Math in Finance !

There are always some basic questions that haunt us more than the complex puzzlers. Invariably, simpler and logical answers to these basic questions make you feel a lot better than finding a scientific solution which hardly makes anyone feel any better than not knowing in the first place.

Some Basic questions in Finance

1. What the hell is a market portfolio ?
2. How does firm value vary with Capital Structure ?

Sharpe and Miller , who addressed these questions are both Nobel Laureates . Lets see how difficult it would have been if they never knew basic Maths !

Market Portfolio

Leading finance books in the market claim that

" Market Portfolio is a portfolio that contains all of the available risky assets in proportion to their total market values " .

Remember what we studied in grade 6 ?
a/b = c/d = e/f = (a + c + e) / (b + d + f )

This is what Market Portfolio means . For simplicity , let us assume that there are just 2 stocks Infy and TCS and just 2 people (P1 and P2).
Infy costs Rs. 10 and TCS costs Rs. 20
P1 has Rs. 100 to invest and P2 has Rs.200 to invest ( they can have different resources) and they invest all their money

Now, in ideal market conditions (equilibrium ) , P1 and P2 would have equal information and hence would expect equal returns. If this is the case,both would have to invest in the stock in the same proportions so as to yield the same returns.

If P1 buys infy for Rs. 20 , he spends 20 % on infy
P2 will also buy in the same proportion , hence he buys for Rs. 40
Total value of infosys = Rs.60
Total value of all stocks in the market = ( 100 + 200 ) =300

20/ 100 = 40 /200 = 60 /300

The above logic holds good for TCS and for any other stock available in the market ( two, in our case)

Now in a real life scenario, one cant really find what proportion each person invests in a particular stock , but i can always know the total market value of Infy and TCS . Hence i can find total market value as sum of Infy + tcs

infy / (infy + tcs ) is the proportion in which every rational investor in an equilibrium condition would invest. This easily perceivable logic is what drives the concept of a Market Portfolio . Most of all, it got Sharpe a Nobel

Firm Value

Another smart execution of a grade 6 concept called additivity

If i have to buy 4 kgs of rice , i should be charged the same whether or not i buy in bulk ( ideal scenario )

ie 4 = 2 + 2

If this is not the case, arbitrage will set in . Lets see how .
Lets say 3 kgs are given at Rs. 30 ( ie 10 /kg) but if i buy 1kg i have to pay Rs. 11/kg . A smart buyer will arbitrage by buying 3 kgs for Rs. 30 and selling 1 Kg packs for Rs.11 each, there by making Rs.3 on the transaction . Markets under equilibrium conditions shouldnt allow such things , hence 4 has to be 2 + 2 or
30 = 10 + 10 + 10 . Agreed ?

Now, lets link this to what Miller said,
D = Debt
E = Equity
Firm Value = FV

Miller said that FV = D + E and the firm value is independent of the capital structure.
We know,100 = 60 + 40

can 100 > 70 + 30 ? ( thats it we got the idea )

Just by changing the composition of debt and equity, if i can change the value of the firm, then the firm's only business would be to keep changing the debt- equity ratio and make arbitrage profit .

This cannot happen . Hence firm value is independent of capital structure .

Remember the concept assumes a frictionless world ( world without bankruptcy costs or differntial treatment of tax for Debt and Equity ,etc )

Now Miller got a Nobel prize for this.

Points to Pop

These ideas were noble because they were simple and hence won the Nobel .
Why noble ? Many economists later used these ideas and the wide spread use of them guaranteed the Nobel.

Moral of the story,Maximum impact can happen only when we keep things straight and simple. We can never influence people with complex things . Its simple things with deeper meaning that can take us places.

PS : This post is dedicated to my juniors who i had to disappoint by not posting a much more interesting , much awaited , game changing information ! Sincere Apologies !