가치결정...(김근용).hwp

Transcription

1 2001 Application of Financial Engineering Method on Real Estate: Value Assessment and Risk Management on MBS and REITs

2 2001 / / 2-22 / / ( ) ( ) / ,.

3 , , 2001., (ABS), (MBS), (REITs)..,.,.

4 ,.,.,,

5 ,..,,.,,,,.,,,,.,

6 (ABS), (MBS) (REITs).., MBS.,,,.. 3 MBS REITs, MBS (KoMoCo) MBS MBS,,, (MBB). MBB, MBS (MPTS) (MPTB). MBB MBB

7 MBB. MBB, MBB. MBB. n (accrued interest) MBB (3.1). MB B non = n t = 1 MB B n on I ( 1 + y ) t + P ( 1 + y ) n = I 1-1 ( 1 + y ) n y : MBB, I : P :, y : ( ) + P ( 1 + y ) n (3.1) MBB MBB MBB. MBB MBB(callable MBB). MBB MBB, (call option). MBB (3.2). MB B cop = MB B n on - C p C p = MB B n on - MB B cop (3.2) MB B cop : MBB, C p : (3.1) MBB ( C p ) (3.2) MBB. Cox, Ross & Rubinstein(1979) Black(1976), MBB.

8 KoMoCo MBS , MBS, 5 MBS 1% MBS 4.33%., MBS, MBS 1 Black, 2 5 MBS MBS , %., KoMoCo MBS MBS 1, 2 5 MBS MBS , %. KoMoCo MBS %, % %. KoMoCo, KoMoCo MBS. Capozza & Lee(1995, 1996) REITs,. (REITs) (CR-REITs), REITs CR-REITs, (r), (g), 1 ( T R 1 ), (x), REITs ( V R ) CR-REITs ( V CR ) (3.29), (3.30).

9 V R = ( x ) TR 1 r - g V CR = ( x ) TR 1 r - g (3.29) (3.30),., 8% 18%, 12%.,,, ,.,,,,

10 ,.,,. VaR(Value at Risk). VaR,,,, ,.

11 ) 8 2) 15 3) ) 24 2) 25

12 3 1. MBS 29 1) 29 2) MBS 30 3) MBB 32 4) MBB 33 5) REITs 48 1) Capozza & Lee 48 2) REITs ) 59 2) ) 64 2) VaR SUMMARY 87

13 < 3-1> KoMoCo MBS < 3-2> KoMoCo MBS < 3-3> KoMoCo MBS < 3-4> KoMoCo MBS n 44 < 3-5> KoMoCo MBS ( : 1 ) 46 < 3-6> KoMoCo MBS (Black : 1 ) 46 < 3-7> KoMoCo MBS (Black : MBS 1 ) 47 < 3-8> REITs 55 < 3-9> 1 8% 56 < 4-1> VaR 75

14 < 2-1> 9 < 2-2> 13 < 2-3> 19 < 2-4> 3 21 < 3-1> MBB MBB 34 < 3-2> 3 MBB 36 < 3-3> KoMoCo MBS < 3-4> 2 KoMoCo MBS 44 < 3-5> 2 KoMoCo MBS 45

15 1 C H A P T E R (ABS; Asset Backed Securities) 49 3,832, , % ABS 1 1

16 ., (mortgage loan) ( KoMoCo ) ,440 ( ) (MBS; Mortgage Backed Securities), 3% , MBS ,,,,.,,,.., KoMoCo KoMoCo MBS., ABS. 2

17 .,,,.,,.,.,,.,,,.,,..,,,,,.. 1 3

18 2.. ABS, MBS,., ABS MBS MBS.,,,. MBS MBS, 1), Cox, Ross & Rubinstein(1979) Black(1976)., Capozza & Lee(1995, 1996) (REITs). (financial engineering),,,,,.. 1) (term structure of interest rate). 4

19 ,. 1 5

20 2 C H A P T E R. ABS, MBS (REITs).., MBS.,,,.. 2 7

21 1. 1) (1). (required yield). (noncallable bond, option-free bond) n (accrued interest) (2.1). B n on = n t = 1 B n on I ( 1 + r) t + P ( 1 + r) n = I 1-1 ( 1 + r) n r :, I : P :, r : ( ) + P ( 1 + r) n (2.1) (2.2). B n on = n t = 1 I ( 1 + r) v ( 1 + r) t P ( 1 + r) v ( 1 + r) n - 1 (2.2) v : ( ), (pure discount bond) (2.3), (2.4). : B n on = : B n on = I r P ( 1 + r) n (2.3) (2.4) 8

22 (2) (2.1), (convex), < 2-1>.,,,,,. < 2-1> B * n on y* (3) (current yield) (yield to maturity)..,., ( 0 ) ( ) 2 9

23 .. (y) (IRR; internal rate of return) (2.5). B n on = n t = 1 I ( 1 + y) t + P ( 1 + y) n = I 1-1 ( 1 + y) n y + P ( 1 + y) n (2.5) (2.5),., (2.6). B n on = P ( 1 + y ) n y = [ P B n on ] 1/ n - 1 (2.6) (4) ( ) (price volatility). (risk hedging), (price value of a basis point, dollar value of a basis point 2) ), (yield value of a price change), (duration).. ( ) (duration), 3) 2) 1 basis point 0.01% 3). n 10

