Transcription of Markowitz Mean-Variance Portfolio Theory
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Markowitz Mean-Variance Portfolio Theory
Markowitz Mean-Variance Portfolio Return RatesAn investment instrument that can be bought and sold is often calledanasset. Suppose we purchase an asset forx0dollars on one date andthen later sell it forx1dollars. We call the ratioR=x1x0thereturnon the asset. Therate of returnon the asset is given byr=x1 x0x0=R ,x1=Rx0andx1= (1 +r) it is possible to sell and asset that we do not own. Thisis calledshort selling. It works somewhat as follows. Suppose you wishto short (or short sell) a particular stockXXX. You begin by askingyour stock broker if their firm is holdingXXXin the total pool ofstocks owned by all of their customers. If the brokerage does hold (ormanage) some of stockXXX, you can ask them sell any number ofstockXXXup to the number that they hold. This sale is creditedagainst your account as a debt equal to the number of stockXXXthey sell on your behalf.
n)T is a set of weights associated with a portfolio, then the rate of return of this portfolio r = P n i=1 r iw i is also a random variable with mean mTw and variance wTΣw. If µ b is the acceptable baseline expected rate of return, then in the Markowitz theory an opti-mal portfolio is any portfolio solving the following quadratic program: M ...
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