But why do we care about these things? Their income pays for their mortgage, transportation, food, clothing, and medical care. Here are a few:. The Averages invest their savings in mutual funds that own stocks and bonds from companies around the world. Introduction to Derivatives way is low. As a result, the Averages are not heavily exposed to any one company. The Averages live in an area susceptible to tornadoes and insure their home. The local insurance company reinsures tornado risk in global markets, effectively pooling Anytown tornado risk with Japan earthquake risk and Florida hurricane risk.
This pooling makes insurance available at lower rates and protects the Anytown insurance company. The bank in turn sold the mortgage to other investors, freeing itself from interest rate and default risk associated with the mortgage. Because the risks of their mortgage is borne by those willing to pay the highest price for it, the Averages get the lowest possible mortgage rate. XYZ Co. In addition to having property and casualty insurance for its buildings, it uses global derivatives markets to protect itself against adverse currency, interest rate, and commodity price changes.
By being able to manage these risks, XYZ is less likely to go into bankruptcy, and the Averages are less likely to become unemployed. A bank that sells a mortgage does not have to bear the risk of the mortgage. A single insurance company does not bear the entire risk of a regional disaster. Risk-Sharing Risk is an inevitable part of our lives and all economic activity. Drought and pestilence destroy agriculture every year in some part of the world. Some economies boom as others falter.
Given that risk exists, it is natural to have arrangements where the lucky share with the unlucky. There are both formal and informal risk-sharing arrangements. On the formal level, the insurance market is a way to share risk. Total collected premiums are then available to help those whose houses burn down. The lucky, meanwhile, did not need insurance and have lost their premium.
This market makes it possible for the lucky to help the unlucky. On the informal level, risk-sharing also occurs in families and communities, where those encountering misfortune are helped by others. There is one important risk that the Averages cannot easily avoid. This could be an important reason for the Averages to avoid investing in XYZ. If the dollar becomes expensive relative to the yen, some companies are helped and others are hurt.
It makes sense for there to be a mechanism enabling companies to exchange this risk, so that the lucky can, in effect, help the unlucky. Even insurers need to share risk. Consider an insurance company that provides earth- quake insurance for California residents.
Thus, insurance companies often use the reinsurance market to buy, from reinsurers, insurance against large claims. Reinsurers pool different kinds of risks, thereby enabling insurance risks to become more widely held.
Bondholders willing to accept earthquake risk can buy these bonds, in exchange for greater interest payments on the bond if there is no earthquake. An earthquake bond allows earthquake risk to be borne by exactly those investors who wish to bear it. Risk is diversifiable risk if it is unrelated to other risks. Risk that does not vanish when spread across many investors is nondiversifiable risk.
Financial markets in theory serve two purposes. Thus, the fundamental economic idea underlying the concepts and markets discussed in this book is that the existence of risk-sharing mechanisms benefits everyone. Derivatives markets continue to evolve. A recent development has been the growth in prediction markets, discussed in the box on page One is a functional perspective: Who uses them and why?
In this section, we discuss these different perspectives. Uses of Derivatives What are reasons someone might use derivatives? Here are some motives: Risk management. Derivatives are a tool for companies and other users to reduce risks. With derivatives, a farmer—a seller of corn—can enter into a contract that makes a payment when the price of corn is low. This contract reduces the risk of loss for the farmer, who we therefore say is hedging.
Introduction to Derivatives BOX 1. See the box on occurrence of a natural disaster, or the value of a page As of this writing, a law outcome of presidential and other elections. For example, if the Re- Trading Commission. If you destroy your car in an accident, your insurance is valuable; if the car remains undamaged, it is not. Derivatives can serve as investment vehicles.
Reduced transaction costs. For example, the manager of a mutual fund may wish to sell stocks and buy bonds. Doing this entails paying fees to brokers and paying other trading costs, such as the bid-ask spread, which we will discuss later. It is possible to trade derivatives instead and achieve the same economic effect as if stocks had actually been sold and replaced by bonds. Using the derivative might result in lower transaction costs than actually selling stocks and buying bonds.
Regulatory arbitrage. It is sometimes possible to circumvent regulatory restrictions, taxes, and accounting rules by trading derivatives. This transaction may allow the owner to defer taxes on the sale of the stock, or retain voting rights, without the risk of holding the stock.
