Solved by a verified expert :9. Assume that the spot position comprises 1,000,000 units in the
stock index. If the hedge ratio is 1.09, how many units of the futures contract
are required to hedge this position?
10.
You have a position in 200 shares of a technology stock with an
annualized standard deviation of changes in the price of the stock being 30.
Say that you want to hedge this position over a one-year horizon with a technology
stock index. Suppose that the index value has an annual standard deviation of
20. The correlation between the two annual changes is 0:8. How many units of
the index should you hold to have the best hedge?
11. You are a portfolio manager looking to hedge a portfolio daily
over a 30-day horizon. Here are the values of the spot portfolio and a hedging
futures for 30 days.
Day
Spot
Futures
0
80.000
81.000
1
79.635
80.869
2
77.880
79.092
3
76.400
77.716
4
75.567
77.074
5
77.287
78.841
6
77.599
79.315
7
78.147
80.067
8
77.041
79.216
9
76.853 79.204
10
77.034
79.638
11
75.960
78.659
12
75.599
78.549
13
77.225
80.512
14
77.119
80.405
15
77.762
81.224
16
77.082
80.654
17
76.497
80.233
18
75.691
79.605
19
75.264
79.278
20
76.504
80.767
21
76.835
81.280
22
78.031
82.580
23
79.185
84.030
24
77.524
82.337
25
76.982
82.045
26
76.216
81.252
27
76.764
81.882
28
79.293
84.623
29
78.861
84.205
30
76.192
81.429
Carry out
the following analyses using Excel:
(a)
Compute ( S), ( F ),
and .
(b)
Using the results from (a), compute the hedge ratio you would use.
(c)
Using this hedge ratio, calculate the daily change in value of the
hedged portfolio.
(d) What is the standard deviation of changes in value of the hedged
portfolio? How does this compare to the standard deviation of changes in the
unhedged spot position?
12. Use the same data as presented above to compute the hedge ratio
using regression analysis, again using Excel. Explain why the values are di
erent from what you obtained above.
13. A US-based corporation has decided to make an investment in
Sweden, for which it will require a sum of 100 million Swedish kronor (SEK) in
three-months ‘ time. The company wishes to hedge changes in the US dollar
(USD)-SEK exchange rate using forward contracts on either the euro (EUR) or the
Swiss franc (CHF) and has made the following estimates:
If EUR forwards are used: The standard deviation of quarterly
changes in the USD/SEK spot exchange rate is 0.007, the standard deviation of quarterly
changes in the USD/EUR forward rate is 0.018, and the correlation between the
changes is 0.90.
If CHF forwards are used: The standard deviation of quarterly
changes in the USD/SEK spot exchange rate is 0.007, the standard deviation of
quarterly changes in the USD/CHF forward rate is 0.023, and the correlation
between the changes is 0.85.
Sundaram
& Das: Derivatives – Problems and Solutions . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . 58
Finally, the current USD/SEK spot rate is 0.104, the current
three-month USD/EUR forward rate is 1.071, and the current three-month USD/CHF
forward rate is 0.602.
(a)
Which currency should the company use for hedging purposes?
(b) What is the minimum-variance hedge position? Indicate if this is to
be a long or short position.
14. You use silver wire in manufacturing. You are looking to buy
100,000 oz of silver in three months’ time and need to hedge silver price
changes over these three months. One COMEX silver futures contract is for 5,000
oz. You run a regression of daily silver spot price changes on silver futures
price changes and nd that
s = 0:03 +
0:89F +
What should be the size (number of contracts)
of your optimal futures position. Should this be long or short?
15. Suppose you have the following information: = 0:95,S = 24,F = 26, K = 90, R = 1:00018. What
is the minimum-variance tailed hedge?
16. Using the equation for tailing the hedge, can you explain why the
tailed hedge ratio is always less than the ratio for untailed (static) hedge?
