Formula+Sheet+Fall+2011

Formula+Sheet+Fall+2011 - when: w D = [ r Df E 2 – r Ef...

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Formulas that may be useful 1. Utility function: U = E( r ) – ½ A 2 2. The utility function when holding a complete portfolio (investing y in a risky portfolio P and (1 – y ) in the riskfree asset f ): U C = r f + y [E( r P ) – r f ] – ½A y 2 P 2 The partial derivative of the above utility function with respect to y : U C / y = [E( r P ) – r f ] – Ay P 2 3. Portfolio variance when investing w in risky security D and (1 – w ) in risky security E : P 2 = w 2 D 2 + (1 – w ) 2 E 2 + 2 w (1 – w ) DE The minimum P 2 is achieved when: (at this point,  P 2 / w = 0) w = ( E 2 DE ) ÷ ( D 2 + E 2 – 2 DE ) 4. When there are two risky securities, D and E , the maximum Sharpe ratio is achieved
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Unformatted text preview: when: w D = [ r Df E 2 – r Ef DE ] ÷ [ r Df E 2 + r Ef D 2 – ( r Df + r Ef ) DE ] w E = 1 – w D ( r Df E( r D ) – r f and r Ef E( r E ) – r f ) 5. If every security has the same expected return E(r) and the same standard deviation , and the correlation between any two securities is , the expected return E(r p ) and the standard deviation p for an equally-weighted portfolio of n securities are given by: E(r p ) = n ( E(r) / n ) = E(r) p = [ 2 / n + ( n-1)/ n × 2 ] 1/2...
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This note was uploaded on 11/27/2011 for the course FINA 3104 taught by Professor Darwin during the Spring '11 term at HKUST.

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