EXECUTIVE SUMMARY

• Largest UK REIT by capital value & FTSE 100 member.
• Statistical analysis performed on the differences in the changes between the daily opening and closing share price for the calendar year 2015.
• 254 sets of data were used.
• 253 sets of daily returns.

• Share price range between;
  • High of 1363p on 19^th May 2015
  • Low of 1140p on 14^th December 2015

• Mean of 0.015%
• Mode of 0.0000%
• Median of 0.0000%
• Variance of 0.0165%
• Frequency distribution of between -4.9219% and +4.2079%
• Grouped frequency distribution where 60% of the daily movements were between -1% and +1% around the mean.
• Results indicate small daily changes in share price movements.

• Land Securities share price statistic performance compared to that of the FTSE 100 over the same period calculating a beta of 0.775204
• Results indicate that on a historical basis in 2015, for every 1% change in the daily returns of the FTSE 100, the Land Securities’ daily returns moved by 0.775%.
• This may guide a potential investor when seeking to make investment decisions, with the Land Securities share price performance less volatile than the FTSE 100 overall.
• This may, or may not, be acceptable to an investor, as this will relate to their appetite for risk and target returns.
• Although these results over the calendar year of 2015 are useful indicators of share price performance, they cannot be seen as predictors of future performance.
• It may be prudent to complete this exercise over a longer period, for example over three or five years.

INTRODUCTION

As a long established member of the FTSE 100, Land Securities is recognised, by capital value, as the largest UK REIT.

With a significant portfolio of assets, totalling over 26 million sq ft, the organisation focuses its activity on the acquisition, development, management and disposal of property.

This report focuses on the statistical analysis of the organisation’s daily closing share price performance for the calendar year 2015, after calculating the following descriptive statistics;

• Mean
• Mode
• Median
• Variance
• Standard Deviation
• Frequency Distribution

Additionally, a comparison has been made of the XXXXX to the performance of the FTSE 100’s daily closing share price for the same period.

STATISTCAL ANALYSIS

The data set for the analysis of Land Securities’ closing share price, for the calendar year January 1^st to December 31^st 2015, produced 254 sets of data (closing share prices) and therefore 253 daily returns, with the first closing price of the year being considered as having no movement in price from the previous trading day.

This data set used as the basis of all calculations was produced using excel, along with excel’s ability to perform the required calculations, and is included as appendix 1.

BACKGROUND/RANGE

To place the share price results into some context, the share price had a high closing price on 19/05/2015 of 1363p, versus a yearly low closing price of 1140p on 14/12/2015. This represents a range of 223p during the period. The graph below shows the daily closing share price.

MEASURES OF CENTRAL TENDANCY

MEAN

The mean of the percentage changes in daily returns was derived from summing the values of the daily changes in closing share price and dividing by the number of values (in this instance by 253).

The sum of the daily changes was 3.806%.

With the calculation for the mean being;

Therefore, the mean daily percentage change in closing share price was calculated as 0.015%.

MODE

The mode represents the most frequently occurring value from the data set. With regards to the changes in daily share price, the mode is 0.0000%.

This most repeated value appears seven times.

Therefore, on seven occasions, and as the most occurring, the modal daily change in share price was 0% (no change from the previous day’s closing price).

An excerpt form the excel spreadsheet is included below;

Table i – Land Securities Close Of Day Share Price Movement – Mode

MEDIAN

With the median representing the value in the data set which represents the central value, the value 50% along when the data was placed in rank (ascending) order was 0.0000% (the 127^th value). Therefore, the median value is 0%.

An excerpt from the data set table used to calculate the median value is shown below;

Table ii – Land Securities Close Of Day Share Price Movement – Median

MEASURES OF DISPERSION

VARIANCE AND STANDARD DEVIATION

The variance, also known as the mean square deviation, is the average of the squared differences from the mean.

Whereas the standard deviation is a measure of the spread of the numbers, and is calculated as the square root of the variance.

When the differences of the spread of numbers is large, the larger the value of the standard deviation.

The mathematical calculation for the standard deviation is;

The variance for the differences in the daily closing share prices is calculated as 0.00165%.

The standard deviation for the differences in the daily closing share price is calculated as 1.2856%.

FREQUENCY DISTRIBUTION & GROUPED FREQUENCY DISTRIBUTION

The distribution around the mean ranged from -4.9219% to +4.2079%.

