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46) A U.S. firm holds an asset in Great Britain and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
2.50
/£
$
2.00
/£
$
1.60
/£
P*
£
1,800
£
2,250
£
2,812.50
P
$
4,500
$
4,500
$
4,500
where,
P* = Pound sterling price of the asset held by the U.S. firm
P = Dollar price of the same asset
The "exposure" (i.e. the regression coefficient beta) is
Hint: Calculate the expression .
A) 7,500
B) 2,500
C) −2,500
D) none of the options
47) A U.S. firm holds an asset in Great Britain and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
2.50
/£
$
2.00
/£
$
1.60
/£
P*
£
1,800
£
2,250
£
2,812.50
P
$
4,500
$
4,500
$
4,500
where,
P* = Pound sterling price of the asset held by the U.S. firm
P = Dollar price of the same asset
Which of the following conclusions are correct?
A) Most of the volatility of the dollar value of the British asset can be removed by hedging
exchange risk because b2[VAR(S)] and VAR(e) are 0 ($)2 and 0 ($)2 respectively.
B) None of the volatility of the dollar value of the British asset can be removed by hedging
exchange risk because b2[VAR(S)] and VAR(e) are 0 ($)2 and 0 ($)2 respectively.
C) Most of the volatility of the dollar value of the British asset cannot be removed by hedging
exchange risk because b2[VAR(S)] and VAR(e) are 125,000 ($)2 and −127,500 ($)2 respectively.
D) Most of the volatility of the dollar value of the British asset can be removed by hedging
exchange risk because b2[VAR(S)] and VAR(e) are 125,000 ($)2 and −127,500 ($)2 respectively.
48) A U.S. firm holds an asset in Great Britain and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
2.50
/£
$
2.00
/£
$
1.60
/£
P*
£
1,800
£
2,250
£
2,812.50
P
$
4,500
$
4,500
$
4,500
where,
P* = Pound sterling price of the asset held by the U.S. firm
P = Dollar price of the same asset
Which of the following would be an effective hedge?
A) Sell £2,278.13 forward at the 1-year forward rate, F1($/£), that prevails at time zero.
B) Buy £2,500 forward at the 1-year forward rate, F1($/£), that prevails at time zero.
C) Sell £25,000 forward at the 1-year forward rate, F1($/£), that prevails at time zero.
D) none of the options
49) A U.S. firm holds an asset in Israel and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
0.30
/IS
$
0.20
/IS
$
0.15
/IS
P*
IS
2,000
IS
5,000
IS
3,000
P
$
600
$
1,000
$
4,50
where,
P* = Israeli shekel (IS) price of the asset held by the U.S. firm
P = Dollar price of the same asset
The expected value of the investment in U.S. dollars is:
A) $2,083.33
B) $762.50
C) $6,250.00
D) $6,562.50
50) A U.S. firm holds an asset in Israel and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
0.30
/IS
$
0.20
/IS
$
0.15
/IS
P*
IS
2,000
IS
5,000
IS
3,000
P
$
600
$
1,000
$
4,50
where,
P* = Israeli shekel (IS) price of the asset held by the U.S. firm
P = Dollar price of the same asset
The variance of the exchange rate is:
A) 0.001901
B) 0.002969
C) 0.0039
D) 0.0049
51) A U.S. firm holds an asset in Israel and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
0.30
/IS
$
0.20
/IS
$
0.15
/IS
P*
IS
2,000
IS
5,000
IS
3,000
P
$
600
$
1,000
$
4,50
where,
P* = Israeli shekel (IS) price of the asset held by the U.S. firm
P = Dollar price of the same asset
The "exposure" (i.e., the regression coefficient beta) is
Hint: Calculate the expression .
A) −52.6316
B) 1,289.80
C) 12,898.00
D) none of the options
52) A U.S. firm holds an asset in Israel and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
0.30
/IS
$
0.20
/IS
$
0.15
/IS
P*
IS
2,000
IS
5,000
IS
3,000
P
$
600
$
1,000
$
4,50
where,
P* = Israeli shekel (IS) price of the asset held by the U.S. firm
P = Dollar price of the same asset
Which of the following conclusions are correct?
A) Most of the volatility of the dollar value of the Israeli asset can be removed by hedging
exchange risk because b2[Var(S)] and VAR(e) are 236,717 ($)2 and 493,751 ($)2 respectively.
B) Most of the volatility of the dollar value of the Israeli asset cannot be removed by hedging
exchange risk because b2[Var(S)] and VAR(e) are 236,717 ($)2 and 493,751 ($)2 respectively.
