Question

Suppose a five year treasury bond with for years left until it's maturity date had a 2.5% coupon and a 100,000 face value and it's market price had risen from $100,000 to $104000 during the 1 year since it was issued (i.e. just after the year 1 coupon was paid).

A) Write down the equation to justify the YTM an investor who bought it at that market price would obtain.

B) has the required yield to maturity increased or decreased during the year? Explain how you know from the data given in this problem, (even without using a calculator to find the new YTM)

C) What rate of return would an investor who bought the five year treasury right after it was issued and then sold it right after collecting the first year's coupon earn?

Answer 1

Answer:

Given that,

A five year treasury bond with for years left until it's maturity date had a 2.5% coupon and a 100,000 face value

market price had risen from $100,000 to $104000 during the 1 year

A)   The equation to justify the YTM an investor who bought it at that market price would obtain.

Coupon = 2.5%*100,000 = 2500

104,000 = 2500/ (1+ YTM) + 2500/ (1+ YTM)^2 + 2500/ (1+YTM)^3+ 2500/ (1+YTM)^4 + 100,000/ (1+YTM)^4
Coupon and the face value are discounted at the YTM to arrive at the market price

B) The required yield to maturity increased or decreased during the year

YTM at year 0:

100,000 = 2500/ (1+YTM) + 2500/ (1+YTM)^2 + 2500/ (1+YTM)^3 + 2500/ (1+YTM)^4 + + 2500/ (1+YTM)^5 + 100,000/ (1+YTM)^5

YTM at year 1:

104,000 = 2500/ (1+YTM) + 2500/ (1+YTM)^2 + 2500/ (1+YTM)^3 + 2500/ (1+YTM)^4 + 100,000/ (1+YTM)^4

Now, since the face value is equal to the market price in the first case, the YTM shall be equal to the coupon rate i.e. 2.5%, however in the second case the market price is greater than the face value which means that the YTM is greater than the coupon rate and therefore greater than YTM at year 0.

C) Rate of return would an investor who bought the five year treasury right after it was issued and then sold it right after collecting the first year's coupon earn

Rate of return = (Coupon + Capital gains) / Original investment
= (2,500+(104,000-100,000)) / 100,000 = 6.5%