To create a portfolio with duration of 4 years using a 5 year zero-coupon bond and a 3 year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest of the portfolio value in the zero-coupon bond.

One would have to invest 55%

Duration of 3-year bond is 2.78

Then 5wZ + 2.78(1 - wZ) = 4

2.22wZ = 1.22

wZ = .5495

Explanation:

To properly understand the concept behind the above calculation, let us define some basic concept:

Portfolio:  This can be refereed to as a phrase in finance. It refers to the collection on investment that is being held by an investment company, a financial institution such as a bank ,persons or an individual.

Zero coupon bond: A zero-coupon bond is a bond where the nominal or return on investment (ROI)  value is repaid at the time of maturity. This definition usually reflects a positive time value of money.

We should also recall that the formula for zero coupon bond as:

price = M / (1 + i)^n

where: M = maturity value

i = required interest yield divided by 2

Applying this formula, we were able to arrive at the investment percentage.

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