Monday, September 10, 2012

Measuring Market Risk – The Delta



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 2: Bond cash flow maturity buckets
Chart 3: Current Interest rate curve

 
  

Chart 4: Measuring the Delta
Say the current interest rates are as shown as a curve in 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.

1 comment:

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

    ReplyDelete