Question

Suppose an individual has $100 and wants to invest it for the next 3 years. He has the choice between two investments:

1- a 3-year bond with a yield to maturity of i3,t
2- a series of 1-year bonds at rates i1,t+j for j = 0.1 and 2;
For simplicity, suppose there is no uncertainty, so our individual knows all the sequence of future interest rates. We assume that he can also borrow at will at the same interest rates.
a) Write the condition that ensures that our individual cannot arbitrate

Answer 1

The price of a bond is adjusted according to the market interest rates to provide a competitive yield. If market rates exceed the bond's coupon rate, its price will be lowered below face value. The pricing formula used is based on the expected payments and the market rate, such as $964 invested at 12% yielding $1,080 after one year.

Step-by-step explanation:

Understanding Bond Pricing and Interest Rates

When an investor is considering buying a bond, the decision often comes down to comparing the yield of the bond with the prevailing market interest rates. If a bond's interest rate is less than the market rate, its price will generally be below its face value to make the yield competitive. For example, if the market interest rate is 12%, and a bond with face value of $1,000 is expected to pay $1,080 (which includes the final year's interest payment and the principal repayment) in one year, the bond must be priced at a discount to attract buyers.

Therefore, the bond's price would be set in such a way that investing $964 at the current market rate of 12% would yield $1,080 after one year, ensuring the bond’s yield is competitive with the market. This is computed using the formula $964(1 + 0.12) = $1080.

When it comes to the risk of the bond, it's important for the price to reflect this as well. A risk-free bond will sell at its face value, whereas if market interest rates rise over time, indicating an increase in risk or better alternatives, the price of the bond will decrease to offer a yield that compensates for the lower coupon rate and higher market rates.