Questions tagged [fixed-income]

Securities which obligate the borrower/issuer to make payments on a fixed schedule. Fixed income securities include sovereign, corporate and municipal bonds, corporate loans, and securitized lending (e.g., ABS). "Fixed" refers only to the schedule of obligatory payments, not the amount, and may include inflation linked bonds, variable-interest rate notes, and the like.

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73 views

Fixed Income portfolio type

Could someone kindly point me toward a primer that would cover the various type of fixed income portfolio strategies under modern portfolio theory ? In a nutshell, I would like to know what kind of ...
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How is the integral relationship between current yield curve and forward yield curve derived?

$$y(\tau) = \frac{1}{\tau} \int_{0}^{\tau} du \Big(f(u)\Big)$$ As far as I understand the forward rate is the future rate based on the expectation hypothesis. But it is unclear how many years into the ...
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Relative order of curve for coupons for Upward Sloping Yield

Why would the forward curve be above zero and coupon bond yield be at the bottom for a sloping up yield curve.
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549 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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Pricing Options on Fixed Income ETFs

The market for trading options on fixed income ETFs like HYG has become increasingly prominent in the past couple years, but I've been unable to find any discussion related to the pricing methodology ...
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Jamshidian's trick for Swaptions

Following Brigo$^1$ p.77, we can decompose the price of a swaption as a sum of Zero-Coupon bond options (Jamshidian's Trick). To do so, the authors suggest to find $r^*$ the value of the spot rate at ...
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Correct form for State Space Equation for Kalman Filter for DNS

In this paper: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf in eqns 3,5 the state eqn has the mean removed. $(z_t-\mu)=A(z_{t-1}-\mu) + \epsilon_t$ $y_t=C z_t + \delta_t$ ...
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Fed Funds Rate: longer maturities

FFR published by Fed Bank of NY is the average rate US banks charge each other for the overnight loans of their reserves required by the Fed regulations. Since Fed acts similar to a clearing house ...
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Calculating Net Annualized Return on LendingClub historical data

I am interested in the formula LendingClub provides as their measure of "Net Annualized Return": $\big(1 + \frac{\sum_{i=1}^N{((I_i + L_i - S_i - C_i + R_i) / P_i) P_i}}{\sum_{i=1}^N{P_i}}\big)^{12}-...
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769 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 ...
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Pre- Versus post-2008 Crisis Rates Modeling

Modeling for interest rate derivatives (such as bermudan swaptions) is said to have undergone significant changes since the crisis. Prior to the crisis, counterparty default risk was often ignored, ...
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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 ...
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Opimization on a Bond Portfolio

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How to properly interpret accrued interest of bonds

Ever since I work in finance I was wondering what accrued interest (AI) are good for (see the wikipedia article for a short introduction). I think I have a clear picture in mind now and the usual ...
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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 ...
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3answers
241 views

Comparing asset swap spreads

I am a bit confused when it comes to asset swap spreads of fixed rate bonds vs the same issuers floating rate bonds of the same maturity and issued at the same time. Should these not be comparable (if ...
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684 views

Treasury futures basis & calendar spd [multiple questions]

How do I determine if a bond will become CTD in a futures contract and how likely there a CTD switch is? Also, how do you use implied repo/actual repo to assess richness/cheapness of two calendar ...
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Is there a Bloomberg field for a bonds (upcoming) coupon dates?

For a specific bond I need to calculate the time until each of the upcoming cash flow payments (for obvious reasons). So I wondered if there is a field (bulk data) that gives me all the dates of the ...
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191 views

Origin of the $-\frac{1}{P}$ in Macaulay Duration?

Changes in the yield curve affect the total return of a coupon bond instrument, hence I want to compare different bond instruments in how sensitive they are to $y$. Well, I just take the derivative, ...
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1k views

How does one price the market value and estimate the fair value of a bond futures roll?

Consider the current situation: we are entering December, meaning that the December futures are being rolled into the March futures (i.e. traders are selling their holdings of December futures ...
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Roll down Treasury curve (Coupon effects)

I'm currently working on roll down calculations for the Treasury curve (3-month roll, 6-month roll, etc..). One of the senior guys (I just started out of college) asked me to adjust for the coupon ...
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1answer
2k views

How to trade interest rate futures calendar spread?

This has always been difficult to understand for me. How is the second futures contract valued in relation to the front month contract? My understanding is there are carry considerations (3 more ...
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2k views

RQuantLib, Hoadley and Bloomberg YAS: fixed rate bond pricing differences?

I'm trying to price a fixed rate bond one year from now on. The bond is the PEUGOT 7 ⅜ 03/06/18, whose ISIN code is FR0011439975. I'm using such a specific example because in this way everyone can ...
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1answer
321 views

Price difference between bond cash and futures

I used to trade German and US govt. bond futures and I am now having trouble understanding the price difference of these markets against the cash market. For example, the 10 year german government ...
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1answer
164 views

What does a electronic dealer track in a RFQ market?

If you have mid price for rfq market in fixed income. What is the internal order book tracking at a bank? Customers dont place limit orders or do they? There arent any other market makers on your ...
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Principal Component Analysis and Yield Curves

I've been tasked with researching trading strategies relating PCA to trading fixed income futures instruments. Apparently PCA is frequently used in this area. I'm just looking for some references for ...
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211 views

What is the best way to interpret changes in Treasury yields?

