Security Markets III Miloslav S Vosvrda Theory of Capital Markets

Derivative Security A derivative security is a security whose value depends on the values of other more basic underlying variables. In recent years, derivative securities have become increasingly important in the field of finance. Futures and options are now actively traded on many different exchanges. Forward contracts, swaps, and many different types of options are regularly traded outside of exchanges by financial institutions. And their corporate clients in what are termed the over- the-counter markets. Other more specialized derivative securities often form part of a bond or stock issue.

Derivative securities are also known as contingent claims. Very often the variables underlying derivative securities are the prices of traded securities. A stock option, for example, is a derivative security whose value is contingent on the price of a stock. However, as we shall see, derivative securities can be contingent on almost any variable, from the price of hogs to the amount of snow falling at a certain ski resort.

FORWARD CONTRACTS A forward contract is a particularly simple derivative security. It is an agreement to buy or sell an asset at a certain future time for a certain price. The contract is usually between two financial institutions or between a financial institution and one of its corporate clients. It is not normally traded on an exchange.

A forward contract assumes a long position and agrees to buy the underlying asset on a certain specified future date for a certain specified price. A short position agrees to sell the asset on the same date for the same price. The specified price in a forward contract will be referred to as the delivery price. At the time the contract is entered into, the delivery price is chosen so that value of the forward contract to both parties is zero. This means that it costs nothing to take either a long or a short position.

A forward contract is settled at maturity. The holder of the short position delivers the asset to the holder of the long position in return for a cash amount equal to the delivery price. A key variable determining the value of a forward contract is the market price of the asset. A forward contract is worth zero when it is first entered into. Later it can have a positive or a negative value depending on movements in the price of the asset. For example, if the price of the asset rises sharply soon after the initiation of the contract, the value a long position in the forward contract becomes positive and the value of a short position in the forward contract becomes negative.

The forward price The forward price for a certain contract is defined as the delivery price which would make that contract have zero value. The forward price and the delivery price are therefore equal at the time the contract is entered into. As time passes, the forward price is liable to change while the delivery price, of course, remains the same.

Spot and Forward Foreign Exchange Quotes, September day forward day forward Spot day forward1.6929

PAYOFFS FROM CONTRACTS The payoff a long position in a forward contract on one unit of an asset is where K is the delivery price and is the spot price of the asset at maturity of the contract. This is because the holder of the contract is obligated to buy an asset worth for K. Similarly, the payoff from a short position in a forward contract on one unit of an asset is These payoffs can be positive or negative

FUTURE CONTRACTS A future contract, like a forward contract, is an agreement between two parties to buy or sell an asset at a certain time in the future for a certain price. Futures contracts are normally traded on an exchange.

Question You are interested in trading 1$ US for 1 CHF. Finded quotations look as follows: How much costs 10000CHF in 6 months and how much costs 10000CHF now? Spot price1$US=1.2CHF 30-dayforward1$US=1.19CHF 90-dayforward1$US=1.18CHF 180-dayforward1$US=1.17CHF

OPTIONS Options on stock were first traded on an organized exchange in Since then, there has been a dramatic growth in options markets. Options are now traded on many different exchanges throughout the word. Huge volumes of options are also traded over the counter by banks and other financial institutions. The underlying assets include stocks, stock indices, foreign currencies, debt instruments, commodities, and futures contracts.

There are two basic types of options. A call option gives the holder the right to buy the underlying asset by a certain date for a certain price. A put option gives the holder the right to sell the underlying asset by a certain date for a certain price. The price in the contract is known as the exercise price or strike price; the date in the contract is known as the expiration date, exercise date, or maturity. American options can be exercised at any time up to the expiration date..

European options can only be exercised on the expiration date itself. Most of the options that are traded on exchange are American. However, European options are generally easier to analyze that American options, and some of the properties of an American option are frequently deduced from those of its European counterpart

PAYOFFS If X is the strike price and is the final price of the underlying asset, the payoff from a long position in a European call option is The payoff to the holder of a short position in the European call option is or

The payoff to the holder of a long position in a European put option is and the payoff from a short position in a European put option is or

HEDGERS Hedgers are interested in reducing a risk that they already face

SPECULATORS Speculators wish to take a position in the market. Either they are betting that a price will go up or they are betting that it will go down. There is an important difference between speculating using forward markets and speculating by buying the underlying asset (in this case, a currency) in the spot market. Buying a certain amount of the underlying asset in the spot market requires an initial cash payment equal to the total value of what is bought.

