suppose that the 6-month, 12-month, 18-month and 24-month zero rates are 5.10%, 5.00%, 4.80% and 4.75%, respectively. what is the two-year par yield?

To find the two-year par yield, we need to calculate the coupon rate that makes the price of a bond equal to its face value, given the zero rates. The par yield is essentially the yield on a bond that is priced at par, meaning that the bond's price is equal to its face value.

### Steps:

1. **Zero Rates:**
   - \( R_{0.5} = 5.10\% \)
   - \( R_{1.0} = 5.00\% \)
   - \( R_{1.5} = 4.80\% \)
   - \( R_{2.0} = 4.75\% \)

2. **Assume a bond with face value 100 and semi-annual coupon payments.**
   - Let the par yield be \( y \% \) per annum.
   - The bond pays \( \frac{y}{2} \) every 6 months.

3. **Present value of coupon payments and face value:**
   - The bond pays \( \frac{y}{2} \) at 6 months, 12 months, 18 months, and 24 months.
   - It also pays 100 (face value) at the end of 24 months.
   - The present value of the bond should be equal to its face value of 100.

4. **Formula:**
   The present value (PV) of a bond is the sum of the present values of all coupon payments plus the present value of the face value at the final maturity.

   The formula for the present value of a 2-year bond paying semi-annual coupons is:

   \[
   \text{PV} = \frac{y}{2} \times \frac{1}{(1 + \frac{R_{0.5}}{2})} + \frac{y}{2} \times \frac{1}{(1 + \frac{R_{1.0}}{2})^2} + \frac{y}{2} \times \frac{1}{(1 + \frac{R_{1.5}}{2})^3} + \left( \frac{100 + \frac{y}{2}}{(1 + \frac{R_{2.0}}{2})^4} \right)
   \]

   Set the above equation equal to 100, and solve for \( y \).

Let me calculate this for you.The two-year par yield is approximately **4.76%**.

Would you like a detailed explanation of the calculations or have any questions?

Here are five related questions you might find interesting:
1. How would the par yield change if the 24-month zero rate increased?
2. What is the relationship between zero rates and par yields?
3. How does the frequency of coupon payments affect the par yield?
4. What is the par yield for bonds with different maturities?
5. How are par yields used in bond pricing?

**Tip:** Par yields are important in bond pricing because they represent the coupon rate at which a bond would be issued at par value, given current market interest rates.

Learn how to calculate the two-year par yield using zero rates. Understand the concept of par yield and how it relates to bond pricing. Detailed step-by-step solution provided with specific zero rates: 5.10%, 5.00%, 4.80%, and 4.75% for 6-month, 12-month, 18-month, and 24-month maturities respectively.

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