How traders manage their risks, Assignments of Credit and Risk Management

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HOW TRADERS MANAGE THEIR

RISKS

Dr. Ika Pratiwi Simbolon Risk Management Reference: Hull, John C. 2012. Risk Management and Financial Institutions

Learning Outcomes

• To understand delta and gamma

• To understand the linear products

• To understand the nonlinear products

• To understand the simulation of delta

hedging

The value of your portfolio is

currently $117,000.

One way of investigating the risks

you face is to revalue the portfolio

on the assumption that there is a

small increase in the price of gold

from $1,800 per ounce to

$1,800.10 per ounce.

In general, the delta of a portfolio with respect to a market variable is where ΔS is a small increase in the value of the variable and ΔP is the resultant change in the value of the portfolio.

Using calculus terminology, delta is the partial derivative of the portfolio value with respect to the value of the variable:

In our example, the trader can

eliminate the delta exposure by

buying 1,000 ounces of gold.

The position gains value at the

rate of $1,000 per $1 increase in

the price of gold. This is known as

delta hedging.

When the hedging trade is

combined with the existing

portfolio the resultant portfolio

has a delta of zero.

Such a portfolio is referred to as

delta neutral.

Linear Products

A linear product is one whose value at any given time is linearly dependent on the value of an underlying market variable (see Figure 7.1). Forward contracts are linear products; options are not. A linear product can be hedged relatively easily.

Example As a simple example, consider a U.S. bank that has entered into a forward contract with a corporate client where it agreed to sell the client 1 million euros for $1.3 million in one year. Assume that the euro and dollar interest rates are 4% and 3% with annual compounding.

This means that the present value of a 1 million euro cash flow in one year is … euros. The present value of 1.3 million dollars in one year is … dollars.

This means that the present value of a 1 million euro cash flow in one year is 1,000,000/1.04 = 961,538 euros. The present value of 1.3 million dollars in one year is 1,300,000/1.03 = 1,262,136 dollars.

This shows that the value of the contract is linearly related to the exchange rate, S. The value of the contract today in dollars is: 1,262,136 − 961,538S The delta of the contract is -961,538. It can be hedged by buying 961,538 euros.