13. Assume you own the following portfolio: Stock A B C D Price #shares beta 140 20,000 1.2 600 8,000 2.0 50 30,000 0.8 120 30,000 1.4 It is 2/15 and you want to hedge till 7/31. You have the following contracts on the S&P500 index available to you. The correlation between your portfolio and the E-mini S&P500 index is 0.85 Maturity March June September December futures value 3120 3140 3150 3180 a. Which is the appropriate maturity of the contract? b. Should you go long or short on the futures contract? c. What are the optimal number of contracts? d. How effective can you expect your hedge to be? Answer: a. Since contract has to expire after the hedge date the appropriate contract is September b. I have a long position and the correlation is positive so I would take a short position in the futures contract c. Number of futures contract is given by Ny = () ) Stock Price #shares beta MV=P*Q ABCD 140 20,000 1.2 2,800,000 0.22 600 8,000 2.0 4,800,000 0.37 50 30,000 0.8 1,500,000 0.12 120 30,000 1.4 3,600,000 0.28 MVs= 12,700,000 Rounding weights to 2 decimal places: ẞs = .22*1.2 + .37*2.0+.12*0.8+.28*1.4 = 1.5 (rounding to 1 decimal place) Market value of portfolio (S) = 12,700,000 f=3150 * 50 = 157,500 № 1.5*(12,700,000/157,500) 120.9 = 121 contracts d. Hedging effectiveness = 0.85^2 = .72 = 72%
13. Assume you own the following portfolio: Stock A B C D Price #shares beta 140 20,000 1.2 600 8,000 2.0 50 30,000 0.8 120 30,000 1.4 It is 2/15 and you want to hedge till 7/31. You have the following contracts on the S&P500 index available to you. The correlation between your portfolio and the E-mini S&P500 index is 0.85 Maturity March June September December futures value 3120 3140 3150 3180 a. Which is the appropriate maturity of the contract? b. Should you go long or short on the futures contract? c. What are the optimal number of contracts? d. How effective can you expect your hedge to be? Answer: a. Since contract has to expire after the hedge date the appropriate contract is September b. I have a long position and the correlation is positive so I would take a short position in the futures contract c. Number of futures contract is given by Ny = () ) Stock Price #shares beta MV=P*Q ABCD 140 20,000 1.2 2,800,000 0.22 600 8,000 2.0 4,800,000 0.37 50 30,000 0.8 1,500,000 0.12 120 30,000 1.4 3,600,000 0.28 MVs= 12,700,000 Rounding weights to 2 decimal places: ẞs = .22*1.2 + .37*2.0+.12*0.8+.28*1.4 = 1.5 (rounding to 1 decimal place) Market value of portfolio (S) = 12,700,000 f=3150 * 50 = 157,500 № 1.5*(12,700,000/157,500) 120.9 = 121 contracts d. Hedging effectiveness = 0.85^2 = .72 = 72%
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Transcribed Image Text:13. Assume you own the following portfolio:
Stock
A
B
C
D
Price
#shares
beta
140
20,000
1.2
600
8,000
2.0
50
30,000
0.8
120
30,000
1.4
It is 2/15 and you want to hedge till 7/31. You have the following contracts on the S&P500 index
available to you. The correlation between your portfolio and the E-mini S&P500 index is 0.85
Maturity
March
June
September
December
futures value
3120
3140
3150
3180
a. Which is the appropriate maturity of the contract?
b. Should you go long or short on the futures contract?
c. What are the optimal number of contracts?
d. How effective can you expect your hedge to be?
Answer:
a. Since contract has to expire after the hedge date the appropriate contract is September
b. I have a long position and the correlation is positive so I would take a short position in the futures
contract
c. Number of futures contract is given by
Ny = () )
Stock Price
#shares
beta
MV=P*Q
ABCD
140
20,000
1.2
2,800,000
0.22
600
8,000
2.0
4,800,000
0.37
50
30,000
0.8
1,500,000
0.12
120
30,000
1.4
3,600,000
0.28
MVs= 12,700,000
Rounding weights to 2 decimal places:
ẞs = .22*1.2 + .37*2.0+.12*0.8+.28*1.4 = 1.5 (rounding to 1 decimal place)
Market value of portfolio (S) = 12,700,000
f=3150 * 50 = 157,500
№ 1.5*(12,700,000/157,500) 120.9 = 121 contracts
d. Hedging effectiveness = 0.85^2 = .72 = 72%
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