The fixed income securities world stands tall on the support of 2 pillars, the interest and the principle. While the principal is more of a dormant participant to the fury and the pleasure of the FIS, interest is the main actor. The same interest that is taught in the schools starting as what we call the simple interest and then compounding itself in to a compound interest.
I=PNR/100 the simple equation for SI, then comes
A=P(1+r/100)n for compound interest.
The n here denoting the frequency of compounding.
Here the variable r is the rate of interest for the period. Hence for a 10% pa bond paying half yearly the r would be 10/2 and the eqn would become
A=P(1+r%/n)^n
As the frequency of compounding becomes lesser and lesser the value of n increases, hence for a bond that is compounded instantaneously n-> infinity (∞).
Applying these limits to the above equation we get
A =P ltn->∞ (1+r/n)^n
A = P e^(rn) is the equation for comtinuous compounding
Equating the previous 2 eqns
e (rcn) = ltn->∞ (1+r/n)^n
(rc)= n ln (1+r/n)
Where rc is the rate of continuous compounding.
Hence comparison of 2 bonds of varying payment frequency is done by comparing the rc value which is a obviously a direct measure since the rates compared are the instantaneous compounding rates.
Never knew bond math could be so simple to calculate, but simple or not it is simply fascinating.
Hope my journey in to this fascinating field of bond math continues…
Monday, July 30, 2007
Sunday, July 29, 2007
Math again...
Mathematics.. one word that is fundamental to life, if I may say so, but peculiarly a rather long word for something this fundamental. A word that could havoc terror on me just by its mention with the noun wxam along with it, especially from 8 grade when I shifted to a new school in the heart of the city where 90% is below average. Inspite of all this I always felt math to be a wonderful subject and saw it more as a beautiful rich land that needs to be conquered, more like Steve Waugh's final frontier of winning a test sereis in India against India. It didnt help much that I had amazing skills of making my paper look like a make of WW II cryptic message communicated in numbers and graphs. Adding to the woes were the audacity that I had against the math teachers for that matter any teacher but for a 1 or 2. With such an attitude the teachers felt obligated not to help me much in math, this aggravated in the 11th and 12th grade where I enjoyed a great love hate relationship with the math teacher resulting in my scores resembling a tan Q graph in the second quadrant. It was a period when I was probably made of anti matter of Midas in maths. Everything I did went wrong. The rules of integration that were very logical and applicable made themselves illogical and not world acceptable certainly not for my classmates and especially the math teacher. Such phenomenal rendezvous with math ensured that I hate the class and the exam though deep down I wanted to love it, and make it my darling.
Then came what was called Engineering college where I am very confident that I managed to engineer absolutely nothing. As they call it, engineering was a perfect educational masturbation for me. Me being what I am did a wonderful job of masturbating for the whole 4 years learning pretty much little but for how to use the jargons and manage to score above 67% which ensured that I was considered as somewhere between above average to good student. What helped this best was the pale competition that I had overall, which helped me in being in the top 15 or 20 in the class. This Im sure would have been the average if not the below average in the grading restricted to the part of the class that masturbated on engineering since a section of the class appeared more interested in actual masturbation or alcohol or those innumerable things that life has to offer other than being serious in studies. Interestingly I managed to score tops in any practical exams, which on the retrospect I think should be attributed to my decent communication skills and ability to think and talk on my feet rather than do the hard work of digesting the concept and making a true research in it. This suited most since here was a guy who could talk something that bordered on making sense and could communicate it better, actually better than the questioner. This certainly not because of my superior knowledge of the particular field in engineering but more because of the superior English that 14 years of English medium education competing with the one of the groups of the best of the competitors in the city.
But math being more of a subject where one has to answer on a answer paper, I managed to score just above the border line. I guess the gods of algebra and calculus had and probably still have a strong vow of apathy towards me. I never managed to come out good in these two domains but geometry was fun and trig was generally a cake. Another perspective for this could be that I never tried taking on complex geometry or trigonometry.
In spite of such a long history of non performance and incompetence in maths the discipline has not ceased to amaze and lure me into conquering it. Just that recently the motivation to conquer it is so that I can master the complex looking calculations of the world of finance. With this high hope I have convinced a gentle man to help me out and take me through the complex looking puzzle of math that can be and is used in finance. Hope the gods are kind with me this time, hope I can put the demons of mathematics to rest this time. It should be a worthy wait to see the results.
Then came what was called Engineering college where I am very confident that I managed to engineer absolutely nothing. As they call it, engineering was a perfect educational masturbation for me. Me being what I am did a wonderful job of masturbating for the whole 4 years learning pretty much little but for how to use the jargons and manage to score above 67% which ensured that I was considered as somewhere between above average to good student. What helped this best was the pale competition that I had overall, which helped me in being in the top 15 or 20 in the class. This Im sure would have been the average if not the below average in the grading restricted to the part of the class that masturbated on engineering since a section of the class appeared more interested in actual masturbation or alcohol or those innumerable things that life has to offer other than being serious in studies. Interestingly I managed to score tops in any practical exams, which on the retrospect I think should be attributed to my decent communication skills and ability to think and talk on my feet rather than do the hard work of digesting the concept and making a true research in it. This suited most since here was a guy who could talk something that bordered on making sense and could communicate it better, actually better than the questioner. This certainly not because of my superior knowledge of the particular field in engineering but more because of the superior English that 14 years of English medium education competing with the one of the groups of the best of the competitors in the city.
But math being more of a subject where one has to answer on a answer paper, I managed to score just above the border line. I guess the gods of algebra and calculus had and probably still have a strong vow of apathy towards me. I never managed to come out good in these two domains but geometry was fun and trig was generally a cake. Another perspective for this could be that I never tried taking on complex geometry or trigonometry.
