By Jasvin Josen

*This article appeared in TheEdge Malaysia on June 23, 2012*

In the previous article, I explained what
delta is in the market risk context and illustrated the case of a bond dealer measuring
the delta in a bond portfolio. After knowing his delta exposure, he next
decides how to manage the delta.

In this article, I expand the previous example
by introducing interest rate swaps to hedge the delta. Next I illustrate the
delta measurement for options.

**Bond and Swap Portfolio**

Let
us assume that the bond dealer mentioned in the previous article decides to
hedge his simple 3-type bond portfolio with interest rate swaps. He decides
only to hedge the delta in the 5-year maturity bucket. He enters into a 5-year bullet
interest rate swap (IRS) with the following terms:

__5 year bullet IRS:__

Pay Fixed Rate: 4.4%

Receive Floating Rate: 6m
LIBOR + margin

Notional: $50,000

The cash flows from the portfolio of bonds and the IRS
will look like in

**Chart 1**. To keep it simple, say the 6m LIBOR (+ margin) rate at the 5Y point (obtained from the forward interest rate curve) is also at 4.4%.**Chart 1: Cash flows for Bonds and Swap**

Next,
the dealer measures his delta exposure for the expanded portfolio. The delta
profile will look like in

**Chart 2**.**Chart 2: Delta Exposure for Bonds and Swap**

We
can see that his delta exposure at the 5-year point has almost eliminated. This
was possible with the bullet IRS where the cash flow on the floating leg also
increases when the interest rate is bumped upwards. Specifically, the cash flow
increased by $5, which is obtained by multiplying the notional value of the
swap ($50,000) by 1 basis point (or 0.01%).

**Macro Hedging**

The
practical way to hedge at trading desks of investment banks however is to
conduct macro hedges rather than specific hedges. Here, the bond desks position
will be combined with the interest rate swaps desk and the currency swaps desks
portfolios to observe the net interest rate risk (or delta) exposure. Based on this
net exposure, hedging of the interest rate risk is done at a macro level at the
bank.

**Other market risk factors affecting the bond price**

In measuring the delta, a price engine is
involved which theoretically prices the bond. However this assumes that the
theoretical price is similar to the observed market price. Most probability
this will not be so. This is because there are factors other than interest
rates that cause the bond price to change. These factors are like liquidity and
creditworthiness of the bond, which can be measured as well.

**Equity Options Portfolio**

In
this example, we assume that an options trader has three equity options on the
same share, shown in

**Chart 3.****Chart 3: Option Portfolio and Delta Measurement**

The
trader defines his delta in options as the difference in the options price when
the underlying share price moves by $0.10. He uses the Black Scholes model to
compute the option price when the underlying share price moves from $3 to $3.10.
We assume that the implied volatility is 12% and the risk-free interest rate is
3%.

He
will see that the call option delta has a positive value whilst the put options
delta has negative values. This is simply because when the underlying share
price increases, the call option increases in value whereas the put options
loses value.

The
delta of the in-the-money call seem be set off mostly by the delta of the
in-the-money put. On a net position, his delta position is quite small. He does
not see the need to further hedge this portfolio at the moment.

**Market risk other than the Delta**

Delta
is often the most significant risk that the market player must be aware of. Other
risk factors that many option-like portfolios are also sensitive to are
volatility (vega), interest rates used in models (rho) and gamma, the risk that
the delta does not change in a linear manner.

**Conclusion**

We
can appreciate that measurement of delta is important for any market
practitioner, be he a trader, market maker, fund manager or the Treasury
department in a corporation. Delta measurement enables the market practitioner
to know his risk and hedge the risk accordingly. If he can do this proficiently,
he will be more confident in investing, trading and dealing in a wider range of
financial instruments and derivatives in the market.

To be able to know the risk and how to hedge the risk properly is the best thing that market practitioner must be aware of.

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