Page 145 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Derivatives & Risk Management

Notes 10.5 Convexity

The duration measure can be supplemented with an additional measure to capture the curvature
or convexity of a bond portfolio. For all option free bonds, a standard result is that as yield
increases (decreases), duration decreases (increases). When yields decrease, the estimated price
change will be less than the actual price change, thereby underestimating the actual price. On the
other hand, when yields increase, the estimated price change will be greater than the actual price
change, resulting in an underestimate of the actual price. For small changes in yield, the duration
does a good job in estimating the actual price. The accuracy of the approximation depends on the
convexity of the price-yield relationship for the bond. The second derivative of the price function
is used as a proxy measure to correct for the convexity of the price-yield relationship. The
second derivative divided by price is a measure of the percentage change in the price of the bond
due to convexity and is referred to as the convexity measure. The Fisher-Weil version of convexity
is,
n
2
 CF t  v i t

i
i

i n
Convexity
P
Task During the settlement month on a particular day, futures settlement price is
` 101.3. For the deliverable bond and conversion factor is 0.854 and the accrued interest is
` 3.33. What is the invoice price?

Self Assessment

Fill in the blanks:
14. The accuracy of the approximation depends on the convexity of the …………relationship
for the bond.
15. The ……….. derivative of the price function is used as a proxy measure to correct for the
convexity of the price-yield relationship.

10.6 Summary

 According to RBI guidelines, interest rates derivatives have been launched in India on
National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) on June 24, 2003.

 Interest-rate futures are contracts of the future delivery of interest-bearing securities (debt).
 Interest-rate futures allow speculators and hedgers to buy and sell these contracts through
the locking prices of these securities for future delivery.

 Eurodollar futures work the same as T-bill contracts except the rate is based on LIBOR.
 A Forward Rate Agreement (FRA) is a widely used financial derivative by various
participants in the money and securities market to manage interest rate risk.

 The term duration has a special meaning in the context of bonds. It is a measurement of
how long, in years, it takes for an investment in a bond to be repaid by its internal cash
flows.
 The duration measure can be supplemented with an additional measure to capture the
curvature or convexity of a bond portfolio.

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