Spread estimation from daily price 
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  Spread is defined as the difference between ask and bid

  Generally, the difference between two prices or interest rates. In stock trading, 
    the difference between the current bid and ask prices for a stock (the bid/ask or 
    bid/offer spread). In futures trading, the price difference between delivery 
    months for the same commodity or asset. In bond trading, the difference between 
    yields of bonds with similar quality and different maturities, or of different 
    quality and the same maturity. In underwriting, the difference between what the 
    issuer receives from the underwriter and what the underwriter receives from the 
    public (underwriting spread).

         http://lexicon.ft.com/Term?term=spread

Roll (1984) designs a method to estimate the spreads by using the 
    first order covariance of price changes. 

       S=2 *sqrt(-cov(A, B) )                         (1)

          where A= deltaP(t-1)
                B= deltaPP(t)	

 Objectives for this term-project
      1) understand how to download and process daily data from Yahoo!finance
      2) understand the logic behind the above formula
      3) estimate Roll's spread for a dozen stocks 	
      4) comment on your results

 Source of data: CRSP 

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What is VaR?
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   The maximum loss for a given confidence level 

       over a fixed period. 

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A few simple examples 
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Today, I own 300 shares of IBM stock worth $2,942. 
          The maximum loss tomorrow is $ 239 with a 99% confidence level.

Our mutual fund has a value of $10m today. The maximum loss over 
        the next 3 months is 0.5m with 95% confidence. 


The value of our bank is $350m. The VaR of our bank is $10m 
        with 99% confidence over the next 6 months. 

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Monte Carlo Simulation to mimic Black Jack 
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This is a 2-player game: a dealer and a player. Below, we assume 
     that you are the player. 

  Rule #1: cards 2 to 10 have their face value, while J, Q, and K 
            are worth 10 points and Ace is worth either 1 or 11 
            points (player's choice).
  Terminology:
    Blackjack          : one A plus any card worth 10 points. 
    Lose               : the player's bet is taken by the dealer.
    Win                : the player wins as much as he bet.
    Blackjack (natural): the player wins 1.5 times the bet.
    Push               : the player keeps his bet, neither winning nor losing money.

 Step 1: the dealer draw two cards, one face up, while the player draw two cards (face up) 

  Step 2: the player could draw the third card 

   Win or lose: if the sum of your cards is less than 21 and 
         is bigger than dealer s, you win. 

    http://www.pagat.com/banking/blackjack.html

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