# Questions tagged [duration]

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3k views

### What is the basis risk between cash and futures government bonds?

I am currently working in a team responsible for maintaining a simple risk application for our bond desk and I am interested in knowing how to provide some sort of basic basis risk metric. Our desk ...
2k views

### Can one use options on Treasury futures to hedge a portfolio?

Can one use options on Treasury bond futures to hedge a typical fixed income portfolio? If so, how can one estimate the duration for an option on a Treasury futures contract, and taking this a step ...
4k views

### Is Duration really the slope of the Price-Yield curve?

When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right? Duration is (change in price) divided ...
2k views

### Is duration additive? $C_{newDur}=A_{fundDur}w_{a} + B_{fundDur}w_{b}$?

Suppose quantified duration (like Macaulay duration with changing intervals) $Dur = \frac{\sum t_{i} PV_{i}}{\sum PV_{i}}$ and two funds having durations $D_{a}$ and $D_{b}$. You own them in the ...
352 views

### Investment Grade Bond vs Junk Bond, whose duration is larger?

Just wondering how to calculate duration when take credit risk into consideration. I think if duration is calculated as weighted average of cashflow time, and weights are calculated using present ...
2k views

### Closed-form formula for approximate maximum duration of a bond?

In teaching myself about bonds, I am writing some software, one piece of which will calculate the maturity of a bond given the yield curve as a function and a requested duration. The tricky part is ...
434 views

### How can we have negative probabilities in finance? Can we have negative payments in bonds? If not, how else can we have negative probabilities?

In Half of a Coin: Negative Probabilities, the author mentions bond duration. Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is ...
795 views

### What are some simple algorithms for hedging vanilla bonds?

My team will soon be implementing an auto hedger for our bond trading desk which will be integrated tightly with our risk application and I am interested in researching how this may work. Any advice ...
7k views

### Can the duration of a bond be greater than Time to Maturity

In the case of a vanilla bond I know that the duration will be less than the time to maturity. But I am observing that for a non-vanilla bond, the duration is greater than time to maturity. Can ...
773 views

### Can duration gap analysis be applied to mortgages?

Can a mortgage loan be treated like a bond and its duration calculated using the bond duration formula? More precisely, can I calculate the loan portfolio duration for duration gap analysis, with ...
2k views

### Is duration really inversely related to the maturity time length of a bond?

It is always said that longer bonds are more sensitive to interest rates. Intuitively this makes perfect sense, since longer bonds have a larger portion of its cash flow being subjected to stronger ...
2k views

### What curve are you shifting when you calculate DV01 for a swap?

I understand that a general swap has 4 curves attached to it: the flat forecast curve associated with the fixed leg, the forecast curve associated with the floating leg, the fixed leg discount curve ...
448 views

### Why is the duration of a bond important?

I know what duration measures, but now in the age of computers why is it useful? If the yield changes, we could just simply plug the new yield into a program, or excel or something like that, and ...
27k views

### What's the intuition behind DTS(duration times spread) in fixed income?

I am having some difficulty grasping the concept of using DTS to measure credit risk. In the equity world, one typical measure of risk is beta, which is quite well-defined as the exposure to a common ...
1k views

### Key Rate Duration for MBSs greater than Key Rate Tenor

Key Rate Durations (KRD) are essentially some fixed income instrument's price sensitivity to a non-parallel shift in interest rates (i.e., a shift at the "Key" Rate). For example, a 10-year bond's ...
122 views

### When would dedicated portfolios do better than 'immunized' portfolios?

We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ...
3k views

### What are the limits of bond portfolio immunization against interest rate changes?

I'm currently reading through an article on bond portfolio immunization against changes in the interest rate. I learned that the immunization can be done against instant changes in interest rate etc.,...
564 views

### Duration: Parallel shift in yield curve assumption

General Intro I'm trying to really understand the assumptions of dollar duration for a portfolio of bonds. In particular I don't fully understand that the assumption that there are parallel shifts ...
875 views

If $P$ is price, $D$ modified duration and $y$ yield then we have the relationship, $$dP=-D \cdot P \cdot dy$$ Why is there a minus sign and what does correspond to?
961 views

### Yield Curve Volatility

Let you have several issuers, and let each issuer have its yield curve built up with liquid plain vanilla fixed rate bonds. Each yield curve has its slope and its curvature, and they obviously change ...
9k views

### Interpretation of Macaulay Duration

I am having a difficulty conceptualizing the meaning of "Macaulay duration" - I want to note I completely understand the math, this isn't the issue. Modified duration & Efficitive Duration make ...
93 views

### How to derive and interpret the duration of a call option?

I read here that CFA students are taught that $$D_{C} = \frac{\Delta_{C} D_{B} B}{C}$$ Where $D$ is the duration, $\Delta_{C}$ is the first derivative of the options price with regards to the ...
332 views

### A question on immunization and Macaulay duration

I am studying for the Society of Actuaries - Exam FM and encountered the following problem: Let $x$ be the face amount of the 5-year bond and let $y$ be the face amount of the 10-year bond. Since ...
2k views

### What is the intuition behind the fact that Modified duration = Macaulay Duration / (1+r)?

I understand the derivation of both:take dP/dR and divide by P which will give you both 1) modified duration OR 2) macaulay duration / (1+r) (notice the weighted average time built into the function ...
533 views

