Question

Explain why yield to maturity is higher than current yield when you buy a coupon-bearing bond for less than its $1000 face value?

If interest rates suddenly fall, would you rather be holding a portfolio composing of short-term securities or long-term securities?

A zero-coupon bond with face value of $10,000 that matures in two years goes on sale today for $9,100. What is the bond’s yield to maturity?

Using the bond described in the previous question, imagine that you purchase this bond. Within an hour of purchasing it, the market interest rate changes to 5 percent. If you decide to sell your bond, what profit (loss) can you expect to make?

Answer 1

1) The Yield to maturity considers all the cashflows that are remaining till bond matures which includes coupon payements and the final face value principal repayment, whereas, Current yield only considers the current cashflow of coupon at the current price of bond. When you buy a bond for less than its face value of 1000, then, Current yield would be lower because Same coupon payment is divided over a lower denominator as Current yield is a Return on investment type of yield which looks at the present, whereas, Yield To maturity for bond lower than 1000 would be higher because buyer of the bond would be getting more return because of incremental cashflow in final principal repayment of 1000 which remains same irrespective of bond's price in market.

2) If interest rates suddenly fall, then Price of the bonds will increase and since bonds with longer duration changes more than shorter duration bonds with change in interest rates, I would rather be holding a portfolio of long-term assets over short-term assets for higher capital gains. However, if interest rates were to go in the reverse direction, that is, increase, then I would like to hold a portfolio of short-term bonds as they are less affected by interest risks because of their shorter duration. In general, to minimize interest rate risk, shorter duration bonds are a better choice, however, as the scenario is specific to only interest rate fall, then longer-term bonds are a better choice.

3) Price of the zero-coupon bond = 9,100

Face value = 10,000 | Time = 2 years

Formula for Price of zero-coupon bond = Face Value / (1+YTM)^T

=> 9,100 = 10,000 / (1+R)²

=> (1+R)² = 10,000 / 9,100

=> R = (10000/9100)^1/2 - 1

YTM of the bond = 0.048285 or 4.83%

4) New YTM = 5%

New Price = 10000 / (1+5%)²

New Price of the bond = 9,070.29

I paid 9,100 for the bond and New price at 5% YTM is 9,070.29.

If I sell the bond now, I'd make a loss and My Loss would be = 9100 - 9070.29 = $29.71