LOS d: Determine the notional principal value needed on an interest rate swap to achieve a desired level of duration in a fixed income portfolio.

Q1. A manager of a $40 million dollar fixed-income portfolio with a duration of 4.2 wants to lower the duration to 3. The manager chooses a swap with a net duration of 2.1. What notional principal (NP) should the manager choose for the swap to achieve the target duration?

A)   $22,857,143.

B)   $56,000,000.

C)   $70,000,000.

Q2. If a fixed-income portfolio manager wants to double the duration of a portfolio with a swap that has the same duration as the portfolio, then the notional principal would be:

A)   half the value of the portfolio.

B)   equal to the value of the portfolio.

C)   twice the value of the portfolio.

Q3. A manager of a $2 million dollar fixed-income portfolio with a duration of 3 wants to increase the duration to 4. The manager chooses a swap with a net duration of 2. The manager should become a:

A)   pay-floating counterparty in the swap with a notional principal of $2 million.

B)   receive-floating counterparty in the swap with a notional principal of $1 million.

C)   pay-floating counterparty in the swap with a notional principal of $1 million.

LOS d: Determine the notional principal value needed on an interest rate swap to achieve a desired level of duration in a fixed income portfolio. fficeffice" />

Q1. A manager of a $40 million dollar fixed-income portfolio with a duration of 4.2 wants to lower the duration to 3. The manager chooses a swap with a net duration of 2.1. What notional principal (NP) should the manager choose for the swap to achieve the target duration?

A)   $22,857,143.

B)   $56,000,000.

C)   $70,000,000.

Correct answer is A)

NP = $40,000,000 × (3 ? 4.2) / -2.1

NP = $22,857,143

Since the manager wants to reduce the duration of his portfolio, he should take a receive-floating/pay-fixed position in the swap with that notional principal. Remember that a receive-floating swap has a negative duration, so we enter –ffice:smarttags" />2.1 in the equation.

Q2. If a fixed-income portfolio manager wants to double the duration of a portfolio with a swap that has the same duration as the portfolio, then the notional principal would be:

A)   half the value of the portfolio.

B)   equal to the value of the portfolio.

C)   twice the value of the portfolio.

Correct answer is B)

If we let V and D equal the current value and duration of the portfolio respectively, then we see that:

NP = V × (2 × D ? D) / D = V

Q3. A manager of a $2 million dollar fixed-income portfolio with a duration of 3 wants to increase the duration to 4. The manager chooses a swap with a net duration of 2. The manager should become a:

A)   pay-floating counterparty in the swap with a notional principal of $2 million.

B)   receive-floating counterparty in the swap with a notional principal of $1 million.

C)   pay-floating counterparty in the swap with a notional principal of $1 million.

Correct answer is C)       

To increase duration, the manager should be a pay-floating/receive-fixed counterparty in the swap with a notional principal equal to:

NP = $2,000,000 × (4 ? 3) / 2

NP = $1,000,000.

Thx!

Thx!