Questions tagged [duration]
The duration tag has no usage guidance.
144
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FRN duration when discount curve and projection curve have non-perfect correlation
The textbook example assumes that discount curve and projection curve are the same (or have a perfect correlation). What happens with the FRN's duration when it is not the case?
For example, there are ...
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1
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138
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Macaulay Duration of a Callable Bond [closed]
I could not find any formula of Macaulay duration for a callable bond in the literature. Can anybody show how to derive it or give a reference where it is already obtained.
EDIT My goal is to find a ...
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2
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310
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mathematical proof of the hedge ratio formula for bond futures
We know that the hedge ratio ϕ_F that we should use in order to to the duration-hedging through bond futures is:
$$ϕ_F= -(DV01_B / DV01_{CTD} )\cdot CF_{CTD}$$
Where $\textrm{DV01}_B$ is the dollar ...
2
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1
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409
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Using CME SOFR Futures in practice
I'm looking for numerical examples on how CME SOFR futures contracts are used in practice for hedging purposes. Book references containing this discussion are appreciated.
Bloomberg's FLDS function ...
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112
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Portfolio immunization in time
The company will have to pay out an amount of liabilities $13594$ at the moment $t=9$. In $t=0$ they want to cover it with 4-years zero-coupon bonds and yearly perpetual annuity that is due in arrears ...
2
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2
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459
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Quantifying the impact of rates change on bond prices
How can I quantify the impact of a change in interest rates on bond prices?
I know that in a classical textbook setting the answer would be to compute the modified duration of the bond and, to account ...
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1
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84
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What is $\sum_{i=1}^n i^2 \frac{CF_i}{CF_{Total}}$
I know that $$\sum_{i=1}^n i \frac{CF_i}{CF_{Total}}$$ is Macaulay Duration, but what is $$\sum_{i=1}^n i^2 \frac{CF_i}{CF_{Total}}$$. I have given it a thought like it is a second moment of something ...
2
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938
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Simplified formula for duration of interest rate swap
Lets consider the simple interest rate swap instrument as 5-year maturity interest rate swap. I found an interesting simplification to calculate the duration of such swap as,
$\frac{\left(1 - e^{-r_t *...
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2
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211
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Are there names from the third term onwards in the Taylor approximation for bond pricing?
The first terms are duration and convexity, but are there common names for the terms beyond this?
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2
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807
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Is duration of a bond a convex function?
I understand that in general, the NAV of a bond is a convex function.
However, I am not too sure if the same can be said for its duration.
Are there references on this? Thanks
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0
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67
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Modified Duration as interest risk [closed]
I am new to bond pricing and I am studying the sensitivity measures of a bond (with discrete compounding) and even though I understand the mathematical concepts of modified duration and convexity ...
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2
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665
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ATM interest rate swap dv01 vs off-market swap dv01
How significant is impact on dv01 of an at-the-money swap if rates move significantly?
For example: lets say a 5Y USD at the money swap has 4.6 duration. now, if the rate curve move by 150-200bps, ...
2
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1
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235
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Macaulay Duration - Liability matching
Can someone provide a detailed example to prove the following statement:
"When the investment horizon is equal to the Macaulay duration of the bond, coupon reinvestment risk offsets price risk.&...
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1
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201
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Bond value as a function of spread change and duration/maturity
I am trying to calculate the change of value in a universe of bonds given a series of shocks to the credit spread of each bond. As a constraint, the initial dataset only contains the spread change for ...
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164
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Formula to calculate the sensitivity of a bond to curve steepening
https://github.com/jerryxyx/TreasuryFutureTrading/blob/master/README.pdf
On page 2 of the pdf above, the sensitivity of a bond to increases in the slope of the curve, is given as $\ln(T)$, where $T$ ...
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264
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Convert spreads to prices for bonds via duration
I have the price of a bond and would like to convert it to spreads. Is this possible by just having dollar duration?
Secondly, if I just care about the relative spreads of multiple bonds, is it enough ...
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2
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584
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"The five year swap has the same dv01 as a par five year treasury bond" Why?
