Lecture_2

# Lecture_2 - Lecture 2 Review of statistical concepts...

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Lecture 2 Review of statistical concepts Institutional background

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Expected Value The expected value (or mean) of a random variable measures what we think of as an average outcome If a random variable takes on the values r(1), r(2)… with probabilities p(1), p(2) , then the expected value is calculated as: or )] 3 ( * ) 3 ( [ )] 2 ( * ) 2 ( [ )] 1 ( * ) 1 ( [ ) ( r p r p r p r E + + = i N i i r p r E * ) ( 1 = =
The Variance and STD of the return The variance of return: Standard deviation of the return: 2 )] ( [ ) ( r E r E r Var - = ) ( ) ( r Var r sd = = σ 2 1 )) ( ( * ) ( r E r p r Var i N i i - = =

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Using Historical Data Assume you want to get an idea of the mean and variance of MSFT stock returns You could use historical data on returns For the period August 1999 until September 2006 what was the mean and STD of MSFT stock returns?
Sample Mean and Variance Using the data on stock returns you (r(1),r(2),…,r(N)), you can calculate the mean and standard deviation in the spreadsheet. You can calculate the sample average and sample variance For MSFT the mean and STD for period 8/1999 to 8/2006 the annual mean=1% , the annual SD=38% = = N i i X N X 1 _ 1 2 1 2 ) ( 1 1 - = - - = X X N S N i i

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Financial markets Broadly speaking we can divide financial markets into: Money Markets -Short-term,highly liquid, low-risk securities -Often referred to as cash or cash equivalent Capital Markets -Longer-term and riskier securities
Financial Markets: Institutional Background Markets and Instruments Money market instruments Bonds Equities Derivatives Institutional Asset Managers Mutual Funds Hedge Funds Issuance and Trading of Securities Primary vs Secondary Trading Market Structures Order Flow and Price Dynamics

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Money Market Instruments T-Bills Treasury Bills CDs: Certificates of Deposit CP: Commercial Paper Fed Funds: Federal Funds Repos: Repurchase Agreements Eurodollars
Money Market Instruments T-Bills Treasury Bills Maturity 1 year or less "Risk Free": no credit risk Still bear interest rate risk (or "price risk") - Minimum denomination of \$1000 - Exempt from all state and local taxes "Pure discount" (no coupon) If required return is r = 1.00%, P = \$990.1 Suppose r, required yield, rises to 1.25 What is the new price of T-bill? 1 . 990 01 . 1 1000 \$ 1 = = + = r Face P

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Money Market Instruments T-Bills Treasury Bills Maturity 1 year or less "Risk Free": no credit risk Still bear interest rate risk (or "price risk") - Minimum denomination of \$1000 - Exempt from all state and local taxes "Pure discount" (no coupon) If required return is r = 1.00%, P = \$990.1 Higher yield causes lower price. Suppose r, required yield, rises to 1.25
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## This note was uploaded on 04/17/2008 for the course ECON 171A taught by Professor Yusim during the Spring '08 term at Brandeis.

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Lecture_2 - Lecture 2 Review of statistical concepts...

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