# Fnce

2999 Words Oct 10th, 2014 12 Pages
FNCE 370v8: Assignment 4

Assignment 4 is worth 5% of your final mark. Complete and submit Assignment 4 after you complete Lesson 12.

There are 12 questions in this assignment. The break-down of marks for each question is presented in the table below. Please show all your work as this will help the marker give you part marks as well as serve as a good study aid as you prepare for the Final Examination.

Question | Marks Available | Reference | 1 | 5 | Lesson 10 | 2 | 5 | Lesson 10 | 3 | 5 | Lesson 10 | 4 | 5 | Lesson 10 | 5 | 10 | Lesson 11 | 6 | 15 | Lesson 11 | 7 | 10 | Lesson 11 | 8 | 10 | Lesson 11 | 9 | 5 | Lesson 12 | 10 | 10 | Lesson 12 | 11 | 10 | Lesson 12 | 12 | 10 | Lesson 12 | Total | 100 | |

1. Explain the
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Security | Expected Return | Variance of Returns | Correlation | | | | A | B | C | D | A | 0.17 | 0.0169 | 1.0 | 0.4 | 0.7 | 0.2 | B | 0.13 | 0.0361 | | 1.0 | 0.6 | 0.5 | C | 0.09 | 0.0049 | | | 1.0 | 0.9 | D | 0.07 | 0.0050 | | | | 1.0 |

a. Determine the expected return and variance for a portfolio composed of 25% of security A and 75% of security B.
Portfolio Expected Return = A*r(a) + B*r(b)
Portfolio Expected Return = 25%*0.17 + 75%*0.13 = 0.0425+0.0975 = 0.14 =14%

Standard Deviation (SD) = sqrt( Variance) = Sqrt(V)
SD (A) = Sqrt (0.0169) = 0.13
SD(B) = sqrt(0.0361) = 0.19

Correlation(a,b) = Covariance(a,b) / ( St.Dev.(a)* St.Dev.(b) )
Covariance(a,b) = Correlation(a,b) *( St.Dev.(a)* St.Dev.(b) ) = 0.4*0.13*0.19 = 0.00988

Variance(a,b) = sq(A)*var(a) + sq(B)*var(b) + 2*A*B*cv(a,b) = sqrt(25%)*0.17 + sqrt(75%)*0.13+2*25%*75%*0.00988 ie Var(a,b) = 0.085+0.1126+0.0037 = 0.2013

b. Determine the expected return and variance of a portfolio that contains 78% security A and 22% security B. Is this portfolio superior to that one in (a) above?

Portfolio Expected Return = 78%*0.17 + 22%*0.13 = 0.1326+0.0286 = 0.1612=16.12%
Variance(a,b) = sq(A)*var(a) + sq(B)*var(b) + 2*A*B*cv(a,b) = sqrt(78%)*0.17+sqrt(22%)*0.13+2*78%*22%*0.00988
= 0.15+0.061+0.0034 = 0.2144

Yes. This Portfolio is superior to the one in (a).