Am reading a book (The Complete Practitioner's Guide to the Bond Market by Steven Dym, 2009) where the author gives an example of someone buying a 5 year par 4.65% treasury and someone else entering ...
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161
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What is the definition of horizon current coupon spread duration
Trying to understand the meaning of current coupon spread duration? Is this same as empirical mortgage spread duration?
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166
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Calculate the duration of group of Bond ETFs
Is it correct to get the weighted average of a bunch of bond ETFs to get the duration? Is it theoretical correct to say that.
I have 6M AGG (duration 8.39), 30M BND (duration 8.7), 60M SHY (duration 1....
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1
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86
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Duration and convexity of an open term loan/bond!
Imagine an open term loan with monthly interest payments of [x]% and the principle due when the loan is closed. Both the lender can call the loan, and the borrower can return the loan (with no penalty)...
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91
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Floating rate bond valuation and Duration
I would like to know how a floating rate bond will be valued when LIBOR is used to compute the coupon cashflows and the bond is discounted using an OIS rate. Normally I have seen valuation of a FRB ...
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153
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Hedging Curve Risk with Futures
Please help confirm/correct my understanding of hedging curve risk using futures.
For example, if I purchased a 9y bond and hedged the duration risk (parallel shift) by shorting 10y treasury futures ...
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1
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1k
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Does credit default swaps have interest rate duration and credit duration?
Will a CDS have interest rate duration and credit duration?
It does seem likely that the value of the CDS would depend on the underlying interest rate, or the spread. But when I try to Google this I ...
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149
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Spread duration curve by issuer or by sector
I was surprised to see that spread duration was not offered as a curve in Bloomberg. As a result, I'm trying to find a curve (in Bloomberg) or build a curve (maybe using the Excel API) which ...
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1k
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Duration of Floating rate bond
I have read in several places that the duration of a floating rate bond is simply the time until next coupon payment, because the upcoming coupon payments are not known. I have 2 questions here:
Why ...
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145
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Bond Future and Bond Yield relation
I recently read, that yield changes during a short time window can be approximated by dividing the returns of futures on the bond by its Duration. Has anybody heard this before and can shed some light ...
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273
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Is this simple model used to calculate the interest rate duration and credit duration of a floating rate note? Other models?
I found this model for floating rate bonds in a book I am reading and I am wondering if it is used anywhere in practice?
$$MV=\frac{\frac{(Index+QM)\cdot FV}{PER}}{\left(1+\frac{Index+DM}{PER}\right)^...
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154
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Bond yield with known DV01
Is there a way to calculate the yield of a bond knowing the DV01 and duration (numerical values) and knowing all other parameters of $V$ (maturity, coupon, etc.)?
$$DV01=-\frac{\partial V}{\partial y}$...
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3
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2k
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How can a deep discount bond with a longer time to maturity have a LOWER duration than an otherwise identical bond with a shorter time to maturity?
Here is a brief excerpt on the fixed income chapter from the 2020-2021 level 1 CFA curriculum:
Generally, for the same coupon rate, a longer-term bond has a greater
percentage price change than a ...
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1
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2k
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QuantLib Python: how to calculate duration and convexity for irregular cashflows? Can I use SimpleCashFlow or must I define a custom bond?
I have 2 questions:
If I want to discount a set of irregular cashflows, I can do it using the SimpleCashFlow class, or defining a bond with custom cashflows (thank you to Ballabio and David Duarte for ...
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62
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What is the duration of a rolling 5 year investment?
I have difficulty with the duration of a 5 year investment (like GIC). In such an investment, the investment (GIC) rate is reset as the current market rates. So the market value is equal to the face ...
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1
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376
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Modified Duration and how it explains bond price sensitivity to changes in the yield to maturity [closed]
My questions is the following: why is it that the modified duration can explain so well the change in price of bonds? I don't get the mathematical relationship behind this, that is between modified ...
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2k
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Gamma/Convexity of a Swap vs a similar bond
As a rule of thumb, how would the duration and convexity of a 30y UST bond paying X% compare to the duration and convexity of a matched maturity vanilla interest rate swap, with a similar fixed rate.