24 . Macaulay ( D m ac ) 4) (modified duration ; D m od ), (2.7), (2.8). D m ac = [ n t = 1 ti ( 1 + y ) t + np ( 1 + y ) ] 1 (2.7) n B n on B non = I ( 1 + y) + I ( 1 + y) I ( 1 + y) n +. d B non 1 I = - dy 1 + y [ ( 1 + y) + 2I ( 1 + y) = - d B non dy 1 B non 1 I 1 + y [ ( 1 + y) + 2I ( 1 + y) B non Macaulay ( D mac = [ I ( 1 + y) + 2I ( 1 + y) ni ( 1 + y) n + ni ( 1 + y) n + P ( 1 + y) n ni ( 1 + y) n + D m ac ). np ( 1 + y) ] n np ( 1 + y) ] 1 n B non np ( 1 + y) ] 1 n B non = [ n t = 1 ti ( 1 + y) t + (modified duration ; np ( 1 + y) ] 1 n B non D m od ). D mod = -, - B non = I d B non dy 1-1 B non = 1 ( 1 + y) n y 1 B non. D mod = - d B non dy 1 B non = D mac 1 + y + P [ 1 ( 1 + y) ] n 1 I y [ ( 1 + y) ] n + n (P - I/ y) ( 1 + y) n + 1 B non 4) F. Macaulay Some Theoretical Problems Suggested by the Movement of Interest Rates, Bond Yields, and Stock Prices in the U.S. Since New York : National Bureau of Economic Research. 2 11

25 D m od = - d B n on dy 1 B n on = D m ac 1 + y = I y [ ( 1 + y ) ] n + n ( P - I/ y ) ( 1 + y ) n + 1 (2.8) B n on (percentage price change). B n on B n on - D m od y (2.9) < 2-1> y ( : 10 basis point), y ( : 200 basis point). 5) ( ) - (convexity) (curvature).. < 2-2> - y * y *,. -. (Taylor series expansion) 6) 5) (convex). 6) f ( x ) x = x 0, f (x ) x 0. 12

26 (2.10), 2. B n on = d B n on dy y d 2 B n on d y 2 ( y ) 2 + (2.10) 7), B n on. < 2-2> } B * non } y * ( ) y 1 y2 y * y 3 y4 B non = d B non B non dy 1 B non y d 2 B non 1 d y 2 ( y) 2 + (2.11) B non f (x) - f ( x 0 ) = f ' ( x 0 )(x - x 0 ) + f ' ' ( x 0 ) 2! (x - x 0 ) f ( n + 1) ( x 0 ) ( n + 1)! (x - x 0 ) n + 1 7) (dollar duration ; DD)., DD = - d B non dy = D m od B non 2 13

27 , 2 8), -. (dollar convexity ; DC) (convexity ; C). D C = d 2 B n on d y 2, C = d 2 B n on d y 2 1 B n on (interest rate volatility). < 2-2> ( y 1 y 4 ), ( y 2 y 3 ).. = - D m od y = 1 2 C ( y ) 2 = - D m od y C ( y ) 2 8) 2. B non = d 2 n t = 1 B non d y 2 =, B non = I d 2 B non d y 2 = I ( 1 + y) t n t = 1 P 2, ( 1 + y) n t( t + 1)I ( 1 + y) t ( 1 + y) n y n( n + 2)P ( 1 + y) n P [ 1 2 ( 1 + y) ]. n 2I y [ ( 1 + y) ] n - 2nI y 2 ( 1 + y) n n ( n + 1)(P - I/ y) ( 1 + y) n

28 2) (1) (minimum interest rate) (base interest rate, benchmark interest rate), (on-the-run) ( ). (risk premium, spread). (intermarket or intramarket sector spread), (quality or credit spread), (maturity spread),,,. (2) ( ) (term structure of interest rate), (yield curve). (normal or positive yield curve). ( 1996),, ABS MBS. ( ) (spot rate) 2 15

29 .. (theoretical spot rate). n r n, n ( z n ) (bootstrapping). ( CI n ) : ( P) ( r n P ) CI n = ( 1 + r n )P ( CO 0 ) : ( B n on ) CO 0 = B non - r n [ z ( 1 + z 2 ) ( 1 + z n - 1 ) n - 1 ] P 1 n : z n = ( CI n n - CO 0 ) 1 (2.12) ( ) (forward rate).. n n-1 n, f n (2.13). ( 1 + z n ) n = ( 1 + z n - 1 ) n - 1 ( 1 + f n ) f n = ( 1 + z n ) n ( 1 + z n - 1 ) n (2.13). 16

30 ( ) (expectation theory), (liquidity preference theory), (market segmentation theory).., ( ) ( ).,. 9) (uncertainty)..,..,, ( ),., 9) Eugene F. Fama "Forward Rates as Predictors of Future Spot Rates". Journal of Financial Economics. Vol. 3, No

31 ,. 3) (1) (option). (contingent claim), (underlying security). (exercise price, strike price), (European option), (American option). (call option), (put option). (2.14), (2.15). C p = M ax [ 0, ( B T - X ) ] (2.14) P p = M ax [ 0, ( X - B T ) ] (2.15) C p B T :, P p : :, X :. (period of call protection) (callable bond).,. (reinvestment risk), 18

