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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1answer
121 views

Data on Options on US-Treasury Futes

I am working on an assignment on the Implied Volatility Surface for the options on US-Treasury futures (ZB, ZN, ZF, etc.). I need data on bid and ask, Imp. Vol, Price of underlying etc. Do you know a ...
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59 views

Calculating a firm's cost of debt using bond issues

When a firm issues coupon bonds that are traded on the open market these bonds can trade at either a premium or discount during the lifetime of the bond. If, for instance, the bond trades at a ...
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233 views

Need a way to calculate YTM for a bond with a step-up coupon? Thank you!

Would be grateful if someone could guide me on how to calculate a YTM for a step-up coupon.
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42 views

compute r(t) in Vasiceck model, what is $e^{at}r$

I know how to solve the exercise using the hint. But I do not understand where the hint is coming from. Is it just continous compounding? Can anybody explain $f(t,r) = e^{at}r$? What does it stand ...
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Are 3 month t-bill rates in FRED annualized?

Are the 3 month t-bill rates documented by FRED here annualized? For example, the rate for January 1997 is 5.03%. Does that mean one would get a 5.03% return in 3 months, or is that an annualized rate?...
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132 views

Interest rate risk. Books recommendation

Can anyone suggest me some good books for Interest Rate risk and Credit Spread, credit spread duration? I am new to finance so a book focussed on basics will be more helpful. Thanks
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80 views

yield concept for a short maturity zero coupon bond

I am trying to clarify what is the more relevant and appropriate quantity for a discount security / zero-coupon bond, that is defined by a face value, FV, a present value, PV and a time to maturity, t,...
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1answer
161 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 ...
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1answer
414 views

Replication of risky callable bonds

I have the following problem regarding callable bond replication. Let's define: A: 7Y Callable bond with fix coupon K%, which is callable exactly in 2Y @par (European feature) B: 2Y x 5Y Receiver ...
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149 views

Is it possible to use the YIELD() function in Excel to compute the yield of an Italian government bond?

I'm interested in using the YIELD() function in Excel to compute the yield of an Italian government bond. The bond in question is: 0.750% 15-January-2018 Italian government bonds have special ...
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86 views

volatility adjustment on momentum

I am trying to figure out what this text means any advice is greatly appreciated. "volatility-adjusted crossover signal where momentum is measured by comparing a short-horizon (45 days) moving ...
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1answer
81 views

Proxying historical bond futures duration

I am trying to come up with a very simple/approximate way of filling up historical bond futures duration. The proposal I have is - lets say for Mar 17 FV contract, I pick up the on-the-run for that ...
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2answers
128 views

I need liquidity metrics of a portfolio (2-5 bonds) that takes into consideration difference in size of bonds and maturity profile

Context: I have bond A from say Apple, Apple also issued different types of bonds , namely B , C, D, E bonds. Bonds A B C D E are all same, except, they were issued at different times, have ...
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153 views

The ambiguity of the term “duration”

This is a soft question about terminology. Let B be a bond with coupon payments. There seem to be two uses of the word duration in finance: Sensitivity of B's log price to B's continuously ...
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92 views

Bond Fair Value

Im trying to learn bond valuations and working out problems I find online, but I come up with the wrong answer for this one. Im buying a four year coupon bond for 963.54. The coupon is 5.172% paid ...
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1answer
36 views

Why would borrowing rates for repurchase agreements be negative

I was reading this article about repurchase agreements. I don't understand this graph: And this paragraph: Borrowing rates using German and French government bonds as collateral fell to minus 4.9% ...
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2answers
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How to calculate FX hedged bond yield?

How does one go about calculating a 10 year US treasury yield hedged back to EUR? I vaguely understand this but I think there's two methods 1) Calculate 3-month annualized hedging cost 2) Calculate ...
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98 views

Deriving the Forward Rate Formula from the Expectation Hypothesis

The Expectation Hypothesis (EH) states that the current spot yield for any of the maturities is the geometric average of current and future short rates. $$\Big(1 + y(t=0, m=\mu) \Big)^{\mu} = \prod_{t=...
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56 views

Interest rate model with external variables

There are several well-known one-factor interest rate models: Hull-White, Ho-Lee and Black-Derman-Toy just to name a few. There are also multi-factor models such as Longstaff-Schwartz and Chen. But ...
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73 views

Why do Fama French's “Common risk factors in the returns on stocks and bonds” use data starting in 1963? Availability or convenience for results?

What is the reason Fama French's "Common risk factors in the returns on stocks and bonds" use data starting in 1963? Was it availability or convenience for results?
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305 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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1answer
110 views

Is it possible to sell protection on own asset with CDS?

Is it possible for a company to sell protection on their own assets or own country bonds by CDS? The company can buy protection on those assets, but how about selling? I suppose it can not sell. Is ...
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533 views

Question about using binomial interest rate tree to value callable bonds

When we use a binomial interest rate tree to value callable bond, we work backward, right? If any computed bond value is larger than the call price, the bond will be called. The call price will ...
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1answer
678 views

Derivation of convexity formula

Let's say that I have a bond that pays coupon on a semi-annual basis. Therefore, the price of this bond can be calculated using the following formula: $$ P = \sum_{i=1}^N \frac{CF_i}{(1 + YTM/2)^{...
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179 views

Sovereign bond CDS data

Does anyone know where I can download from historical data for sovereign bond CDS (credit default swaps) rates? preferebly free?
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How do traders determine when points in a yield curve are at 'fair value'?

