Minimum Variance Hedge Ratio Practice Questions and Answers PDF

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Professor Joel Rentzler
Additional practice problems using the minimum variance hedge ratio along with answer and explanations...

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Minimum Variance Hedge Ratio Practice Questions & Answers Minimum Variance Hedge Ratio Practice Questions Stock Portfolio Hedge Scenario: On March 31th a portfolio manager is concerned about the market over the next four months. The portfolio has accumulated an impressive profit, which the manger wishes to protect over the period ending July 27th a. What position should the portfolio manager take in the futures market - long or short? b. What is the optimal number of futures contracts the portfolio manager should buy to hedge her position? c. What is the profit (loss) of the portfolio manager after the hedge takes place? d. How much did the portfolio manager's hedge save her? Given the following information about the portfolio manager's positions and futures prices on March 31st and July 27th March 31st

S&P 500 September Futures Contract: Price on March 31st = Contract Multiplier =

452.60

500

Price of one contract =

500 ∗ 452.60 = 226, 300

July 27th

S&P 500 September Futures Contract Price on July 27th =

447.70

Contract Multiplier =

500

Price of one contract =

500 ∗ 447.70 = 223, 850

Part a) Solution A: The portfolio manager should enter into a Short Hedge The portfolio manager enters a short hedge because she is currently long in the spot market and fears that her portfolio value will decrease. To protect the value of her portfolio, she uses a cross hedging strategy and enters a short hedge because if the prices in the spot market decrease, her short position would counteract her losses. Part b) Solution We calculate the MVHR for the stock portfolio which is equal to portfolio's beta

h∗ = BP Where

h∗ = Minimum Variance Hedge Ratio BP = Portfolio Beta

h∗ = 1.06 Now that we have the MVHR, we determine the amount of contracts we need to short is:

3, 862, 713 226, 300

∗ 1.06 = 18.05 ≈ 18

We divide our current spot position ($3,862,713), the value of the entire portfolio, by the cost of a single futures contract ($226,300) the multiply by h* (1.06) and see we must short 18 contracts to hedge our position Part c) Solution The profit (loss) of the portfolio hedger follows the equation of the profit (loss) for an investor who is a Long Hedger

ΠLH (TOT ) = (St+1 − St ) − (t FT −t+1 FT ) ΠLH (TOT ) = (3, 759, 350 − 3, 862, 713) − (4, 073, 400 − 4, 029, 300) ΠLH (TOT ) = (−103, 362) + (44, 100) ΠLH (TOT ) = −59, 262

Part d) Solution Without the hedge, the portfolio manager would have loss -$103,362 which translates into a 2.68% loss

ΠLH (SM) = St+1 − St ΠLH (SM) = 3, 759, 350 − 3, 862, 713 ΠLH (SM) = −103, 362 103, 362 3, 862, 713

= 0.0268

The hedge recuperated a profit of $44,100 in the profit in the futures market which reduced the the overall losses to 1.53%

ΠLH (FM) =t FT −t+1 FT ΠLH (FM) = 4, 073, 400 − 4, 029, 300 ΠLH (FM) = 44, 100 59, 262 3, 862, 713

= 0.0153

Anticipatory Hedge of a Takeover Scenario: On November 17, a firm has decided to begin buying up shares of Locus Development Corporation with the ultimate objective of obtaining controlling interest. The acquisition will be made by purchasing lots of about 100,000 shares until sufficient control is obtained. The first purchase of 1000,000 shares will take place on December 17. The stock is currently worth $54 and has a beta of 1.35 a. What position should the firm take in the futures market - long or short? b. What is the optimal number of futures contracts the firm should buy to hedge their position? c. What is the profit (loss) of the firm after the hedge takes place?

d. What is the effective share price per share after the profits from the hedge? November 17th Sport Market Current Price of the stock is = $54 Current Cost of 100,000 share = $5,400,000 Stock Beta = 1.35 Futures Market: March S&P 500 Futures Futures price = $465.45 Contract multiplier = 500 Price per contract = $232,725 December 17th Sport Market Current Price of the stock is = $57 Current Cost of 100,000 share = $5,700,000 Stock Beta = 1.35 Futures Market: March S&P 500 Futures Futures price = $473.95 Contract multiplier = 500 Price per contract = $236,975 Part a) solution A: The firm should enter a Long Position in the futures market The firm should enter a long position in the futures market as they are short in the spot market. The firm is looking to make a purchase in the future and is worrying about the potential price increasing which would make their takeover investment cost more money. To counteract this, they should enter a long position in the futures market which would allow them to profit from the increasing prices Part b) solution

A: In this instance, we are hedging out position on stocks, we know that the MVHR is equal to the beta of a stock or portfolio which was given to us. We then determine that the optimal number of contracts to by is 31

h∗ = 1.35 5, 400, 000 232, 725

∗ 1.35 = 31.32 ≈ 31

Part c) solution

ΠS H (TOT ) = (St − St+1 ) − (t+1 FT − t FT ) ΠS H (TOT ) = (5, 400, 000 − 5, 700, 000) − (7, 346, 225 − 7, 214, 475) ΠLH (TOT ) = (−300, 000) + (131, 750) ΠLH (TOT ) = −168, 250 Part d) solution A: When the firm purchases the 100,000 shares at $57 dollars per share, they would have had an effective purchase price of $57 per share After the hedge, the firm effectively ended up paying $5,568,250 for the 100,000 shares then dividing the total cost by the total share we get an effective share price of $55.68 per share

(5, 700, 000 − 131, 750)/100, 000 = 55.68...