as372w10a2soln

as372w10a2soln - Solution 1. (a) Average Returns (assume...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solution 1. (a) Average Returns (assume arithmetic average): x small cap = 5 X i =1 R i = . 1851 + + 0 . 1255 5 = 17 . 384% x market = . 1202 + + 0 . 1453 5 = 11 . 5% (b) Variance and Standard deviation. First note that the sample (unbiased) variance estimates for a sample of N observations is given by 2 = 1 N- 1 N X i =1 ( x i- x ) 2 = 1 N- 1 N X i =1 x 2 i- N x 2 ! . Note, the sample estimate should be divided by N- 1, instead of N for the unbiasedness. Hence 2 small cap = 1 4 (0 . 34644504- 5 . 17384 2 ) = 0 . 048835828 small cap = . 048835828 = 22 . 10% 2 market = 1 4 (0 . 14178322- 5 . 115 2 ) = 0 . 018914555 market = . 018914555 = 13 . 75% (c) (unbiased) Sample covariance: small cap,market = 1 N- 1 N X i =1 ( x small cap,i- x small cap )( x market,i- x market ) = 1 N- 1 N X i =1 ( x small cap,i x market,i )- N x small cap x market ! = 1 4 (0 . 1851(0 . 1202) + + 0 . 1255(0 . 1453)- 5(0 . 17384)(0 . 115)) = 0 . 027085 Sample correlation = small cap,market small cap market = 0 . 891163 3 2. A = 0 . 2( . 123) + . 5(0 . 065) + 0 . 3(0 . 03) = 6 . 61% B = 2 . 26% 2 A = 0 . 2( . 123- A ) 2 + 0 . 5( . 065- A ) 2 + 0 . 3( . 03- A ) 2 = 0 . 00103909 A = . 00103909 = 3 . 22349% B = 3 . 10329% A,B = . 2( . 123)(- . 037) + . 5( .....
View Full Document

This note was uploaded on 06/21/2010 for the course ACTSC 5255 taught by Professor Tan,kens during the Spring '10 term at Waterloo.

Page1 / 4

as372w10a2soln - Solution 1. (a) Average Returns (assume...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online