These are common reasons for using derivatives. The general point is that derivatives provide an alternative to a simple sale or purchase, and thus increase the range of possibilities for an investor or manager seeking to accomplish some goal. Obviously, for society as a whole, hedging may be desirable while regulatory arbitrage is not. In recent years the U. Nevertheless, surprisingly little is known about how companies actually use derivatives to manage risk. The basic strategies companies use are well-understood—and will be described in this book—but it is not known, for example, what fraction of perceived risk is hedged by a given company, or by all companies in the aggregate.
They may have assets and liabilities in different currencies, with different maturities, and with different credit risks. Hence banks could be expected to use interest rate derivatives, currency derivatives, and credit derivatives to manage risks in those areas. Perspectives on Derivatives How you think about derivatives depends on who you are.
In this book we will think about three distinct perspectives on derivatives: The end-user perspective. End-users are the corporations, investment managers, and investors who enter into derivative contracts for the reasons listed in the previous section: to manage risk, speculate, reduce costs, or avoid a rule or regulation.
End- users have a goal for example, risk reduction and care about how a derivative helps to meet that goal. The market-maker perspective. Market-makers are intermediaries, traders who will buy derivatives from customers who wish to sell, and sell derivatives to customers who wish to buy. In order to make money, market-makers charge a spread: They buy at a low price and sell at a high price. In this respect market-makers are like grocers, who buy at the low wholesale price and sell at the higher retail price.
After dealing with cus- tomers, market-makers are left with whatever position results from accommodating customer demands. Market-makers typically hedge this risk and thus are deeply con- cerned about the mathematical details of pricing and hedging.
Introduction to Derivatives The economic observer. Finally, we can look at the use of derivatives, the activities of the market-makers, the organization of the markets, and the logic of the pricing models and try to make sense of everything. This is the activity of the economic observer. Regulators must often don their economic observer hats when deciding whether and how to regulate a certain activity or market participant.
These three perspectives are intertwined throughout the book, with different degrees of emphasis. Financial Engineering and Security Design One of the major ideas in derivatives—perhaps the major idea—is that it is generally possible to create a given payoff in multiple ways.
The fact that this is possible has several implications. First, since market-makers need to hedge their positions, this idea is central in understanding how market-making works. The market-maker sells a contract to an end-user, and then creates an offsetting position that pays him if it is necessary to pay the customer. This creates a hedged position. Second, the idea that a given contract can be replicated often suggests how it can be customized.
The market-maker can, in effect, turn dials to change the risk, initial premium, and payment characteristics of a derivative. These changes permit the creation of a product that is more appropriate for a given situation. Third, it is often possible to improve intuition about a given derivative by realizing that it is equivalent to something we already understand.
These basic transactions are so important that it is worth describing the details. First, it is important to understand the costs associated with buying and selling. Second, it is helpful to understand the mechanisms one can use to buy or sell. Third, a very important idea used throughout the book is that of short-sales.
Even if you are familiar with short-sales, you should spend a few minutes reading this section. Although we will use shares of stock to illustrate the mechanics of buying and selling, there are similar issues associated with buying any asset.
However, we must also account for transaction costs. There are in fact two prices, a price at which you can buy, and a price at which you can sell. The price at which you can buy is called the offer price or ask price, and the price at which you can sell is called the bid price. To understand these terms, consider the position of the broker.
To buy stock, you contact a broker. Suppose that you wish to buy immediately at the best available price. If the stock is not too obscure and your order is not too large, your purchase will probably be completed in a matter of seconds. Where does the stock that you have just bought come from? It is possible that at the exact same moment, another customer called the broker and put in an order to sell.
More likely, however, a market-maker sold you the stock. As their name implies, market-makers make markets. If you want to buy, they sell, and if you want to sell, they buy. In order to earn a living, market-makers sell for a high price and buy for a low price. If you deal with a market-maker, therefore, you buy for a high price and sell for a low price. This difference between the price at which you can buy and the price at which you can sell is called the bid-ask spread.
If you were to buy immediately and then sell, you would pay the commission twice, and you would pay the bid-ask spread. Example 1. The terminology seems backward, but rather than the price you pay, the bid price is what the market-maker pays; hence it is the price at which you sell. The offer price is what the market-maker will sell for; hence it is what you have to pay.