C) Most of the volatility of the dollar value of the Israeli asset cannot be removed by hedging
exchange risk because b2[Var(S)] and VAR(e) are 8.22 ($)2 and 59,211 ($)2, respectively.
D) Most of the volatility of the dollar value of the Israeli asset can be removed by hedging
exchange risk because b2[Var(S)] and VAR(e) are 8.22 ($)2 and 59,211 ($)2 respectively.
53) A U.S. firm holds an asset in Israel and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
0.30
/IS
$
0.20
/IS
$
0.15
/IS
P*
IS
2,000
IS
5,000
IS
3,000
P
$
600
$
1,000
$
4,50
where,
P* = Israeli shekel (IS) price of the asset held by the U.S. firm
P = Dollar price of the same asset
Which of the following would be an effective hedge?
A) Sell 53 Israeli shekels forward at the 1-year forward rate, F1($/IS), that prevails at time zero.
B) Buy 53 Israeli shekels forward at the 1-year forward rate, F1($/IS), that prevails at time zero.
C) Sell 12,898 Israeli shekels forward at the 1-year forward rate, F1($/IS), that prevails at time
zero.
D) none of the options
54) Find an effective hedge financial hedge if a U.S. firm holds an asset in Great Britain and faces
the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
2.20
/£
$
2.00
/£
$
1.80
/£
P*
£
3,000
£
2,500
£
2,000
P
$
6,600
$
5,000
$
3,600
P* = Pound sterling price of the asset held by the U.S. firm
P = Dollar price of the same asset
The CFO runs a regression of the form P = a + b × S + e
The regression coefficient beta is calculated as b =
Where
Cov(P,S) = 0.25 × ($6,600 - $5,050) × ($2.20 - $2.00)
+ 0.50 × ($5,000 - $5,050) × ($2.00 - $2.00)
+ 0.25 × ($3,600 - $5,050) × ($1.80 - $2.00)
Cov(P,S) = 77.50 + 0 + 72.50
Cov(P,S) = 150
b = = 7,500
The variance of the exchange rate is calculated as
E(S) = 0.25 × $2.20 + 0.50 × $2.00 + 0.25 × $1.80
= $.55 + $1 + $.45
= $2.00
VAR(S) = 0.25 + 0.50 + 0.25
= 0.01 + 0 + 0.01
= 0.02
The expected value of the investment in U.S. dollars is:
E[P] = 0.25 × $6,600 + 0.50 × $5,000 + 0.25 × $3,600 = $5,050
Which of the following is the most effective hedge financial hedge?
A) Sell £7,500 forward at the 1-year forward rate, F1($/£), that prevails at time zero.
B) Buy £7,500 forward at the 1-year forward rate, F1($/£), that prevails at time zero.
C) Sell £2,500 forward at the 1-year forward rate, F1($/£), that prevails at time zero.
D) 0.25 × £3,000 + 0.50 × £2,500 + 0.25 × £2,000 = £2,500
55) Find an effective hedge financial hedge if a U.S. firm holds an asset in Great Britain and faces
the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
2.20
/£
$
2.00
/£
$
1.80
/£
P*
£
3,000
£
2,500
£
2,000
P
$
6,600
$
5,000
$
3,600
P* = Pound sterling price of the asset held by the U.S. firm
P = Dollar price of the same asset
The CFO runs a regression of the form P = a + b × S + e
The regression coefficient beta is calculated as b =
Where
Cov(P,S) = 0.25 × ($6,600 - $5,050) × ($2.20 - $2.00)
+ 0.50 × ($5,000 - $5,050) × ($2.00 - $2.00)
+ 0.25 × ($3,600 - $5,050) × ($1.80 - $2.00)
Cov(P,S) = 77.50 + 0 + 72.50
Cov(P,S) = 150
b = = 7,500
The variance of the exchange rate is calculated as
E(S) = 0.25 × $2.20 + 0.50 × $2.00 + 0.25 × $1.80
= $.55 + $1 + $.45
= $2.00
VAR(S) = 0.25 + 0.50 + 0.25
= 0.01 + 0 + 0.01
= 0.02
The expected value of the investment in U.S. dollars is:
E[P] = 0.25 × $6,600 + 0.50 × $5,000 + 0.25 × $3,600 = $5,050
Suppose that you implement your hedge at F1($/£) = $2/£. Your cash flows in state 1, 2, and 3
respectively will be
A) $5,100, $5,000, $5,100.
B) $5,100, $5,100, $5,100.
C) $5,000, $5,000, $5,000.
