INTRODUCTION TO FINANCIAL DERIVATIVES

Chapter 1 :Introduction to the course

What is a financial derivative? A derivative is a financial instrument that derives its value from the value of some more basic underlying instrument or variable. The underlying instrument or variable is commonly referred to as simply the "underlying".
The underlying may be an equity share, the price of barrel of crude oil, a foreign exchange rate, a bond, all of these or – another derivative. A derivative that has another derivative as an underlying is often called a compound derivative (remember compound sentences from English grammar - the same idea).

Derivatives are around us as well. A contract to purchase a flat a year from today is a derivative. The value of the flat purchase contract depends on the price of the flat today in relation to the price fixed by the purchase contract.

Of course, the flat purchase contract itself can be bought and sold i.e. transferred between different owners. That’s trading in the derivative contract!

Derivatives can quickly become very complex. Its easy to think of one, but difficult to price and hedge complex derivatives i.e. to manufacture derivatives.

A derivative is also sometime referred to as a contingent security. That is another way of saying that the value of the derivative security is contingent on the value of some other underlying security or variable. Sometimes you might hear people talk about contingent claim analysis. That’s derivative pricing for the layman.

Once derivatives are defined in this general manner its difficult not to think of all financial instruments as derivatives. Every financial instrument you encounter can be thought of as a derivative. Let's start from the most basic one – an equity share.
The price of a common share depends on the residual value of the firm that issues it. The underlying is therefore the value of the firm. The price of a bond or a certificate of deposit depends on the interest rate level. The underlying is the interest rate. The price of a BSE index futures contract depends on the value of BSE Sensex today.


In order to price and understand derivatives you obviously need to understand how the underlying behaves. This usually involves defining the mathematical process that the underlying variable follows. Most financial variables – such as equity share prices or foreign exchange prices – follow stochastic or probabilistic processes. In other words we can only define approximately what the future value of the variable will be. Of course, if you could define the future value exactly, there would not be any fun in it, right? The range of future values – or the distribution is defined in terms of statistical parameters that are peculiar to the stochastic processes that the financial variable follows. For those mathematically inclined, most derivatives are priced assuming that the underlying variable follows a Normal or a Lognormal process.

Why do people use derivatives?:

While it's conceptually pretty to think about everything as a derivative, it will be helpful to step back for a moment to think about why people use derivatives. Several reasons why:

• Derivatives help alter Risk
  Derivatives offer a simple way for firms or individuals to alter their risk profile - either increase the amount of risk they are running, or reduce (also called hedging) their risk. Derivatives thus transfer risk between market participants - from firms to individuals, between firms from banks to industrial companies and vice versa.
  
  A common example of how an individual could use derivatives is stock grants. Many companies provide their employees with grants on their company's stock. These grants are preferential allotments of shares in the company to its employees awarded at the time of an IPO (Initial Public Offering). These preferential allotments usually come with a lock-in period within which it is not possible to sell the shares.
  Lets say a person owns 100 shares in his/her company that the person cannot sell for the next six months. However, the person believes that there is considerable chance that the share price has peaked and will fall before the shares come out of the lock-in period and can be sold. In order to reduce the risk of losing the current gain implied by today's share price, the person could enter into a forward contract to sell 100 shares six months from today with another counterparty. The forward contract priced off today's share price locks in the price at which the person sells 100 shares six months from today. The risk of share price falling is transferred from the owner of the shares to the forward contract counterparty. Of course, the forward contract counterparty may not have any restrictions on selling shares today and could use this fact to in turn hedge its risk.
  
  Derivatives, such as the forward contract described above, transfer risk from one party to another. But, what is the advantage of doing so? Isn't the system as a whole carrying the same risk? Does hedging risk in this manner using derivatives have any overall economic value? It turns out there are five economic reasons why firms or individuals should use derivatives - taxes, transaction costs, debt capacity, cost of financial distress, and reduction of borrowing costs.
  
  
• Derivatives reduce Expected Taxes
  Most tax laws (as anyone who as read a tax guide or filled out a tax form will tell you) are complex and one-sided. That means they are usually designed to favor the authority raising the tax. These breakages or irrationalities in tax laws allow a firm or an individual to reduce taxes by altering the timing or size of its cash-flows using derivatives.
  One common example is that of carried forward losses. Many firms that set up new projects are allowed to tax incentives in their first few years of operation. During these setup years the firm is allowed to pay tax at a lower rate - sometimes the firm is given a tax holiday. However, paradoxically these are also the years where the firm makes the least amount of money, as it is paying off startup costs and may not have full production and marketing capacities in place. A common derivative used in such cases is a swap that allows the firm to reduce its tax liability. The swap increases the firm's profits in the initial years and reduces the profits in the subsequent years by bringing forward its cashflows.
  Another tax rule that allows firms to profitably use derivatives is one that taxes capital gains at a rate different from revenue gains. Derivatives can be used to change the nature of gains from revenue gains to capital gains or vice versa depending on which is taxed at a lower rate.
  The other manner in which derivatives reduce expected taxes is, they allow a firm to hedge its earnings streams. By hedging its revenue or expense streams, a firm is reducing the uncertainty in the cash-flow streams. By reducing this uncertainty, the firm also reduces its expected tax outflow. (See example below on carry forward losses)
  