32 (price compression).. (2) - < 2-3> aa, ab. - (positive convexity). - ( y * ) convexity). (negative < 2-3> a ' B * b CP a y* (long position) (call option) (short position) 2 19

33 . < 2-3> ( C p ) aa ab. B cop = B n on - C p C p = B n on - B cop (2.16) B cop :, C p :,. B pop = B n on + P p (2.17) B p op :, P p : (3) Black & Scholes(1973),. Cox, Ross & Rubinstein(1979) (Option Pricing Model) 10) (binomial interest-rate tree model) Black(1976). ( ) < 2-4>. ( ), 1 1 r 1H, 1 r 1L. 10) Cox, Ross & Rubinstein (underlying price), (striking price), (range of movement). 20

34 ( y) (random process).., N H N H H N H L , , 1 +. < 2-4> 3 r3 H H H r2 H H N H H H r1 H N H H r3 H H L r0 N H r2 H L N H H L N r1 L N H L r3h L L N L r2 L L N H L L N L L r3l L L N L L L 1 2 3,. 2 21

35 1, 1/ 2.,,. 3 MBS. ( ) Black Black & Scholes(1973), (futures contract) 11)., Black & Scholes Black(1976). Black. (2.18) (geometric Brownian motion) 12). df = F d t + F dz (2.18) F :, : F, : F (volatility) t :, dz : Wiener, (lognormal distribution) 13), (nonstochastic) 14) 11). 12) dz Brownian motion Wiener process., dz dt dz = dt. N ( 0, 1)., 0, 1., dt dz.,, Markov process. 13),.,, 22

36 Black (2.19), (2.20). C p = e - r T [ F N ( d 1 ) - X N ( d 2 ) ] (2.19) P p = e - r T [ X N ( - d 2 ) - F N ( - d 1 ) ] (2.20), d 1 = ln ( F / X ) + T 2 T / 2 d 2 = ln ( F / X ) - T 2 T / 2 T : ( ) X : = d 1 - T r : T N ( d i ) : 15) (2.19), (2.20)., F (2.21). F = ( B - I p v ) e r T (2.21) B : I pv : 16). 14) (stochastic process), (nonstochastic). 15) N ( d i ) 0, 1,, d i. 16). 2 23

37 2. 1).,,,. (2.22). S 0 = t = 1 D t ( 1 + r) t (2.22) S 0 D t r : 0 : t : D, (2.23). S 0 = t = 1 D ( 1 + r) t = D r (2.23) (g), (2.24). 17) S 0 = D 1 r - g (, r>g 18) ) (2.24) 17) S 0 = D 1 ( 1 + r) + D 1 ( 1 + g) ( 1 + r) D 1 ( 1 + g) ( 1 + r) - 1 = D 1 r - g 24

38 S 0 : 1 g : (2.24),,,,. 2) (2.24), g.,, g. (NOI : net operating income), NOI b, k, (2.25). N OI t = N OI t b N OI t - 1 k = N OI t - 1 ( 1 + b k) (2.25) N OI t : t, N OI t - 1 : t-1 (k), (ROE : return on equity). (2.25) (2.26). N OI t = N OI t - 1 ( 1 + b R OE ) (2.26) 18) r g (2.24). 2 25

39 (2.26) b ROE, g, N OI t N OI t - 1 (2.27). N OI t = N OI t - 1 ( 1 + g ) (2.27) (EPS : earning per share) NOI (2.26) (2.27) (2.28). E P S t = E P S t - 1 ( 1 + b R OE ) = E P S t - 1 ( 1 + g ) (2.28) E P S t : t, E P S t - 1 : t-1 EPS, (2.23) (2.29). S 0 = D r = E P S r (2.29) (PVGO : present value of growth opportunity). S 0 = E P S r + P VGO (2.30) PVGO : PVGO (2.31) (NPV : net present value). P VGO = t = 1 N P V t ( 1 + r) t (2.31), (b) (ROE) 26

40 , t ( b E P S t ) t (2.32). 19) N P V t = - b E P S t + b E P S t R OE ( 1 + r) = - b E P S t + b E P S t R OE r + b E P S t R OE ( 1 + r) 2 + (2.32) (2.28) (2.32), (2.33). 20) N P V t = N P V t - 1 ( 1 + b R OE ) (2.33) (2.33) ( N P V t ) N P V 1 (2.34). N P V t = N P V 1 ( 1 + b R OE ) t - 1 (2.34) (2.34) (2.31) PVGO (2.35). 21) P VGO = t = 1 N P V t ( 1 + r) t = N P V 1 r - b R OE (2.35) (2.35) (2.30), (2.36). S 0 = E P S r + P VGO = E P S r + N P V 1 r - b R OE (2.36) 19) (2.32) NP V t >0 R OE > r., NP V t >0 b E PS t R OE r > b E PS t R OE > r. R OE < r, N P V t <0. 20) N P V t = - b E P S t - 1 ( 1 + b R OE ) + b E PS t - 1 ( 1 + b R OE ) R OE r = [ - b E PS t b E PS t - 1 R OE r ] ( 1 + b R OE ) = NP V t - 1 ( 1 + b R OE ) 21) P V GO = t = 1 t - 1 N P V t NP V 1 ( 1 + b R OE ) ( 1 + r) t = t= 1 ( 1 + r) t = NP V 1 r - b R OE 2 27

