Question

Exercise 4:

Consider an Australian financial institution which has Swiss Franc denominated assets worth 50 million CHF and USD denominated liabilities worth 1 million USD. The past exchange rates in over the past 10 months are:

a) Measure the exposure: Calculate the value of the position in AUD.

b) Measure the sensitivity: Calculate the change (in AUD) in the CHF position for a 1% increase in the value of the Swiss Franc. Calculate the change (in AUD) in the USD position for a 1% increase in the value of the USD.

c) Calculate the past changes in the exchange rate in %.
d) Re-evaluate the portfolio position with the past changes in the exchange rate. e) Calculate the Value at Risk for the next month and α = 10%
f) Calculate the Value at Risk for the next month and α = 20%

Month	0	1	2	3	4	5
Swiss exchange rate (AUD x)/ CHF	1.25	1.20	1.23	1.28	1.31	1.24
US exchange rate (AUD x)/ USD	1.38	1.40	1.46	1.53	1.47	1.47

Month	6	7	8	9	10 (today)
Swiss exchange rate (AUD x)/ CHF	1.18	1.08	1.21	1.27	1.32
US exchange rate (AUD x)/ USD	1.40	1.32	1.39	1.31	1.27

Answer 1

a
Value of position in AUD today-
Position	Position value (foreign currency)	Exchange rate	Position value in AUD
Assets (CHF)	50,000,000	1.32	66,000,000
Liability (USD)	1,000,000	1.27	1,270,000
Net			64,730,000

b
Sensitivity of the position-
Position	Position value (foreign currency)	Exchange rate	Position value in AUD	+1% change in position	Position value in AUD	-1% change in position	Position value in AUD
Assets (CHF)	50,000,000	1.32	66,000,000	50,500,000	66,660,000	49,500,000	65,340,000
Liability (USD)	1,000,000	1.27	1,270,000	1,010,000	1,282,700	990,000	1,257,300
Net			64,730,000		65,377,300		64,082,700
Change in position					647,300		(647,300)
Change in position					1.00%		-1.00%

c
% changes in past exchange rates
Month	0	1	2	3	4	5	6	7	8	9	10 (today)
Swiss exchange rate (AUD x)/ CHF	1.25	1.2	1.23	1.28	1.31	1.24	1.18	1.08	1.21	1.27	1.32
US exchange rate (AUD x)/ USD	1.38	1.4	1.46	1.53	1.47	1.47	1.4	1.32	1.39	1.31	1.27
% change in Swiss exchange rate		-4.00%	2.50%	4.07%	2.34%	-5.34%	-4.84%	-8.47%	12.04%	4.96%	3.94%
% change in US exchange rate		1.45%	4.29%	4.79%	-3.92%	0.00%	-4.76%	-5.71%	5.30%	-5.76%	-3.05%

d
Past portfolio position
Position	Position value (foreign currency)
Assets (CHF)	50,000,000
Liability (USD)	1,000,000
Month	0	1	2	3	4	5	6	7	8	9	10 (today)
Swiss exchange rate (AUD x)/ CHF	1.25	1.2	1.23	1.28	1.31	1.24	1.18	1.08	1.21	1.27	1.32
US exchange rate (AUD x)/ USD	1.38	1.4	1.46	1.53	1.47	1.47	1.4	1.32	1.39	1.31	1.27
Asset value in AUD	62,500,000	60,000,000	61,500,000	64,000,000	65,500,000	62,000,000	59,000,000	54,000,000	60,500,000	63,500,000	66,000,000
Liability value in AUD	1,380,000	1,400,000	1,460,000	1,530,000	1,470,000	1,470,000	1,400,000	1,320,000	1,390,000	1,310,000	1,270,000
Net Portfolio value	61,120,000	58,600,000	60,040,000	62,470,000	64,030,000	60,530,000	57,600,000	52,680,000	59,110,000	62,190,000	64,730,000

e, f
The VAR can be calculated by multiple methods. We will calculate the VAR value by 2 methods
Historical returns method-

Returns from lowest to highest

52,680,000

57,600,000

58,600,000

59,110,000

60,040,000

60,530,000

61,120,000

62,190,000

62,470,000

64,030,000

64,730,000

VAR at alpha= 10% is the lowest 10% return value. In this case, there are 11 values, Hence, 10% of 11 is 1.1. We take the 1st and the 2nd lowest return and extrapolate
52,680,000+ 0.1* (57,600,000-52,680,000)
53,172,000
VAR= 64730000- 53172000
11,558,000
Hence, 10% VAR= 11,558,000

VAR at alpha= 20% is the lowest 20% return value. In this case, there are 11 values, Hence, 20% of 11 is 2.2. We take the 2nd and the 3rd lowest return and extrapolate
57,600,000+ 0.2*(58,600,000-57,600,000)
57,800,000
VAR= 64730000- 57800000
6,930,000
Hence, 20% VAR= 6,930,000

Parametric (mean-std dev) method
Average portfolio returns over 10- months
3.90%
Std dev of return over 10-months
4.46%

Alpha= 10%
Min Return with 90% prob	-1.8157	=NORM.INV(10%,3.9%,4.46%)
Value of Portfolio	(52,801,554)	=64,730,000*(1-1.8157)
Value at Risk	11,928,446	=64,730,000-52,801,554
Alpha= 20%
Min Return with 80% prob	(0.1464)	=NORM.INV(20%,3.9%,4.46%)
Value of Portfolio	55,255,515	=64,730,000*(1-1.1464)
Value at Risk	9,474,485	=64,730,000-55,255,515

Based on the flow of question asked in the problem, I suggest historical VAR is the expected method for providing the answer. We were asked to provide values of portdolio for historical period. This would suggest a VAR calculation based on historical values.