How to calculate the duration and the volatility of a bond - YouTube

hello everyone uh this is uh professor xun bian  in this video tutorial I want to show you how  

to calculate the duration and the volatility of a  bond if you have to use the tiba 2 plus financial  

calculator to run the calculation so before  we jump into the calculation the first thing  

i want to say is that if you have a tiba 2 plus  professional you should not be watching this video  

because there is a much easier way that's going to  allow you to handle the calculation automatically  

but unfortunately if you have to use the tiba  2 plus right so you should actually be able to  

use the method that i will be discussing here  to do on the calculation so the question that  

i want to go over here to demonstrate you  how to run the calculations is this one here  

we ask the question what is the duration and the  volatility of a four-year bond with a coupon rate  

of two percent and a yield to maturity of three  percent so before we run the calculation the  

first thing that i want to do here is to make sure  the cash flow is clear to everyone we're talking  

about four year bond we're assuming the bonds  are making annual coupon payment so this is why  

for the first year you're getting two percent of  the face value whatever the face value might be  

in the second year you're getting another two  percent of the face value paid to you as the  

coupon payment so on and so forth and in the last  year this is the time of maturity you're getting  

paid the last coupon payment of two percent of the  face value plus you're also getting paid the face  

value at the time of maturity this is why at the  end at the time of maturity you'll be receiving  

102 of the face value as you can see here i'm  using the percentage of the face value as the  

unit right so um and also later when you actually  use the worksheet that is the basically the unit  

that i use of course you can also choose to use  the you know the dollar number right if you want  

to use that that's fine which is going to give  you the same answer but the advantage of using the  

percentage of the face value as the unit is you  don't actually have to know what the face value is  

so hopefully the cash flow is clear to everyone so  my suggestion to you is if you have to calculate  

the duration and the volatility right without  the automatic function to calculate that i think  

the best way is to use a worksheet like this in  this case you have five columns right to complete  

the first column here because we're talking about  a four year bond i'm simply creating a time index  

it runs all the way from year one to year four  right because we have a four year bond and then  

what i want to do in the second column here is  to list the cash flow you have two percent in  

the first year two percent in the second year  two percent in year three and then last but  

not least you have 102 paid to you at the  end of year four that is consisted of the  

two percent coupon payment and then also the  the the face value returned to you at the end  

of maturity so no calculation so far just you know  trying to summarize all the information and then  

what we want to do here in column number three is  using our financial calculator we will one by one  

calculate what is the present value of each  individual cash flow so for example for this blank  

box here we're trying to calculate what is the  present value of the first two percent coupon that  

you're getting at the end of the first year so  let me bring in my financial calculator here the  

first thing obviously you want to do is you want  to clear the memory of your financial calculator  

before you jump into any new calculation so  what you want to do is you want to do second  

reset and enter right so that clears up everything  and then the other thing that i would also suggest  

you do is because when you're doing the volatility  and you know the the the duration calculation very  

often you're dealing with very small numbers to  have enough precision what you want to do is you  

want to carry at least four decimal numbers  you can actually change uh the setting of  

your financial calculator to accomplish that so  what you do is you can do second and a format  

right now you see the default value is two  which means that the calculator allows you  

to see only two decimal numbers but we want to see  at least a four so what i can do here is i can do  

four and enter right so immediately you see now  you can see four decimal numbers so after that  

what you want to do you want to do second and quit  right so now you can start your calculation like  

i said for the first the cell here what i want  to do is i want to calculate the present value  

of the first two percent that i receive at the end  of the first year this is a very straightforward  

uh present value calculation for a single lump  sum so to calculate that what i want to do is i  

simply want to put in 1 for n right and i have  you know a yield to maturity of 3 i'm going to  

use that as my discount rate 3 for iy we're trying  to calculate the present value but we're receiving  

you know two percent uh at the end of the first  year so two for fv then we can go ahead and  

calculate the present value so we don't need the  negative sign we just put in 1.9417 in this box  

right here all right so this is basically how  uh the entire column is calculated i just did  

