Question

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, we first need to determine the selling price of the bond after 3 years, when the yield to maturity (YTM) is 3%.

A zero-coupon bond pays no interest until maturity, thus its price can be calculated using the present value formula:

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

Where:
- \(P\) = price of the bond
- \(F\) = face value of the bond ($1000)
- \(r\) = yield to maturity (0.03 for 3%)
- \(n\) = number of years to maturity at the time of sale

Since the bond was purchased for a 5-year term and 3 years have passed, there are \(n = 2\) years remaining before maturity.

Now substituting the known values into the formula:

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

Calculating it step by step:

1. Calculate \(1 + r\):

\[
1 + 0.03 = 1.03
\]

2. Raise it to the power of \(n = 2\):

\[
(1.03)^2 = 1.0609
\]

3. Now calculate the price \(P\):

\[
P = \frac{1000}{1.0609} \approx 941.76
\]

Now we know that the selling price of the bond after 3 years is approximately $941.76.

Next, we calculate the holding period return (HPR):

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

Here:
- Selling Price = 941.76
- Purchase Price = 800

So, substituting the values:

\[
HPR = \frac{941.76 - 800}{800}
\]
\[
HPR = \frac{141.76}{800} \approx 0.1772
\]

To express the holding period return as a percentage, we multiply by 100:

\[
HPR\ (as\ a\ percentage) = 0.1772 \times 100 \approx 17.72\%
\]

Therefore, the holding period return if you sell the bond at that time is approximately:

**17.72**