In spite of such a long history of non performance and incompetence in maths the discipline has not ceased to amaze and lure me into conquering it. Just that recently the motivation to conquer it is so that I can master the complex looking calculations of the world of finance. With this high hope I have convinced a gentle man to help me out and take me through the complex looking puzzle of math that can be and is used in finance. Hope the gods are kind with me this time, hope I can put the demons of mathematics to rest this time. It should be a worthy wait to see the results.
Saturday, June 9, 2007
Oops you earn too much.
Among the best things that can happen thru chain mails is that once in a blue moon you one can get a pearl or an absolute diamond... listed below is my recollection of 1 such mail, which sounded better in the original chain.
An economics professor explaining the concept of taxation and tax breaks to the poor to his rapt attentive class....
9 men used to meet at a specific pub every day for their group beer session, of the nine 2 were in the rich category, 3 in the middle income category and 4 in the poor category. Considering their differences in income they decided to split the bill of $ 9 thus. the rich 2 pay $ 3 each and the middle 3 pay $ 1 each. The poor 4 being poor were allowed the luxury of having their drink free. This seen as a fair arrangement continued for quite some time. Considering that the 9 were his long time customers the pub decides to provide them with a discount of 10% on their beer. This 10 % was split based on the contribution of the individual, resulting in a 30p discount per rich guy and a 10p discount per middle income guy. based on the new arrangement, the poor felt cheated that they didnt gain anything from the discount, the middle felt that their discount was far less than the rich 3's. The middle and the poor hence accused the rich of cornering all the benefits and beat them up and the rich 3 didnt turn for drink the next day. The next day the pub wouldn't allow the remaining 6 to enter since they couldnt pay for the drinks.
This is the probably one of the best description of taxation and tax breaks system. There is a limit that a government can impose tax on the tax payers. After a threshold it is inevitable that the tax payers simply run away, then wonder who will be paying the tax.
One of the first things that came to my mind on hearing PM Dr.MS comment on CEO earnings was the above story. How many times have we heard the story of killing the golden hen laying goose. But nope the story is relevant only for the 4-8 year old kids with the adult politicians however educated and smart they be, refuse to go by that.
Today the CEOs are earning much hence make them cut their salaries, get brownie points of being an Aam Aadmi guy but then tomorrow not many would prefer to be CEOs in the country. Then what, run a Vodafone or Airtel or Tata Group with Aam aadmis? or even better sarkari bureaucrats? The former I dont thing will be an option in the wildest of imaginations of the aam aadmi himself and the latter, well the infamous hindu rate of growth stands testimony to the approach.
Interestingly if you keep slashing everyone's salary but the fraternity of politicians and the allied to bring about an equality, then who will fund the country's bill? do we print rupee notes to fund our deficits? All this will portend to the '91 pawing of our gold assets to BoE which would be 1 backward step for the government and a giant leap backward in terms of progress for India.
Also by then the aam aadmi would be completely empowered since there would be ne one else left.
A better way to decrease the inequality would be if the govt cuts on its bureaucratic spending and use the savings for better infrastructure and social support systems. But then that wouldnt win yo political votes would it, hence what a stupid thing to say from me. huh.
An economics professor explaining the concept of taxation and tax breaks to the poor to his rapt attentive class....
9 men used to meet at a specific pub every day for their group beer session, of the nine 2 were in the rich category, 3 in the middle income category and 4 in the poor category. Considering their differences in income they decided to split the bill of $ 9 thus. the rich 2 pay $ 3 each and the middle 3 pay $ 1 each. The poor 4 being poor were allowed the luxury of having their drink free. This seen as a fair arrangement continued for quite some time. Considering that the 9 were his long time customers the pub decides to provide them with a discount of 10% on their beer. This 10 % was split based on the contribution of the individual, resulting in a 30p discount per rich guy and a 10p discount per middle income guy. based on the new arrangement, the poor felt cheated that they didnt gain anything from the discount, the middle felt that their discount was far less than the rich 3's. The middle and the poor hence accused the rich of cornering all the benefits and beat them up and the rich 3 didnt turn for drink the next day. The next day the pub wouldn't allow the remaining 6 to enter since they couldnt pay for the drinks.
This is the probably one of the best description of taxation and tax breaks system. There is a limit that a government can impose tax on the tax payers. After a threshold it is inevitable that the tax payers simply run away, then wonder who will be paying the tax.
One of the first things that came to my mind on hearing PM Dr.MS comment on CEO earnings was the above story. How many times have we heard the story of killing the golden hen laying goose. But nope the story is relevant only for the 4-8 year old kids with the adult politicians however educated and smart they be, refuse to go by that.
Today the CEOs are earning much hence make them cut their salaries, get brownie points of being an Aam Aadmi guy but then tomorrow not many would prefer to be CEOs in the country. Then what, run a Vodafone or Airtel or Tata Group with Aam aadmis? or even better sarkari bureaucrats? The former I dont thing will be an option in the wildest of imaginations of the aam aadmi himself and the latter, well the infamous hindu rate of growth stands testimony to the approach.
Interestingly if you keep slashing everyone's salary but the fraternity of politicians and the allied to bring about an equality, then who will fund the country's bill? do we print rupee notes to fund our deficits? All this will portend to the '91 pawing of our gold assets to BoE which would be 1 backward step for the government and a giant leap backward in terms of progress for India.
Also by then the aam aadmi would be completely empowered since there would be ne one else left.
A better way to decrease the inequality would be if the govt cuts on its bureaucratic spending and use the savings for better infrastructure and social support systems. But then that wouldnt win yo political votes would it, hence what a stupid thing to say from me. huh.
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