Question

What is the duration of your bond portfolio if you invest 30% of your portfolio in a bond with a duration of 12.2 (let’s denote it BA), 30% in a 20-year zero-coupon bond (let’s denote it BZ), and 40% in a 3-year bond with a 12% annual coupon, par value of $1000, and a yield to maturity of 7% (let’s denote it BB)? 10.74 years 12.5 years 9.3 years 4 years

Answer 1

Duration of bond portfolio is its weightage average of its bonds’ duration

Duration of bond portfolio = proportion of bond BA in portfolio * Duration of Bond BA + proportion of bond BZ in portfolio * Duration of Bond BZ + proportion of bond BB in portfolio * Duration of Bond BB

Where,

Proportion of bond BA in portfolio = 30%

Duration of Bond BA = 12.2 years

Proportion of bond BZ in portfolio = 30%*

Duration of Bond BZ = 20 years (Duration of zero coupon bonds are equals to its maturity period because zero-coupon bond has no cash flow until maturity)

Proportion of bond BB in portfolio = 40%

Duration of Bond BB =?

Now first calculate the duration of Bond BB

Year (t)	Cash Flow from coupon payments (12% of $1000)	Cash Flow from maturity amount	Total Cash Flow from coupon payments and maturity amount (CF)	Present value (PV) discounted at 7% of yield to maturity [CF/(1+7%)^t]	PV *t
1	$120.0		$120.0	$112.15	$112.15
2	$120.0		$120.0	$104.81	$209.63
3	$120.0	$1,000.0	$1,120.0	$914.25	$2,742.76
sum				$1,131.22	$3,064.54
				Bond's Price↑
			Duration = sum of (PV*t)/sum of PVs =	$3,064.54/$1,131.22	2.71

Therefore the Duration of Bond BB is 2.71 years

Now putting the all values in Duration of bond portfolio equation

Duration of bond portfolio = 30% * 12.2 + 30% * 20 + 40% * 2.71

= 10.74 years

Therefore the correct answer is option 10.74 years