Question

(a) Suppose you hold a bond, and the current one-year holding period rate of return is 6%. And we further know that the yield to maturity for this bond is also 6% now. Could you tell me which rate will be higher if the interest rate decreases? Why? (b) Suppose there are two bonds with the same yield-to-maturity and date to mature; but one is sold at premium, the other one is sold at discount. Could you tell me which bond has a higher coupon? Why? (c) Is there any difference in prices between these two bonds mentioned in (b) at the end of their duration? Why?.

Answer 1

a)

Here one year holding period retunr =6%

Yield to maturity = 6%

If interest rate decreases than the YTM will decrease but the holding period return will increase. Reason as the bond is sold at lower yield the price increases, price inversely proportional to yield of a bond and hence the bond holder also gains due to capital gains thus his holding period return increases, but the YTM in which he sells will be lower.

So holding period return high, yield to maturity (YTM) low

b)

Now if bond 1 and 2 are same, than bond with higher coupon will sell at a premium while bond with low coupon will sell at a discount.

Let's say there are two bonds one with coupon9% and other with coupon 7% both maturing in 1 year

let's say YTM is 8%

Now if face value is 100

So 7% coupon will trade at a discount, lets see from the cash flow

one year later return = 100+7 = 107

So present Value = 107/(1.08), since 8% in YTM

PV = 99.07407

So 9% coupon will trade at a discount, lets see from the cash flow

one year later return = 100+9 = 109

So present Value = 109/(1.08), since 8% in YTM

PV =100.9259

Hence higher coupon will trade at premium while lower coupon will trade at a discount

c)

At the end of duration the net inflow will be different for both, one will bee 107 while other will be 109