     Example : Carry Forward Losses and Derivatives:
  
  Let there be equal probability of the firm having a pre-tax income of +500 and -300. The firms expected earnings are then:
  
  E(Earnings) = ½ * (500) + ½ * (-300) = 250 -150 = 100
  
  If the tax rate on earnings is 30%, then the tax on expected earnings is:
  Tax(E(Earnings)) = T(100) = 30
  
  If the firm is allowed to carry-forward all its losses, then in a multi-period case, the firm can always reduce its profits by deducting prior period losses. Thus, a loss creates an equivalent amount of tax credit that can be used in later periods (like a tax refund).
  
  The expected tax of the firm then is:
  
  E(Tax) = ½ * Tax(500) + ½ * Tax(-300) = ½ * 150 + ½ * (-90) = 75 - 45 = 30
  The expected tax of the firm and tax on expected earnings is the same.
  
  The situation changes if the firm is allowed to carry forward only half its losses. Under this regime the tax on expected earnings remains the same.
  Tax(E(Earnings)) = 30
  
  However, the expected tax changes as losses now provide only half the tax credit as before. The expected tax is:
  
  E(Tax) = ½ * Tax(500) + ½ * Tax(-300) = 75 + ½ * (30% * -150) = 75 - ½ * 45 = 75 - 22.5 = 52.5
  
  You may have intuitively reached the same conclusion. The expected tax is higher than the tax on expected earnings. In such a case, if a firm is able to hedge its earnings so that its earnings are always equal to the expected earnings level, its expected tax will be:
  
  E(Tax) = 1 * Tax(100) = 30
  
  
  
• Derivatives reduce Transaction Costs
  Derivatives are such convenient ways to transfer risks, that firms and institutions can now choose exactly which risks they wish to run and which they would rather discard.
  This leads to a natural specialization in risk taking ability. Firms that refine crude can choose to assume crude oil price risk, whereas banks and financial institutions can choose to assume interest rate and foreign exchange risk. They can each transfer non-core risk elements to other firms by using derivatives. This leads to a natural accumulation of risk in the hands of financial intermediaries such as banks and insurance companies.
  Firms can then use economies of scale to manage risk more efficiently. Many risks cancel each other at the portfolio level, and the firm need manage only the net residual risk. This naturally reduces the number of hedging transactions that need to be executed to hedge the same portfolio. Large banks and financial institutions acting as market makers make the financial system more efficient. None of this would have been possible without the use of derivatives to smoothly transfer risk amongst market participants.
  
  
• Derivatives reduce cost of financial distress and increase the debt capacity of the firm
  When firms use derivatives to hedge their income or expense streams, they reduce the volatility of the stream of future cash-flows. A firm's expected cost of financial distress depends on:
  1. the probability of financial distress or default and
  2. the cost when in a defaulted situation.
  Hedging derivatives reduce expected cost of financial distress by reducing factor (a). As the firm is less likely to default if its earnings are less volatile, derivatives directly reduce the expected cost of financial distress. Naturally, a firm less likely to default will also be charged a smaller credit spread by its lenders and given larger amounts of debt by its lenders. Thus, derivatives increase the debt capacity and reduce borrowing costs as well.
  
  
• Derivatives "arbitrage" Regulations
  Finally, while few practitioners like to admit this, derivatives are commonly used to get around regulations relating to flow of capital (sovereign regulations), accounting and securities ownership.
  A foreign equity investor may wish to hedge its exposure to foreign exchange rate fluctuations. However, country regulations may prohibit the investor from hedging directly.
  Enter from left stage - Mr. Derivative in the form of a non-deliverable forward contract¹ !

  
  

  These derivatives are described in greater detail in the sections that follow.
  
  
  ¹ A non-deliverable forward contract is like a standard forward contract, except that only the net value of the contract is settled on maturity. The net value is determined by looking at a standard fixing page. Principal cash-flows are not delivered, hence the name.

  
  

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  This is part of the course :'INTRODUCTION TO FINANCIAL DERIVATIVES'.
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