This is sometimes called a simple finance approach.

Now, the thing is that the analysis of fixed income

securities is actually a vast area, and that in

detail goes fundamentally beyond the scope of this course and this specialization.

And this is a long and complex piece, but

now I'm just showing some of the important things that are studied there.

So here you can see all cash flows are mispriced and

there is one idea that is very important here is that if,

these rs change,

what happens to the value of the bond?

Let's say if all rs, they change by 1%, by a small percent each points, you can

see that all cash flows their discounted, their present values are changed.

And therefore, so is the value of the bond.

And what people do they basically take some

point of this interest rate and then going around this we study

the small changes of the value of the bond with respect to changes in this r.

Basically as in math, we can always expand that into serious and

there are some approximations to that.

And one idea is the idea of duration, well,

duration is sort of, double quoted, effective maturity.

So basically, the idea is as follows what if we put all cash flows of the bond,

at one point.

So as the PV of newly created security where all coupons and

the principal, they come at this point, we discount that

at the rate that is observed at this point, and then the PV is the same.

So that is called duration.

So the idea is if we put a chart here, again,

this is T, and this is a term structure.

So we basically put all of them at one point.

This is a point D so that the distribution is like delta function.

And all cash flows they just come here, sort of artificially.

Now, you can say, well, it's kind of a strange way to do that.

Well, this is basically an explanation, because the formula for

the duration is like this.

D is = to the sum from i = 1 fto T- 1.

PV(C1) divided by the P times i, so this is the term.

And the final number here is PV(CT + F) times T and divided by P.