What happens to your shares after you buy them? Unless you make other arrange- ments, shares are typically held in a central depository in the U. Such securities are said to be held in street name. Ways to Buy or Sell A buyer or seller of an asset can employ different strategies in trading the asset.
You implement these different strategies by telling the broker or the electronic trading system what kind of order you are submitting. The advantage of a market order is that the trade If you think a bid-ask spread is unreasonable, ask what a world without dealers would be like.
The search would be costly and take time. Dealers, because they maintain inventory, offer an immediate transaction, a service called immediacy. Introduction to Derivatives is executed as soon as possible. The disadvantage of a market order is that you might have been able to get a better price had you been more patient.
Thus, the advantage of a limit order is obtaining a better price. There are other kinds of orders. For example, suppose you own shares of XYZ. The box on page 17 illustrates bid and offer prices for one prediction market. Short-Selling The sale of a stock you do not already own is called a short-sale. For example, if we buy the stock of XYZ, we pay cash and receive the stock. Some time later, we sell the stock and receive cash. This transaction is a form of lending, in that we pay money today and receive money back in the future.
For many assets the rate of return we receive is not known in advance the return depends upon whether the stock price goes up or down , but it is a loan nonetheless.
The opposite of a long position is a short position. A short- sale can be viewed as a way of borrowing money. With ordinary borrowing, you receive money today and repay it later, paying a rate of interest set in advance.
There are at least three reasons to short-sell: 1. Speculation: A short-sale, considered by itself, makes money if the price of the stock goes down. This is very common in the bond market, for example. Hedging: You can undertake a short-sale to offset the risk of owning the stock or a derivative on the stock. This is frequently done by market-makers and traders. Most brokerage agreeements give your broker the right to lend your shares to another investor. The broker earns fees from doing this.
You generally do not know if your shares have been loaned. Here is a table showing the contract. An immediate sale would earn you bid-ask spreads in the U. If you bought both the Democratic and from the Iowa Presidential Nomination Market Republican contracts, you would be guaranteed on May 24, The prices in the table are limit orders placed by other traders.
You also cannot Democratic 0. Total 0. Example: Short-Selling Wine. Because short-sales can seem confusing, here is a detailed example that illustrates how short-sales work. If you believe prices will rise, you would buy the wine on the market and plan to sell after the price rises. However, suppose there is a wine from a particular vintage and producer that you believe to be overpriced and you expect the price to fall. How could you speculate based on this belief? The answer is that you can engage in a short-sale.
You can do this by borrowing a case from a collector. The collector, of course, will want a promise that you will return the wine at some point; suppose you agree to return it 1 week later. Having reached agreement, you borrow the wine and then sell it at the market price. After 1 week, you acquire a replacement case on the market, then return it to the collector from whom you originally borrowed the wine. If the price has fallen, you will have bought the replacement wine for less than the price at which you sold the original, so you make money.
If the price has risen, you have lost money. Either way, you have just completed a short-sale of wine. The act of buying replacement wine and returning it to the lender is said to be closing or covering the short position. Note that short-selling is a way to borrow money. Initially, you received money from selling the wine.
A week later you paid the money back you had to buy a replacement case to return to the lender. The rate of interest you paid was low if the price of the replacement case was low, and high if the price of the replacement case was high.
S0 and S90 are the share prices on days 0 and Note that the short-seller must pay the dividend, D, to the share-lender. It is easy to buy, at a fair price, satisfactory wine to return to the lender: The wine you buy after 1 week is a perfect substitute for the wine you borrowed. The collector from whom you borrowed is not concerned that you will fail to return the borrowed wine.
Example: Short-Selling Stock. Now consider a short-sale of stock. As with wine, when you short-sell stock you borrow the stock and sell it, receiving cash today. At some future date you buy the stock in the market and return it to the original owner.
Suppose you want to short-sell IBM stock for 90 days. Observe in particular that if the share pays dividends, the short-seller must in turn make dividend payments to the share-lender. This issue did not arise with wine! This dividend payment is taxed to the recipient, just like an ordinary dividend payment, and it is tax- deductible to the short-seller. Thus, short-selling is literally the opposite of buying.
The Lease Rate of an Asset We have seen that when you borrow an asset it may be necessary to make payments to the lender. Dividends on short-sold stock are an example of this. We will refer to the payment required by the lender as the lease rate of the asset.
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