# Questions tagged [duration]

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90 questions
0answers
43 views

### Average Duration of a Swap versus normal duration of a swap? [closed]

This came up in a lecture and I'm slightly confused on the difference - how is the average calculated versus the normal way of calculating the duration of a swap? Using Macaulay's Method and floaters (...
0answers
55 views

### Macaulay Duration Calculation on LIBOR/Swap term structures

I'm a bit confused as to how to use the Macaulay Duration Calculation method to calculate the duration of a swap in which the rates for both paying and fixed change every six months (LIBOR/Swap Term ...
1answer
40 views

### MBS Market Duration & Convexity

Soft question...hopefully. I am working on a swaption hedging strategy. Part of this strategy calls for a forward looking indication of changes in implied volatility, using 1m10y implied as a proxy ...
1answer
43 views

### Interest Rate Sensitivities of a FRA [closed]

A basic question perhaps ? How to compute the Duration, MDuration, Convexity and PV01 of a FRA ?
0answers
51 views

### Duration and yield

I have some basic questions about mainly duration and yield. 1) Almost no-one defines what yield they are talking about when talking about duration and discount rate, I've seen some talk about ...
1answer
43 views

### Does it make sense to combine different modified durations?

Does it make sense to aggregate different modified durations into one overall duration measure? In the context of insurance liabilities: ...
1answer
39 views

### Generalization of Macaulay/modified duration under non-parallel shift of spot curve

The generaliztaion of Macaulay duration (which is defined in terms of yield to maturity) is known as Fisher-Weil duration. How is Fisher-Weil duration or modified duration defined under non-parallel ...
0answers
47 views

### Effective duration and recalibration

I am calculating the effective duration of an interest rate instrument with optionality. I do the following calibrate an interest rate model to market data: discount curve and ATM swaption vols use ...
0answers
59 views

### Spread Duration weighted OAS vs. Mkt Cap Weighted?

I am curious what the differences might be in rolling up OAS spreads across a portfolio by duration weighting vs. mkt cap weighting. @Alex yes I meant S.D. weighted not Duration weighted
1answer
52 views

### Calculation of duration based on spot rates

As I know, Macaulay and modified durations are defined in terms of yield to maturity (YTM), in other words, in order to calculate durations we use yield to maturity as a discount factor. Suppose, ...
2answers
150 views

### How should we calculate the duration of a convertible bond?

For callable bonds we can use the effective duration to approximate the modified duration, since the future interest rates will affect the expected cash flows. For convertible bonds the underlying of ...
2answers
97 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 ...
1answer
90 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 ...
3answers
2k views

### Modified or Macauley Duration in python

are there any existing python modules that can calculate Modified and/or Macauley Duration of a bond.
1answer
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 ...
6answers
318 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 ...
2answers
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 ...
1answer
165 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/...
0answers
122 views

### Duration adjusted credit spread

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 ...
1answer
61 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 ...
2answers
188 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?
2answers
163 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 ...
0answers
112 views

### Duration of a FRN in continuous time interest rate model

This question was inspired by my attempt to understand the duration of a floating rate note, or FRN for short. Several answers, like this, say the duration of a FRN is just time to next coupon payment....
1answer
126 views

### Units of Modified Duration and Macauley Duration

I know that the unit of the mod. Duration is % (actually no unit, because every number can be written as %) and the Macauley Duration has the unit time. If you want to convert the Macauley Duration ...
1answer
467 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 ...
2answers
108 views

### Data for daily real interest rates

In a high frequency model i would like to add daily real interest rates (preferably short-term) as a variable. However, I cannot seem to find either daily CPI data, or daily real interest rates (...
0answers
234 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 ...
1answer
77 views

### Macaulay's Duration with Zero Rates

The definition of Macaulay's Duration is the weighted average maturity of cash flows and is calculated as- $$D_{mac}=\frac{\sum_ttPV(C_t)}{V}$$ where $PV(C_t)$ is the present value of the cash flow ...
3answers
26k 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 ...
0answers
120 views

### Calculating DTS only have Effective Duration

This is a relatively simple question but I have a global index of bonds and have been asked to calculate the DTS of each bond within the index. I have only the OAS and effective duration. I have no ...
1answer
75 views

### Portfolio duration

What is the correct way to calculate duration of a fixed income portfolio with long and short bond positions? And how to calculate portfolio YTM with long and short positions. For long only (or short ...
1answer
639 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 ...
2answers
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 ...
1answer
978 views

### DV01 approximation

I often approximate DV01 using: DV01 = Market value of position * 1bps * Duration in years. Here, for Bond or CDS, I generally assume duration = residual maturity. My query: Assume I buy a bond. So ...
2answers
326 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 ...
1answer
783 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 ...
1answer
143 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 ...
2answers
230 views

### Duration vs. Convexity Contradiction

A lower coupon bond exhibits higher duration, which means higher price volatility with changing YTM. A lower coupon bond also exhibits higher convexity. However, with higher convexity, bond prices ...
0answers
280 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 ...
3answers
169 views

### Alternate explanation of Duration

In many reputed sites such as, Investopedia, bond duration is explained as a measurement of how long, in years, it takes for the price of a bond to be repaid by its internal cash flows. My ...
3answers
1k 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 ...
1answer
10k views

### Duration of perpetual bond

I am trying to derive the duration of a perpetual bond with coupon $c$ in two ways: $$D=-\frac{\frac{\partial P}{\partial r}}{P},$$ $$P=\frac{c}{r}$$ \Rightarrow D = -\frac{-\frac{c}{r^2}}{\frac{c}{...
0answers
118 views

### What is relation between option adjusted duration and volatility

I am calculating oasd using implied vol of 15%. What is relation between OASD vs Implied volatility in theory for various maturities. I am running using MMD curve. If anyone recommend any good ...
1answer
121 views

### Curve to curve hedging for treasury

Please correct my conceptual understanding if needed, but I'm trying to calculate the mod duration of treasury curve pieces when the curves are DV01 hedged. For example: DV01 of 10 Year Note is 896....
0answers
44 views

### How to estimate bond price returns via an index?

Let's say I have a corporate bond, for which I know current yield, modified duration, coupon and maturity. I want to estimate how it would have performed under certain market conditions by looking at ...
2answers
200 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 ...
1answer
506 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.
2answers
552 views

### Why Is Bond Time Value Risk Not Considered in Bond Immunization?

I know bond portfolio immunization includes duration and (if the hedging period is longer) convexity matching. These are equivalent to taking the first and second partial derivatives of the bond ...
2answers
949 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 ...
2answers
856 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 ...