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In: Finance

A portfolio manager wants to exchange one bond in a portfolio for another. The old bond...

A portfolio manager wants to exchange one bond in a portfolio for another. The old bond position has a market value of 6.5 million, a price of $81.90 per $100 of par value, and a duration of 4.33. The new bond has a duration of 4.33 and a price of $85.52 per $100 of par value.

What is the total market value of the new bond that the portfolio manager must buy in order to keep the same portfolio duration?

Correct Answer: 6,500,000

Solutions

Expert Solution

The old bond position has a market value of 6.5 million, a price of $81.90 per $100 of par value and duration of 4.33

Duration of portfolio is its weightage average.

Weightage Duration of old bond in portfolio = (market value of old bond * duration of old bond)/ total value of portfolio

Where,

Duration of old bond = 4.33 years

Market Value of old bond = $6.5 million

Weightage Duration of old bond in portfolio = ($6.5 million * 4.33)/ total value of portfolio

To keep the same portfolio duration; the portfolio manager must keep the weightage duration of new bond equal to weightage duration of old bond in portfolio.

Weightage Duration of new bond in portfolio = (total market value of new bond * duration of new bond)/ total value of portfolio

Where,

Duration of new bond = 4.33 years

Therefore, Weightage Duration of new bond in portfolio = (total market value of new bond * 4.33)/ total value of portfolio

Therefore,

Weightage Duration of old bond in portfolio = Weightage Duration of new bond in portfolio

($6.5 million * 4.33)/ Total value of portfolio = (Total market value of the new bond * 4.33)/ Total value of portfolio

Or ($6.5 million * 4.33) = (Total market value of the new bond * 4.33)

Or Total market value of the new bond = ($6.5 million * 4.33) / 4.33 = $6.5 million or $6,500,000

The portfolio manager must buy $6,500,000 total market value of the new bond in order to keep the same portfolio duration.

jeff jeffy answered 2 hours ago
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