Factors Influencing Interest Rate Risks | CFA Level I Fixed Income

Today, we’ll discuss the factors that affect a bond’s interest rate risk.

Properties Affecting Interest Rate Risk

Three main properties determine a bond’s interest rate risk:

• Time to maturity
• Coupon rate
• Yield-to-maturity

These factors impact the Macaulay duration, which is a measure of interest rate risk. Keep in mind that these principles also apply to other duration measures.

Time to Maturity

For bullet bonds, the balloon payment at maturity has the largest weight. Therefore:

• Shorter time to maturity means lower Macaulay duration
• Longer time to maturity means higher Macaulay duration

However, this relationship is not linear and has an upper limit.

Perpetual bonds have no maturity and an interesting Macaulay duration. The relationship between time to maturity and Macaulay duration changes when bonds are purchased at a discount, following a curve that first increases, then decreases over a range of long maturities.

For zero-coupon bonds, the Macaulay duration is equal to the number of years to maturity, as there is only one cash flow.

Coupon Rates

Higher coupon rates result in lower Macaulay duration and interest rate risk. This is because a higher coupon rate shifts the weights towards cash flows closer to payment.

Yield-to-Maturity

Higher yields-to-maturity decrease the discount factor of cash flows in the near term and increase the discount factor of cash flows in the far term, resulting in lower Macaulay duration.

Interest Rate Risk and Yield Volatility

Investors are concerned with not only the sensitivity of a bond’s price to changes in yield but also the volatility of the bond’s yield. The relationship between yield volatility and time to maturity is referred to as the term structure of yield volatility.

Duration and convexity calculations often assume a parallel shift in the yield curve, but this is not always the case in practice. For instance, central bank policies can impact the yield curve, causing it to steepen or flatten.

In conclusion, the Macaulay and modified duration of a fixed-rate bond depend primarily on its time-to-maturity, coupon rate, and yield-to-maturity. Longer time-to-maturity usually leads to higher duration, while a higher coupon rate or a higher yield-to-maturity reduces the duration.