The GBM doesn't model big shocks to stock prices, due to quarterly announcements, news, public policy change etc.

# Month: September 2013

# Combination Sum question – no solution yet

Note:

All numbers (including target) will be positive integers. Elements in a combination (a1, a2, … , ak) must be in

non-descending order. (ie, a1 ≤ a2 ≤ … ≤ ak). The solution set must not contain duplicate combinations.

For example, given candidate set 2,3,6,7 and target 7, A solution set is:

[7]

[2, 2, 3]

# Useful tips – series summation puzzles

Facts to internalize, so when you see them in the middle of a puzzle, you could recognize them.

Fact A:

Fact A2:

1/5 + 1/5^{2} + 1/5^{3} … = 1/4

Fact C: (I call this a geometric-arithmetic series)

1/5 + 2/5^{2} + 3/5^{3 }… = 5/ 4*4

Fact C2: (similar)

1/5 + 4/5^{2} + 9/5^{3 }+ 16/5^{4}… is also tractable

# book value of leverage

Book value of EQ is still 600-480 = $120k, but current EQ would be 1.2m – 480k = 720k.

(Book value of) Leverage in “literature” is defined as

(book value of) ASset / EQuity (book value)

The denominator is much lower as book value than the current value. For a listed company, Current value of total equity is total market cap == current share price * total shares issued so far. In contrast, Book value is the initial capital of the founder + actual dollars raised through the IPO, ignoring the increase in value of each share. Why is this book value less useful? We need to understand the term “shareholder equity”. This term logically means the “value” of the shares held by the shareholders (say a private club of …. 500 teachers). Like the value of your house, this “value” increases over time.

# OLS ^ AutoRegressive models

Given some observed data Y, you first pick some explanatory variables X_1, X_2 etc

If you pick a linear model to explain the observed Y, then OLS is the best, linear, unbiased and efficient (BLUE) solution using a computer. It will give you all the parameters of your linear model – the b_0, b_1, b_2 etc.

If you feel the relationship isn’t linear, you still can use OLS. As an alternative to a linear model, you could use AR(1) models to explain Y using the X1 X2 etc. You use AR models when you believe there’s strong serial correlation or autocorrelation.

I believe AR models use additional parameters beside the b1, b2 etc. The computation is more efficient than OLS.

# asset^liability on a bank’s bal sheet

When a bank issues a financial statement, the meaning of AS (asset) and LI (liability) tend to confuse me.

Suppose JPMC bank has client IBM…

Liability – Deposits (incl. CD) at the bank

Liability – overnight borrowing. This interest rate could surge like in 2008.

Liability – Commercial papers issued by the bank

Liability – Bonds issued by the bank

Asset – securities owned by the bank (treasury department?), including stocks, govt bonds and corp bonds etc. Securities could devalue like bad loan!

Asset – Loans to corporations like IBM — on the balance sheet treated like a govt bond!

Asset – Loans/mtg to retail — on the balance sheet treated like a govt bond!

Asset – spare cash

AS = LI + share holders’ equity

If the bank issues 600M shares in an IPO, the $600mil collected is considered share holders’ equity capital or simply “capital” or simply “equity”.

Chronologically, the balance sheet starts with the initial share holders’ equity. Then Deposits come in and sitting there as spare cash. Similarly the bank can issue bonds.

Then the bank could use the spare cash to buy securities — without change on the LI side.

The bank can also use the spare cash to give loans — without change on the LI side.

Each type of transaction above affects the balance sheet only in a “realized” sense i.e. book values —

Big warning – all the AS numbers and LI numbers and equity values are book values.

* Latest share price doesn’t enter the equation. Those 600M shares will always be recorded as worth $600M on the balance sheet.

* market value (m2m) of the loans lent out doesn’t matter

* market value (m2m) of the securities owned by the bank doesn’t matter.

Fair Value accounting tries to change that. Mark-to-market is a big effort in GS and many investment banks.

# Professionals “always” trade pairs

Professionals “always” trade pairs like

– Relative value pairs

– Option “strategies”

My problem with pair trading is the commission or bid/ask spread.

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