Workshop 14 (Revision)2019 PDF

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Workshop Week 14 Revision Lecture (please see the tutorial questions and the formulae list at the end of the note) Final examination (a note): 1. Date of the final exam: 6 November, 2019. Students are advised to check their own timetable and room number. 2. Students are advised to cover week 1 to 14 lecture materials and week 1 to 14 tutorial questions for the preparation of the final examination. All tutorial questions, additional questions and the questions discussed during the lecture will be included in the final exam. No sample exam paper will be given. 3. The final examination is worth 50% of the total assessment. 4. There will be 5 questions in the final exam (5 10=50 marks). 5. Student should answer all questions (approximately 50% numerical and 50% theoretical). Each question will involve few part questions. 6. The tutors and the unit coordinator (if needed) will be available for consultation at 1PSQ (ph: 9685 9664, email: [email protected]). Please make an appointment to your tutor. 7. There will not be any multiple choice questions in the final exam. 8. All students are requested to check their assessment marks (in the vUWS) within 4 November 2019 and inform to the unit coordinator in case there is any mistake. After 6 November 2019 it will be difficult for me to correct your marks (in case there is a mistake. 9. Please do not hesitate to contact the unit coordinator if you have any question/s. 10. Please note that to pass the exam student must get overall 50% and minimum 50% marks in the final examination (threshold mark is 25 (out of 50) for final exam). 11. The formula list at the end of this note will be in the Final Exam. 12. Please practice the revision questions (discussed during week 14) first. After practicing the revision questions, students should practice the tutorial questions and the questions in the lecture notes. Students must not think that if they can solve the practice questions they will pass the final exam.

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Question 1: How to calculate i) mean; ii) standard deviation, iii) variance and iv) correlation coefficient using calculator for the following set of data: Year 2010 2011 2012 2013 2014 2015

Return A 3 -2 7 10 6 5

Return B -1.1 5.2 8.5 4.9 0.6 3.1

Please show the results using calculator. (a)

In the following table, observed returns on two assets (A and B) are given for four consecutive years. Year 2010 2011 2012 2013 (i)

(ii)

Return A 3% -2% 7% 10%

Return B -1% 5% 8% 4%

Use the information in the table to estimate the mean and standard deviation of the distribution of returns for each asset. If needed, express your estimates rounded to two decimal places. Use the information in the table to estimate the mean and standard deviation of the probability distribution of returns for a portfolio consisting of assets A and B with portfolio weights of 0.7 and 0.3, respectively. Again if needed, express your estimates as percentages rounded to two decimal places.

(i) Sample mean returns – For Asset A: For Asset B:

(3−2+7+10)/4=4. 5% (−1+ 5+8 + 4 )/ 4=4 %

Sample standard deviations of returns – For Asset A:

√

(3−4.5)2 +(−2−4.5 )2 +( 7−4.5 )2 +(10−4.5)2 3 ¿ √ 27≈5.20%

For Asset B:

√

(−1−4 )2 +( 5−4 )2 +( 8−4 )2 +( 4−4 )2 3 ¿ √ 14≈3.74%

(ii)

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Return 2010

=0 . 7 (3 )+ 0 .3 (−1 )=1 . 8 %

Return 2011

=0 . 7 (−2 )+ 0. 3 (5 )=0 . 1 %

=0 . 7 ( 7 )+0 . 3 ( 8 )=7 . 3 % Return 2013 =0 . 7 ( 10 )+0 .3 ( 4 )=8. 2 % Return 2012

Sample mean return =(1. 8+0.1+7 .3+8. 2)/ 4=4. 35% Sample standard deviations of returns

√

(1.8−4. 35)2 +( 0.1−4.35 )2 +( 7.3− 4.35 )2 +( 8.2−4 .35 )2 = 3 ¿ √ 16.03≈4 .00% Note: students are advised to use calculator for the above calculation. It will be much easier to use the calculator. These extended answers are given for better understanding. (b)

According to the capital asset pricing model the expected return on shares in the Gamma Corporation is 10.6%. The beta value associated with these shares is 1.1 and the risk free rate of interest is 4%. Given this information, calculate the market risk premium and the expected return on the market portfolio?

Answer : r  R  b ( r  R )  0.106 0.04  1.1( r  0.04) j F j m F m 0.066 0.06 or ,6% 1.1(r  0.04) 0.066  r  4  m m 1.1 The market risk premium is thus 6%. The expected return on the market portfolio is r  0.04 0.06 or ,6% m r 0.06  0.04 0.10 or,10% m

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Question 2: Calculation of IRR using scientific calculator: Example: Consider projects A Year 0 1 2 3

Expected net cash flow -50 20 10 40

Suppose r 0.15 (or15% pa) a) What are the NPV of the project? b) Calculate the IRR for the project. Answer a) 20 10 40 NPVA     50 51.25  50 1.25 2 1.15 (1.15) (1.15)3 Answer b) n

CFt  CF0 t t 1 (1  IRR)

We know that; NPV 0  

n

CFt

 (1  IRR ) t1

t

CF0     (1)

We need to find out IRR, when equation (1) is satisfied; i.e. NPV =0 Please note that, when, r=0.15  NPV 1.25,  to get NPV 0, r must be greater that 0.15 20 10 40 Firstly, we consider r 0.16  NPV     50 0.30  0 2 1.16 (1.16) (1.16)3 20 10 40 if , r 0 .17  NPV     50  0.63  0 2 1.17 (1.17) (1.17 3  it is now clear that 0.16...