Key rate duration is a measure of a bond's sensitivity to changes in interest rates. It is calculated by multiplying the modified duration of a bond by its key yield. Key rate duration can be used to hedge against interest rate risk or to take advantage of changes in interest rates.

Modified duration is a measure of a bond's sensitivity to changes in interest rates. It is calculated by dividing the percentage change in the price of a bond for a 1% change in interest rates by the bond's current yield.

The key yield is the yield of a bond that is most sensitive to changes in interest rates. It is usually the yield of the bond with the longest maturity. What is the difference between par rate and spot rate? The par rate is the interest rate that results in a zero net present value for a series of future cash flows. The spot rate is the current market yield on a security.

##### What is the par yield curve?

The par yield curve is a curve that shows the relationship between the interest rates on bonds of different maturities. The par yield curve is used to price new bonds. The term "par" refers to the face value of the bond. The par yield curve is also sometimes referred to as the "zero coupon yield curve."

What does negative key rate duration mean? Negative key rate duration (KRD) is a measure of a bond's sensitivity to changes in interest rates. It is calculated by taking the negative of the sum of the present values of the cash flows from the bond, weighted by the applicable key rate.

A bond with a negative key rate duration is said to have negative convexity. This means that the bond's price will increase at a faster rate than the underlying interest rate when rates decline, and vice versa.

Negative key rate duration can be a desirable trait in a bond, as it can provide some protection against rising interest rates. However, it also means that the bond's price will be more volatile than a bond with a positive key rate duration. What does key rate mean? Key rate is a financial ratio that measures the percentage of a company's outstanding key debt that is current and not in default. This ratio is important because it provides insight into a company's ability to make interest and principal payments on its debt. A high key rate indicates that a company is in good financial health and is able to meet its debt obligations. A low key rate, on the other hand, may indicate that a company is struggling to meet its debt obligations and is at risk of default.

##### What does duration mean in bonds?

Duration is a measure of a bond's price sensitivity to changes in interest rates. It is calculated by taking the weighted average of a bond's cash flows, with the weights equal to the time each cash flow is received. The longer a bond's duration, the more sensitive it is to changes in interest rates.

For example, consider a bond with a face value of $1,000 that pays interest semiannually and matures in 10 years. Assume that the bond's yield to maturity is 5%. The bond's duration would be calculated as follows:

The first cash flow (the interest payment) occurs in 6 months, so its weight is 0.5. The second cash flow (the interest payment) occurs in 12 months, so its weight is 1. The third cash flow (the interest payment) occurs in 18 months, so its weight is 1.5. The fourth cash flow (the interest payment) occurs in 24 months, so its weight is 2. This process is continued until the final cash flow (the maturity payment), which occurs in 120 months, so its weight is 10.

The weighted average of the cash flows is then calculated:

0.5 x $50 + 1 x $50 + 1.5 x $50 + 2 x $50 + ... + 10 x $1,050 = $7,500

Duration is therefore equal to 7.5 years.

A bond's duration will increase as its maturity date approaches and will decrease as its yield to maturity decreases.