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Limits: Trading Limits – Duration, Convexity and PVBP Limits

Other Limits

Duration Limits

Duration measures the sensitivity of the price of the product/ value of the portfolio to changes in the interest rate. In order to limit the sensitivity the company needs to decide what the acceptable level of duration for the product/ portfolio should be. For example it may want the portfolio duration to be not more than 2 years. In other words it would like to limit its exposure to interest rate changes so that an increase in interest rates of 1% would not result in a decline in the portfolio value of greater than 2%. For example if the portfolio value was AED 1 million then the limit will be breached if the portfolio’s value fell below AED 980,000.

Convexity Limits

Duration does not account accurately for large changes in the interest rates. So in order to assess sensitivity more accurately the convexity measure may also be included in the calculation. The duration & convexity metric will then be used in setting the exposure limits. This metric is calculated as follows for duration and convexity:

A 1% increase in interest rates leads to an x% decrease in price where x = absolute value of {-1 × Duration × (0.01) x 100 + Convexity × (0.01)2 x 100}.

This is illustrated in the following example for 3-year bond issues. The duration limit is set at 2.3% whereas the duration& convexity limit is set at 2.2%:

3-year BondP0P-P+Duration metric (%)Duration & Convexity metric (%)Duration LimitDuration & Convexity Limit
Issue 197.5199.9595.142.462.42BreachBreach
Issue 297.5699.9395.272.392.35BreachBreach
Issue 397.6799.9295.472.282.24SafeBreach
Issue 498.0299.9496.151.931.91SafeSafe

Figure 9: Setting Duration & Convexity limits

PVBP Limits

PVBP is the change in present value of an instrument brought about by a 1 basis point change in interest rates. PVBP limits may be set separately for each maturity bucket or may be evaluated across all buckets. The PVBP metric is calculated to determine the change in present value by increasing the underlying interest rates by 0.01%. If the PVBP metric calculated for the portfolio exceeds this limit, a limit violation occurs. This is illustrated below:

Interest Rate 6%Maturity Bucket
Total Across Buckets0-11-22-33-44-5
Amount125,00025,00025,00025,00025,00025,000
PV @ time zero105,30923,58522,25020,99019,80218,681
PVBP metric292.224.205.947.478.81
Limit as a % of PV0.02%0.01%0.02%0.03%0.03%0.04%
PVBP Limit272.173.536.386.937.52
Limit StatusBreachBreachBreachSafeBreachBreach

Figure 10: Setting PVBP limits

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