Duration and convexity

It is considered a canonical religious masterpiece and greatly influenced both Thomas Aquinas and Duns Scotus. I have no such aspirations for this commentary, except perhaps remind readers that it is never different this time. Such is the case that while a professional investing career of forty years may be termed robust, in actuality it will likely capture only a pair of economic cycles; too few to fairly opine. Only a few years separated me from being drafted to serve in another ill-fated conflict.

Duration and convexity

Portfolio Duration Duration is an effective analytic tool for the portfolio management of fixed-income securities because it provides an average maturity for the portfolio, which, in turn, provides a measure of interest rate risk to the portfolio.

The duration for a bond portfolio is equal to the weighted average of the duration for each type of bond in the portfolio: Minimize Duration Risk When yields are low, investors, who are risk-averse but who want to earn a higher yield, will often Duration and convexity bonds with longer durations, since longer-term bonds pay higher interest rates.

But even the yields of longer-term bonds are only marginally higher than short-term bonds, because insurance companies and pension funds, who are major buyers of bonds, are restricted to investment grade bonds, so they bid up those prices, forcing the remaining bond buyers to bid up the price of junk bondsthereby diminishing their yield even though they have higher risk.

Indeed, interest rates may even turn negative. In Junethe year German bond, known as the bund, sported negative interest rates several times, when the price of the bond actually exceeded its principal. Interest rates vary continually from high to low to high in an endless cycle, so buying long-duration bonds when yields are low increases the likelihood that bond prices will be lower if the bonds are sold before maturity.

This is sometimes called duration risk, although it is more commonly known as interest rate risk. Duration risk would be especially large in buying bonds with negative interest rates.

On the other hand, if long-term bonds are held to maturity, then you may incur an opportunity cost, earning low yields when interest rates are higher. Therefore, especially when yields are extremely low, as they were starting in and continuing even intoit is best to buy bonds with the shortest durations, especially when the difference in interest rates between long-duration portfolios and short-duration portfolios is less than the historical average.

On the other hand, buying long-duration bonds make sense when interest rates are high, since you not only earn the high interest, but you may also realize capital appreciation if you sell when interest rates are lower.


Convexity Duration is only an approximation of the change in bond price. For small changes in yield, it is very accurate, but for larger changes in yield, it always underestimates the resulting bond prices for non-callable, option-free bonds.

This is because duration is a tangent line to the price-yield curve at the calculated point, and the difference between the duration tangent line and the price-yield curve increases as the yield moves farther away in either direction from the point of tangency.

Giddy/ABS Mortgage -Backed Securities/ 2 Copyright © Ian H. Giddy Mortgage -Backed Securities 4 Structure of the US MBS Market Mortgage Loan Bank (mortgage. Jun 18,  · HI David, A short call has -ve duration and -ve convexity. A short bond seems to be similar. As yield increases short seller will benefit. When I calculate modified duration for a continuously compounded zero, for short sale it comes out to be exactly opposite of long bond. I have questions relating to convexity and duration. Could you explain them conceptually and the practical uses for them? An example of why a certain convexity bids up a bond, or something along.

A diagram of the convexity of 2 representative bond portfolios, showing the general relationship between the percentage change in the value of bond portfolios to a change in yield. Convexity is the rate that the duration changes along the price-yield curve, and, thus, is the 1st derivative to the equation for the duration and the 2nd derivative to the equation for the price-yield function.

Convexity is always positive for vanilla bonds. Furthermore, the price-yield curve flattens out at higher interest rates, so convexity is usually greater on the upside than on the downside, so the absolute change in price for a given change in yield will be slightly greater when yields decline rather than increase.

Consequently, bonds with higher convexity will have greater capital gains for a given decrease in yields than the corresponding capital losses that would occur when yields increase by the same amount. Some additional properties of convexity include the following: Convexity increases as yield to maturity decreases, and vice versa.

Convexity Bias | Treasury Today

Convexity decreases at higher yields because the price-yield curve flattens at higher yields, so modified duration is more accurate, requiring smaller convexity adjustments. This is also the reason why convexity is more positive on the upside than on the downside.

Among bonds with the same YTM and term length, lower coupon bonds have a higher convexity, with zero-coupon bonds having the highest convexity. This results because lower coupons or no coupons have the highest interest rate volatilityso modified duration requires a larger convexity adjustment to reflect the higher change in price for a given change in interest rates.

Convexity is calculated by the following equation:Given particular duration, the convexity of a bond portfolio tends to be greatest when the portfolio provides payments evenly over a long period of time.

Duration and convexity

It is least when the payments are concentrated around one particular point in time. Notes Page 2 Economics of Capital Markets Version Outline Page 3 Bond Duration and Convexity Introduction Bond Duration and Convexity Introduction We already know the relationship between bond prices and yields (or required rates of.

Vanguard research May Distinguishing duration from convexity Authors Donald G. Bennyhoff, CFA Yan Zilbering Executive summary.

For equity investors, the perception of . In a few recent columns, we’ve talked about duration and convexity in the context of changing market prices. They are some of the most misunderstood and misused terms in finance, and clarifying.

Analytic-Calculus Duration and Convexity- 12 Duration is the d+ quantity divided by the bond price. This weighting adjustment of duration allows comparison of the interest rate sensitivity of bonds with different principal amounts.

d However, duration is not constant. To obtain more accurate estimates of price changes, we need to measure convexity in order to determine the sensitivity of duration itself to changes in interest.

Use Duration And Convexity To Measure Bond Risk