41 ,,,. 22) 22) (2.24), (2.36) S 0 = S 0 = = E PS 1 r E PS 1 r E P S ( = E PS 1 ) r + ( E P S 1 b)( (R OE - r)/ r). r - b R OE D 1 r - g = E PS 1 ( 1 - b) r - b R OE + P V GO= E PS 1 r +, NP V 1 r - b R OE + ( E P S 1 b)( (R OE - r)/ r) E PS 1 ( 1 - b). r - b R OE r - b R OE 28

42 3 C H A T E R 1. MBS 1) MBS.., 23) (value additivity rule) Vasicek(1977). Cox, Ingersoll & Ross(1980), (Brownian motion). (1996), (2001), 23)

43 .. MBS (1999), Fabozzi(1996) (binomial interest-rate tree model) MBS. 2) MBS (MBS). MBS,. (equity-type), (bond-type), (hybrid-type). MBS MBS. MBS (MPTS ; Mortgage Pass-Through Securities). MBS MBS. MBS (MBB ; Mortgage Backed-Bond). MBS., MBS, MBS. MBS 30

44 (MPTB ; Mortgage Pay-Through Bond). MPTB (Multi-class Securities) (CMO ; Collateralized Mortgage Obligation). MBS MBB. MBB, MBS MPTS MPTB. MBB MBB. (mortgage loan) (prepayment). MBB MBB MBB (call option). MBB, MBB MBB MBB. Cox, Ross & Rubinstein(1979) (option pricing model) Black(1976), MBB. KoMoCo MBS MBS. KoMoCo MBS,,,. 3 31

45 3) MBB (1) MBB MBB. MBB MBB. n MBB 2 (2.1) (3.1). MBB non = n t = 1 MB B n on I ( 1 + y) t + P ( 1 + y) n = I 1-1 ( 1 + y) n y : MBB, I : P :, y : ( ) + P ( 1 + y ) n (3.1) (3.1) MBB (y) (n). MBB, MBB., 2 < 2-1> (convex). MBB.,. (2) MBB MBB (price volatility) MBB MBB, (risk hedging). 32

46 2, MBB.. MBB,.. MBB -. MBB -. 2 < 2-2> MBB -., y * y * MBB. MBB - MBB. 2.,.,., MBB, MBB. 4) MBB (1) MBB MBB MBB MBB. MBB (period of call 3 33

47 protection) MBB MBB(callable MBB). MBB MBB MBB,., MBB (reinvestment risk)., MBB (price compression). MBB MBB. MBB MBB -, MBB - 2 < 2-1> (positive convexity)., MBB - < 3-1> MBB MBB MBB a ' MBB MBB * b CP MBB a y* ( y * ) 34

48 (negative convexity). < 3-1> aa MBB -, ab MBB -. (2) MBB MBB MBB, (call option). < 3-1> ( C p ) aa - ab, 2 (2.16) MBB (3.2). MB B cop = MB B n on - C p C p = MB B n on - MB B cop (3.2) MB B cop : MBB, C p : (3) MBB ( ) 2 (binomial interest-rate tree model) MBB. MBB MBB. 24) MBB MBB,. (interest-rate volatility) MBB. < 3-2> 24) Andrew J. Kalotay, George O. William, and Frank J. Fabozzi "A Model for the Valuation of Bonds and Embedded Options". Finacial Analysts Journal. pp

49 (node : ) ( 1 ), 1 1 r 1H, 1 r 1L. < 3-2> 3 MBB r3 H H H N H H H r2 H H r1 H N H H r3 H H L r0 N H r2 H L N H H L N r1 L N H L r3 H L L N L r2 L L N H L L N L L r3 L L L N L L L ( y) (random process), 1, 2 (3.3). r 1H = r 1L ( e 2 y ), r 2HH = r 2L L ( e 4 y) (3.3) y : 1 25) MBB MBB 25) e 2 y y, 1. r e 2 y - r 2 r + 2 y r - r 2 = y r 36

50 MBB., N H MBB N HH N H L MBB. 1 MBB 1 (coupon payment). 1, 1 MBB 1. 1 MBB + 1 MBB +., N H N H H MBB + N H L MBB +., MBB. 1. 1, 1/ 2 N MBB (3.4). MB B ( n ) = 1 2 [ V H + I r * V L + I 1 + r * ] (3.4) MB B ( n ) : N MBB V H : 1 MBB I V L : 1 MBB :, r * : N MBB, MBB (K), n MBB, MB B ( n ) cop. 3 37

51 MB B ( n ) cop = M in [ MB B ( n ), K ] (3.5) ( ) Black Black(1976), 2 (2.19) MBB. (2.19) F (2.21) MBB (3.6). F = ( MB B n on - I pv ) e r T (3.6) I pv : 26) MBB (volatility). MBB. MBB MBB (3.7). MB B n on MB B n on - D m od y = - D m od y y y (3.7) (3.7) MBB MBB y., (3.7) (3.8). = D m od y y (3.8) 26) I pv. 38

