VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY
INTERNATIONAL UNIVERSITY
SCHOOL OF BUSINESS
INTERNATIONAL FINANCIAL MANAGEMENT
ASSIGNMENT – GROUP 2
(Chapter: Management of economic exposure)
Group members:
Full name
Student ID
Contribution
Nguyễn Đặng Trâm Anh
BABAIU19007
100%
Nguyễn Phan Quốc Minh
BABAIU19060
100%
Nguyễn Đức Tâm
BABAIU19089
100%
Lê Thảo Nguyên
BABAIU15072
0%
Problem 1:
Notes
Do not practice
a)
Probability
P
S
P* (P*= PxS)
Boom
0.6
￡2000
$1.4/￡
$2800
Slow down
0.4
￡1500
$1.5/￡
$2250
The Expected Price of asset (Land) is:
𝐸(𝑃) = 2,800 × 0.6 + 2,250 × 0.4 = $2,580
The Expected Exchange rate is:
𝐸(𝑆) = 1.4 × 0.6 + 1.5 × 0.4 = 1.44
We have:
𝑉𝑎𝑟 (𝑆) = 0.6 × (1.44 − 1.4)2 + 0.4 × (1.44 − 1.5)2 = 0.0024
𝐶𝑜𝑣 (𝑃, 𝑆) = 0.6 × (2,800 − 2,580) × (1.4 − 1.44) + 0.4 × (2,250 − 2,580) × (1.5 − 1.44) = −13.2
The exposure (b) to the exchange risk is calculated by:
𝐶𝑜𝑣 (𝑃, 𝑆) −13.2
𝑏=
=
= −5,500 (￡)
𝑉𝑎𝑟 (𝑠)
0.0024
Hence, The the value of exposure is ￡5,500.
b) The variance of the dollar value of property that is attributable to exchange rate
is:
𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝑏2 × 𝑉𝑎𝑟 (𝑆) = (−5,500)2 × 0.0024 = $72,600
c) We can hedge our exchange risk exposure by using a hedging strategy. Buying
forward contract for amount that is equal to ￡5500. This minimizes the volatility
of the dollar versus the pound, lowering the risk of exposure to exchange risk.
Problem 2:
a) Compute the exchange exposure faced by the U.S. firm.
The Expected Exchange rate is:
E(S)=𝛴 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 (𝑠𝑝𝑜𝑡 𝑟𝑎𝑡𝑒)
= 0.25*(1.2+1.10+1.00+0.90)
=0.25*4.20
=$1.05/€
The Expected Price of asset:
E(P)=0.25*(1,800+1,540+1,300+1,080) = $1,430
We have:
Var(S)=0.25 × [(1.20 − 1.05)2 + (1.10 − 1.05)2 + (1.00 − 1.05)2 + (0.90 − 1.05)2]
= 0.0125
Cov(P,S) = 0.25*[(1,800 - 1,430)(1.20 - 1.05) + (1,540 - 1,430)(1.10 - 1.05) + (1,300 1,430)*(1.00-1.05) + (1,080 - 1,430)(0.90 - 1.05)] =30
The exchange exposure faced by the U.S firm is:
b=
𝐶𝑜𝑣(𝑃,𝑆)
𝑉𝑎𝑟(𝑆)
=
30
0.0125
= €2,400
b) What is the variance of the dollar price of this asset if the U.S. firm remains
unhedged against this exposure?
Var(P)=0.25 × [(1800 − 1430)2 + (1540 − 1430)2 + (1300 − 1430)2 + (1080 − 1430)2] =
$72100
c) If the U.S. firm hedges against this exposure using a forward contract, what
is the variance of the dollar value of the hedged position?
Var(P) - [𝑏2 *Var(S)]== 72,100 − (2,4002 × 0.0125) = $100
It means that most of the volatility of the dollar value of the French asset can be removed
by hedging exchange risk. The hedging can be achieved by selling €2,400 forward.
Problem 3
Estimate your exposure to the exchange risk
Boom
Probability
Asset Value (P) in dollars
Recession
70.00%
30.00%
$1,000,000
$500,000
Spot Exchange Rate (s)
Asset Value (P) in pounds (≃)
$1.4
$1.6
£714,285.71
£312,500
£0.71
£0.63
Spot Exchange Rate (s) in Pounds (≃)
a. Estimate your exposure to the exchange risk
Expected Return on Spot Rate (Es) in pounds
E(s) = ((0.70)/(1.40) + (0.30)/(1.60) = £0.6875/$
Expected Return on Asset value in in pounds
E(P) = (0.70)*(714,285.71) + (0.30)*(312,500) = £593,750/$
Variance of spot rate V(s)
Var(s) = 0.7 × (0.71 − 0.6875)2 + 0.3 × (0.63 − 0.6875)2 ≃ 0.0014
Cov(P,S) = 0.7*(714,285 - 593,750)*(0.71 - 0.6875) + 0.3*(312,500-593,750)
*(0.63-0.6875) =6,750
𝑏=
𝐶𝑜𝑣 (𝑃, 𝑆)
6,750
=
≃ 4,821,428.571
𝑉𝑎𝑟 (𝑆)
0.0014
b. Compute the variance of the pound value of your American equity position that
is attributable to the exchange rate uncertainty
𝑏2 *Var(S) = (4,821,428.571)2 × 0.0014 = 33,254,464,285
c. How would you hedge this exposure? If you hedge, what is the variance of the
pound value of the hedged position?
𝑉𝑎𝑟(𝑃) = 0.7 × (714,285.71 − 593,750)2 + 0.3 × (312,500 − 593,750)2 =
33,900,668,920
Variance of Exchange Rate
Var(e) = Var(P) - b^2*Var(S) = 33,900,668,920 − 33,254,464,285 = 646,304,635
⇒ You can hedge this exposure by selling $4,821,428.571 forward