While on my last day on an internship last summer, I heard on the morning call a UK rates trader say something along the lines of: "Most of the curve is at fair value at the moment, so nothing ...
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53 views

Returns on actively trading bonds compared to equity?

Long term equities outperform bonds (equity premium puzzle). However this kind of misses the nature of returns: in equity it is mostly the total return from "the principal" (and a little from ...
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1answer
71 views

$R^{2}$ Measure for Functions (Yield Curves)

I am used to applying $R^{2}$ (relative explained variance) as a measure for point estimates. I am now confronted with forecasting the whole of the yield curve and would like to see what fraction of ...
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125 views

How are short rate models used to construct the whole of the yield curve? [closed]

There are a number of short rate models that give $r(t)$. How can those be used to construct the whole of the yield curve $y(t,T)$ (where $y(t, 0) = r(t)$)?
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1answer
102 views

Calculating expected loss using actual probabilities

I'm calculating expected loss on fixed-income using actual default probabilities and risk-free rate as the discount factor. I understand this is not theoretically correct. In absence of risk-neutral ...
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1answer
131 views

Anyone have good literature on buying bullet vs barbell returns?

I am trying to understand the concept, weighting schemes, real\$ vs fast\$ view, etc... On the desk today, I used some third party tool to run analysis on some trade ideas but I'm blindly running ...
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1answer
179 views

Convexity for historical bond data

I'm trying to write a program to calculate the convexity of a bond. The bigger idea is, that if I have access to the actual price for each point in time, I should be able to calculate various features ...
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0answers
379 views

Definition of carry [closed]

Trying to understand this answer here, but having difficulty. Would appreciate it if someone formally, mathematically wrote down the precise definitions here. https://quant.stackexchange.com/a/25330 ...
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43 views

Is return required by a bond investor a function of base interest rate and credit worthiness of the issuer?

The price of a non-zero coupon bond (with dicrete discounting) is found using $$B = \frac{C}{r}\Bigg(1-\frac{1}{(1+r)^n}\Bigg) + \frac{P}{(1+r)^{n}}$$ or for a continuously dicounted version: $$B = C\...
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1answer
343 views

Using PCA model to capture Risk on a box trade on Swap spread

I have PCA models to capture Risk for Swaps trading I have a question regarding a multi-leg package which has 4 legs (box spread). Typically, a box spread is a switch between two Swap Spread, where ...
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3k views

Pricing a fixed rate bond in Quantlib Python

I'm trying to implement a pricing model for fixed rate bonds with the code below. ...
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4answers
3k views

What are some of the best textbooks on Fixed Income securities?

I'm looking for something that might be considered the 'Bible' of fixed income. Ideally it would contain everything from the basics of PV and discounting cash flows all the way up to some of the most ...
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122 views

What's a covered bond?

I'm reading both the wikipedia page and investopedia page about covered bonds, and I'm not sure I understand its definition. From what I could tell a covered bond it's a 'lump' of other loans put ...
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3answers
109 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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2answers
125 views

Choosing a proxy for asset credit event correlations

I'm interested in modeling the joint likelihood for rating changes and default events across a portfolio of bonds. To estimate the correlation between these assets, I can use a third-party factor ...
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53 views

Adjust a bond for PIK option

Is there any literature that discusses adjusting a bond for various PIK (Pay-in-Kind) options? I'm trying to benchmark a loan with a PIK option with non-PIK bonds. Edit: The loan has a payment in ...
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235 views

Negative correlation between interest rates and credit spreads - Why?

In fixed income markets a stylized fact seems to be that there is a negative correlation between interest rates and credit spreads: Spreads tend to widen as rates fall. Why is that?
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Valuation of Fixed-Income Securities [closed]

Could one of you please assist with question 4 shown in the image above? Thank you in advance! JR
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135 views

What is the “maturity” of an “investment option”?

i am reading an article regarding convertible bonds and it keeps saying: ......firms facing investment options that are expected to mature shortly after issuance....... OR .......firms with ...
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How to compare the value of bank Certificates of Deposit (CDs) with brokered CDs?

I am interested in comparing the value of bank Certificates of Deposit (CDs) with brokered CDs, to determine whether one is undervalued relative to the other. A brokered CD is basically a vanilla bond ...
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1answer
2k views

Question on pure carry for two bonds

If two bonds have yield of 5% and 2% and assume there's no price change, can we say that the carry is simply 5%-2% = 3% for a year. Does this take into account coupons? Equivalently, let's say the ...
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509 views

Riding the Yield Curve

Can someone explain how/why bond prices have not changed at t=1. I would expect that even though the curve is not changing, the price at t=1 would not be same at it was at t=0? Shouldn’t new prices ...
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68 views

How do you quantify the impact on bond if it becomes special?

If the bond is trading at 5% and it becomes special, how do you quantify the impact this has on the bond? Or am I misunderstanding the concept of specialness?
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360 views

How do bond traders get all the different moving parts?

I've been working with this trader and every time he explains something to me, it sound like foreign language. There's so many things going on. I'm a graduate analyst on the bond trading desk and I ...
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734 views

Treasury Bill and Treasury Bond : Quoted Price VS Cash Price VS Value of Bond

I have confused by three concepts and following is my understanding: Quoted Price and Cash price are totally different things ...