# Tag Info

• 14.9k

### Modified Duration and how it explains bond price sensitivity to changes in the yield to maturity

Bond price in terms of yield (denoted "$y$") is just the Present Value (PV) of the Bond coupons (denoted "$C$") and the final Notional (denoted $N$), discounted at the yield. ...
• 5,523

### 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?

It's a very good question. This is also mentioned in "Bond Math: the theory behind the formulas" - but the author doesn't get into a lot of details, he just mentions it as some kind of a ...

### 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?

Probably easier to see with the $Dur, which can be expressed as follows (assuming principal=1):${\rm Dur}=\frac{c}{y^2}\left(1-{\frac { yT+y+1}{ \left( 1+y \right)^{T+1} }}\right)+\frac{T} {\left( ...

### Is duration of a bond a convex function?

Recall that duration is defined as the average time to receive the cashflow, with the weights being the present values of the cashflows. So when interest rates rise very high, the long dated ...
• 15.2k
Accepted

### A question on immunization and Macaulay duration

Duration is not linear. It is the weighted average of the duration of the underlyings with the weightings being their values. To get a linear system multiply the durations by the associated pvs and ...
• 6,833

### Why is 'duration' not the same as 'spread duration' for risky bonds

Adding to the answer of Tim: If you consider a fixed-rate bond then IR-duration and spread-duration have the same effect on the bond. For a floating-rate bond, on the other side, you have IR-risk ...
• 13.4k
Accepted

This is an approximation (to first order) based on the idea that the option gives you access to the underlying, but with leverage. Let the duration of the underlying be $D_B$. The expression $\... • 9,212 4 votes ### US 10yr future and ED future The duration of a bond is the percentage change in the value of the bond for a 1% change in yield. For example, a 10Y bond with a duration of 8Y will lose approximately 8% for every 1% increase in ... • 5,718 4 votes ### Can you calculate modified duration for swaps? If you know how to calculate them for bonds, you know how to calculate them for swaps. Assuming you refer to fixed-income swaps where a party receives a fixed rate and pays a floating rate or vice ... • 153 4 votes Accepted ### Duration of a floating rate bond with spread Is formula (1) correct? Yes, follows from first definition - floater with deterministic spread is composed (sum) of two components: (1) pure floater and (2) deterministic coupon strip via contractual ... • 161 4 votes Accepted ### Is the risk the same for two different tenor bonds with the same DV01? To a first order of approximation,$dV=\frac{\partial V}{\partial r}dr$, and assuming normally distributed rate shifts,$dr\sim N(0,\sigma_r^2)$, then your risk is -- again to a first oder of ... • 6,175 3 votes ### Duration of a floating rate bond Yes. the duration of a floating rate bond is the time t until the next coupon payment, as your equation shows. The payments that come after are not known yet and will be determined based on interest ... • 9,212 3 votes Accepted ### Duration of perpetual bond You were on a right track. In the first approach you've shown Modified Duration of perpetuity is$ModDur=\frac{1}{r}$. In your second approach keep in mind that$ModDur=\frac{MacDur}{(1+y_k/k)}$so ... • 722 3 votes ### Macaulay Duration: Duration for 2 bonds Macaulay duration is simply a weighted average.$MacD(A,B)=\frac{V(A) \cdot MacD(A)+ V(B) \cdot MacD(B)}{V(A)+V(B)}$• 768 3 votes ### Interpretation of Macaulay Duration There are many ways to understand the Macaulay Duration, one of them is from "the interest rate risk" point of view. For a fixed coupon bond, there are two risks that is caused by the change ... • 187 3 votes Accepted ### Bond Portfolio Immunization - Duration Matching If I understand correctly the question, you wish to completely hedge the interest rate risk (defined as a parallel shift in the yield curve). If that is the case, you should use modified duration, ... • 520 3 votes ### To compute key rate duration, shall I use par curve or zero curve? You can do either. It depends on what you're trying to do and how you build your curve. If you're trying to match bond index duration, then shocking par curve is the way to go, because index providers,... • 11.1k 3 votes ### duration and modified duration Modified duration is the right concept to use to estimate change in price in response to an infinitesimal change in yield. It works very well for a small change in yield (say a few basis points). ... • 9,212 3 votes ### High convexity vs low convexity bond definition Do not forget the effect of passing time (the theta) on your portfolio. If two portfolios have the same value and duration, then the portfolio made up of the difference has locally zero sensitivity ... • 5,592 3 votes ### How should we calculate the duration of a convertible bond? Unfortunately, convertible bonds are quite complex so you don't have simple formulas or approaches as with vanilla bonds. However, this does not mean you are powerless. You can follow different ... 3 votes ### US 10yr future and ED future If your notional is 100mm, and you buy a 10Y treasury note worth 10mm (10% of 100mm) then you own 100 contracts (since each contract specification is officially a nominal of \$100,000), and the DV01 ...
• 8,217
You need Gamma to answer this question really. Gamma tells you how much your delta moves for a change in rates. Taking a 5y \$receiver swap with a DV01 of \$4333.60 on 10MM notional we get a Gamma ...