23.single_index_ex

23.single_index_ex - 370.61670 0.004105009 1-0.0043 0.94...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
University of California, Los Angeles Department of Statistics Statistics C183/C283 Instructor: Nicolas Christou Single index model - example For three stocks you are given the following data based on the single index model: Stock α β σ 2 ± A -0.0043 0.94 0.0033 B 0.0059 0.61 0.0038 C 0.0048 1.12 0.0046 Assume ¯ Rm = 0 . 01 and σ 2 m = 0 . 0018. Below you are given the solution to the problem (point of tangency) when short sales are allowed and R f = 0 . 005 using two methods: A. Using the formula Z = Σ - 1 R : Z = Σ - 1 R = 0 . 00489048 0 . 00103212 0 . 00189504 0 . 00103212 0 . 00446978 0 . 00122976 0 . 00189504 0 . 00122976 0 . 00685792 ! - 1 0 . 0051 - 0 . 005 0 . 0120 - 0 . 005 0 . 0160 - 0 . 005 ! = - 0 . 883563202 1 . 327096101 1 . 610164293 ! . The sum of the z i ’s is 3 i =1 z i = 2 . 053697192 and therefore the x i ’s are: x 1 = - 0 . 4302 ,x 2 = 0 . 6462 ,x 3 = 0 . 7840. B. Using the single index model: Ranking the stocks based on the excess return to beta ratio. Stock i α i ˆ β i ¯ R i ˆ σ 2 ±i R i - R f ˆ β i ( ¯ R i - R f ) ˆ β i ˆ σ 2 ±i i j =1 ( ¯ R j - R f ) ˆ β j ˆ σ 2 ±j ˆ β 2 i ˆ σ 2 ±i i j =1 ˆ β 2 j ˆ σ 2 ±j C i 2 0.0059 0.61 0.0120 0.0038 0.0114754098 1.12368421 1.123684 97.92105 97.92105 0.001719548 3 0.0048 1.12 0.0160 0.0046 0.0098214286 2.67826087 3.801945 272.69565
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 370.61670 0.004105009 1-0.0043 0.94 0.0051 0.0033 0.0001063830 0.02848485 3.830430 267.75758 638.37428 0.003208254 From the table above we get C * = 0 . 003208254 (short sales are allowed therefore C * is the last C i . Using, z i = i 2 i R i-R f i-C * we compute the z i s . We get: z 1 = . 94 . 0033 [0 . 0001063830-. 003208254] =-. 8835632 z 2 = . 61 . 0038 [0 . 0114754098-. 003208254] = 1 . 3270961 z 3 = . 1 . 12 . 0046 [0 . 0098214286-. 003208254] = 1 . 610164 The sum of the z i s is: 3 X i =1 z i = 2 . 053697 , and therefore using x i = z i n i =1 z i we compute the x i s : x 1 =-. 8835632 2 . 053697 =-. 4302305. x 2 = 1 . 3270961 2 . 053697 = 0 . 6461985. x 3 = 1 . 610164 2 . 053697 = 0 . 7840320. The two methods give exactly the same answer....
View Full Document

Ask a homework question - tutors are online