Question

a. Write down the formula used to calculate the Present Value (PV) of a future Cash Flow (CF)  

for ‘n’ years. Using this formula, explain why the price of a coupon bond and the yield to maturity are negatively related.  

b. If there is an increase in interest rates, which would you rather be holding, long-term bonds or short-term bonds? Why? Which type of bond has the greater interest-rate risk?

Answer 1

A) formula of present value of future cash flow is as follows

Present value of future cash flow = Future cash flow / (1+r)^n

R = rate of interest

N = no. of period

Now coupon bond carries interest rate say 10% which is paid on the par value. This interest rate is paid every year till maturity of bong where investor gets redemption amount as well. Thus to find value of bond one needs to discount all future cash flow and determine it's present worth. Present worth of future cash flow depends on rate at which cash flows are discounted. Higher the rate less is the present worth of cash flow,hence the price.

Thus there is negative correlation between price of bond and interest rate(YTM)

B) If interest rates are rising than one should prefer holding short term bonds rather than long term bonds. This is because long term bonds have more number of years to mature and thus more no. of coupon payments which are discounted at higher interest rate.

Long term bonds are more sensitive to interest rate changes and thus have higher interest rate risk