...
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437
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Duration and Convexity
I am searching to estimate the evolution of my portfolio duration following a yield increase/decrease.
Can i use the convexity?
I mean IR delta x (- convexity) = Duration delta
Is it correct?
Thanks a ...
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1
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2k
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Duration of a futures contract
I have tried to find an answer to this question but have come up with nothing.
So, it is my understanding that to find the duration of a futures contract (assuming no switch risk), all you need to do ...
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1
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118
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Is the risk the same for two different tenor bonds with the same DV01?
I have two different bonds (for e.g. 1yr and 10yr) that have the same DV01. The notional for 1yr bond is definitely more than the 10yr bond. Is the risk same for the bonds the same because DV01 for ...
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64
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Hedge Active Duration by Issue Currency or Country of Risk
For example, lets say I own a bond issued by a company in Mexico that's denominated in USD and I want to hedge my duration exposure. I obviously need to hedge duration to the US yield curve. Do I ...
2
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1
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2k
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Duration of a floating rate bond with spread
I need to calculate the duration of a floating rate bond with spread. With zero spread the price of the bond is given by:
$$p_\tau=(1+c_1)e^{-r(\tau_1) \cdot \tau_1}$$ so the duration is:
$$-\frac{\...
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0
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499
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How to calculate the new price of a bond using duration rule and duration with convexity rule?
A bond with a 30 year maturity, par value of $1000 and is 8% p.a. coupon is selling at an yield to maturity of 8% p.a. The modified duration of the the bond at its yield is 11.26%, and its convexity ...
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Why is the effective duration of a floating rate bond the time to the next payment?
I am wondering why the effective duration of a floating rate note is the time to the next payment. Effective duration is is defined as
$$\frac{V_{-\Delta y}-V_{+\Delta y}}{2V_0\Delta y},$$
for a small ...
2
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0
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293
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How to optimise Fixed Income portfolio (Yieldbook) based on YTM, duration, rating and exchange rate
I have a fixed income portfolio built up in the Yieldbook and BBG Port.
However due to some bad performance of my portfolio compared to the benchmark I would like to build up an optimisation which ...
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0
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149
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Interest rate hedging using treasury futures – timing and duration
I'm pondering over the following (rather standard) problem:
We have \$10 million invested in government bonds and are concerned with highly volatile interest rate over the next six months. We want to ...
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Step-up bonds should be more, not less sensitive to market interest rates, shouldn't they?
I keep reading that "a step-up bond provides more protection to an investor in the face of market interest rate fluctuations", that "a step-up bond typically performs better than any ...
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Bond Change in Absolute or Relatively Percentage
Since most of the bonds prices are quoted in price, for example, bond price of 103 means 103% of the principal or face value (ex. $1000). Suppose a bond has modified duration of 4.62 years. If yield ...
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277
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Question About Negative and Positive Convexity
I read the following paragraph from investopedia:
https://www.investopedia.com/terms/c/convexity.asp
If a bond's duration increases as yields increase, the bond is said to have negative convexity. In ...
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Macaulay or modified duration in Python
i was wondering to ask, is there any function in pyhton, that calculates macaulay or modified duration, when time to maturity is not a whole number, for example time to maturity is 1514 days, and you ...
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Can you calculate modified duration for swaps?
I know how to calculate them for bonds. But it came to my mind this.
In bonds, Macaulay duration technically is a weighted average of coupon payments. But can it be somehow calculated for swaps? Or ...
0
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1
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322
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Macaulay duration of an IRS receiver [closed]
how can I compute the duration of an IRS receiver? and how can I use it to compute the Delta of IRS?
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232
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Calculate duration of zero coupon bond
I am currently studying interest rate risk management, and i can't seem to get the derivation right, and I would like to do all of the steps, to be sure that I understand what is going on.
Let Pz (t, ...
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How required yield affects price of the bond and how the durations changes
can somebody answer, those two theoretical questions?
How does the bond price depend on the desired yield (market interest
rates)?
How the duration changes if we have a shorter / longer
maturity and ...