52 5) (1) KoMoCo MBS KoMoCo ,440 ( ) MBS. KoMoCo KoMoCo MBS MBB. < 3-1> KoMoCo MBS MBS ( ) 2, Tranche % 3 AAA : / KoMoCo MBS MBS Tranche, MBS, MBB., Tranche KoMoCo. 27), 5 MBS 27) KoMoCo( MBS

53 . 7 Tranche MBS. MBS MBS (mortgage loan) (prepayment risk) (interest rate risk). KoMoCo MBS , MBS. (2) KoMoCo MBS MBS < 3-2>, < 3-3> (normal or positive yield curve).. < 3-2> KoMoCo MBS ( : %) (6.59) : ( ) KoMoCo MBS ( ) 40

54 < 3-3> KoMoCo MBS MBS 4 MBS. MBS.,, KoMoCo MBS , MBS < 3-3>., 5 MBS 1% MBS ( D m od ) 4.23% (C) 0.10%. 28) 1% MBS 4.33%. MBS. 28) (C) MBS C/ 2 ( y) 2 1% C MBS 0.10%. 3 41

55 < 3-3> KoMoCo MBS ( D m od ) (C) MBB ( + ) (3) MBS ( ) KoMoCo MBS MBS., KoMoCo MBS MBB., MBS 100.,,., 4, 1., MBS 1.,,,., ( y) ) ( ) 2 MBS, 1 : t r t, 2 MBS 1 29) KoMoCo MBS. MBS %, 0.15, %,

56 ( r 1 ) (0.07) r 1 e 2 y(0.085). 2 : r 1, r 1 e 2 y 1 MBS MBS. 2 MBS. 2 MBS 100, MBS ( V H ) MBS ( V L ) [ V H + I 1 + r * + V L + I 1 + r * ] N MBS. r * %, MBS : 2 MBS (99.86 ) MBS (100 ) r 1. r 1 1, r

57 < 3-4> 2 KoMoCo MBS N V = 100 C = 0 r 0 = 6.57% N H N L V = C = 6.57 r1,h = 8.37% V = C = 6.57 r1,l = 6.85% N H N H N L L V = 100 C = 6.57 r2,h H =? V = 100 C = 6.57 r2,h L =? V = 100 C = 6.57 r2, L L =? 3 MBS. 3 MBS 1 r 1 2 r 2. r 1 r 2 (0.0664). r 2, r 2 e 2 y, r 2 e 4 y 3 MBS. 4, 5 MBS, 3, 4 < 3-4>. < 3-4> KoMoCo MBS n ( : %) MBS MBS 44

58 MBS. KoMoCo 2 MBS < 3-5> (3.5), MBS = Min[ MBS, ] MBS < 3-5> 2 KoMoCo MBS N V = C = 0 r0 = 6.57% N H N L V = C = 6.57 r1,h = 8.37% V = 100 ( ) C = 6.57 N H N H N L L V = 100 C = 6.57 r2,h H =? V = 100 C = 6.57 r2,h L =? V = 100 C = 6.57 r2,l L =? MBS MBS, (3.2). KoMoCo 2 MBS, MBS 100 MBS KoMoCo MBS MBS < 3-5>, 2 5 MBS MBS MBS. 3 45

59 MBS MBS. (3.1) 3 MBS, MBS 7.41% MBS 7.31%., 3 MBS 0.1%. 2 5 MBS %.. < 3-5> KoMoCo MBS ( : 1 ) ( : / MBS 100 ) MBS MBS ( ) Black Black(1976) KoMoCo MBS , < 3-6>.,. < 3-6> KoMoCo MBS (Black : 1 ) ( : / MBS 100 ) MBS

60 KoMoCo MBS MBS 1, 2 5 MBS < 3-7> MBS , %. KoMoCo MBS %, %,, %. MBS,,. MBS,. KoMoCo 30%, KoMoCo MBS (LTV; Loan-to-Value) 30%, 1 2%, AAA %. MBS MBS. < 3-7> KoMoCo MBS (Black : MBS 1 ) ( : / MBS 100 ) MBS

61 2. REITs 1) Capozza & Lee REITs Capozza and Lee(1995, 1996). Capozza and Lee. REITs (3.9). P V = N OI 1 r - g (3.9) PV : NOI1 : 1 r : g : (3.9) (r - g) (capitalization rate), R, (3.10). P V = N OI 1 R (3.10) R : (capitalization rate) Capozza and Lee REITs (property asset valuation) 30) (value additivity 30) REITs. 48

62 principle) (capital structure irrelevance). 31) REITs n REITs (3.11). RV = TV + OV = E + D (3.11) RV : REITs TV : REITs = n i = 1 P V i OV : PVi : REITs i E : REITs D : REITs, REITs REITs. n REITs TV (3.10) (3.12). T V = n i = 1 P V i = n i = 1( N OI i 1 R i ) (3.12) NOI1i : i 1 Ri : i Capozza and Lee, (3.10) N OI i 1 = ( P V i R i ), (3.13). 31) REITs, Modigliani & Miller(1958). 3 49

63 n i = 1 N OI i 1 = n i = 1 (R i P V i ) = T V w (3.13) w : (3.13) (3.14), REITs i 1. T V = n i = 1 N OI i 1 w i (3.15). (3.14) wg t i = n i = 1 PR i SF i ( PR i SF i ) (3.15) wgti = i ( n i = 1 wg t i = 1) PRi = 1 SFi = i i (wgti) (Ri). (3.16). w = n i = 1 ( wg t i R i ) (3.16), (3.14) REITs. (3.11) REITs (net asset value) (3.17), Capozza and Lee (Main Street Valuation Model). 50

