Question

Which bond would have more interest rate risk: a long-term bond or short-term bond? Why? Will there be other risks in these bonds?

If possible, please give numeric example.

Answer 1

Long term bond has higher duration and hence higher interest rate risk because there are more number of coupons in the future and the current price is equal to present value of all cash flows. Present value is highly dependet on interest rate and as longer maturity bond has more number of cash flows, it is very sensitive to changes in interest rates.

Other risk is callable risk, reinvestment risk, inflation risk.

For example:
Bond A with par of 1000, 10% annual coupon, 10 years to maturity and yield to maturity 10% is priced at 1000
Bond B with par of 1000, 10% annual coupon, 5 years to maturity and yield to maturity 10% is priced at 1000

Lets say rates rise by 1%
Price of Bond A=10%*1000/11%*(1-1/1.11^10)+1000/1.11^10=941.1076799

Price of Bond B=10%*1000/11%*(1-1/1.11^5)+1000/1.11^5=963.0410298

As both had same price initially, percentage change in Bond A is higher as it is longer maturity bond