Question

Question 6
Suppose you bought a five-year zero-coupon Treasury bond for $800 per $1000 face value. Suppose after 3 years, the yield to maturity on comparable bonds declines to 3%. Calculate the holding period return if you sell the bond at that time.

*Make sure to input all currency answers without any currency symbols or commas, and use two decimal places of precision.

Answer 1

To calculate the holding period return (HPR) on the five-year zero-coupon Treasury bond, we first need to determine the bond's price after three years, given that the yield to maturity (YTM) has declined to 3%.

### Step 1: Calculate the price of the bond after 3 years.

The bond initially has a maturity of 5 years, and after 3 years, it has 2 years remaining until maturity (5 - 3 = 2).

The price of a zero-coupon bond can be calculated using the formula:

\[
P = \frac{F}{(1 + r)^n}
\]

where:
- \(P\) is the price of the bond
- \(F\) is the face value of the bond (which is $1000)
- \(r\) is the yield to maturity (3% or 0.03)
- \(n\) is the number of years until maturity (2 years)

Substituting in the values:

\[
P = \frac{1000}{(1 + 0.03)^2}
\]
\[
P = \frac{1000}{(1.03)^2}
\]
\[
P = \frac{1000}{1.0609}
\]
\[
P \approx 941.76
\]

### Step 2: Calculate the holding period return (HPR).

The holding period return is calculated as follows:

\[
HPR = \frac{Selling\ Price - Purchase\ Price}{Purchase\ Price}
\]

Where:
- Selling Price = Price of the bond after 3 years = $941.76
- Purchase Price = $800 (the price at which the bond was initially bought)

Substituting in the values:

\[
HPR = \frac{941.76 - 800}{800}
\]
\[
HPR = \frac{141.76}{800}
\]
\[
HPR \approx 0.1772 \text{ or } 17.72\%
\]

To express this in decimal form (which is often used in financial contexts), the HPR is approximately:

**17.72** (without the percent sign or any currency symbol).