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., :.,,,.,. (3.),,.,,. :,, ; ; ; ;,. (3.), ( ),... : ; ;, (,,.) ;,.,,,,.., ( x = ). (3.) : ρ / / = = = x = = =. (3.),., (3.),.,,. /, (3.) 4

., x =, (. 0 < <, ρ = Cost, = = Cost )., (3.) ρ j j... = : ρ / + + ρ ρ = = = = = /, (3.3) (3.3) 0, ρ., ρ.,. : ( ρ < ), ( ) j ;, ;.,....,,,., [,. 495]. 3..., r, =, [,. 46]. M{ r } µ, c ( c = D r })., µ, c, =, { r, c = cov( r, r ) = M{( r µ )( r µ )}, (3.4) j j j j 5

,. ( + ) + = ( + 3), µ ( + )/ c j (, c = c ). (, = 00 ( + 3) = 550 ).. W 0. W,, P., j j r W + P W W 0 =, (3.5) 0 r. S. = S = W 0, (3.6) W 0. x = S W0. W 0,., x 0 =, (3.6) x = =, (3.7), ( ), (3.8) W+ P= S + P = r ( S + P ) S S + P S = = W S = =, 0 = S W 0 (3.9) 6

( + ) S P S S, r. r = r x, (3.0) = r, r. M{ r } = E = M{ r } x = µ x, D{ r } = V = = = = j= x x j cov( r, r ) = j = j=, (3.) c x x. j j V., E µ x, = V = c x x, = V, j = j= = = j x =, x 0, =,. (3.), U E, U = U( E, ), U E U > 0, < 0, (3.3) [3,. 55].,, U > 0,.. 7

( E ) ( E V ) U E,, (,, ) ( ) = U 0 = Cost. (dfferece curve).. 3. 3.3. U 0. (, ) U E = E τ, (3.4) E = U0 + τ, (3.5), τ. τ. (, U E U ( ) ;,, ( ) ( ) E..) U 0 U > U 0 U 0 U > U U > U 0 U > U E E 3. ( ) 3.3 ( ). 8

x =, x 0, =,, (3.6) = (3.7) E = µ x, = c xx, (3.7) j = = ( E ) (. 3.4). j,..,,,,,., E. (E, ) 9 E 3.4,,, (lower rght-had boudary),,. ( ) (effcet set), (effcet ortfolos).,.,.,..

,,. () () ( x x () () ( ) (,, x3, K, x ) ( x x ) ( ) ( ),, x3, K, x ) E E., x = αx () + α x ( ( ) ), =,, 0 α, (3.8) E. ( ) ( ) ( ( ) ) E = µ x = µ αx + α x = = = () ( ) = α µ x + ( α ) µ x = αe + ( α) E, = =, (3.9) () ( ) () ( ) ( ( ) )( j ( ) j ) = c αx + α x αx + α x =, j= j ( ) ( ) ( ) ( ) ( ) ( ) = α c x x + α( α) c x x + ( α) c x x =, j j j j j, j=, j=, j= = α + α( α) V + ( α), j (3.0) V = c x x, j= j ( ) ( ) j. (3.9) α α= E E E E, (3.) (3.0), : 30

(3.), V + j, j= ( ) ( ) ( ) ( ) V + = c ( x x )( xj xj ), (3.3), C = c j. E, = a E + b E + c, (3.4) a > 0. ( E, ) ( ( E ), ),, (. 3.5).,,, (, ) (, ). E E ( E, ) ( E, ) ( E, ) ( E, ) E E 3.5 E 3 3.6,, () () x x () (),, x3, K, x, ( )

( ) ( ( x x ) ( ) ( ),, x3,, x ) () ( ) K x = αx + ( α) x. (, ) E, (, ) (, ). E E () ( ) ( x = αx + ( α) x ), (, ) (, ). E E,. = 3. E = V = 3 = = = µ x, j= c x x j j x =, x 0, x 0, x 0. 3 3 3, 3, (3.5) x 3 x = ` x x 3 E V :, (3.6), ( x, x ). x 0, x 0, x3 = x x 0 ( x, x) x = 0, x = 0, x + x = (. 3.7). E, E = µ 3+ x( µ µ ) + x( µ µ 3) ( x, x ), E. µ, µ µ 3. V = Cost C. V ( ( 0 ), ( 0 x x ) ), V 3

. (. 3.7), ( 0) ( 0) ( 0) ( 0) 3.9). ( x, x, x x ),. E. V m E. E 3.7 ( x, x), V. ( 0) ( 0) ( 0) ( 0) ( x, x, x x ) P( ) (corer ortfolo). E, (3.6),,. E., E V, (3.6). E,,, ab, (crtcal le)., 33

, x + x =. P( ).,,,., (. 3.8). P(3) P() P() 3.8, E x + x =, x =, x = x3 = 0. P( 3 ), E,., P( ) P( 3 ),, P( ) P( 3).,,, P( ), P( ) P( 3 ).. 3.9, V., 4 P( ), P( ), P( 3) P( 4 ),,,.,.,,,, (3.).,.,, (3.),,. -. E 34

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.,,., [,. 80].,,.,,,» [4,. 366].,,.,,..,.,,,,,.. 3.,.,,,.,.,. [4,. 6]. E k 0 g P P P =, (3.7) 0 g P + P k P ; 0 P ; g P ( )., x < 0,..,.,, 36

., x =.,,,. 3.3,., :,....,,. β,. =, (3.8) M M M ; M.,.,,..,,,.,..,,.,. : r = + r +, (3.9) 37

r ; r ; α, β, ; ε.,.,» ( ).»,. (3.8),,. : x y x y = = = =, (3.30) x x = = x, y ;. ( ),. y = = = x, (3.3), -... (9),, : 38

