1. Suppose ICT stock has a volatility (standard deviation) of 40%, and an expect

ID: 2743028 • Letter: 1

Question

1. Suppose ICT stock has a volatility (standard deviation) of 40%, and an expected return of 16%. DFW stock has a volatility of 20%, and an expected return of 10%. ICT and DFW have a correlation coefficient of 0.15. Plug in these numbers into the worksheet “2 risky securities” on my file “PS7 Spring 2016 portfolio examples” for parts b and c below. a. What is the expected return and standard deviation of a portfolio that is weighted 60% in DFW and 40% in ICT. b. What portfolio consisting of both ICT and DFW stock has the same standard deviation as being 100% invested in DFW? c. What portfolio consisting of both ICT and DFW stock has the smallest possible standard deviation?

Explanation / Answer

(‘a) Expected Return and Standard Deviation of Portfolio

Security

Weight

Expected Return

Weighted Return

DFW

60 %

0.10

6.00

ICT

40 %

0.16

6.40

Expected Return of Portfolio

12.4 %

Standard Deviation after considering correlation coefficient

‘p = [ ( A )2 ( WA)2 x ( B )2 ( WB)2 + 2 ( A ) ( B ) ( WA) ( WB) Cor AB ]1/2

Where

A = 20 %, and WA = 60 % for DFW stock

B = 40 %, and WB= 40 % for ICT stock

Cor AB = 0.15

By applying above formula we get the standard deviation of portfolio

Standard Deviation of Portfolio = 21.39

(‘b) Standard deviation of DFW = 20 %

If 100 % will be invested in DFW then Standard deviation of portfolio will be 20 % as same to DFW.

In this case 0 % will be invested in ICT and 100 % will be invested in DFW

(‘c) To minimise the standard deviation of portfolio weight of securities will be as follows

Weight of ICT ( WB ) = [ (A )2 - Cov AB ] / (A )2 + (B )2 - 2Cov AB

CovAB = Covariance between A and B stock = Corr AB x A x B

CovAB = 0.15 x 20 x 40 = 120

Hence

WB (ICT ) = [ (20 )2 – 120 ] / [(20 )2 + (40)2 -2 x 120]

WB (ICT ) = 15.91 %

Hence weight of DFW = 100- 15.91 = 84.09 %