When grouped together, 60% of the of the distribution of the closing difference in daily share price is grouped between -1% and + 1% around the mean.

The table below highlights both the grouped and cumulative results.

Table iii – Land Securities Grouped & Cumulative Frequency Distribution

The graph below represents the table above in graphical form;

Frequency Distribution & Cumulative Grouped Distribution

MARKET COMPARISON

The selection of statistics produced describe the performance of the set of data relating to Land Securities’ closing share price over the calendar year 2015; however, it may be useful and of greater value to compare the statistical output against the performance of a similar set of data.

If an investor was considering purchasing shares in Land Securities, and wanted to assess the risk of doing this, the statistical data obtained could potentially be of greater use if this was able to be reviewed against the performance of a similar set of data or asset class.

As Land Securities is member of the FTSE 100, it this instance, it may be prudent to compare the data across 2015 to that of the FTSE 100 over the same period.

The beta (which is used as a measurement of investment portfolio risk) is calculated in this regards as the covariance of the share’s returns with the benchmark returns, divided by the variance of the benchmark’s returns.

When the results are compared, if the beta is 2, it translates that for every 1% change in the value of the benchmark (in this case the FTSE 100), the value of Land Securities’ value changes by 2%.

Therefore, providing the party analysing the data with some statistical guidance of the historical changes in share price of the two comparables.

For this calculation, 242 data items were available for the FTSE 100, therefore, the data for the comparable days for the Land Securities closing share price was removed, ensuring the identical number of days were evaluated.

When the calculation was completed, a beta () of 0.7752 is achieved.

The statistical interpretation of this being that for every 1% move in the daily closing price of the FTSE 100 in 2015, the closing share price of Land Securities moved by 0.7752%.

The data for this calculation is included in as Appendix ii.

Furthermore, it is possible to use excel to run a complete regression test to compare the returns of Land Securities to that of the FTSE 100.

A scatter plot (as below) is produced, depicting the daily deviations from the mean return (as plotted on the x-axis) and the corresponding values for Land Securities (on the y-axis).

Scatter Plot OF The Weekly Land Securities & FTSE 100 Deviations From Mean Return

The straight line of best fit is overlaid, the gradient of which is equal to Land Securities’ beta.

The regression table output is shown below;

Regression Test Output

It is noted that the standard error of beta is 0.009783357 amongst 242 daily return observations of Land Securities and the FTSE 100.

CONCLUSIONS

The daily returns for Land Securities closing share price over the calendar year for 2015 resulted in relatively small movements on a daily basis.

Even though the share price range was 223p over the year (16%), with regards to the statistics regarding central tendencies, the mean movement was 0.015%, with a median result of 0% and a seven times occurring mode also of 0%.

With reference to the measures of dispersion, a variance of 0.0165% was calculated and a standard deviation of 1.2856%.

Perhaps most interestingly, the cumulative frequency distribution highlighted that 60% of the daily closing return movements were with between -1% and +1% around the mean.

When the prices were subsequently compared to the FTSE 100 over the same period, the results produced a beta of 0.775204, resulting in an observation that for every 1% move in the daily returns for the FTSE 100, Land Securities’ returns move by 0.775%.

This could be interpreted as Land Securities being a more stable and less volatile stock, when compared to the overall FTSE 100 performance.

This may support analysts when taking potential investment decisions.

However, it is prudent to highlight that firstly, analysis over a longer period of time may also be undertaken,  and secondly, that the future share price of an organisation will largely be determined by the market in operates in, the wider economic landscape, and the news emanating from within the business, rather on historical data analysis.

