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What is the difference between a long futures position and a short futures position?
- A trader who enters into a long futures position is agreeing to buy the underlying asset for a certain price at a certain time in the future.
- A trader who enters into a short futures position is agreeing to sell the underlying asset for a certain price at a certain time in the future.
Explain the difference between hedging, speculation and arbitrage.
- A company is hedging when it has an exposure to the price of an asset and takes a position in futures or options markets to offset the exposure.
- In a speculation the company has no exposure to offset. It is betting on the future movements in the price of the asset.
- Arbitrage involves taking a position in two or more different markets to lock in a profit.
Supose that you write a put contract with a strike price of $40 and an expiration date in three months. The current stock price is $41 and one put option contract is on 100 shares. What have you committed yourself to? How much could you gain or lose?
- You have sold a put option. You have agreed to buy 100 shares for $40 per share if the party on the other side of the contract chooses to exercise the right to sell for this price. The option will be exercised only when the price of stock is below $40.
- Suppose, for example, that the option is exercised when the price is $30. You have to buy $40 shares that are worth $30; you lose $10 per share, or $1,000 in total. If the option is exercised when the price is $20, you lose $20 per share, or $2,000 in total.
- The worst that can happen is that the price of the stock declines to almost zero during the three-month period. This highly unlikely event would cost you $4,000. In return for the possible future losses, you receive the price of the option from the purchaser.
You would like to speculate on a rise in the price of a certain stock. The current stock price is $29 and a three-month call with a strike price of $30 costs $2.90. You have $5800 to invest. Identify two alternative strategies. Briefly outline the advantages and disadvantages of each.
- One strategy is to buy 200 shares. Another is to buy 2,000 options (20 contracts). If the share price does well, the second strategy will give rise to greater gains. For example, if the share price goes up to $40, you gain
- [2,000 ($40 - $30)] - $5,800 = $14,200 from the second strategy and only
- 200 ($40 - $29) = $2,200 from the first strategy.
- However, if the share price does badly, the second strategy yields greater losses. For example, if the share price goes down to $25, the first strategy leads to a loss of 200 ($29 - $25) = $800, whereas the second strategy leads to a loss of the entire $5,800 investment.
Options and futures are zero-sum games. What do you think is meant by this statement?
The statement means that the gain (loss) to the party with the short position is equal to the loss (gain) to the party with the long position. In total, the gain to all parties is zero.
A stock when it is first issued provides funders for a company. Is the same true of an exchange-traded stock option?
- No, an exchange-traded stock option is a security traded from one investor to another. It provides no funds for the company. Stocks when first listed are do, however, as they are oldfrom company to investor.
- An exception is company options. Company call options allow for buying of new stocks in the company at the option expiration date.
- Mining example: The use of company stock options is best explained by example - for a mining company, the option could fund the exploration phase of a new mine, while the issue of new shares at option expiration could be used to fund development of the mine ready for extraction.
The ASX offers a furture contract on 10 year Commonwealth Trasury bonds. Characterse the investors likely to use this contract.
- HEDGING: Portfolio managers: A short position in the contract could be used to hedge bond price risk. If bond prices fall then a short futures contract generates a profit that will offset the loss made on the bond portfolio.
- HEDGING: Bond investors: A long position in the contract could be used to lock in interest rates today for until they are ready to make their bond investment. A long position will rise in value when interest rates fall, thus covering the bank against losses from lower interest rates in the future.
- SPECULATING: Speculators: If the speculator takes a short position and interest rates rise, the bond yield will increase and the bond price will decrease leading to a profit on the short bond futures contract position.
A futures contract is used for hedging. Explain why the daily settlement of the contract can give rise to cash flow problems.
- Suppose an investor takes a short position in a futures contract to hedge the sale of an asset in 6 months. If the asset price rises sharply, the futures price will also rise, and they may get margin calls,leading to cash outflows. Eventually the cash outflows will be offset by the extra amount received when the asset is sold, but there is a timing mismatch in the cash flows.
- A similar situation could arise if you took a long position in a futures contract to hedge the purchase of an asset and the asset's price fell sharply (e.g. Metallgesellschaft)
Is the futures price of a stock index greater than or less than the expected future value of the index? Explain.
The futures price of a stock index is always less than the expected future value of the index. This is because E(S_T) = S_o x e^((r x mu - q)T). Because mu > r and F_o=S_o x e^((r-q)T), it follows that E(S_t) > F_o.
Explain why the liquidity preference theory is consistent with the onservation that the term tructure of interest rates tends to be upward sloping more often than it is downward sloping.
If long term rates were simply a reflection of expected future short-term rates, the term structure should be as much upward sloping as it is downward sloping (assuming half the time investors expect rates to increase and other half the time to decrease). Liquidity preference theory argues that long term rates are high relative to expected future short term rates. This means that the term structure should be upward sloping more than it is downward sloping.
How were the risks in ABS CDOs misjudged by the market?
- Investors underestimated how high the default correlations between mortgages would be in stressed market conditions.
