Duration Risk – Longterm Bond vs Shortterm Bond
Longer-term bonds are generally more sensitive to inflation expectations than shorter-term bonds. This phenomenon is known as “duration risk.”
Here’s why longer-term bonds tend to be more sensitive to inflation expectations. The word is “Time”. You are supposed to hold a bond for longer amount of time, so the risk for that is higher too. It can be explained from four different prespective.
Time Horizon: Longer-term bonds have a more extended period until maturity. Therefore, their fixed interest payments are exposed to the effects of inflation for a more extended period. If inflation erodes the purchasing power of money over time, it can have a more substantial impact on the real (inflation-adjusted) returns of longer-term bonds.
Fixed Payments: Bonds pay fixed interest payments (coupon payments) throughout their term. In an inflationary environment, the real value of these fixed payments diminishes. Investors holding longer-term bonds may experience a more significant reduction in the real value of their coupon payments compared to shorter-term bondholders.
Interest Rate Risk: Longer-term bonds are subject to greater interest rate risk. If market interest rates increase due to rising inflation expectations, the prices of existing longer-term bonds tend to fall more significantly than those of shorter-term bonds. This is because the fixed interest payments of longer-term bonds become less attractive compared to newly issued bonds with higher coupon rates.
Market Expectations: When investors expect future inflation to rise, they typically demand higher yields (interest rates) on longer-term bonds to compensate for the potential loss of purchasing power. As a result, longer-term bond prices tend to be more sensitive to changes in interest rates driven by inflation expectations.
In contrast, shorter-term bonds have shorter durations and maturities. They are less exposed to the long-term effects of inflation and interest rate fluctuations. While shorter-term bond prices can still be influenced by changes in interest rates driven by inflation expectations, the impact is typically less pronounced compared to longer-term bonds.
Bond Pricing Model - Present Value Formula:
The Present Value formula is a fundamental model used to determine the fair price of a bond based on its expected future cash flows and the prevailing interest rates. The formula can be expressed as:
Bond Price (P) = Σ [CFt / (1 + r)^t]
Where:
- P = Bond Price
- CFt = Cash Flow at time t (typically coupon payments and principal repayment)
- r = Current interest rate (yield to maturity)
- t = Time until cash flow occurs
Duration as a Measure of Bond’s Sensitivity:
Duration is a key concept in bond analysis that quantifies how sensitive a bond’s price is to changes in interest rates. It provides a measure of the weighted average time it takes for an investor to receive the bond’s cash flows.
Mathematically, Macaulay Duration (D) is calculated as:
D = Σ [t * (CFt / P)]
- D = Macaulay Duration
- t = Time until cash flow occurs
- CFt = Cash Flow at time t
- P = Current price of the bond
Understanding Duration Risk: Longer-term bonds have higher durations than shorter-term bonds. This means that they have more extended weighted average cash flow periods. Now, let’s see how inflation expectations come into play:
When inflation expectations rise, investors typically demand higher nominal interest rates to compensate for the anticipated loss of purchasing power due to inflation. The Fisher equation illustrates this relationship:
Nominal Interest Rate (r) = Real Interest Rate (r) + Expected Inflation Rate (π)*
- r = Nominal Interest Rate
- r* = Real Interest Rate
- π = Expected Inflation Rate
As investors expect higher inflation (π), nominal interest rates (r) increase.
Impact on Bond Prices: The relationship between duration, interest rates, and inflation expectations becomes evident when we consider how bond prices react to rising nominal interest rates:
When nominal interest rates (r) rise due to higher inflation expectations, the present value of future cash flows (CFt / (1 + r)^t) decreases for each cash flow, especially for cash flows that are further in the future (higher ‘t’).
Longer-term bonds have a more substantial proportion of their cash flows that occur further in the future. [Remember the story of Compound Interest where it is said that the magic happens at the end of the story.] Therefore, the impact of rising interest rates on the present value of these cash flows is more pronounced.
As a result, the prices of longer-term bonds decline more significantly than the prices of shorter-term bonds when inflation expectations increase.