Percentage Change in Price if Yield changes from 6 to 5 % ?

What is the percentage change in the price of each bond if its yield to maturity falls from 6%
to 5%?

P (A) to P(B)

Since Price and Yield are inversely proportional therefore:-

Zero Coupon Bond
1 + YTM =  (FV/P)^1/n

P (b) / P(a)   - 1  = { (1+r(a)  / (1+r(b)) }^n - 1
i.e

{1.06/1.05}^15 -1

-------------------------------------------x

Bid/Ask Scenario

Bid/Ask  explains everything sometimes authors are referring Bid as Buyers than that is from Perspective of Bank or Stock Exchange example.

If there are any errors please contribute and help me fix it. :)
That's all 

Are You stupid - check here! Why U need YTM or IRR ?

Why U need YTM or IRR ?  and please convert a investment to Coupons or vice versa

Talking about Yield of a Bond and IRR are same but IRR is usually calcuated on Bond simple one i guess and the Yield is used when there is a bond with constant payments like Annuinity or maybe pert..not sure

So lets take an example.

One imp. Point replace the values of initial investment with 900 and we will learn why not to use formulas and simplification rather process everything in end to be more accurate but it makes things confusing so start with 800

Suppose  interset is .11111  so u need to learn where are u loosing money and it will need a new post .
Simple Investment
800----------*------------*---------------*---------------*------------*----------*
                    1                  2                        3                       4                5                6

for 1yr -----820
            800*(1,0125)
---2 yr ----------------840,5
                          800*(1,0125)^2
----------------------------------------861,5
------------------------------------------------------883,05
-------------------------------------------------------------------905,126
---------------------------------------------------------------------------------927,75

Bond with Coupon conversion
800----------20-----------20---------------20--------------20----------20---------20
                     1                    2                        3                       4                5                6
-for 1 yr----820

-----2 yr ----20---------820 + 20*(1.025) = 840.5 - Present value of 20 that YOu got 1 yr before so now they are 20.5

----------
-----3 yr with coupon-----------------------820 + 20*(1,025) + 20(1,025)^2 = 861.5



Above is a simple bond that shows if u have it for One , two or three or how many yrs u want .
If for Four yrs u get 883,05 in the end.

How do you know what is the Rate there well that's what IRR is for  .When bonds its YTM

Q- Invest X and get $10 every yr. and in end of 6 yrs get 800 back.

P= C/R
R= 10/800  = ,0125
Wrong way to calculate in Coupon bonds . WE USED  800 specifically to show that wrong method and that is why we need IRR in coupons 
Calculated the R here again

Now how to Equate this with coupons and how much you get every year must be the same  and you can see that above .

IRR and YTM thing well.

Everything is done now what is IRR or YTM here for then ?

Well you wanna sell the bond for what price that gives 20 per yr and 800 in end.
so u use YTM and excel to get that

Selling Price=BW(0,0125;6;20;800) = -857,46
Rate =ZINS(6;20;-857,46;800) = ,0125 or 1,25%

yr = 6
COUPON = 20
800 u get in end.
You can get rate from selling price here by 

If u sell it at 800 u are stupid sell it at 857,46
that's all !




Simpliest way to do this .

How I understood EAR & apr

We know

1 + EAR =  ( 1+ APR/x )^x

Example:- 100 bond 5% coupon seminannual payments . Current price 957.35

Compute Rate  =ZINS(10;25;-957,35;1000) = 3%

3%

So APR = 6%
EAR = 6.09%

How ?

APR is computed like Simple interest so semiannualy in this ques.
Both APR and EAR are expressed in annual terma´s


957.35(1.03)(1.03) = 1015.652615

EAR
957.35(1 + ear) = 1015.652615
957.35 + 957.35*ear = 1015.652615
 957.35*ear = 1015.652615 - 957.35
ear  = 58,302615/957.35

ear = 0,0609

Just the compounded % of how much u earned ! 

= HOW MUCH U EARNED PER YR / INITIAL MONEY

Now see the first equation and see this 

957.35(1.03)^2= 1015.652615

(1.03)^2= 1015.652615/957.35      =  1+rate = (1 + ear)1/2   /* This is the imp. point to understand because compounded semianually*/

So half of the ear return  is the apr return per 6 months.

