Lecture10_winter09

# Lecture10_winter09 - PORTFOLIO THEORY PORTFOLIO THEORY...

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PORTFOLIO THEORY

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PORTFOLIO THEORY Learn how to characterize the Return and the Risk of Portfolios of Assets Determine the Portfolio or Portfolios that have the best relation between Return and Risk Determine the correct price of Risk in terms of the added Return needed to compensate for it.
STATISTICS REVIEW Suppose you have two Random Variables: X and Y. Suppose you create another Random Variable Z=X+Y Then it is true that: E(Z)=E(X+Y)=E(X)+E(Y) VAR(Z)=VAR(X+Y)=VAR(X)+VAR(Y)+2COV(X,Y)

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STATISTICS REVIEW Suppose you have a Random Variable X Suppose you multiply it by a scalar c and create a new Random Variable Z=cX Then, it is true that: E(Z)=E(cX)=cE(X) V(Z)=V(cX)=c 2 V(X)
PORTFOLIO THEORY A Portfolio is a collection of Assets Will be defined by: The Assets it contains (X i , i =1,…,N) The weights of the Assets in the Portfolio (w i , i =1,…,N), where w 1 +w 2 +…+ w N =1 The weight is the fraction of the money invested in that Asset

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PORTFOLIO THEORY The weights can be positive or negative If positive it means you have a LONG position. It means you are BUYING the Asset If negative it means you have a SHORT position. It means you are SHORT SELLING the Asset.
SELLING SHORT Is, in essence, SELLING SOMETHING YOU DON’T HAVE YET , but you promise to deliver it in a later date. You receive the Money for it immediately and you will deliver the Asset to the Buyer in a agreed date. If the Asset makes payments before that date (dividends, coupons) you should give them to the buyer. You need to buy the Asset at some point. Very Risky .

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TWO ASSET PORTFOLIO Portfolio is a combination of two assets P=w 1 X 1 +w 2 X 2 , where w 1 +w 2 =1 E(R P )=w 1 E(R 1 )+w 2 E(R 2 ) V(R P )=(w 1 ) 2 V(R 1 )+(w2) 2 V(R 2 )+2w 1 w 2 COV(R 1 ,R 2 )
TWO ASSET PORTFOLIO

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## This note was uploaded on 01/28/2012 for the course ECON 134a taught by Professor Lim during the Winter '08 term at UCSB.

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Lecture10_winter09 - PORTFOLIO THEORY PORTFOLIO THEORY...

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