**By Jasvin Josen**

*This article appeared in The Edge, Malaysia on June 18, 2012*

Maintaining a portfolio of financial
instruments is an everyday thing for financial market investors, fund managers,
dealers and traders at commercial banks and investment banks. Hand in hand with
maintaining the portfolio is managing the risk that the portfolio will incur
losses from fluctuation in the securities prices in the portfolio. This is market
risk.

Say a trader holds a portfolio of palm oil
futures. She knows what its market value is today, but she is uncertain as to
its market value a week from today. The trader wants to identify this risk and
reduce any exposures that she considers excessive. In other words, she wants manage
the market risk. How does she do it?

In order to manage market risk, the trader
must first be able to measure this risk. In a series of two articles, I describe
the delta, the most common kind of market risk. After explaining what delta
means and how it is measured, I show practical applications on how delta is used
in portfolio management using simple hypothetical portfolios.

**What is Delta**

The delta is simply the change in a financial
product’s price when the underlying asset changes in value.

For example, a bond’s price will change when
interest rates move in the market. Gold futures’ price change when the underlying
spot gold prices changes. Interest rate swaps value change when underlying interest
rates change. Equity options price change when the underlying equity price
changes.

However the change in the price of the
financial instrument is not linear with the change in the underlying asset
value. If interest rates go up by 1%, bond prices will not move by 1%.
Moreover, bonds with different maturities and payoffs will respond differently
to the changes in interest rates.

If we try to conceptualise the delta with a
graph (see

**Chart 1**), the delta is simply the steepness (or gradient) of the price graph of a particular financial instrument. Note that the curve is now represented by a straight line to measure its steepness. The steepness is measured by dividing the price move of the financial instrument over the price move of the underlying asset. The more sensitive the particular financial instrument is to the price change of the underlying asset, the steeper its price curve will be and hence the larger the delta.**Chart 1: The Delta**

**How is Delta measured in practice?**

In practice, global market practitioners use
a very simple technique to quantify delta risk. This method is frequently
referred to as “bumping”. First, the underlying asset’s price is “bumped” by a
small decimal point. Next all financial instruments that are sensitive to that
particular underlying asset is priced again with the newly “bumped” underlying
asset’s price. The difference in the value of the financial instruments with the
bumping is known as the trader’s delta exposure. He can now decide how to
manage this delta risk.

The next example will illustrate this
concept.

**Portfolio of bonds**

A bond dealer that makes a market by buying
and selling bonds will maintain a portfolio of bonds at any given time. The
dealer faces the risk that the bonds in his portfolio will change in price as the
underlying interest rates move up or down. He wants to measure this delta exposure,
which will help him next to decide whether or not to reduce this risk. A bond
delta is also known as its duration.

First, he arranges his bond portfolio
according to maturity buckets of cash flows. These grouped cash flows are then
valued (or discounted) using the present underlying interest rates in the
market.

For simplicity, say his portfolio is
constructed with three different bonds:

100 of Bonds A : 2-year
zero coupon bond

100 of Bonds B : 3-year
bond with $5 yearly coupon

100 of Bonds C : 5-year
bond with $8 yearly coupon

Each bond has a nominal value (or principal)
of $100.

The bond cash flows in maturity buckets will
look like

**Chart 2**. In the chart we also see the present value of the cash flows in each maturity bucket, discounted using the current interest rates.**Chart 3: Current Interest rate curve**

**Chart 3**.

In order to measure the delta exposure, he assumes
that interest rates jumps by 1 basis point (0.01%), in parallel across all
maturities. He will now re-value the cash flows using the newly “bumped”
interest rate. The delta is simply the change in the discounted value of cash
flows.

**Chart 4**illustrates this. He now notices that the delta exposure is the biggest in the 3-year and 5-year maturity buckets.
His next task is to manage the delta risk, in
this case, essentially his interest rate risk. He will first decide whether to
keep the risk or not. If he does keeps the risk, perhaps he is of the view that
the interest rates at Year 3 and Year 5 may go down in future which makes the
cash flows of the bonds increase in value, resulting in a profit.
Alternatively, he may not think so and decide to reduce the risk.

He can reduce the delta by engaging in other
financial instruments to offset the interest rate risk. Most common techniques
are using derivatives like interest rate swaps, interest rate forwards or
interest rate futures.

**Convexity**

Readers may note that in

**Chart 1**, a straight line instead of a curved line represents the price change in the financial instrument. This is a simplified way. In reality, the price of the financial instrument does not move in a straight line. The delta can be further improved by measuring this convexity effect.**Conclusion**

By knowing the delta, the dealer was able to
manage the interest rate risk in his bond portfolio. However, he now needs to keep
track of the delta in the new portfolio, which will consist of bonds and
interest rate derivatives. We will
explore the delta in this expanded portfolio in the next article.

Simple Example and easy to understand.Thanks for sharing your experience.

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