that for the first one let's also you know do that  for the second one again we're trying to calculate  

what is the present value of your second year cash  flow again this is two percent of the coupon this  

is your two percent coupon right so in this case  i actually don't have to rerun the calculation  

right if you compare the first calculation which  you just did and the second one right um all you  

really have to do is to replace your end because  again you're getting two percent coupon payment so  

all you really have to do is to change from one  to two so i'm gonna do that i'm gonna use two  

for n and then go ahead and recalculate my present  value so this is how you get your second number so  

you one by one you fill this um you know column  here right by calculating the present value of  

each individual cash flow so let's do that for  year three and year four again for year three  

you're still getting two percent the eot maturity  is still three percent we don't have to change  

that the only thing that we have to change is we  want to use three for my n and then i can go ahead  

and calculate the present value that's your third  number right and then last but not least right  

here we actually have to make two modifications  because you're talking about year four and you're  

also talking about 102 percent of the face value  because at the end you're getting both the coupon  

payment and also the face value returned  to you so in this case i'm going to use  

four from my end but i'm going to use 102 for  my future value then i'm going to go ahead and  

calculate the present value so this is your last  number here all right so hopefully that's clear to  

everyone and then what you do is you add up those  four numbers that you just calculated together  

that should be pretty straightforward for  everyone too i'm not going to show you that  

but if you add up you know 1.9417 1.8852  1.8303 and the last number here you should get

96.2829 all right and then what do you do after  that is for each individual present value that you  

just calculated you want to take that number  and divide that by the total present value  

so essentially what we're doing here in column  number four is we try to calculate what's the  

percentage of present value you're getting back  each year as we all know duration volatility  

they're trying they're basically measuring how  quickly you're getting your money back so for the  

first one here what i want to do is i want to take  1.9417 divide that by the total present value here  

nine six point two eight two nine right so in the  first year um you know roughly speaking you're  

getting back about two percent of the present  value of this particular investment and then what  

you do is you do the same calculation for all  the other years for example for the second one  

you take 1.8852 divide that by 96.2829 and then  here you do the same thing here you do the same  

thing and that is basically how you get those  numbers all right and then at the end if you  

want to you don't actually have to do this but  i think it's a nice verification if you add up  

the four numbers that you calculated you should  get one all right so if you're not getting one  

and that's indication that you probably made  a mistake somewhere but uh you know those are  

basically just the individual present value  as a percentage of the total obviously you're  

supposed to get one at the end and then the last  thing that you do here right we have only one  

column left what you do is you want to multiply  column four by column one so whatever number  

that you have in column four multiply that  by column one so here you're taking point  

zero two zero 0.0202 multiplied by 1. obviously  that's going to give you 0.0202 and here you're  

taking .0196 multiply that by 2 right we can  actually do that using our financial calculator

.0196 multiply that by two right this is why you  have .0392 here then take this one multiply by  

three take this one multiply by four this  is how you get the other two numbers right  

that's what do i mean by column four times  column one and then at the end what do you do  

is again you add up the four numbers that you  calculated and you know sum them up and that's  

the total this is actually the duration of the  bond again like i said if you have the tiba  

uh two plus professional you don't actually  have to go through this uh you know uh  

process to calculate there is actually a function  in there too you know for you to calculate this  

thing automatically but unfortunately if you have  to do this by hand right uh like i just show you  

you can still do that right it does take a little  bit more time so uh going back here right so this  

is the summation this is basically your duration  right and then to go from duration to volatility  

what we do is we take the duration divide by one  plus yield to maturity the yield to maturity here  

is given to us as three percent so in this  case the volatility which is also called the  

modified duration by the way can be calculated as  three point eight eight divide that by one plus  

point zero seven and that is going to give you a  duration sorry it's going to give you a volatility  

of 3.77 so this is basically how do you calculate  you know the duration and the volatility if you  

have to use the ba the tiba 2 plus to run the  calculation so as always please let me know  

if you have any questions i'll be more than  happy to answer any questions that you have  

as always thanks for watching and i  will see you in another video tutorial