# Tagged Questions

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### Modified or Macauley Duration in python

are there any existing python modules that can calculate Modified and/or Macauley Duration of a bond.
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### 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 ...
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### Duration calculation for perpetuity with continuous compounding

Let's say we have a continuously compounded perpetuity. Does macaulay duration = modified duration? I've read from wikipedia for Bond Duration that macaulay duration = modified duration for ...
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### 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 ...
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### Why is the duration of a bond important?

I know what duration measures, but now in the age of computers why is it useful? If the yield changes, we could just simply plug the new yield into a program, or excel or something like that, and ...
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### Bond Portfolio Immunization - Duration Matching

**Question is at the bottom** Suppose you have a portfolio of bonds A, B, and C with the following characteristics: (the "Frequency" column is the # of coupon pmts per year and also the # of ...
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### 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 ...
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### If we modify duration, should we modify bond price? Options Futures and Other Derivatives

In Example 4.5 of Section 4.8 on Duration of Options, Futures and Other Derivatives (p.92), a bond's price and duration are computed assuming continuous compounding where the bond yield is y = 12%. ...
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### Can the duration of a bond be greater than Time to Maturity

In the case of a vanilla bond I know that the duration will be less than the time to maturity. But I am observing that for a non-vanilla bond, the duration is greater than time to maturity. Can ...
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### How do bond futures affect effective rate when used to hedge a bond's duration?

I'm trying to wrap my head around what happens to the net interest received when an invester goes short a bond future to fully hedge the duration of his long position in an actual bond. Does it ...
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### Bond duration as estimation to holding return

I am really struggling to prove to myself that when we can estimate the one-year holding period return for a three-year zero by using the following estimation: S3 - Duration2*(f1,3- S3) Where Sn is ...
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### Is duration really inversely related to the maturity time length of a bond?

It is always said that longer bonds are more sensitive to interest rates. Intuitively this makes perfect sense, since longer bonds have a larger portion of its cash flow being subjected to stronger ...
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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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### 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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### Can duration gap analysis be applied to mortgages?

Can a mortgage loan be treated like a bond and its duration calculated using the bond duration formula? More precisely, can I calculate the loan portfolio duration for duration gap analysis, with ...
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### What are the limits of bond portfolio immunization against interest rate changes?

I'm currently reading through an article on bond portfolio immunization against changes in the interest rate. I learned that the immunization can be done against instant changes in interest rate ...
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### Is Duration really the slope of the Price-Yield curve?

When looking at the Price-vs-Yield graph for a fixed rate instrument, we are often told that the duration is the slope of that curve. But is that really right? Duration is (change in price) divided ...
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### Can one use options on Treasury futures to hedge a portfolio?

Can one use options on Treasury bond futures to hedge a typical fixed income portfolio? If so, how can one estimate the duration for an option on a Treasury futures contract, and taking this a step ...
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### What is the basis risk between cash and futures government bonds?

I am currently working in a team responsible for maintaining a simple risk application for our bond desk and I am interested in knowing how to provide some sort of basic basis risk metric. Our desk ...
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### Closed-form formula for approximate maximum duration of a bond?

In teaching myself about bonds, I am writing some software, one piece of which will calculate the maturity of a bond given the yield curve as a function and a requested duration. The tricky part is ...
### Is duration additive? $C_{newDur}=A_{fundDur}w_{a} + B_{fundDur}w_{b}$?
Suppose quantified duration (like Macaulay duration with changing intervals) $Dur = \frac{\sum t_{i} PV_{i}}{\sum PV_{i}}$ and two funds having durations $D_{a}$ and $D_{b}$. You own them in the ...