Financial Risk Manager

Zero Rate from Zero Coupon Bonds 10 Year

2009-09-04T06:10:31-08:00

Hi David,
Could you please throw some light, how to go about in the below Question?

A 10-year, 8% coupon bond currently sells for $90. A 10-year, 4% coupon bond currently sells for $80. What is the 10-year zero rate?
Choose one answer.
a. 7.3%
b. 6.4%
c. 5.7%
d. 3.57%

Thanks
Rahul

How did they solve for duration in this question? GARP paractice Exam

2009-10-19T09:13:18-08:00

Hi David,

This question is from GARP Practice Exam 2, 2006 (Question 61)

How do they find the Duration input of the 6% coupon bond?, in the following question:

What is the best estimate of the market value of a portfolio of USD 100 Million invested in recently issued 6% 10 year bonds and USD 100 million of long 10 year zero coupon bond if intrest rates decline by 0.50%?

a) USD 219 million
b) USD 195 million
c) USD 209 million
d) USD 206 million

The solution says:

ANSWER C

To calculate the best estimate of the market value of the portfolio if interest rates decline 0.5%, one needs to calculate the change in the market value of each bond using duration. The duration of the 10 yr zero coupon bond is 10.Thus, the change in the value of this bond equals 10x0.005x100,000,000 which equals 5 million.

The duration of the newly issued 6% bond is 7.802 assuming that the price of the bond is par. Given a duration of 7.802 assuming that the price of the bond is par.

Given a duration of 7.802 the change in the value of the bond equals 7.802x0.005x100000000=3.91million.

I understand there rational of assuming that the bond is at par because it is recently issued. However, I STILL DONT SEE HOW THEY SOLVE THE DURATION TO BE 7.802 FROM THAT ONE ASSUMPTION!!

*I have looked at all the duration formulas and I can not make the connection!

Secondly, not as important- but why cant one solve for portfolio duration and then work out the Market value estimate?

David Please help I am sure I am not the only one who would like to know the answer for this.

Thanks!

DavidM

on-year zero rate???

2010-02-21T04:27:01-08:00

Hello
please can you help me
because there is quite a difficult task for me

zero-coupon government bonds with maturities ranging 1-5 years now have the following yields: 6%, 7%, 8%, 8,5%, 10,5%. using the expectations theory of the term structure what will you say the market expects the on-year zero rate to be one year from now???

Thanks in advance

Eurodollar and Fed Funds Futures

2010-02-08T21:36:33-08:00

Can anyone help me solve this question….

As of February 5, 2002, two Treasury bonds were priced as follows:
Coupon Maturity TED Spread DV01
3.625 8/31/2003 31.1 1.53
4.500 11/15/2003 35.7 1.75
Qualitatively describe a spread of spreads trade suggested by these
numbers. How much would a trade involving $100,000,000 of the
4.5s of November 15, 2003, make if the TED spread of the two
bonds immediately equalized?

mahen

A quick Q: DIV01 Hedging of a written call option using a long bond

2009-11-17T09:49:01-08:00

A quick question on the example presented in Tuckman page 95-98.

It appears the DIV01 hedge is being created based on the face value of the bond. But the definition of DIV01 is dollar change in price given 1 bp shift in rates. Should the text be using Price instead of the face value in the calculations (eg. Price * Div01)? Or the FV is being used instead of the price as yield chosen is the same as coupon rate and hence FV = Price. I am a bit confused by the usage of Face Value in DIV01 formula.

Please help.

key rate shft

2009-11-16T09:48:47-08:00

David,

In the key rates example (5.b.3) it appears that when the 2 year key rate is shifted it affects only the rates above it up to 5 years…shouldn’t it also affect the rates below it i.e from .5 years to 2 years?

Very quick Clarification Needed on bond duration formula

2009-11-16T02:04:54-08:00

Dear David,
For modified duration = duration/(1+yield) , does it also apply to non-annually paying bond as well?
Or should I use modified duration = duration/(1+yield/k) where k is the number of coupon payment per year?

Thanks

Liming
16/11/09

Confusion over your answer to P&L impacts ranking for a MBS

2009-11-15T06:12:50-08:00

Dear David,
I’ve had some confusion, misunderstanding and doubts when doing 09 Level I Annotated Boot Camp. Appreciate your kind help on this!

In sub question 8e under question 8 (see below), the P&L impacts are ranked for a MBS, with the duration approach having the highest impact and full re-pricing having the lowest impact. I’m just wondering if this is the case because I think what should always hold for MBS is that the duration approach will gives the highest price in the valuation and full re-pricing gives the lowest price in the valuation. What is not necessarily the case is the impact or the change in MBS valuation, considering that the impact refers to the absolute value of change in prices. For example, under duration approach, bond prices increases versus the old price; under full pricing, the prices decreases versus the old price, so the first price is higher than the latter but the absolute deviation from the initial price is yet to determine and compare.

8. Consider the following four methods for estimating the P&L of a bullet bond: Full-repricing, Duration (PV01),and Duration plus convexity. Third-order Taylor series approximation.
8a. [sample exam] Ranking the estimated P&L impact of a large negative yield shock from the lowest P&L impact to the highest P&L impact, what is the ranking of the methods to estimate the P&L impact?
8e. Replace the bullet bond with a mortgage-backed security (e.g., a pass through on a pool of 30-year mortgages), assume the initial yield is low, and then recast the rankings based on MBS.

Your Answer: 8e. Replace the bullet bond with a mortgage-backed security (e.g., a pass through on a pool of 30-year mortgages), assume the initial yield is low, and then recast the rankings (i.e., the ranking of estimated P&L impact based on large negative yield shock) based on MBS. The MBS will exhibit negative convexity at low yield (why?). Therefore the situation is reversed: Full re-pricing will have the lowest impact and duration (being the least accurate) will have the highest impact.

Thank you for your enlightenment and correction!
Cheers
Liming
16/11/09

Early Retirement of Zero-Coupon Bond

2009-11-10T23:54:39-08:00

Dear David,

Appreciate your helpful insight on the early retirement of zero-coupon bond. I’m wondering whether zero-coupon bond shall NEVER be possible to be called before its maturity but it can be put before its maturity day. And if this is correct, do we, in reality, sometimes see zero-coupon bonds issued with embedded put feature and never see zero-coupon bond with embedded call feature?
Thanks a lot!

Cheers
Liming

11/11/09

Wealth Transfer..

2008-08-10T21:00:33-08:00

Hi David

Am not clear intuitevely about how increase in leverage transfers wealth from nondholders to share holders?Please help me out ..

Anil