リスクとは何か?

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1

2 Agenda Value at Risk 2

3 3 TOPIX 10 95%

4 4 TOPIX or Value at Risk

5 5 TOPIX = log TOPIX N

6 6

7 7 N TOPIX x, x, 1 2, L x N

8 8 x = N 1 EXCEL AVERAGE N i= 1 x i

9 9

10 10 σˆ 2 = 1 N ( x x) i 2 EXCEL VAR N 1 i= 1 STDEV σˆ EXCEL

11 11

12 EXCEL MEDIAN 25% 75% EXCEL QUARTILE, PERCENTILE 12

13 13 EXCEL AVEDEV N 1 x i x N 1 i=

14 TOPIX 14

15 15

16 X 16

17 17

18 18

19 19 p p 28 pˆ = = 0.07 = 400 7%

20 20

21 21 s x 1.96 < µ < x n s n µ, n : x :, s : 1.96 = NORMSINV(0.975)

22 (1 0.07) 0.07(1 0.07) < p < < p < 0.095

23 23

24 24

25 25

26 26

27 27

28 : : 50 :, 20 : p p H p p H p p > = + = ) (1 n n p p p p t 50 : 20 : : n n p

29 29 ) ( 1 NORMSDIST p = (1.521) ) 0.085( > = = = + = NORMSDIST p t

30 30

31 ˆ) ( 1 ˆ 0 1,, ˆ,,, µ σ µ = + = = + = > > = = N i i t i i i N i i N i i t i N t t t x w N N w w w w x x x x t L 1) (0 ) 1 ( < < = λ λ λ i w i

32 32 Box-Car N Moving-Window N t N N

33 33 t σ = σ annual daily 250 Box-Car Moving-Window

34 34 TOPIX TOPIX = β + β β 1 2 L + β K 2 K

35 35 ARCH GARCH = = = + + = + = + = q i i t i p i i t i t p i i t i t t t t t t t b a a p,q a a p N x , ) (0,, :, σ ε σ ε σ σ ε µ ε µ ) GARCH( ) ARCH( ARCH: AutoRegressive Conditional Heteroskedasticity GARCH:Generalized ARCH

36 Value at Risk(VaR) Value at Risk 36

37 37 Value at Risk Value at Risk(VaR) -N VaR N BIS BIS 99, N = 10

38 Value at Risk Value at Risk(VaR) X + Y ( X + Y ) Conditional VaR(CVaR)... VaR VaR CVaR 38

39 39

40 40 VaR

41 41 VaR

42 42 vs TOPIX 10 VaR t

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