Question

Flight-to-safety, is a financial market phenomenon occurring when investors sell what they perceive to be higher-risk investments and purchase safer investments, such as gold and US treasury bonds (Wikipedia). When you first heard the outbreak of COVID-19 on Jan 22, 2020, in fear of the potential harm to the economy, you decide to purchase 10 -year US treasury note. YTM of available 10-year US treasury note was around 1.70% (annualized rate), with coupon rate of 1.12% (annualized rate). Coupon is paid every 6 months. 6 months later the YTM of the same bond drops to 0.64% (right before the first coupon payment). Assuming the maturity date of the bond you invested is Jan 22, 2030. Q4: What is the annualized bond rate of return in percentage term after holding the bond for 6 months (right before the first coupon payment)?

Answer 1

To calculate the bond rate of return after holding the bond for 6 months, we can use the following steps:

1. Determine the present value of the bond at the time of purchase. Since the coupon is paid every 6 months, the bond has 20 semi-annual coupon payments.

PV = Coupon Payment * [1 - (1 + YTM)^(-n)] / YTM + Face Value / (1 + YTM)^n

PV = (Coupon Rate * Face Value / 2) * [1 - (1 + YTM)^(-n)] / YTM + (Face Value / (1 + YTM)^n)

Here,

Coupon Payment = Coupon Rate * Face Value / 2

YTM = Yield to Maturity as an annualized rate (0.0170)

n = Number of coupon payments remaining (19)

2. Calculate the present value of the bond after 6 months.

PV_after_6_months = Coupon Payment * [1 - (1 + YTM_after_6_months)^(-n)] / YTM_after_6_months + Face Value / (1 + YTM_after_6_months)^n

PV_after_6_months = (Coupon Rate * Face Value / 2) * [1 - (1 + YTM_after_6_months)^(-n)] / YTM_after_6_months + (Face Value / (1 + YTM_after_6_months)^n)

Here,

Coupon Payment = Coupon Rate * Face Value / 2

YTM_after_6_months = Yield to Maturity after 6 months as an annualized rate (0.0064)

3. Calculate the bond rate of return.

Bond Rate of Return = (PV_after_6_months - PV) / PV

Remember to convert the bond rate of return into a percentage term.

Please note that the above calculation assumes that coupon payments and the face value will be paid in full at maturity. It also assumes there are no transaction costs or taxes involved.

Step-by-step explanation:

Answer 2

Answer and Explanation:

To calculate the annualized bond rate of return after holding the bond for 6 months, we need to consider the change in yield to maturity (YTM) and the coupon payments.

1. Calculate the bond's purchase price:

The bond has a coupon rate of 1.12% and a face value of $100 (assuming it's a $100 bond).

The coupon payment is made every 6 months, so the bond will receive 2 coupon payments during the 10-year period.

Purchase price = Present value of future cash flows

PV = (Coupon payment / (1 + YTM/2)^1) + (Coupon payment / (1 + YTM/2)^2) + ... + (Coupon payment + Face value / (1 + YTM/2)^20)

Using the given YTM of 1.70% and coupon rate of 1.12%, we can calculate the present value of the bond using the formula above.

2. Calculate the bond's value after 6 months:

The YTM drops to 0.64% right before the first coupon payment. Since the coupon payment is made every 6 months, we need to calculate the present value of the remaining coupon payments and the face value using the new YTM.

3. Calculate the bond rate of return:

The bond rate of return is the percentage increase in value from the purchase price to the value after 6 months, expressed as an annualized rate.

Bond rate of return = ((Value after 6 months - Purchase price) / Purchase price) * (1 / 0.5)

Multiply by (1 / 0.5) to annualize the rate of return since it's based on a 6-month holding period.

By following these steps, you can calculate the annualized bond rate of return after holding the bond for 6 months (right before the first coupon payment).