what two factors in bond markets lead to a positive risk premium?
Duration & Convexity: The Price/Yield Human relationship
Investors who own fixed income securities should be aware of the human relationship between interest rates and a bond's price. Every bit a general rule, the price of a bond moves inversely to changes in interest rates: a bail'south price will increment as rates decline and volition decrease as rates move up. Macaulay duration is the weighted-average maturity of a bond's cashflows, which is measured in years. Modified duration attempts to guess how the price of a bond will change in response to a change in interest rates and is stated in terms of a percent change in price. Typically when duration is quoted information technology is referring to a bond'southward modified elapsing rather than Macaulay elapsing. Taking this concept 1 step further, a bail'due south convexity is a measurement of how duration changes as yields change. These 2 measurements tin provide insight into how a bond is expected to perform should interest rates change and tin can help investors understand the price run a risk of fixed income securities in different interest rate environments.
What is Duration?
In simple terms, modified duration gives an idea of how the price of a bond will be affected should involvement rates change. A higher duration implies greater price volatility should rates move. Duration is quoted as the per centum alter in price for each given percentage change in interest rates. For case, the price of a bail with a duration of ii would be expected to increase (refuse) by about 2.00% for each ane.00% move down (up) in rates.
The elapsing of a bond is primarily affected by its coupon rate, yield, and remaining fourth dimension to maturity. The duration of a bond volition be higher the lower its coupon. Duration will be higher the lower its yield. Duration will also be higher the longer its maturity. The following scenarios of comparison ii bonds should aid clarify how these three traits affect a bond's duration:
- If the coupon and yield are the aforementioned, duration increases with time left to maturity
- If the maturity and yield are the aforementioned, duration increases with a lower coupon
- If the coupon and maturity are the same, duration increases with a lower yield
Example: Price/Yield Relationship for Bonds with Differing Maturities (5.00% coupon)
Example: 5.00% Coupon Bail at Par:
Cost Change for a Given Rise in Rates
| If Rates Move Up ... | 2-Year Bond | 10-Year Bond | 30-Twelvemonth Bond |
|---|---|---|---|
| 1.00% | -1.0% | -6.9% | -13.7% |
| 2.00% | -i.nine% | -xiii.two% | -24.vii% |
| 3.00% | -ii.8% | -19.0% | -33.6% |
(Source: Raymond James)
These are hypothetical examples for illustrative purposes only. They are not intended to reverberate the bodily performance of any security.
Convexity:
Equally the yield on a bond changes so too does its duration. A bond's convexity measures the sensitivity of a bond's duration to changes in yield. Duration is an imperfect mode of measuring a bond's toll change, equally it indicates that this change is linear in nature when in fact it exhibits a sloped or "convex" shape. A bond is said to have positive convexity if elapsing rises equally the yield declines. A bond with positive convexity will have larger price increases due to a decline in yields than price declines due to an increase in yields. Positive convexity can exist idea of equally working in the investor's favor, since the toll becomes less sensitive when yields rising (prices downwardly) than when yields pass up (prices upward). Bonds can likewise have negative convexity, which would indicate that duration rises as yields increase and tin can work against an investor'southward interest. The table below highlights the types of bonds that exhibit each blazon of convexity.
Examples of Bonds with Positive and Negative Convexity
| Type of Convexity | Typical Types of Bonds |
|---|---|
| Positive Convexity | Non-callable bonds, bonds with make-whole calls |
| Negative Convexity | MBS (most), bonds with a traditional phone call, preferreds |
(Source: Raymond James)
A useful style to visualize a bail's convexity is to plot the potential toll change against various yields. If ii bonds take the aforementioned duration and yield but differing convexities, a change in interest rates will affect each bail differently. For example, the chart below shows three bonds: a bond with higher positive convexity (Bond A) will exist less afflicted past interest rates than a bond with lower positive convexity (Bond B). On the other hand, a bond with negative convexity (Bond C) will showroom larger toll fluctuations should rates rise than if they were to fall.
Bonds Can Have Very Different Convexities: Positive vs. Negative
Conclusion:
Duration and convexity are 2 metrics used to help investors understand how the price of a bond volition be afflicted by changes in interest rates. How a bond'south toll responds to changes in interest rates is measured by its duration, and can help investors sympathise the implications for a bond's price should interest rates change. The alter in a bail's elapsing for a given modify in yields can exist measured by its convexity.
- If rates are expected to increase, consider bonds with shorter durations. These bonds volition be less sensitive to a ascension in yields and will fall in cost less than bonds with college durations.
- If rates are expected to decline, consider bonds with higher durations. Equally yields decline and bail prices move up, higher duration bonds stand to proceeds more their lower elapsing counterparts.
Source: https://www.raymondjames.com/wealth-management/advice-products-and-services/investment-solutions/fixed-income/bond-basics/duration-and-convexity