Asset Pricing Undergrad

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2007

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:: DNA ............................ 3 ............................................................ 7 , ...............................................................11 .................................................................................................... 15 ......... 41 ............................................................................... 43 ... 45 ................ 50 ................................................................................. 52 ............................................................................ 55 ................................................................................................................. 61 beta............................................................................. 66 ..................... 68 ; ........................................................................................................ 72 ................................................... 73 .............................................................. 74 ; ................................................................................. 81 : 84 ..................................................................................................................... 86 .101 ............................................105 Epstein-Zin.109 : ................................................................................................................ 119

2

: DNA . , , ; ; ; .

: CAPM, ICAPM, APT . . , 10-15 , (Consumption Capital Asset Pricing Model, C-CAPM). .

3

. . .

. , . , , , .

, .

, , , .

, 4

.

, DNA CCAPM. , CCAPM . . , CAPM CCAPM. CCAPM CAPM CCAPM. CCAPM .

: = .

:

Pt = E ( M t +1 X t +1 ) M t +1 = f ( , )5

P: , X: , : .

f(.). , :

M t +1 = a + bFt +1 F ( ) . F. , CCAPM : F = , c, CAPM : F = , ICAPM : F = c + .

. . , . . .

6

,

( ) . , . .

, ( ) :

r = + + + z (r ) = () + ( ) + ( ) + ( z )

7

(.. ) .

() .

; . ,

(marginal rate of substitution (MRS) elasticity of intertemporal substitution (EIS) rate of time preference).

. 10%

(0,10), 1 EUR , 1+0,10 EUR .

( 1)

8

Individual 1 Period 2 Period 2

Individual 2

I1Y2 C2 C2 Y2

I2

1+r Y1 C1 Period 1 C1 Y1

1+r Period 1

Borrowing

Lending

Figure 1: Determination of real interest rate

.

, , ( ) :r = +

. ,

9

( ) . :

r = + +

2.

Nominal interest rate (r)

Liquidity premium ()

Expected inflation ()

Real interest rate ()

Term to maturity

Figure 2: Decomposition of nominal interest rate

. .

(CAPM, CCAPM, ICAPM, APT .). : : .

10

:r = + + + z

3.

Nominal interest rate (r) Risk premium

Liquidity premium ()

Expected inflation ()

Real interest rate ()

Term to maturity

Figure 3: Decomposition of nominal interest rate

,

F P

r T m.

F ()

:

F = P(1 + r ) T : P = 1000

EUR,

r = 0,1011

(10%),

T = 2

F = 1000(1 + 0,1) 2 = 1210

EUR

F m :r F = P(1 + m ) mT

:

r = 0,10

(10%),EUR

T = 2 , m = 2

F = 1000(1 + 0,1 / 2) 4 = 1215, 51

:

r = 0,1 (10%) = (1 +r m m

)

1:

F

(1 + r )

1, 100000 1, 1025001, 103813

(1 + 2r )2(1 + 4r )4r (1 + 12 )12

1, 1047131, 105156

r (1 + 365 )365

r F = P(1 + m ) mT

12

( m )

F = Pe rT e = lim (1 + m1/ r )m m/r

= 2, 71828.

,

e r = (2.71828) 0,1 = 1,105171

F T ,

P F T .

. () P F T :

P=

F (1+ r )T

= F (1 + r ) T

: zero coupon

10% 5 1000 EUR

P = F (1 + r ) T = 1000(1 + 0,1) 5 = 620, 92 EUR (1 + r ) T

13

m , P F T :

P=

F r (1+ m ) mT

r = F (1 + m ) mT

( m ) , F r (1+ m ) mT r = F (1 + m ) mT

P=

P = Fe rT

, d t t = 1,..., T ,1 (1+ r )

,

P0 =

T

t =1

( )dt 1 (1+ r )

t

: ,

d t t = 1,..., T , F r , :

P0 =

T

t =1

( )dt 1 (1+ r )

t

+ F (1 + r ) T

r

( ) ( F).

