Question

Using the parametric form of a 2-year coupon bond with coupon rate C and face value F, prove the following facts: (Do not use numbers, just parameters!)

1. The Duration is decreasing in coupon rate (The higher is the coupon rate, the lower is the Duration)

2. The Duration is decreasing in yield (The higher is the yield, the lower is the Duration).

Answer 1

ANSWER DOWN BELOW. FEEL FREE TO ASK ANY DOUBTS. THUMBS UP PLEASE.

Golden line:
Duration refers to volatility or risk of the bond.

A. The higher is the coupon rate, the lower is the Duration.

It is because the coupon rates are intermediate cash flows and as cash flows in the middle(issuance date to maturity date) increases. The risk decreases, as the holder is getting the cashflows before itself.

B. The higher is the yield, the lower is the Duration.

As the yield increases in the market and bondholders coupon rate remain constant.

There is a less chance that there will be a default in the bond repayment, that is the risk decreases.

As the risk decreases, the duration decreases.