Question

QUESTION 5

Consider the performance of two securities, J and K over the five year period from 2014 to 2018. The annual return earned on each one of them is as provided in the table below:

Year	J	K
	%	%
2014	37.9	-15.8
2015	28.4	19.8
2016	-0.1	12.8
2017	-50.0	-20.8
2018	31.7	58.6

Required:

Compute the following:

1. Assume your organization had K150 million to invest on 01st January, 2014. If 70% was invested in security J over the holding period, the annual returns would you have earned from a portfolio comprising the two securities.

[05 Marks]

2. The annual volatilities of the portfolio with the above investment proportions; assuming the correlation coefficient between returns on securities J and K remained constant at 0.04 over the holding period.

[10 Marks]

3. Evaluate the performance of the portfolio for each year of the holding period and advise when the performance was satisfactory. Assume a risk-free rate of 6%.

[05 Marks]

Total 20 Marks

Answer 1

V Amount available for Investment = 150 million 70%. Invested in security I soy, Invested in Sawit Ñ A yout Rp a WR + W₂ R₂ Rp 2 Return on portfolio W, z Weight/proportion of Investment in security I We a weight/proportion of Investment in scenity K. प्रय 2014 2015 2016 2017 Refun on pootfolio 0.1831.9 t 0.3XC-15-8)= 21.79% OTX 28.4+ 0.3809.6.) 2 25.82% fool) XOT+0.34 12-8 = 3.77% 6500) X 0.7 + 0-3* (-208)=-41•Ay. 319 X 0.7 t 0.3858.6 34.0/ 2018

(6) Let us compute the standard deviation Lividual stocke first va! i I year Retung. Deviation Deviation from mean squared 2014 37.9 uns 28.32 802.02 2015 28.4 18.82 354.19 2016 - orl + -4.59 29.97 2017 -5000 -59.58 3549.78 2018 31.9 22.12 489.29 arts 47.9 mb ] 5289-25 Average 249 -9 29.56 Variance - 5287:25 - 1057.45 Standard deviation : 1105745. 32-52%.

- year Rotunt - 2014 - 2015 - 2016 2011 - 2016 15.0 19.2 12.2 -2008 59.6 Doriation foron mean -26.72 8.88 1988 -31.72 47.68 Desiating squared 113.96 76085 3.53 1006-16 2273.38 1075:26 54.6 - Average 2 546 210.92 Variance a 4075.88 a 815.18 - standard deviation J8 15.18 z 28.55 %

C portfolio variance =N, 6 + W 26 2 + 2W,W Coravianes, Covariance & 6,6 correlation 32.52X28.55 0.04. e 37.14 III portfolio variance = (0.70%(32-52)*+C0-33(2655) t2(0.7)(0:3)(37:14) 20-49x1057.45 + 0.09% 815.18 +- 15.6 = 5184-15 +78-37 +15-6 2 607.12 portfolio Standouddeviation Sportfolio variance a 1607.12 z 24.64.6

O Evaluation of the performance of portfolio I year Retun of portfolio Sharpe Ratio 2014 21.79 = 64 0.2179-0-0120-4 0.2464 - 2015 25.82 0:2582,-0.06 0.80 - 2016 3.07 0.0377.0.062 -0.09 2017 ~41-24 2-0.4124 -0.06 2-1092 0.2464 2018 39077 2 0.3977-0.06 z 1037 0·2444 Sharpe Ratio 2 Portfolio Return - Riskfree rate standard deviation. Now from the above calculation one can decifee that performance was satisfactory during the years 2014, 201562018. 2018 year is the best. 2016 & 2017 performance was not good as shoppe Ratio is negative