64 = + - (3.17) Capozza and Lee, REITs. Capozza and Lee REITs ( ), REITs., REITs(equity REITs) 7% (discount). REITs REITs (capital structure), (diversification strategy), (management contracts).. REITs REITs, REITs REITs, REITs REITs, REITs REITs, (premium). 2) REITs. REITs, REITs, CR-REITs 3 51

65 . REITs CR-REITs Capozza and Lee (Main Street Valuation Model)., REITs., REITs 2 (3.18) REITs. V R = V R D 1 r - g : REITs (3.18) (3.18) REITs ( V R ) 1 ( ) ( D 1 ), (r), (g).,,, (capital gain)., REITs CR-REITs 32), D 1.., REITs CR-REITs 1, D 1 (, 1 ). 32) REITs CR-REITs,. REITs CR-REITs,. 52

66 D = N OI - R E - TX (3.19) RE : 1 TX : 1 ( ) 1 (RE) 10% (90% ), 10% 33) NOI 9%( 10/ 110). 1 TX REITs NOI 30.8%, CR-REITs 30.8%. REITs CR-REITs (D) NOI (3.20), (3.21). D R = N OI (3.20) D R : REITs 1 D CR = N OI (3.21) D CR : CR-REITs 1 NOI 1 1. N OI = NR - T C (3.22) NR : 1 TC : 1 1 (NR) 1 (TR) 1, 1,, (,,,,,, ) 34) (,, 33) ),, 3 53

67 ,, 1 ), (,,, ). NR = TR - V C (3.23) TR : 1, VC : 1 T C = R T C + OT C (3.24) RTC : 1 OTC : 1 (3.23), (3.24) (3.22), (3.20), (3.21), REITs CR-REITs 1. D R = ( TR - V C - R T C - OT C) (3.25) D CR = 0.882( TR - V C - R T C - O T C) (3.26) (3.25), (3.26). < 3-8> (RTC) (TR) 13.71%, (OTC) TR 14.61%. (VC),,. TR RTC TR OTC (3.25), (3.26), TR VC x, (3.27), (3.28) % 1. 54

68 < 3-8> REITs (bp) %, 30 (B) (30), (30), (30), (35), (12), (5) ( %), ( ( 32-35%) 35% ) (C) (100), agency (100), (10), (5), (48), (1) 1 : 1 (D) / 100 5% ( ), 18%. 0.1% ( 72bp) (100), (5), (10), (E) 116 (1) (F) 2 CR-REIT. 5 1 ( 3, 1) (G) 407 G = B + (C 35%) + (D / 5) + E + F :, D R = ( TR - V C - R T C - OT C) = ( x ) TR (3.27) x : 1 D CR = 0.882( TR - V C - R T C - O T C) = ( x ) (3.28) TR < 3-9>, 8% 1 REITs CR-REITs 1 %. 3 55

69 < 3-9> 1 8% ( : %) REITs CR- REITs , 3%( 2%, 1% ), 8% 1 REITs 19.28%, CR-REITs 13.21%. REITs CR-REITs, REITs CR-REITs.,, 1, REITs CR-REITs (3.18), (3.27), (3.28) (3.29), (3.30). V R = ( x ) TR 1 r - g V CR = ( x ) TR 1 r - g (3.29) (3.30) V CR : CR-REITs 1 ( T R 1 ), (r), (g), (x), REITs,,. 56

70 V R TR 1 = ( x ) ( r - g) - 1 V R r V R g V R x = - { ( x) TR 1 } ( r - g) - 2 = { ( x) TR 1 } ( r - g ) - 2 = ( TR 1 ) ( r - g) - 1 REITs CR-REITs,,, REITs CR-REITs (2.40) (3.27), (3.28) (3.31), (3.32). V R = ( x ) TR 1 r - b R OE V CR = ( x ) TR 1 r - b R OE (3.31) (3.32) (3.31) (3.32) (x) 71% CR-REITs REITs, CR-REITs. REITs CR-REITs 0 x 71.9%, 71.6%. 3 57

71 4 C H A P T E R 1. 1) (volatility).,.., (business risk), (strategic risk), (financial risk). 35), (business risk) (competitive advantage),.,,.. 35) Jorion, P Value at Risk : The New Benchmark for Controlling Market Risk. IRWIN. 4 59

72 , (strategic risk). (hedge)., (financial risk) (financial market).,,., (financial risk). MBS,,, Block(1998)., VaR(Value at Risk). 2) (1) MBS, (, ),,.. (liquidity risk)., 60

73 . 1,. (credit risk) (default risk) (delayed payment risk)...,,, (LTV; Loan-to-Value), (PTI; Payment-to-Income).. LTV 20 30%, 70%.. KoMoCo MBS 1% (mortgage loan) MBS MBS. 36) 36) MBS,,. MBS 4 61

74 , MBS (MBB) MBS (MPTB), MBS (MPTS) MPTS. MPTS MPTS. (interest risk).,.. MBS 3 MBS MBS MBS. KoMoCo 5 MBS 1% MBS 4.33%. (prepayment risk), MBS, (MPTS; Mortgage Pass-Through Securities). MBS MBS, (MBB; Mortgage Backed-Bond). MBS MBS, MBS (MPTB; Mortgage Pay-Through Bond). 62

