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Questions tagged [duration]

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1answer
42 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 ...
0
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1answer
64 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 ...
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0answers
17 views

Duration Calculation with Delayed Amortization

I am trying to calculate Duration for a bond with a 10 year maturity, but experiences 10% Amortization over the last 5 years. It also has a 5% coupon. I am interested in the answer, but more ...
2
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1answer
72 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 ...
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2answers
66 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 (...
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0answers
28 views

RMBS Effective Duration, OAD, and Spread Duration: What's the difference?

I'm reading Fabozzi's "Bond Markets Analysis and Strategies", and I'm reading conflicting things on the definitions of different types of durations. In one section, they seem to say Option Adjusted ...
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0answers
52 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 ...
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0answers
48 views

Should risky gov't bonds be treated differently from riskless ones when it comes to risk computation?

If I were computing: YTM, DV01, OAS, Spread Duration for risk-free gov't bonds (eg, US Treasuries, German Gov't Bonds), and suddenly I'm adding risky gov't bonds to my portfolio, should the ...
1
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1answer
63 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 ...
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0answers
44 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 ...
1
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1answer
66 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 ...
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2answers
188 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 ...
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1answer
284 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 ...
1
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1answer
478 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 ...
1
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1answer
108 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 ...
2
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1answer
337 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 ...
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0answers
188 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 ...
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0answers
114 views

Technical approach to Key Rate Duration Hedging

I currently work for a Firm that hedges Mortgage Servicing Rights using a combination of vanilla swaps, Eurodollar Futures, MBS Pass-Throughs and Swaptions. We asses the fair value of the MSR asset ...
3
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3answers
890 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 ...
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3answers
136 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 ...
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0answers
96 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 ...
0
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1answer
88 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....
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0answers
37 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 ...
2
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1answer
300 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.
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2answers
565 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 ...
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2answers
608 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 ...
2
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2answers
161 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 ...
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1answer
136 views

Use of ACD to model transaction durations

I am using a simple ACD (autoregressive conditional duration) model with expoential or Burr distributed residuals and 1 lag, i.e. ACD(1,1). I am modelling durations for transactions data on a 'medium'...
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0answers
354 views

Duration of callable zero coupon bond

Can anybody please help me out with the below question with a brief explanation:- A 10-year zero coupon bond is callable annually at par (its face value) starting at the beginning of year 6. Assume a ...
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2answers
379 views

Bond Duration hedging with long convexity

How do you build a duration-neutral bond portfolio which is long convexity? can you give me an example?
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1answer
2k views

Definition of spread duration

is there anyone who can explain the concept of spread duration, both from a mathematical point of view and an intuitive one? Providing a practical example would be highly appreciated. Thanks in ...
1
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1answer
2k views

Interest Rate Swap DV01

thank you in advance anyways! I do have a question that drives me mad. How do i calculate the Swap DV01 for a Interest Rate Swap? I think for a bond i multiply the discounted cashflows times the ...
2
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1answer
465 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 ...
1
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1answer
387 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 ...
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2answers
424 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 ...
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1answer
98 views

Calculate historical duration based on current duration & historical prices

Suppose I have today current duration of a bond and it's historical daily prices. How from that I can calculate the historical duration? e.g. the value of duration I would saw if yesterday, week ago, ...
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1answer
655 views

Risky duration formula for what kind of bond?

In a documentation, there is the following formula for "zero interest rate risky duration" of a bond: $\frac{1-exp(-s \cdot T)}{s}$, where $s$ is spread, $T$ time until maturity. What type of bond (...
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0answers
72 views

Bond Duration with Bond portfolio returns

if I have given CRSP bond portfolio returns with different maturities (1m-12m, etc), how is it possible to compute the Future price and the duration? Beside that I do also have the Nelson-svensson-...
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2answers
428 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 ...
2
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1answer
649 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 ...
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1answer
3k views

Duration of a floating rate bond

It is known that the price $p_t$ of a floating rate bond can be calculated discounting $(L+k)$ the sum of the next coupon payment $k$ and the face value $L$ at the relevant risk-free rate. Hence, ...
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6answers
282 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 ...
1
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0answers
167 views

Bond Convexity: Relationship between discrete and continuous interest rate

The interest rate risk of a bond price $P$ is measured by its Duration: $$D=-\frac{\frac{dP}{P}}{dr}$$ However, the explicit formula for the Duration given a function $P$ is different if $r$ is ...
0
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1answer
8k 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}{...
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3answers
205 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 ...
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2answers
191 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 ...
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1answer
2k 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 ...
0
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1answer
105 views

Macaulay Duration: Duration for 2 bonds

Using Macaulay Duration, determine the duration of Bond B if Bond A and B (market value of 600 000 dollars and 400 000 dollars respectively) have a duration of 6.7 years and the duration of A is 8.5 ...
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2answers
251 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 ...
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1answer
627 views

Why the negative sign in modified duration relationship

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?