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