My question is quick and simple. However, I would like to use this answer to further my understanding of bonds and yields. If the YTM on a 10yr Note yesterday was 1.00% and the YTM on the same 10yr ...
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1answer
318 views

Forward bond yield with QuantLib

I'm looking into way to calculate forward bond yield using QuantLib. In Python QuantLib book I see an example for bond futures, where ...
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3k views

Carry and Rolldown of a Premium bond

I'm hoping that you may help me understand how the pull to par of a premium bond impacts the carry and roll calculations over a year. I understand that carry = Coupon income - cost of funds and that ...
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3answers
116 views

Why bond (individual or their benchmark index) graphs predominantly display yield rather than price?

Yield graphs seem to be predominant. This is in contrast to price graphs in equity based products. I can work out the price if I know the face value, but still -- would imagine for consistency ...
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203 views

Why aren't option pricing models more frequently used to value risky cash flows?

One way to think of the value of a risky firm is through expected measure theory. On the most basic level, the value of any asset is the convolution of the probability density function of its risky ...
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270 views

How do dealers price benchmark treasury bonds?

My understanding is that in practice, off the run treasury bonds are priced using a spread to the on the run bonds. How then are the on the run bonds priced - e.g. 5 year treasury? If a discounting ...
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24k views

how to calculate a cross-currency swap in basis pt?

This question has been bugging me for awhile now and I've been trying to find a definite answer, however, no avail... My question, in specific, relates to the USD/CNH CCS rate. From what I understand ...
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1answer
536 views

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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Convention for computing returns on bond futures

From the CME website, we know that the contract unit for bond futures is "face value at maturity of $100,000". Which of the following is more appropriate the convention to compute "...
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1answer
841 views

Hedging a trade for PCA component neutrality

Suppose I am given a set of financial instruments, e.g. {1Y, 2Y, ..., 30Y} interest rate swaps or {Barclays, Lloyds, .. } FTSE100 companies. It doesn't matter which so let's go with IRS. I have ...
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2answers
303 views

Carry vs Roll-Down on a zero-coupon IRS

I am trying to understand the differences between carry vs roll-down on a zero-coupon interest rate swap. Lets say we have a 10 day ZC IRS, meaning we will only swap once on maturity. We are a payer ...
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1answer
333 views

If 10s20s steepener have equal DV01 weighting on each swap then why does convexity play a role in MtM

Receiver Swap 10yrs Notional: 1,000,000 DV01: +1,300 Tenor: 10yrs Rate: 4% Payer Swap 20yrs Notional: 500,000 DV01: -1,300 Tenor: 20yrs Rate: 5% Looking at this fictitious example, I want to ...
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1answer
413 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 ...
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2k views

Measuring bond fair value (richness/cheapness) using basic regression models?

Background Due to the nature of the curve (bond curve, swap curve etc), bond traders typically have some model that allows them to measure the "fair value" (FV) of a bond vs other bonds on the curve. ...
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1answer
504 views

discrepancy in calculating 30/360 day count

I'm trying to calculate 30/360 (US) date differences, but I'm confused by the differences between calculating dates in one order vs the other. When I calculated the difference between date1=2/29/2016 ...
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1answer
1k views

Automatic fixing of missing floating rate in QuantLib's addFixing()

Due to the periodic fixing of floating rate bonds's coupon rates, in order to calculate the bond clean price one must tell the pricing engine to account for previous LIBOR rate fixing. If I am right (...
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4k views

CTD and bond futures

I am reading a chapter on bond futures in Fabozzi's book. It states that without CF (conversion factor) the CTD (cheapest to deliver) would be the bond with the longest maturity and highest coupon. ...
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3answers
2k views

What is the clean price and dirty price of a risky bond?

Following up on this question: Yield of a risky bond, what is the definition of clean and dirty prices for a risky (defaultable, catastrophe, etc.) bond? I would think the dirty price should ...
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1answer
274 views

zero-coupon bond and forward rate

My understanding, in a discrete-time setting, the relationship between a zero-coupon bond price and forward rates is: $$p(t,T)=\frac{1}{\Pi_{j=1}^{T-1}f(t,j)}.$$ where $p(t,T)$ represents the price ...
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2answers
862 views

Misunderstanding of 'day counts' and accrued interest

I'm totally new to the fixed income world. My goal with this question is to gain an understanding how interest is accrued day-by-day for a particular instrument. This will obviously be done by an app ...
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3answers
390 views

Systematic credit "liquidity provider" strategy

I was reading a piece published by Bloomberg today, where it says the following: “A systematic process lends itself to providing liquidity rather than taking it because our models have views on ...
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1answer
314 views

Funding Treasury net basis trades and balance sheet

I am trying to extend my understanding of Treasury futures net basis trading by understanding the funding markets. If net basis is cheap, an investor can buy the basis. This means that the investor ...
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2answers
190 views

Standardized numerical values for ratings

Is there a standardized way of transforming the ratings of any of the major ratings agencies (S&P, Moody's, Fitch) to a numerical value. Ideally, it might be possible to create a similar scale for ...
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647 views

Reconstruct yield curve from principal components

I am currently building a model which aim is to model shocks to the yield curve (i.e. 25bps hike in the short rate). Currently I am looking at a swap curve from which I derive the PCs. Assessing the ...

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