- They also did not realise that the tranches underlying ABS CDOs were usually quite thin, so they were either wiped out or untouched.
- There was a tendency to assume that a tranche with a particular rating could be considered to be the same a a bond with that rating. This assumption is not valid for the reasons just mentioned.
Explain why the arguments leading to put-call parity for European options cannot be used to give a similar result for American options.
When early exercise is not possible, we can argue that two portfolios that are worth the same at time T must be worth the same at earlier times. When early exercise is possible, the argument falls down. Suppose that P + S > C + Ke^(-rT). This situation does not lead to an arbitrate opportunity. If we buy the call, short the put and short the stock, we cannot be sure of the result because we do not know when the put will be exercised.
A portfolio manager announces that the average of the returns realised in each of the last 10 years is 20% per annum. In what respect is this statement misleading?
A certain sum of money, say $1000, when invested for 10 years in the fund would have realised a return (with annual compounding) of less than 20% per annum. The average of the returns realised in each year is always greater than the return per annum (with annual compounding) realised over 10 years. The firt is an arithmetic average of the returns in each year, the second is a geometric average of these returns.
Explain how a stop-loss hedging trading rule can be implemented for the winter of an out-of-the-money call option. Why does it provide a relatively poor hedge?
- It can be done by having a covered position when it is in the money and a naked position when it is out of the money. This would mean that the writer of an out-of-the-money call would by the underlying asset as soon as the price moved above the strike price, K, and sell the underlying asset as soon as the price moved below K.
- However, it provides a relatively poor hedge as there is no way of knowing whether the price of the underlying asset will move up or down after it equals K. The asset will therefore be bought at K + E and sold at K - E for some small E.The cost of hedging depends on the number of times the asset price equals K - if it never does, the hedge will cost nothing, but if the asset price equals K many times it will be very expensive. In a good hedge, the cost of hedging is known in advance to a reasonable level of accuracy.
What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1000 call options be made delta neutral when the delta of each option is 0.7?
A delta of 0.7 means that when the price of the stock increases by a small amount, the price of the stock increases by 70% of this amount. Similarly, when the price of the stock decreases by a small amount, the price of the option decreases by 70% of this amount. A short position in 1000 options has a delta of -700 and can be made delta neutral with the purchase of 700 shares.
A portfolio manager has maintaned an actively managed portfolio with a beta of 0.2. During the last year the risk free rate was 5% and equities performed very badly providing a return of -30%. The portfolio manager produced a return of -10% and claims that in the circumstances it was good. Discuss this claim.
The portfolio has a beta of 0.2 which means that it does not and is not expected to perform the same as the market. To determine how it should perform in the market conitions we can use the CAPM. E(R_i(portfolio)) = 0.05 + 0.2 x (-.30 - 0.05) = -0.02 or -2%. Therefore, the portfolio under their management performed much worse than it could have been expected to, and the portfolio managers claims are very poor.
Why was there a transparency problem in the subprime residential mortgage market? Why is a lack of transparency in financial markets considered to be bad? What steps can be taken to improve transparency?
- Creation of tranches from tranches in the subprime residential mortgage market created highly complex securities whose successf dpeneded on several factors, including other securities, which were often not understood by investors.
- Furthermore, as an ABS or ABS CDO is typically governed by a complex legal document that is several hundred pages long, many investors did not pay sufficient attention to the detail contained in the document, instead relying on the rating label.
- The tranches became almost impossible to trade once hey were perceived as risky, as investors did not sufficiently understand the underlying asset and the algorithms that determined cash flows to the various tranches.
- The difficulties in trading, brought about by the lack of transparency, could be improved by ensuring that the documentation governing the products contains software, rather than words, that is capable of calculting the cash flows realised by certain tranches in varying circumstances. This would be in addition to providing data on the attributes of the mortgages or other instruments underlying the security.
On 7 January 2011, an investor owns 1,000 BHP shares. As indicated in Table 1.2, the share price is $44.60 and an April put option with a strike price of $44 costs $1.61. The investor is comparing two alternatives to limit downside risk. The first involves buying one April put option contract with a strike price of $44. The second involves instructing a broker to sell the 1,000 shares as soon as BHPs price reaches $44. Discuss the advantages and disadvantages of the two strategies.
The second alternative involves what is known as a stop or stop-loss order. It costs nothing and ensures that $44,000, or close to $44,000, is realised for the holding in the event the stock price ever falls to $44. The put option contract costs $1,610 and guarantees that the holding can be sold for $44,000 any time up to April. If the stock price falls marginally below $44 and then rises the option will not be exercised, but the stop-loss order will lead to the holding being liquidated. There are some circumstances where the put option alternative leads to a better outcome and some circumstances where the stop-loss order leads to a better outcome. If the stock price ends up below $44, the stop-loss order alternative leads to a better outcome because the cost of the option is avoided. If the stock price falls to $40 in March and then rises to $45 by April, the put option alternative leads to a better outcome. The investor is paying $1,610 for the chance to benefit from this second type of outcome.