A $300 million bond portfolio currently has a modified duration of 6.53. By using a futures contract priced at $105,250, the portfolio manager wants to reduce potential loss of the bond portfolio to $30 million when the yield on the bond portfolio increase by 2%. The futures contract has an implied modified duration of 9.25. The manager estimates that the yield on the bond portfolio is about 12% more volatile than the implied yield on the futures contract.
A) Indicate whether the portfolio manager should enter a short or long futures position.
B) Calculate the target modified duration of the bond portfolio.
C) Calculate the number of futures contracts needed to achieve what the manager wants to do.
Please show answers using excel and formulas. Thank you!
Indicate whether the portfolio manager should enter a short or long futures position.
To determine whether the portfolio manager should enter a short or long futures position, we need to compare the modified duration of the bond portfolio to the implied modified duration of the futures contract.
If the portfolio manager wants to reduce the potential loss of the bond portfolio when the yield on the bond portfolio increases, they should use futures to hedge against rising interest rates. In this case, they should use a short futures position because a short position in futures will increase in value when interest rates rise, offsetting the potential loss in the bond portfolio.
Now, let’s move on to the next part.
B) Calculate the target modified duration of the bond portfolio.
The target modified duration of the bond portfolio can be calculated using the following formula:
Target Modified Duration = Current Modified Duration – (Hedge Ratio x (Implied Modified Duration – Portfolio Modified Duration))
Where:
We are trying to reduce the potential loss of the bond portfolio from $300 million to $30 million when the yield on the bond portfolio increases by 2%. So, the change in portfolio value is $300 million – $30 million = $270 million.
The change in futures value can be calculated as the implied modified duration multiplied by the change in yield (2%):
Change in Futures Value = Implied Modified Duration x Change in Yield Change in Futures Value = 9.25 x 0.02 = $0.185
Now, we can calculate the Hedge Ratio:
Hedge Ratio = $270 million / $0.185 = 1,459,459.46 (rounded to the nearest whole number)
Now, plug these values into the formula to calculate the target modified duration:
Target Modified Duration = 6.53 – (1,459,459.46 x (9.25 – 6.53))
Target Modified Duration ≈ 6.53 – (1,459,459.46 x 2.72) Target Modified Duration ≈ 6.53 – 3,974,109.97 ≈ -3,973,103.44
The target modified duration of the bond portfolio is approximately -3,973,103.44.
Now, let’s move on to the final part.
C) Calculate the number of futures contracts needed to achieve what the manager wants to do.
To calculate the number of futures contracts needed, we can use the following formula:
Number of Futures Contracts = (Change in Portfolio Value / Change in Futures Value) x (-1)
We have already calculated the change in portfolio value as $270 million and the change in futures value as $0.185.
Number of Futures Contracts = ($270 million / $0.185) x (-1) Number of Futures Contracts ≈ 1,459,459.46 x (-1)
Number of Futures Contracts ≈ -1,459,459.46
Since you cannot have a fraction of a futures contract, you would need to round this number to the nearest whole number. Therefore, the portfolio manager would need approximately 1,459,459 futures contracts to achieve their hedging objective.
In summary, the portfolio manager should enter a short futures position to hedge against rising interest rates. The target modified duration of the bond portfolio is approximately -3,973,103.44, and approximately 1,459,459 futures contracts are needed to achieve the manager’s objective of reducing potential losses in the bond portfolio when the yield increases by 2%.
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