75 . (prevailing mortgage rate) (contract rate),,,,,.,. MBB, MPTS MPTB.. KoMoCo MBS 1 2% 1%.,. 3, MBS, MBS. (title risk), (hazard risk), (pipeline risk),. 4 63

76 (2)..,. 37) REITs 56%, REITs 37%. 2. 1) (trade-off) 38). 37) Block, R. L Investing in REITs. Bloomberg Press. 38).. 64

77 (hedge),.,,,. (hedge)..,, 1 1,. 1,.. 2 MBS -,..,,,,.,. MBS. MBS MBB, MPTS MPTB 4 65

78 . MBB MBB, MBB,,. MBB. MPTS, MPTS,,,. MPTS., 1. MPTB, MPTS,,., MBB MBB, MPTS MPTB. MBS., MBS (reference rate ; ) MBB(Floating-rate MBB) MBB(Inverse floating-rate MBB) MBB. 66

79 100, 7.5% MBB + 1% ( = 15%) MBB 14% - ( = 0%) MBB 50 MBB. 39) MBB MBB. SWAP 40), MBS. (systematic risk) 41) (unsystematic rick)..,, (hedge ratio),. 39) MBB MBB 0.5 ( +1%) (14%- ) = 7.5% 7.5% MBB. 40) SWAP. SWAP SWAP. 41),. 4 67

80 2) VaR.. VaR(Value at Risk). (1) VaR VaR,., 1 VaR 95 % 10, %. VaR,.. VaR VaR. (2) VaR VaR. (Delta Analysis Method), 68

81 (Historical Simulation), (Stress Testing), (Monte Carlo Simulation). VaR (parametric method), VaR (nonparametric method).. ( ) (Delta Analysis Method) VaR..,. (risk factor) (delta)., (linear approximation).,.. VaR

82 1,. (duration), (beta) 42)., -. VaR n.. V p = V p p i n p i i = 1 : : i (4.1) ( t) (4.2). V p = n i = 1 p i (4.2) V p : (4.3), (4.4). E [ V p ] = n i = 1 E [ p i ] (4.3) 2 V p = E [ ( n i = 1 p i - n i = 1 E [ p i ]) 2 ] (4.4) E [ ] : (operator), 2 V p : V p (t) V p ( t) E [ V p ( t) ], 42). 70

83 VaR (4.5), (4.6). E [ V p ] = E [ V p ( t) ] - V p ( 0) (4.5) VaR = E [ V p ( t) ] - V p ( t) (4.6) VaR,,,. 43) VaR,., (+) (-)., VaR. VaR.,, -VaR, VaR. (F) k, (4.7). V p V p = k j = 1( V p / V p F j / F j ) F j F j (4.7),. 43) VaR. :. 4 71

84 p i p i = k j = 1( p i / p i F j / F j (4.2), (4.8) (4.9). V p = n i = 1[ k F j / F j j = 1( p i / p i ) F j F j (4.8) )( F j F j )] p i (4.9),, (nonlinear payoff). ( ). ( ) (Historical-Simulation Method) VaR., VaR. 95% 1 VaR ,, VaR., 72

85 .,. ( ) (Stress Testing) (Scenario Analysis).,.,,., 1% VaR.. VaR.. VaR.. VaR... VaR. 4 73

86 ( ) (Structured Monte Carlo)..., (stochastic process). ( )....,.. VaR... VaR. VaR.,,, < 4-1>. 74

87 < 4-1> VaR (avoid model risk) (communicability).,. VaR, VaR..,

88 ...,, VaR.. (3) VaR VaR,.,. VaR,., VaR,. VaR, VaR. VaR (stable).,. VaR.,. VaR. 76

89 VaR.,,. VaR.. VaR. VaR..,,. MBS ABS,,,, REITs.,.,,,. 4 77

90 5 C H A P T E R,. 1998,, ,..,. 5 79

91 , (ABS) (MBS),. MBS,,,, REITs., (KoMoCo),,. MBS MBS 2 5 MBS , 7.41% 6.59% 0.82% (spread) 3 MBS, %, 0.10%,, MBS. 1 MBS , 80

92 . 8% 18%, 12%., ( ).,...,,, ( ).,

93 .,,,,,.,. VaR. VaR....,. 82

94 : VaR. :.. : : (REITs)? Black, F The Pricing of Commodity Contracts. Journal of Financial Economics. Black, F., Derman, E. & Toy, W One-Factor Model of Interest Rate and its Application to Treasury Bond Options. Financial Analysts Journal. Black, F., & Karasinski, P Bond and Option Pricing when Short Rates are Lognormal. Financial Analysts Journal. Black, F., Scholes, M The Pricing of Options and Corporate Liabilities. Journal of Political Economy. Block, R. L Investing in REITs. Bloomberg Press. 83