39 = = = = y x y y, (3.3),.,,,. : x x = = =, (3.33) : = = = x x, (3.34). R-squared (R ),,. R-squared. = = = = = = = = y y x x y x y x R, (3.35),

.,,.,,,..,. (, ), 3.: 3. < 0, β <, α < 0, R 0 β β > 0, α > 0, R 0 > 0, β >, α < 0, R 0 β β < 0, α > 0, R 0 α, β, R.,. β.. β. 3.4,,,., ( ). r, E ( r f ) = r f, ( r f ) = 0 cov( rf, r ) = 0 0,,.,,,. ( ) > 0 =,. r., Θ = (,, ) ( ), f, f Y = ( Θ) f + Θ, (3.36) 40

, (0, r f ) (, r ), r f r. ( ),., (0, r ) T (. 3.0). r A T V r f 3.0.,,.,.,.,,,. (, T)., T.,,,,,.,,,,,,,.,.,,, V,,..,. 4

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r., r r, r r. α,,, α<0. r P T, (. 3.). P T P T. P T P T (E T, T ) (E, ) (r, 0) (r, 0) (r, 0) 3. : r > r 3.3 r r, r = r (. 3.3);. E T T., (, r 0) ( E T, T ). : α,, 0 α,, α <0, r., α,. E = E = αr + ( α) = ( α). E T,, (3.37) α,, E 43

E r = E T r, (3.38) T E = r+ ( ET r), (3.39) T (Catal Market Le, CML). :.. (Catal Asset Prcg Model, CAPM),. [ 6 ]. :.,.... 3.,. 4.. 5.,., [ 6 ]., (, )....,,,.,?,.,,.,,,... 44

r,,,. r T.,, : α α. r = αr + ( α) rt. : M{} r = E = αµ + ( α) E, T Dr {} = = α + α( α ) T + ( α) T,, (3.40) = α + α( α ) + ( α). T T α= ; α=0. α 0 ( α<0), (, ) ( E, ).,,.., ( E T, T )., (. 3.4),,,.. (E T, T ) µ., E de dα d dα = µ E T, α + ( α ) ( α ) T T = α + α( α ) T + ( α) T, (3.4). α=0 ( α=0 (, ) ) E 45

α = α < 0 α = 0 E T, T ( r, 0 ) E 3.4 ( ) de dα d T T = µ ET; =,, (3.4) dα α= 0 α= 0 T de d T ( µ ET ) =., (3.43) T T, 3.39, de d E T r =, (3.44) T, 3.45 de d = de d, (3.45) 46

( µ ET) T ET r =, (3.46) T T T µ T T T ET = ( ET r) = ( ET r) ET + r, (3.47) T T, µ T = r+ ET r ( ), (3.48) T (Securty Market Le, SML). β, SML T T µ = r+ β ( E r), (3.49) T β = 0 µ = r,. β, µ,,., (3.49)..,, E, U = E, E = U +, (3.50) τ τ, U, : de d( ) =, τ =, (3.5) d( ) τ de 47

E., (,) r 0 (. 3.5), E E T r T r =, (3.5) ( E T, T ) ( E, ) ( r, 0 ) E 3.5 ( E r) = T ( E r), (3.53) T,, d( ) de = T E r ( E r) T, (3.54),,,. (3.5) (3.54). 48

τ= E r ( E r), (3.55) T T ). 3.5.,..,,. (arbtrage).,.,.,..,, 600.,,,.,.,,.?. :..». (arbtrage ortfolo)., r = α + β I + ε, (3.56) α β ; I ; ε., M{}= I 0 ( M{}= I I0 0, β I 0 α ), D {}=, M{ ε } =0, D{ ε } = ε. I ( x, x, K, x ), 49

x = = 0. = x 0,.,. x < 0, (short sale) j, x j > 0.. ( 3.57-3.58). r = = r x = = = α x + I β x + x ε, (3.57) =, (3.58) 3.58 ( ) ( )... β x = = 0, (3.59) = x ε =., x = = 0;, (3.60) 50

= = E = α x, = x ε, (3.6).?,.,,, x = = 0, β x = 0, (3.6) =. α x =0, =? K β β β3 K β, (3.63) α α α3 K α α x =0 x = 0 = = β x = = 0,., =, α = λ0 + λβ, (3.64) r µ = λ 0 + ( λ + I ) β = M{ r } = λ 0 + ε + λ β, (3.65). β = 0 µ = λ 0.,?. λ 0 = r. 5

,, β =.. E T E T = λ r +, (3.66) 0 + λ = λ λ = E T r µ = r + β ( E r), (3.67) T SML, E T β. 3.5.3, r r = α + βi+ βi+ K + βkik + ε, (3.68) M{ Ir } = 0, r=, k M{ Ir Is}= crs. x = 0 = k r = xα + Ir xβr + xε, (3.69) = r= = = E = = = k α x k k rs r= s= = c x β r k = x β s + = x ε, (3.70) 5

k xβ r = 0 =, k, (3.7) = x = = k 0; xβ r = 0 =, k, (3.7) = = α x =0, (3.73) K β β β3 K β β β β3 K β, (3.74) K K K K K βk βk β3k K β k α α α3 K α, k + : α = λ + λβ 0 s s s= k, (3.75) r µ = λ 0 + k s= λ = M{ r } = λ s ( β + I ) 0 s + k s= s λ β s + ε s, (3.76) 53

β s = 0, λ 0 = r. β s = β l = 0, l s, s E s, Es = r+λ s, λ s = E s r k µ = r + βs( Es r), (3.77) s= (3.67) k., 95...., ( ) ( )..,,. [6].,,,.,,.,,,.,»,,,,,,,,. 54

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