Entering into a forward contract on the same amount of the asset requires no initial cash payment. Speculating using forward therefore provides an investor with a much higher level of leverage than speculating using spot markets

ARBITRAGEURS Arbitrageurs are a third important group of participants in derivative securities markets. Arbitrage involves locking in a riskless profit by simultaneously entering into transactions in two or more markets.

SUMMARY Hedgers are in the position where they face risk associated with the price of an asset. They use derivative securities to reduce or eliminate this risk. Speculators wish to bet on future movements in the price of an asset. They use derivative securities to get extra leverage. Arbitrageurs are in business to take advantage of a discrepancy between prices in two different markets. If, for example, they see the futures price of an asset getting out line with the cash price, they will take offsetting positions in the two markets to lock in a profit.

QUESTIONS and PROBLEMS Suppose that you write a put option contract on 100 IBM shares with a strike price of $120 and an expiration date in 3 months. The current price of IBM stock is $121. What have you committed yourself to? How much could you gain or lose ?

You would like to speculate on a rice in the price of a certain stock. The current stock price is $29 and a 3-month call with a strike of $30 costs $2.90. You have $5,800 to invest. Identify two alternative strategies, one involving an investment in the stock and the other involving investment in the option. What are the potential gains and losses from each?

Suppose that a European call option to buy a share for $50 costs $2.50 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustrating of the profit from a long position in the depends on the stock price at maturity of the option

FUTURES MARKETS

BASIC RISK The basis in a hedging situation is defined as follows: Basis = Spot price of asset to be hedged / Futures price of contract used If the asset to be hedged and the asset underlying the futures contract are the same, the basis should be zero at the expiration of the futures contract.

When the spot price increases by more than the futures price, the basis increases. This is referred to as a strengthening of the basis. When the futures price increases by more than the spot price, the basis declines. This is referred to as a weakening of the basis. To examine the nature of basis risk we will use the following notation:

From the definition of the basis : The price realized for the asset is and the profit on the futures position is. The effective price that is obtained for the asset with hedging is therefore

The hedging risk is the uncertainty associated with. This is known as basis risk. Consider next a situation where a company knows it will buy the asset at time and initiates a long hedge at time. The price paid for the assets is and the loss on the hedge is The effective price that is paid with hedging is therefore

For investment assets such as currencies, stock indices, gold, and silver, the basis risk tends to be fairly small. The basis risk for an investment asset arises mainly from uncertainty as to the level to the risk-free interest rate in the future.

CHOICE OF CONTRACT One key factor affecting basis risk is the choice of the future contract to be used for hedging. This choice has two components: The choice of the asset underlying the futures contract The choice of the delivery month.

If the asset being hedged exactly matches an asset underlying a futures contract, the first choice is generally fairly easy. In other circumstances, it is necessary to carry out a careful analysis to determine which of the available futures contracts has futures prices that are most closely correlated with the price of the asset being hedged.

OPTIMAL HEDGE RATIO The hedge ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure. Up to now we have always assumed a hedge ratio of 1.0. We now show that, if the objective of the hedger is to minimize risk, a hedge ratio of 1.0 is not necessarily optimal.

Define: Change in spot price, S, during a period of time equal to the life of the hedge Change in futures price, F, during a period of time equal to the life of the hedge Standard deviation of Coefficient of correlation between and h: Hedge ratio

The hedger‘s position during the life of the hedge is For a long hedge it is In either case the variance, v, of the change in value of the hedged position is given by

so that Setting this equal to zero, and noting that is positive, we see that the value of h that minimizes the variance is

The optimal hedge ratio is therefore the product of the coefficient of correlation between and and the ratio of the standard deviation of to the standard deviation of. If and, the optimal hedge ratio, h, is 1.0. This is to be expected since in this case the future price mirrors the spot price perfectly. If and, the optimal hedge ratio h is 0.5.

Options are referred to as in the money, at the money, or out of the money. An in-the-money option is one that would lead to a positive cash flow to the holder if it were exercised immediately. Similarly, an at- the-money option would lead to zero cash flow if it were exercised immediately, and an out-of-money option would lead to a negative cash flow if it were exercised immediately.

If S is the stock price and X is the strike price, a call option is in the money when S > X, at the money when S = X, and out of the money when S < X. A put option is in the money when S < X, at the money when S = X, and out of the money when S > X.

QUESTIONS and PROBLEMS If the minimum variance hedge ration is calculated as 1.0, the hedge ratio is always 1.0. Is this statement true? If there is no basic risk, the minimum variance hedge ratio is always 1.0. Is this statement true?