QM Summative Assignment:

(Q1):

Below are the 30 observations and the log returns for my three chosen stocks: G4S, GKN and GLAXOSMITHKINE. Below is the logarithmic returns formula:
• rLOG = (Final amount of investment / Initial amount of investment) * 100
G4S - PRICE INDEX GKN - PRICE INDEX GLAXOS- PRICE INDEX
871674(PI) Log Return 900754(PI) Log Return 900479(PI) Log Return
264.5 1208 64980.3
284.6 0.073243434 964 -0.225630084 58890.7 -0.098400964
278 -0.023463572 1011 0.047603924 56365.7 -0.043822366
208.9 -0.285765445 968.3 -0.043153262 66651.1 0.167610733
211 0.010002465 1100.2 0.127705304 73557.6 0.098597222
197.4 -0.066626006 1142.4 0.037639331 70178.6 -0.047025352
224.6 0.129088915 1044.5 -0.089593011 71552.4 0.019386627
204 -0.096201048 1058.7 0.013503438 71366.8 -0.002597273
232.8 0.132059722 1108.9 0.046326793 73557.6 0.030235998
230.3 -0.010796909 835.7 -0.282854115 76045.4 0.033261758
235.3 0.021478489 978.8 0.158057635 73669 -0.031748444
227 -0.035911278 951.6 -0.028182553 76379.6 0.036133558
257.1 0.124515097 876 -0.082778687 70178.6 -0.084672224
256.6 -0.001946662 1029.6 0.161559565 66651.1 -0.051571871
273.9 0.065244624 997.4 -0.031773763 70735.6 0.059477432
252.5 -0.081351828 895.2 -0.108104736 68359.1 -0.03417429
274.7 0.084268344 934.8 0.043285446 68581.9 0.003253959
296.1 0.075017642 923.7 -0.011945259 70995.5 0.034587843
271.5 -0.086735096 845 -0.089050716 74263.1 0.044997698
286.3 0.053078073 880.9 0.041607485 75265.6 0.013408998
262.4 -0.087170155 872.8 -0.009237678 67876.5 -0.103333314
192.5 -0.309773903 776.6 -0.116781017 71292.6 0.049102658
167.8 -0.13732336 751.8 -0.032455086 68693.4 -0.03713941
171.1 0.019475387 790.7 0.050448298 65351.5 -0.049872732
193.3 0.121995205 749.7 -0.053245503 63977.7 -0.021245808
200.7 0.03756787 771.6 0.028793155 62715.2 -0.019930743
217.2 0.079007332 831.8 0.075125746 64014.8 0.020510464
200.7 -0.079007332 976 0.159870559 61415.6 -0.041450432
204.8 0.020222637 908.1 -0.072108082 61638.4 0.003621178
214.3 0.045343009 945.6 0.040465142 52132.7 -0.167492662

These log returns can then be used to calculate the descriptive statistics. Through inputting the data into Excel, the data is provided.
Descriptive Statistics:
Statistic Name:
G4S Name:
GKN
Name:
GLAXO SMITH KINE

Time Period:
Start – 31/12/1999
End – 31/05/2002
Mean -0.007257391 -0.008444887 -0.007596267
Standard Error 0.020441715 0.019323072 0.012188405
Median 0.019475387 -0.009237678 - 0.002597273
Mode #N/A #N/A #N/A
Standard deviation 0.110082005 0.104057928 0.065636568
Sample variance 0.012118048 0.010828052 0.004308159
Kurtosis 1.611338969 0.849653662 1.361266742
Skewness -1.182990353 -0.564157907 0.135248479
Range 0.441833625 0.44441368 0.335103395
Minimum -0.309773903 -0.282854115 - 0.167492662
Maximum 0.132059722 0.161559565 0.167610733
Sum -0.210464349 -0.244901732 - 0.220291756
Count 29 29 29

Analysis of statistics:
By examining the derived results, we can come to the following conclusions:
• The scale of difference between the stocks was differing. G4S’ mean return was -0.0073 whilst GKN’s was -0.0084 and GLAXOSMITHKINE’s was -0.0076. We can see that whilst G4S and GLAXOSMITHKINE were close, GKN’s differed greatly.
• The median indicates over half of