Derivative Assets Put-call parity: SEeCP rT −+= − Black-Scholes formula: )d(NEe)d(SNC 2

USEFUL FORMULAS

Measures of risk

Expected returns: ∑ ×= ssi RobPr)r(E

Variance of returns: ∑ −×=σ 2

iss 2

i )]r(ER[obPr Covariance between returns:

( )( ))r(Er)r(ErobPr)r,r(Cov jjsiissji −−∑ ×= Beta of security i:

)r(Var )r,r(Cov

M

Mi i =β

Portfolio Theory Expected rate of return on a portfolio with weights w in securities i and j: )r(Ew)r(Ew)R(E jjiip += Variance of portfolio consisting of securities i and j:

)r,r(Covww2ww jiji 2 j

2 j

2 i

2 i

2 p ×××+σ+σ=σ

Covariance/Correlation coefficient:

j,ijiji Corr)r,r(Cov ×σ×σ= Minimum variance portfolio:

Fixed-Income Analysis Present value of $1 Discrete period compounding:

T)r1( 1PV +

=

Continuous compounding: rTePV −=

Forward rate of interest for period T: 1T 1T

T T

T )y1( )y1(

f −

−+ +

=

Real interest rate: 1 i1 r1R −

- +

=

where r is the nominal interest rate; and i is the inflation rate

…/continued overleaf

)RR( COV 2 – )RVAR( + )RVAR( )RR( COV – )RVAR( = W

BABA

BAB

2

Duration of a security:

Equity Analysis

Constant growth dividend discount model: gk

D gk

)g1(DP 100 − =

− +

=

Growth rate of dividends: bROEg ×=

Price-earnings multiple: bROEk

b1EP ×−

− =

Present value of growth opportunities: PVGO k

E P 10 +=

Derivative Assets Put-call parity: SEeCP rT −+= − Black-Scholes formula: )d(NEe)d(SNC 2

rT 1

−−=

T

T)2r()ESln( d

2

1 σ

σ++ =

Tdd 12 σ−=

Performance Evaluation

Sharpe’s measure: p

fp p

rrS σ −

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