95 Cappzza, D. R. & Sohan Lee Portfolio Characteristics and Net Asset Values in REITs. Canadian Journal of Economics. Cappzza, D. R. & Sohan Lee Property Type, Size, and REIT Value. Journal of Real Estate Research. Cox, J. C., Ingersoll, J. & Ross, S. A An Analysis of Variable Rate Loan Contracts. Journal of Finance. Cox, J. C., Ross, S. A. & Rubinstein, M Option Pricing: A Simplified Approach. Journal of Financial Economics. Fabozzi, F. J Bond Markets, Analysis and Strategies. Prentice Hall. Fama, E. F Forward Rates as Predictors of Future Spot Rates". Journal of Financial Economics. Heath, D., Jarrow, R. & Morton, A Bond Pricing and the Term Structure of Interest Rates: A New Methology for Contingent Claims Valuation. Econometrica, Vol. 60. Ho, T. S. Y. & Lee, S. B Term Structure Movements and Pricing Interest Rate Contingent Claims. Journal of Finance. Vol. 41. Hull, J. & White, A Pricing Interest Rate Derivative Securities. Review of Financial Studies. Vol. 3. Jorion, P Value at Risk : The New Benchmark for Controlling Market Risk. IRWIN. Kalotay, A. J., William, G. O. & Fabozzi, F. J A Model for the Valuation of Bonds and Embedded Options. Finacial Analysts Journal. Kuhn, R. L Mortgage and Asset Securitization. Dow-Jones Irwin. Macaulay, F Some Theoretical Problems Suggested by the Movement of Interest Rates, Bond Yields, and Stock Prices in the U.S. Since New York: National Bureau of Economic Research. Merton, R. C Continuous-Time Finance. Blackwell Publishers Inc. 84

96 Modigliani, F. & Miller, M. H The Cost of Capital, Corporation Finance and the Theory of Investment. American Economic Review. Miller, M. H. & Modigliani, F Dividend Policy, Growth and the Valuation o Shares. Journal of Business. Vasicek, O. A An Equilibrium Characterization of the Term Structure. Journal of Financial Economics. 85

97 SUMMARY Application of Financial Engineering Method on Real Estate: Value Assess ment and Ris k Management of MBS and REITs Geun- Yong K im J u- hy un Y oon Korean economy encountered seriou s liquidity problems, so-called foreign exchange and financial crisis, in Real estate securitization w as so urgently needed to aid restructuring of entrepreneurs and banks that government has implemented several measures to promote real estate finance in Korea. Asset securitization including mortgage securitization w as introduced to Korea in 1998 with the enactment of the Asset Securitization Law that was followed by the Act on Housing Mortgage Securitization Companies. And real estate investment companies were allow ed with the enactment of the Real Estate Investment Companies Law in July 2001 In spite that the new financing methods like securitization and investment finance were institutionally introduced in real estate sector, 87

98 it is early to expect these new methods work efficiently. Since real estate sector in Korea has been working based on the speculative incentives rather than the cash-flow incentives and the supporting system of the new financing methods is in the premature stage. One of the issues in supporting system is that pricing model of financial products concerning real estate properties is very rare to be used. In order to promote securitization and investment in the real estate sector, analytical tools like financial engineering should be applied to evaluate and design financial commodities concerning real estate like ABS, MBS, REITs. This study is the trial to adopt financial engineering method to evaluate MBS and REITs. Thus, the purpose of this study is to set up the pricing model of MBB(mortgage-backed-bond) and REITs, and to identify the financial risks embedded in real estate financial products in order to suggest the risk management method. This study consists of five chapters. The second chapter, next to an introduction, reviews theoretical background of pricing models on general bonds and stocks in advance to the application of the model to real estate financial products. For the case of bond pricing model, option-free bond and option-embedded bond are separately reviewed in consideration of applicability to the MBB with call option that allows prepayment. And for the case of stock pricing model, dividend evaluation model and growth opportunity model are reviewed. In chapter three, pricing models reveiwed in the second chapter are applied to MBS and REITs. This chapter suggests pricing models of MBBwithout option and then MBB with call option by using the principle of pricing bonds. The basic frameworks of the pricing model employed are Option Pricing Models su ggested by Cox, Ross & Rubinstein(1979) and Black(1976). These theoretical models will be used to analyze each value of MBS and call option given to the issuer by exemplifying the MBS that have been issued by KoMoCo, lately. And then, the pricing 88

99 model of REITs is suggested based on Capozza & Lee(1995, 1996), dividend evaluation model, and growth opportunity model that are review ed in the second chapter. The fourth chapter classifies the risk types of real estate financial products and suggests the risks management methods. Securitization is one way to hedge risks prevailed in real estate, however, it is not sufficient since real estate financial products includes intrinsic risks of financial products as w ell as additional risk transferred from real estate. Recently measuring the risks by VaR(Value at Risk) is attempted as a comprehensive management method of each risk. Unfortunately, this study does not attempt to measure VaR due to the lack of concerning data, instead, suggest measurement method like delta analysis, historical simulation method, stress testing method, and structural Monte-Carlo analysis etc. The last chapter summarizes the core contents of each chapter. It insists the necessity of data accumulation for concrete results of the model analysis and the need of infrastructure that is channeling the analytical results to the individual investors. In the case of housing mortgage loans, the loan borrowers have the right to redeem the loan earlier than the date due. By this reason, the financial institutions usually issue MBB with embedded call option that enables them to buy back MBB earlier than its maturity so as to coincide the cash flows of housing mortgage loans to those of MBB. 89