Appendices

Appendix i

Data Set for Land Securities Closing Daily Share Price Movements 2015

Date	Open	High	Low	Close	Volume	Adj Close	Daily Returns
31/12/2015	1189	1193	1177	1177	600200	1148.293	-0.9259%
30/12/2015	1200	1204	1182	1188	1203600	1159.024	-1.1647%
29/12/2015	1193	1203	1187.04	1202	1349600	1172.683	1.3491%
24/12/2015	1186	1187	1178.9	1186	162700	1157.073	0.3384%
23/12/2015	1173	1182	1159.86	1182	1076000	1153.171	1.6337%
22/12/2015	1172	1178	1159	1163	1287900	1134.634	0.1723%
21/12/2015	1172	1190	1161	1161	1013300	1132.683	-0.8540%
18/12/2015	1185	1191	1171	1171	2385000	1142.439	-1.2648%
17/12/2015	1200	1208.85	1182	1186	1516300	1157.073	-0.0842%
16/12/2015	1160	1189	1157	1187	2429600	1158.049	2.3276%
15/12/2015	1148	1165	1140	1160	3010800	1131.707	1.7544%
14/12/2015	1157	1179.6	1140	1140	1828400	1112.195	-1.4693%
11/12/2015	1185	1188	1157	1157	2438000	1128.781	-2.4452%
10/12/2015	1190	1202.9	1185	1186	2090700	1157.073	-1.0017%
09/12/2015	1203	1212	1198	1198	2876300	1168.781	-0.4983%
08/12/2015	1216	1221	1204	1204	1446900	1174.634	-1.1494%
07/12/2015	1214	1234	1209	1218	1463700	1188.293	0.9950%
04/12/2015	1196	1210	1186.85	1206	3071700	1176.585	0.7519%
03/12/2015	1232	1243	1197	1197	2793700	1167.805	-3.7007%
02/12/2015	1248	1253	1241	1243	2016700	1204.732	0.1612%
01/12/2015	1232	1244	1228	1241	1769000	1202.793	0.8123%
30/11/2015	1234	1239	1225	1231	1893400	1193.101	-0.1622%
27/11/2015	1221	1234	1216.3	1233	1037200	1195.04	0.6531%
26/11/2015	1235	1235	1220	1225	1131300	1187.286	-0.5682%
25/11/2015	1215	1241	1215	1232	1605500	1194.07	1.5664%
24/11/2015	1222	1222	1201.3	1213	2243600	1175.655	-0.8987%
23/11/2015	1240	1244	1223	1224	1460000	1186.317	-1.9231%
20/11/2015	1258	1258	1243	1248	2192900	1209.578	-0.1600%
19/11/2015	1248	1256	1241	1250	1989400	1211.516	0.8878%
18/11/2015	1245	1249	1234	1239	1501400	1200.855	-0.5618%
17/11/2015	1243	1255	1238	1246	2626100	1207.639	1.3008%
16/11/2015	1215	1230	1208	1230	1590900	1192.132	0.8197%
13/11/2015	1217	1223	1207	1220	2886600	1182.44	-0.0819%
12/11/2015	1239	1250	1221	1221	2231900	1183.409	-1.6116%
11/11/2015	1249	1249	1223	1241	4224600	1202.793	-0.1609%
10/11/2015	1270	1273	1228	1243	3545700	1204.732	-2.7387%
09/11/2015	1308	1312	1278	1278	2771500	1238.654	-2.2936%
06/11/2015	1328	1329	1305	1308	1694100	1267.731	-1.1338%
05/11/2015	1305	1324	1299	1323	2037300	1282.269	1.7692%
04/11/2015	1323	1327	1299	1300	2671200	1259.977	-1.7385%
03/11/2015	1340	1340	1320	1323	1676500	1282.269	-1.0471%
02/11/2015	1330	1343	1330	1337	1341400	1295.838	-0.1494%
30/10/2015	1341	1349	1336.3	1339	2146300	1297.776	-0.2235%
29/10/2015	1350	1352	1336	1342 Posted in Uncategorized « Environmental studies environmental problems » You can leave a response, or trackback from your own site. Leave a Reply Click here to cancel reply. Name (required) Mail (will not be published) (required) Website Why Choose Us 10+years of experience in the custom writing market Satisfied and retuming customer A wide range of service 6-hour delivery available Money-back guarantee 100% privacy guaranteed Writers are MA/MS or Ph.D degree holders Only custom-written papers Free amendments upon Сonstant access to your paper writen We Accept Paper Features Chose the font you want State the Referencing Style Normal font size is 12 275 Words Double Spacing 550 Words single spacing One Inch Margins Left Text Alignment Home About Us Contact Us Our Guarantees How it Works Order Our Writers Services Term Papers Academic Writing Services Admission Essays & Personal Statements Coursework Writing Services Custom Book/Movie Reviews Dissertation/Thesis Writing Services Editing and Proofreading Services Essay Writing Services Online Classes and Homework Help Research Paper Writing Services Term Paper Writing Services Term Papers Copyright © Informative Papers - Powered by WordPress | Designed by: Premium WordPress Themes | Thanks to Themes Gallery, Bromoney and Wordpress Themes