Hw2a - UNIVERSITY OF TORONTO Joseph L Rotman School of Management RSM332 PROBLEM SET#2 SOLUTIONS 1(a The expected returns on each security are all

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: UNIVERSITY OF TORONTO Joseph L. Rotman School of Management RSM332 PROBLEM SET #2 SOLUTIONS 1. (a) The expected returns on each security are all equal to 17%. As an example of how to calculate this, E [ R 1 ] = 0 . 4(0 . 3) + 0 . 4(0 . 1) + 0 . 1(0 . 1) + 0 . 1(0 . 0) = 0 . 17 or 17% . The standard deviations on each security are respectively, σ 1 = 11%, σ 2 = 46 . 05%, and σ 3 = 10 . 3%. As an example of how to calculate this, σ 1 = h . 4(0 . 3- . 17) 2 + 0 . 4(0 . 1- . 17) 2 + 0 . 1(0 . 1- . 17) 2 + 0 . 1(0 .- . 17) 2 i 1 2 = 0 . 11 . (b) The covariances between the returns are respectively, Cov[ R 1 ,R 2 ] =- . 0479, Cov[ R 1 ,R 3 ] =- . 0084, and Cov[ R 2 ,R 3 ] = 0 . 043. As an example of how to calculate this, Cov[ R 1 ,R 2 ] = 0 . 4(0 . 3- . 17)(- . 3- . 17) + 0 . 4(0 . 1- . 17)(0 . 3- . 17) + 0 . 1(0 . 1- . 17)(0 . 5- . 17) + 0 . 1(0 .- . 17)(1 . 2- . 17) =- . 0479 . The correlations between the returns of different securities are respectively, Corr[ R 1 ,R 2 ] =- 0.9456, Corr[ R 1 ,R 3 ] =- 0.7414 and Corr[ R 2 ,R 3 ] = 0.9195. As an example of how to calculate this, Corr[ R 1 ,R 2 ] ≡ Cov[ R 1 ,R 2 ] σ 1 σ 2 =- . 0479 (0 . 11)(0 . 4605) =- . 9456 . (c) The expected return and standard deviation of a portfolio with equal proportions in two securities ( i and j ) is given by μ p = 0 . 5 E [ R i ] + 0 . 5 E [ R j ] , σ p = q . 25 σ 2 i + 0 . 25 σ 2 j + 0 . 5Cov[ R i ,R j ] . Substituting in the values in parts (a) and (b) above gives us the same mean return on each of the portfolios, i.e. 17%. Substituting in the values in parts (a) and (b), 1 the standard deviations of the portfolios are (i) σ p = 0 . 1792 for the equally weighted portfolio of assets 1 and 2, (ii) σ p = 0 . 0384 for the equally weighted portfolio of assets 1 and 3, and (iii) σ p = 0 . 2778 for the equally weighted portfolio of assets 2 and 3....
View Full Document

This note was uploaded on 11/29/2011 for the course RSM 332 taught by Professor Raymondkan during the Winter '08 term at University of Toronto- Toronto.

Page1 / 5

Hw2a - UNIVERSITY OF TORONTO Joseph L Rotman School of Management RSM332 PROBLEM SET#2 SOLUTIONS 1(a The expected returns on each security are all

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