Financial Risk Manager Part 1
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A financial risk manager at a financial institution is evaluating how a bond portfolio reacts to non-uniform shifts in the spot rate curve. The portfolio consists of a 4-year zero-coupon bond and a 7-year zero-coupon bond. Each bond has a particular sensitivity to changes in its specific spot rates, as illustrated below:
Spot rate duration Impact on portfolio value for a 1-bp increase in the spot rate (AUD) 4 years -189.27 7 years -302.45
To account for the non-parallel movements in the spot rate curve, the risk manager has identified the 2-year, 5-year, and 10-year spot rates as critical rate durations. Using the given data, calculate the portfolio's key rate duration (KR01) in response to a 1-bp increase in the 5-year spot rate.
A financial risk manager at a financial institution is evaluating how a bond portfolio reacts to non-uniform shifts in the spot rate curve. The portfolio consists of a 4-year zero-coupon bond and a 7-year zero-coupon bond. Each bond has a particular sensitivity to changes in its specific spot rates, as illustrated below:
| Spot rate duration | Impact on portfolio value for a 1-bp increase in the spot rate (AUD) |
|---|---|
| 4 years | -189.27 |
| 7 years | -302.45 |
To account for the non-parallel movements in the spot rate curve, the risk manager has identified the 2-year, 5-year, and 10-year spot rates as critical rate durations. Using the given data, calculate the portfolio's key rate duration (KR01) in response to a 1-bp increase in the 5-year spot rate.
Explanation:
The portfolio's key rate duration (KR01) for a 1-bp increase in the 5-year rate is calculated by considering the sensitivity of the bond portfolio to changes in the 5-year spot rate. The key rate duration measures the change in the value of a bond or a portfolio of bonds for a 1 basis point change in the specific key rate. In this case, the risk manager has identified the 2-year, 5-year, and 10-year spot rates as key rates.
The 4-year and 7-year zero coupon bonds in the portfolio have sensitivities to their respective spot rates, which are -189.27 and -302.45 for a 1-bp increase in the spot rate. To find the KR01 for the 5-year rate, we need to determine how the 4-year and 7-year spot rates would change in response to a 1-bp increase in the 5-year rate.
The change in the 4-year spot rate is calculated by the ratio of the distance between the 4-year and the 5-year key rates to the distance between the 2-year and the 5-year key rates, which is . Similarly, the change in the 7-year spot rate is calculated by the ratio of the distance between the 7-year and the 10-year key rates to the distance between the 7-year and the 5-year key rates, which is .
The overall change in the portfolio value for a 1 bp change in the 5-year spot rate is then the sum of the changes in the value of the individual bonds due to the change in their respective spot rates:
This calculation results in a portfolio value decrease of approximately AUD 307.66, which corresponds to option C. This value represents the key rate duration for the 5-year rate, indicating that for a 1 basis point increase in the 5-year spot rate, the portfolio value would decrease by approximately AUD 307.66.