Question

# A bond portfolio is made up of \$14 million in zero-coupon bonds maturing in 2 years,...

A bond portfolio is made up of \$14 million in zero-coupon bonds maturing in 2 years, and \$9 million in zero-coupon bonds maturing in 24 years. The yield curve is flat at 8%. What is the Macaulay duration of this bond portfolio? Please enter your answer in years rounded to two decimal places.

Duration of the portfolio measures the sensitivity of the portfolio when the interest rate changes

Macaulay Duration of the zero coupon bond is equal to years left to maturity.

Duration of \$14 million zero coupon bond(A) = 2 years

Duration of \$9 million zero coupon bond(B) = 24 years

Weight of A = \$14 million/ (\$14 million+\$9 million) = 0.609

Weight of B = \$9 million/ (\$14 million+\$9 million) = 0.391

Duration of portfolio = (Weight of A*Duratio of A) + (Weight ot B*Duration of B)

= (0.609*2)+(0.391*24)

= 1.218+9.384

= 10.608

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