D) none of the options
56) A U.S. firm holds an asset in Great Britain and faces the following scenario:
State 1
State 2
State 3
Probability
25%
50%
25%
Spot rate
$
2.50
/£
$
2.00
/£
$
1.60
/£
P*
£
1,800
£
2,250
£
2,812.50
Where
P* = Pound sterling price of the asset held by the U.S. firm
The CFO decides to hedge his exposure by selling forward the expected value of the pound
denominated cash flow at F1($/£) = $2/£. As a result,
A) the firm's exposure to the exchange rate is made worse.
B) he has a nearly perfect hedge.
C) he has a perfect hedge.
D) none of the options
57) A U.S. firm holds an asset in Italy and faces the following scenario:
State 1
State 2
State 3
Probability
30%
40%
30%
Spot rate
$
2.50
$
1.50
$
0.90
P*
€
1,350.00
€
2,250.00
€
3,750.00
Where
P* = Euro price of the asset held by the U.S. firm
The CFO decides to hedge his exposure by selling forward the expected value of the euro
denominated cash flow at F1($/£) = $1.50/€. As a result,
A) the firm's exposure to the exchange rate is made worse.
B) he has a nearly perfect hedge.
C) he has a perfect hedge.
D) none of the options
58) Suppose a U.S. firm has an asset in Britain whose local currency price is random. For
simplicity, suppose there are only three states of the world and each state is equally likely to occur.
The future local currency price of this British asset (P*) as well as the future exchange rate (S) will
be determined, depending on the realized state of the world.
State
Probability
P*
S
S × P*
1
1/3
£
980
$
1.40
/£
$
1,372
2
1/3
£
1,000
$
1.50
/£
$
1,500
3
1/3
£
1,070
$
1.60
/£
$
1,712
Which of the following statements is most correct?
A) The firm faces no exchange rate risk since the local currency price of the asset and the exchange
rate are negatively correlated.
B) The firm faces substantial exchange rate risk since the local currency price of the asset and the
exchange rate are positively correlated.
C) The firm's exchange rate exposure can be completely hedged with derivatives written on the
British pound.
D) Since randomness is involved, no hedging is possible.
59) Suppose a U.S. firm has an asset in Britain whose local currency price is random. For
simplicity, suppose there are only three states of the world and each state is equally likely to occur.
The future local currency price of this British asset (P*) as well as the future exchange rate (S) will
be determined, depending on the realized state of the world.
State
Probability
P*
S
S × P*
1
1/3
£
1,000
$
1.40
/£
$
1,400
2
1/3
£
1,000
$
1.50
/£
$
1,500
3
1/3
£
1,000
$
1.60
/£
$
1,600
Which of the following statements is most correct?
A) The firm faces no exchange rate risk since the local currency price of the asset and the exchange
rate are negatively correlated.
B) The firm faces substantial exchange rate risk since the local currency price of the asset and the
exchange rate are positively correlated.
C) The firm's exchange rate exposure can be completely hedged with derivatives written on the
British pound.
D) Since randomness is involved, no hedging is possible.
60) Suppose a U.S. firm has an asset in Britain whose local currency price is random. For
simplicity, suppose there are only three states of the world and each state is equally likely to occur.
The future local currency price of this British asset (P*) as well as the future exchange rate (S) will
be determined, depending on the realized state of the world.
State
Probability
P*
S
S × P*
1
1/3
£
1,000
$
1.40
/£
$
1,400
2
1/3
£
933
$
1.50
/£
$
1,400
3
1/3
£
875
$
1.60
/£
$
1,400
Which of the following statements is most correct?
A) The firm faces no exchange rate risk since the local currency price of the asset and the exchange
rate are negatively correlated.
B) The firm faces substantial exchange rate risk since the local currency price of the asset and the
exchange rate are positively correlated.
C) The firm's exchange rate exposure can be completely hedged with derivatives written on the
British pound.
D) Since randomness is involved, no hedging is possible.
61) Suppose a U.S. firm has an asset in Italy whose local currency price is random. For simplicity,
suppose there are only three states of the world and each state is equally likely to occur. The future
local currency price of this asset (P*) as well as the future exchange rate (S) will be determined,
depending on the realized state of the world.
State
Probability
P*
S
S × P*
1
1/3
€
1,000
$
1.40
/£
$
1,400
2
1/3
€
933
$
1.50
/£
$
1,400
3
1/3
€
875
$
1.60
/£
$
1,400
Assume that you choose to "hedge" this asset by selling forward the expected value of the euro
denominated cash flow at F1($/£) = $1.50/€. Calculate your cash flows in each of the possible
states.
A) $1,400, $1,400, $1,400
B) $1,496.6, $1,400, $1,306.40
C) $1,404, $1,404. $1,404
D) none of the options
