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.
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