Ch 3: Hedging Linear Risk Flashcards
The traditional approach to market risk management includes _____, which consists of taking positions that lower the risk profile of the portfolio.
hedging
True or false. This implementation of hedging is quite narrow, however. Its objective is to find the optimal position in a futures contract that minimizes the variance, or more generally the VAR, of the total position.
true
which consists of putting on, and leaving, a position until the hedging horizon.
Static hedging
which consists of continuously rebalancing the portfolio to the horizon. This can create a risk profile similar to positions in options.
Dynamic hedging
arises when changes in payoffs on the hedging instrument do not perfectly offset changes in the value of the inventory position.
Basis risk
Because the amount sold is the same as the underlying, this is called a ______
unitary hedge
True or false. A long hedge position is said to be long the basis, since it benefits from an increase in the basis.
false. Short hedge position
true of false. Basis risk arises when the characteristics of the futures contract differ from those of the underlying position.
true
Basis risk is higher with ________, which involves using a futures on a totally different asset or commodity than the cash position.
cross-hedging
True or false. Basis risk occurs when the hedge horizon match the time to futures expiration
false. Basis risk occurs when the hedge horizon does not match the time to futures
expiration
What feature of cash and futures prices tends to make hedging possible?
(Example #1)
a. They always move together in the same direction and by the same amount.
b. They move in opposite directions by the same amount.
c. They tend to move together, generally in the same direction and by the same amount.
d. They move in the same direction by different amounts.
c. They tend to move together, generally in the same direction and by the same amount.
Under which scenario is basis risk likely to exist?
(Example #2:)
a. A hedge (which was initially matched to the maturity of the underlying) is lifted
before expiration.
b. The correlation of the underlying and the hedge vehicle is less than one and their
volatilities are unequal.
c. The underlying instrument and the hedge vehicle are dissimilar.
d. All of the above are correct.
d. All of the above are correct
This is an example when you implement temporary hedging using derivative contracts
T-bond Futures
This can be used when it is too costly to sell the entire portfolio only to buy it back later and you want to guard the financial asset against interest rate increase.
Temporary Hedge
This is considered a hedging problem because it involves ____________ which involves analyzing demand and supply conditions
Hedging Revenues
This is a strategy used by traders to reduce risk exposures of financial assets.
Hedge
The _________ is obtained from a regression of the (change in the) value of the inventory on the value of the hedge instrument.
Best Hedge
S consists of the number of units (shares, bonds, bushels, gallons) T or F?
True
The ________________ is given by the negative of the beta coefficient of a regression of changes in the cash value on changes in the payoff on the hedging instrument.
Optimal Hedge
If two securities have the same volatility and a correlation equal to −0.5, their minimum variance hedge ratio is
Example 3
a. 1:1
b. 2:1
c. 4:1
d. 16:1
b. 2:1
A bronze producer will sell 1,000 mt (metric tons) of bronze in three months at the prevailing market price at that time. The standard deviation of the price of bronze over a three-month period is 2.6%. The company decides to use three-month futures on copper to hedge. The copper futures contract is for 25 mt of copper. The standard deviation of the futures price is 3.2%. The correlation between three-month changes in the futures price and the price of bronze is 0.77. To hedge its price exposure, how many futures contracts should the company buy/sell?
Example 4
Sell 38 futures
Buy 25 futures
Buy 63 futures
Sell 25 futures
Sell 25 futures
A company expects to buy 1 million barrels of West Texas Intermediate crude oil in one year. The annualized volatility of the price of a barrel of WTI is calculated at 12%. The company chooses to hedge by buying a futures contract on Brent crude. The annualized volatility of the Brent futures is 17% and the correlation coefficient is 0.68. Calculate the variance-minimizing hedge ratio.
Example 5
a. 0.62
b. 0.53
c. 0.48
d. 0.42
c. 0.48
An airline knows that it will need to purchase 10,000 metric tons of jet fuel in three months. It wants some protection against an upturn in prices using futures contracts.
The company can hedge using heating oil futures contracts traded on NYMEX. The notional for one contract is 42,000 gallons. As there is no futures contract on jet fuel, the risk manager wants to check if heating oil could provide an efficient hedge instead. The current price of jet fuel is $277/metric ton. The futures price of heating oil is $0.6903/gallon. The standard deviation of the rate of change in jet fuel prices over three months is 21.17%, that of futures is 18.59%, and the correlation is 0.8243. Find the notional and standard deviation of the unhedged fuel cost in dollars. page 61
$2,770,000 ; $586,409
An airline knows that it will need to purchase 10,000 metric tons of jet fuel in three months. It wants some protection against an upturn in prices using futures contracts.
The company can hedge using heating oil futures contracts traded on NYMEX. The notional for one contract is 42,000 gallons. As there is no futures contract on jet fuel, the risk manager wants to check if heating oil could provide an efficient hedge instead. The current price of jet fuel is $277/metric ton. The futures price of heating oil is $0.6903/gallon. The standard deviation of the rate of change in jet fuel prices over three months is 21.17%, that of futures is 18.59%, and the correlation is 0.8243. Find the optimal hedge ratio. page 61
89.7
An airline knows that it will need to purchase 10,000 metric tons of jet fuel in three months. It wants some protection against an upturn in prices using futures contracts.