Thats all folks :)



1 

Silly mistake in Harvard Business school's Course ;) - Mathematics

Hello Internet,

Last day i was going through the Online course for my semester. The course is quiet informative and simple explains all the basic concepts in a very precise and interactive way. You can give it a try its worth it.

But there's an error here as well .It's an easy one .But yes may bother someone, so save your time
Formula for Annuity and calculating the  bond value !

C(1r−1r(1+r)N)+F(1+r)N

The answer will change from 3.8554 to 3855432894.295317473644036444788 . That's a big change :D. Funny fact is they always end up with correct answers like we do :D ! Let me know if you guys figure out some other mistake as well.

I've dropped an email will be corrected soon. 

That's all Folks
Nitin Arya

IBAN error Deutsche Bank

Deutsche Bank is sending wrong IBAN in new block account letters.

IBAN structure

So today i was about to transfer my funds in my account and the payment gateway kept denying the IBAN number given by the Deutsche bank .

IBAN is of 22 Digits and here  in the  attached letter u'l see they have given a 21 digit IBAN. I am wondering how can they commit a mistake like that when they are opening more than thousands of block account daily. Maybe a lot of people have been facing same problem regarding their IBAN.

Here's Proof of concept I hope they fix it soon.
Full size Image :- https://twitter.com/nitin0arya/status/365517556691386371/photo/1

Deutsche Bank

Simplifying Annuity

The present value of a constant cash flow, C, for t periods is:

Define the discount factor:

Substituting a into the formula, we get

To simplify the present value formula, we need to simplify the expression in the brackets:

To simplify this formula, we first add at+1,at+2, and so on, and then subtract all the terms we added:

We can rewrite this as:

Note that the infinite number of terms in each of the brackets is the same. Define:

+

Now, observe that V = 1 + aV, which means that

Therefore, the expression

Now, replace a with the discount factor 1/(1 + r) and simplify to get:

We can now simplify the present value formula as follows:

Replacing the expression in square brackets with what we derived, we get:

Simplified Annuity

which is the annuity formula.

Given the interest rate, r, this formula can be used to compute the present value of the future cash flows. Given the present value, it can be used to compute the interest rate or yield. Finally, given the present value and the interest rate, it can be used to determine the cash flow.

You can use the formula in different ways as you go through Bond Tutor. The topic Time Value of Money in this chapter lets you calculate the present value of each cash flow for an annuity and also lets you see the annuity value through time. In The Term Structure of Interest Rates topic, you can see how the present value is affected by the interest rate and also calculate the interest rate given the present value.

Courtsey & Source http://www.bondtutor.com/btchp1/topic7/topic7.htm

Nitin Arya

NPV and IRR explained with example.

Hello everyone,

One of the main confusion that pops is regarding the conceptual difference b/w the IRR(Internal Rate of Return ) and NPV(Net Present Value).

Now we can easily understand the underlying formulas and calculations but there is an idea that has to be understood and the best to to understand is by picking up an suitable example.

I would suggest this Wiki article for a warm up.

http://en.wikipedia.org/wiki/Internal_rate_of_return

http://en.wikipedia.org/wiki/Net_present_value 

Example:- We need two investments for which the net NPV should be 50.
Cost of Capital = .2 or 20%

Investment one:       -100                 180

Investment two:       -100000           120060

NPV one = -100 + 180(1 + .2) = 50
NPV two = -100000 + 120060(1 + .2) = 50

You cannot judge an investment based on NVP as both are same but consider the amount of money in investment two but this is just an simple case when the investments are complex its hard to judge so . So that's why we need IRR but IRR is also not the ultimate solution.

Now lets calculate IRR for the same . We need a value r' for which the NVP must be Zero.

IRR one :-  -100  + 180/(1 + r') = 0
                  Simplify we get r' = 0.80 

IRR two :-    -100000 + 120060(1+r'')= 0
                     here r'' = .2006

r < r'  Investment  accepted

  r > r ' Investment rejected

In our case r  = .20 and r'= .80 and r''(Second investment) = .20

So clearly investment one is favorable as compared to investment two although up to fourth decimal place it is also higher or up to second decimal place almost equal but as you read wiki page carefully you see these methods are for mutually exclusive investment selection and thus investment one gives us higher return and thus should be chosen.

Nitin Arya