14

:

P : d:

r : () 1 = 1+ r : ()

:

( ), .

.

, (r), , (r)=r. r :r = + z ,

: z :

:

d ( ) r :

15

(fair price);

= 1 () (fair price) :

P0 =

E (d1 ) E ( P ) 1 + 1+ r 1+ rP0 E ( P1 ) E (d 1 ) r

(1)

1+ r .

1

.

(1),

, .

= 2 ()

(1)

P = 1 E ( d 2 ) E ( P2 ) + 1+ r 1+ r

(2)

(2) (1) P0 = E (d1 ) E (d 2 ) E ( P2 ) + + 2 1 + r (1 + r ) (1 + r ) 216

(3)

= T ()

P0 = t =1

T

E (d t ) E ( PT ) + t (1 + r ) (1 + r ) T

(4)

(4) ( ) ( ). . : :

P0

E ( PT )

(1+ r )T

,

E ( PT ) r

1: 1998-1999, NASDAQ 1998-2000.

.

. (4), r o P.

90

. o . ,

17

( 7,5% 3%). o . , .

,

, T . (4) :

P0 = t =1

E ( PT ) E (d t ) + lim t (1 + r ) T (1 + r )T P0 = t =1

(5)

(6)

E (d t ) (1 + r ) t

limT

T T (1+ r )

( ) = 0.E ( PT )

lim E ( PT ) < , . (1 + r ) T T , r > 0. (6)

r .

()

.

.

r = + z , ,

18

z.

1 : . (5) E (d t ) = 0,

t = 1,...,

P0 = 0.

:

.

2: r .

.

.

, , r .

(6)

P0 .

P0 ,

. d t .

19

1. (random walk):

d t = d t 1 + t

(7)

: =0 . ( ( I 0 ) . :

E (d1 / I 0 ) = E (d 0 + 1 / I 0 ) = d 0 E ( d 2 / I 0 ) = E ( d1 + 1 / I 0 ) = E ( d 0 + 1 + 2 / I 0 ) = d 0...

E (d T / I 0 ) = E (d T 1 + T / I 0 )= E (d 0 + 1 + 2 ... + ... T / I 0 ) = d 0

E ( 1 / I 0 ) = 0,

E ( 2 / I 0 ) = 0,

E ( 3 / I 0 ) = 0,...,

E ( T / I 0 ) = 0.

(6) (7) :

P0 = t =1

d0 (1 + r ) t 1 (1 + r ) t

= d0 t =1

20

= d0 = d0

1 1 (1 + r ) t (1 + r ) t =0

1 1 1 (1 + + + ...) (1 + r ) (1 + r ) (1 + r ) 2 = d0 = d0 1 1 1 (1 + r ) 1 1+r

1 1+ r (1 + r ) r

P0 =

d0 r

(8)

,

, .

,

r.

(7)

Pt ;

(1) E ( P1 / I o ) = (1 + r ) P0 E (d1 / I o ). (7)

E (d 1 / I o ) = d 0

(8)

d 0 = r P0 .

21

:E ( P1 / I o ) = (1 + r ) P0 rP0 = P0

E ( Pt / I o ) = P0 ,

, . .

2. : Gordon

( -- random walk with drift-- d t ):

E (d t ) = (1 + g )d t 1

(9)

E (d t ) = (1 + g ) t d 0 (6) P0 = d 0 t =1

(1 + g )t (1 + r )t

= d0 tt =1

=

(1+ g ) (1+ r )

. ,

1 P0 = d 0 (1 + + 2 + ...) = d 0 ( ) 1

22

= d0

1+ g 1 1 + r 1 1+ g 1+r

P0 = d 0 1+ g rg

(10)

(10) Gordon.

(10),

.

23

1. Real Stock Price: (S&P 500), P(t)*(CPI(2003)/CPI(t), 2. PDV constant discount rate: . PV(t)=RealD(t)+(PV(t+1)/(1+mean(R))), RealD(t)=D(t)* (CPI(2003)/CPI(t) mean(R)=exp(mean(ln(1+R(t))) S&P 5