The company can hedge using heating oil futures contracts traded on NYMEX. The notional for one contract is 42,000 gallons. As there is no futures contract on jet fuel, the risk manager wants to check if heating oil could provide an efficient hedge instead. The current price of jet fuel is $277/metric ton. The futures price of heating oil is $0.6903/gallon. The standard deviation of the rate of change in jet fuel prices over three months is 21.17%, that of futures is 18.59%, and the correlation is 0.8243. Find the variance of the hedge position. page 62
+110,222,250,414
In the early 1990s, Metallgesellschaft, a German oil company, suffered a loss of $1.33 billion in their hedging program. They rolled over short-dated futures to hedge long-term exposure created through their long-term fixed-price contracts to sell heating oil and gasoline to their customers. After a time, they abandoned the hedge because of large negative cash flow. The cash-flow pressure was due to the fact that MG had to hedge its exposure by
Example 6
a. Short futures, and there was a decline in oil price
b. Long futures, and there was a decline in oil price
c. Short futures, and there was an increase in oil price
d. Long futures, and there was an increase in oil price
b. Long futures, and there was a decline in oil price
________________ can be successful at mitigating market risk, it can create other risks. _______________ are marked to market daily.
Futures Hedging ; Futures Contracts
________________ can be viewed as a measure of the exposure of relative changes in prices to movements in yields.
Modified Duration
The _________________ is given by the ratio of the dollar duration of the position to that of the hedging instrument.
Optimal Duration Hedge
A portfolio manager holds a bond portfolio worth $10 million with a modified duration of 6.8 years, to be hedged for three months. The current futures price is 93-02, with a notional of $100,000.We assume that its duration can be measured by that of the cheapest-to-deliver, which is 9.2 years. Provide for the notional of the futures contract.
$93,062.5.
A portfolio manager holds a bond portfolio worth $10 million with a modified duration of 6.8 years, to be hedged for three months. The current futures price is 93-02, with a notional of $100,000.We assume that its duration can be measured by that of the cheapest-to-deliver, which is 9.2 years. Provide for the number of contracts to buy/sell for optimal protection. page 65
79 contracts
On February 2, a corporate treasurer wants to hedge a July 17 issue of $5 million of commercial paper with a maturity of 180 days, leading to anticipated proceeds of $4.52 million. The September Eurodollar futures trades at 92, and has a notional amount of $1 million. Provide for the current dollar value of the futures contract. page 65
$980,000
On February 2, a corporate treasurer wants to hedge a July 17 issue of $5 million of commercial paper with a maturity of 180 days, leading to anticipated proceeds of $4.52 million. The September Eurodollar futures trades at 92, and has a notional amount of $1 million. Provide for the number of contracts to buy/sell for optimal protection. page 65
9 contracts
If all spot interest rates are increased by one basis point, a value of a portfolio of swaps will increase by $1,100. How many Eurodollar futures contracts are needed to hedge the portfolio?
Example 7
a. 44
b. 22
c. 11
d. 1,100
a. 44
Roughly how many three-month LIBOR Eurodollar futures contracts are needed to hedge a position in a $200 million, 5-year receive-fixed swap?
Example 8
a. Short 250
b. Short 3,440
c. Short 40,000
d. Long 250
b. Short 3,440
Albert Henry is the fixed income manager of a large Canadian pension fund. The present value of the pension fund’s portfolio of assets is CAD 4 billion while the expected present value of the fund’s liabilities is CAD 5 billion. The respective modified durations are 8.254 and 6.825 years. The fund currently has an actuarial deficit (assets < liabilities) and Albert must avoid widening this gap. There are currently two scenarios for the yield curve: the first scenario is an upward shift of 25 bps, with the second scenario a downward shift of 25 bps. The most liquid interest rate futures contract has a present value of CAD 68,336 and aduration of 2.1468 years. Analyzing both scenarios separately, what should Albert Henry do to avoid widening the pension fund gap? Choose the best option.
Example 9
a. Do nothing, Buy 7,559 contracts
b. Do nothing, Sell 7,559 contracts
c. Buy 7,559 contracts, Do nothing
d. Do nothing, Do nothing
a. Do Nothing, Buy 7,559 Contracts
What assumptions does a duration-based hedging scheme make about the way in which interest rates move?
Example 10
a. All interest rates change by the same amount.
b. A small parallel shift occurs in the yield curve.
c. Any parallel shift occurs in the term structure.
d. Interest rates movements are highly correlated.
d. Interest rates movements are highly correlated.
_____________________ can be viewed as a measure of the exposure of the rate of return on a portfolio i to movements in the “market” m
Beta or Systematic Risk
A portfolio manager holds a stock portfolio worth $10 million with a beta of 1.5 relative to the S&P 500. The current futures price is 1,400, with a multiplier of $250. Find the notional of the futures contract. page 67
$350,000
A portfolio manager holds a stock portfolio worth $10 million with a beta of 1.5 relative to the S&P 500. The current futures price is 1,400, with a multiplier of $250. Find the number of contracts to sell short for optimal protection. page 67
43 contracts after rounding
The _____________________ is given by the beta of the cash position times its value divided by the _____________________.
Optimal hedge with stock index futures ; notional of the futures contract
A fund manager has a USD 100 million portfolio with a beta of 0.75. The manager has bullish expectations for the next couple of months and plans to use futures contracts on the S&P 500 to increase the portfolio’s beta to 1.8. Given the following information, which strategy should the fund manager follow? The current level of the S&P index is 1250; each S&P futures contract delivers USD 250 times the index; and the risk-free interest rate is 6% per annum.
Example 11
a. Enter into a long position of 323 S&P futures contracts.
b. Enter into a long position of 336 S&P futures contracts.
c. Enter into a long position of 480 S&P futures contracts.
d. Enter into a short position of 240 S&P futures contracts.
b. Enter into a long position of 336 S&P futures contracts.
