Question

What is the relationship between price and yields for fixed income securities? There is a government bond with a par value of $1000, and %4 semi- annual coupon rate. The bond was issued 6 years ago when the market interest rates are 8%. (The yield to maturity is %8). The remaining maturity of this bond is 1,5 years. Make comment about the price of this bond. a- If somehow, the market interest rates remain unchanged (ytm unchanged) b- If the market interest rates rise (ytm goes up) c- If the market interest rates go down. (ytm goes down   

Answer 1

Face vale of bond = 1000

semiannual coupon amount = face value * coupon rate/2

=1000*4%=40

semiannual years to maturity (n) =1.5*2 = 3

a. If market interest rate remains unchanged i.e. 8%

semiannual interest rate = 8%/2 = 4%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(40*(1-(1/(1+4%)^3))/4%) + (1000/(1+4%)^3)

=1000

Bond was issued at par value and if market interest rate is not changed, it will sell at par value. So Bond price will not change, if YTM is not changed.

b. If market interest rate goes up (assume 10%)

semiannual interest rate (i) = 10%/2 = 5%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(40*(1-(1/(1+5%)^3))/5%) + (1000/(1+5%)^3)

=972.7675197

Bond was issued at par value and if market interest rate goes up, then it will sell at discount.

So Bond price will go down, if YTM goes up.

c. If market interest rate goes down (assume 6%)

semiannual interest rate (i) = 6%/2 = 3%

Bond price formula = Coupon amount * (1 - (1/(1+i)^n)/i + face value/(1+i)^n

(40*(1-(1/(1+3%)^3))/3%) + (1000/(1+3%)^3)

=1028.286114

Bond was issued at par value and if market interest rate goes down, then it will sell at premium.

So Bond price will go up, if YTM goes down.

As we can see that there is inverese relationship between YTM and bond price. If YTM goes up, bond price go down. If YTM goes down, bond price goes up. Otherwise it remains unchanged.