ 6.03 0.015625 SUM 13,417363 AUD 655.71233 1.125 -21.417353 453.7034 7.16724140- .39453125 47.2076357 2228.551 59.64253015 7.03125 15.0325357 354.147 22.75913901 2.3125 3.4173633 11.57337 0.364949118 7.03125 19.0325367 354.147_22.75913901 11.25 -3.4173633 11.67337 1.459795473 4.5 -21.417353 458.7034 23.65395552 2.8125 -3.4173533 11.673370.354949118 4.5 -21.417363 453.7034_2.65395562 1.3 35.317353 1282.884 40.09010976 1.7578125 15.0325367 354.147 5.583797253 2.8125 -3.4173533 11.673370.354949118 1.125 -21.417353 458.7034 7.157241404 2.8125 -3.4173633 11.67337 0.354349115 4.5 -21.417353 453.7034_23.55396552 1.s -35.817353 1282.33,4 40.03010376 1.125 -21.417363 45.7034 7.167241404 1. -35.317353 1282.334 40.09010376 0.72 -47.337353 2240.325 35.01290555 93.41735323 SUM 556.7129251 d) AUD Value THREE year from now (USD/AUD) Variance of AUD value THREE year from now Standard Deviation Square Root(Variance) Standard Deviation of AUD value one year from now 25.820785 AUD (SGRI(555.712925)