SMU Classification: Restricted
SELECTED FORMULA LIST
Money Market Yields:
idy =
( Pf − P0 ) 360

Pf
h
(P − P0 ) 360
i spy = f

P0
h
i bey =
(Pf − P0 ) 365

P0
h
i


EAR = 1 + bey 
 365 / h 
365 / h
−1
ibe = isp (365 / 360)
Utility Function
U = E ( r ) − 1 A 2
2
Complete Portfolio, C
Expected return:
Variance:
E ( rc ) = rf + y   E ( rp ) − rf 
 c2 = y 2   p2
MaxU = rf + y[ E (rP ) − rf ] − 12 Ay 
y* =
2
y
2
P
➔ Solution: y*
E (rP ) − rf
A P2
To find max, take derivative w.r.t. y and set equal to 0
[ E (rP ) − rf ] − Ay P2 = 0
Portfolios
Solve forofyTwo Risky Assets
Portfolio Expected return:
Portfolio Variance:
E (rp ) = w D E (rD ) + wE E (rE )  p2 = wD2  D2 + wE2 E2 + 2wD wE Cov ( rD , rE )
Where Cov(rD,rE) = ρ.σD.σE
SMU Classification: Restricted
Sharp Ratio:
Sp =
E (rp ) − rf
p
Markowitz Portfolio Optimization Model
 =  wi w j Cov ( ri , rj )
n
2
p
Portfolio Variance-Covariance:
n
i =1 j =1
Average variance and average covariance of the securities:
2 =
Cov =
1 n
 i2

n i =1
n
n
1
Cov ( ri , rj )

n ( n − 1) j =1 i =1
j i
1
n
 p2 =  2 +
Portfolio variance becomes:
Minimum Variance Portfolio Weights:
Weights of the Optimal Risky Portfolio:
n −1
Cov
n
SMU Classification: Restricted
Single-Index Model
Regression equation:
Ri (t ) =  i + i RM (t ) + ei (t )
Expected return-beta relationship:
E (Ri ) =  i +  i E (RM )
2
Cov ( ri , rj ) = i  j M2

=  i2 M2 +  2 (ei )
i
Variance:
Covariance:
Correlation:
Variance of the equally-weighted portfolio of firm-specific components:
2
1
1
 (e p ) =     2 (ei ) =  2 (e )
n
i =1  n 
n
2
Capital Asset Pricing Model (CAPM)
E ( rP ) =  wk E ( rk ) and
E(ri) = rf + βi [E(rM) – rf ]
k
 P =  wk  k
k
Market Risk Premium
E ( RM ) = A M2