### To compute key rate duration, shall I use par curve or zero curve?

To calculate Key rate duration/Key rate DV01 for bonds, do we move the zero/spot curve or we move the par curve? Or either one is OK? Just want to know the industry standard.
1k views

### duration of a cms swap

in the linked paper kwok_part2_exotic_swaps it says the following: A Swedish company has recently embraced the concept of duration and is keen to manage the duration of its debt portfolio. In the ...
5k views

### Bond Portfolio Immunization - Duration Matching

**Question is at the bottom** Suppose you have a portfolio of bonds A, B, and C with the following characteristics: (the "Frequency" column is the # of coupon pmts per year and also the # of ...
886 views

### Duration and DV01 vs coupon rate

For a vanilla bond, as coupon goes down ,absolute duration goes up, but absolute dv01(absolute change in price for a 1bp increase in rates ) goes down. so ... what is the message to take away from ...
570 views

### Duration calculation with negative cashflows

I have a pool of (mortgage) assets that pay cashflows as below. How could I correctly calculate the duration? Does it have a meaning in the sense of a vanilla/callable bond as the measure of price ...
217 views

### Duration split: treasury curve vs spread duration

I am looking at corporate bond (FR0013367620) in Bloomberg for which I have these values: DUR_ADJ_MID (modified duration performed using the yield to worst): 6.649 DUR_ADJ_OAS_MID (security's price/...
678 views

### The relation between coupon and convexity

Here are three statements: A lower coupon bond exhibits higher duration. The higher the coupon rate, the lower a bond’s convexity. Zero-coupon bonds have the highest convexity. Given particular ...
214 views

### Bond duration and the mathematical proof of 'bond price recovery'

The term duration has a special meaning in the context of bonds. It is a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. I have read this ...
840 views

### Why do people use (spread) Duration times spread (DTS) but no one uses (yield) duration times yield?

According to the DTS paper, the argument for using DTS instead of spread duration itself is that relative spread volatility is more stable than absolute spread volatility. Then surely the same ...
856 views

### Are there any opensource C# libraries for calculating bond duration and other FI Analytics?

I'm doing some Fixed Income analytics work and wanted to know if there where any opensource C# libraries that I could use in order to avoid writing functions for generic calculations like YTM and ...
184 views

I am currently reading two policy papers that construct, for a fixed-income bond, a following credit spread: This one, p. 12, computes the yield to maturity minus the Overnight Index Swap (OIS) rate ...
268 views

### Calculate tenor wise DV01 of a Swap in Quantlib Python, i.e. Key-rate Duration

Is there a way I can get DV01 breakup of a Swap across different tenors of the deal in Quantlib-Python. The question asked here, follows the basic method of re-valuing the swap by shifting the curve ...
297 views

### Modified duration and convexity of a bond in R

A soft question: Are there any existing packages in R that allows one to compute the modified duration and convexity of bonds in R? If there isn't, how can one go about doing so (with formulas) with ...
581 views

### Modified duration in multi-currency portfolio

I was thinking about how to figure aut duration for portfolio of bonds denominated in different currencies… I would like to compare sensitivity of portfolio to shift of yield with competitive ...
100 views

### US 10yr future and ED future

If the the duration of a 10yr future is roughly 8 years, I simplistically think that if I go long 10% notional of my portfolio and yields rise 10bps, then my P&L is 8 x -10bps x 10% = -8 bps In ...
211 views

### Can two bonds have same yield and price but different convexity?

In the market, if there are two bonds that have the same yield and price, then the higher convexity bonds will be more attractive. However, this would mean the market would increase the price of the ...
253 views

### Clean vs. Dirty Price and its impact on duration

When calculating duration would you use the clean price or the dirty price? why for either?
152 views

### duration and modified duration

By modelling duration and modified duration in Excel, I found that modified duration approximates bond price change well when there is a 1% increase in yield, while duration is a good approximation ...
3k views

### Difference between DV01 and IR DV01

What is the difference between DV01 and IR DV01? As far as I can see DV01 is at point on the yield curve and IR DV01 represents a parallel shift of the entire yield curve? My understanding is still ...
77 views

### Eurodollar Future Key Rate Duration

I am having trouble understanding the Key Rate (partial) Duration profile of Eurodollar Future contracts. Using market rates and pricing date as of 11/14/2018 I have calculated the partial duration ...
2k views

### Why is 'duration' not the same as 'spread duration' for risky bonds

For risky bonds, duration is defined as sensitivity of price due to change in underlying yield while spread duration is sensitivity of price due to change in the 'spread in yields to the ...
821 views

### High convexity vs low convexity bond definition

Isn't high convexity always better than low convexity bond from the formula that $$\frac {ΔB} B=-D \frac {Δy} {1+y} + \frac 1 2 CΔy^2$$ Since $\frac 1 2 CΔy^2$ is positive no matter what so the price ...
257 views

### How to get to this answer on Macauley duration?

Can you explain why the answer to the following question is approximately 4.5%: An investor buys a bond that has a Macaulay duration of 3.0 and a yield to maturity of 4.5%. The investor plans to ...
143 views

If you have an index and have measured its beta with respect to the overall market, how would you go about adjusting it against spread dv01 and why would you want this number?