# Statistical Comparison of Stock and Gold

Topics: Statistical hypothesis testing, Gold as an investment Pages: 69 (28845 words) Published: October 1, 2011
Statistics Project| September 26
2011
|
The project statistically studies and compares the daily closing price movement of two investment options – real estate and gold represented by DLF stock and SBI Gold ETF respectively – over the past 3 years.| Comparative study of DLF Stock and Gold ETF price movement|

Contents
Stage 13
Overview3
Problem Statement3
Inferences5
Stage 26
Hypothesis Testing6
Stage 37
Linear Regression Analysis7
Manual Calculations7
Regression Analysis: DLF Closing versus Gold Closing using Minitab7
Appendix A10
Appendix B23
Appendix C38
Appendix D53

Stage 1
Overview
In this stage, the daily closing values of DLF stock price and SBI Gold ETF are analyzed. These two are selected to study the two traditionally important investment vehicles in India – Real estate and Gold. DLF being the largest real estate company India and SBI Gold ETF being the largest ETF in India, they are assumed to represent their underlying sectors for this study. By studying the various statistical parameters such as mean, variance, standard deviation, and confidence interval through this project, one would be in a better position to compare the two investment options. Problem Statement

Any investment has a return component and a risk component. One measure of return is the % appreciation in value of the investment over a period of time. In case of our subjects, the % appreciation/depreciation of daily closing prices is an effective measure of return. The frequency distribution plot of the % change of closing price is a visual representation of the volatility – which is an important measure of risk.

The risk component can also be measured by calculating the mean value of the % change of the investment and the standard deviation, the range etc.., which represents the volatility of the value. % change - DLF|

| |
Mean| -0.08|
Standard Error| 0.12|
Median| -0.08|
Mode| 0.00|
Standard Deviation| 2.81|
Sample Variance| 7.90|
Kurtosis| 1.25|
Skewness| 0.05|
Range| 21.60|
Minimum| -10.53|
Maximum| 11.07|
Sum| -43.66|
Count| 577.00|
Confidence Level (95.0%)| 0.23|
| % change - gold|
| |
Mean| 0.12|
Standard Error| 0.04|
Median| 0.07|
Mode| #N/A|
Standard Deviation| 1.00|
Sample Variance| 1.01|
Kurtosis| 8.12|
Skewness| 0.51|
Range| 12.61|
Minimum| -5.52|
Maximum| 7.09|
Sum| 66.40|
Count| 577.00|
Confidence Level (95.0%)| 0.08|
|

The data for the calculations can be found in Appendix A.
A box plot of the % change in daily closing prices is another visual representation of the risk (volatility). The graph below is the box plot of the % change in daily closing price of both DLF stock and Gold ETF

Inferences
1. From the frequency plot, it’s clear that the % change in daily closing price of DLF stock is more dispersed while that of Gold ETF is concentrated around the centre. This means that the volatility (risk) is more in case of DLF stock (real estate investment). 2. From the descriptive statistics table, DLF has a negative (-0.08) mean for %change of daily closing price, which means that, on an average the stock depreciated over the 3 year period per day. While the same measure of Gold ETF is positive (0.12) – which means the ETF appreciated by 0.12% per day on an average over the 3 year period. 3. From the descriptive statistics table, the standard deviation of DLF stock closing price change is almost 3 times that of the Gold ETF, which means it’s a riskier investment. 4. From the box plot and the descriptive statistics, the median value of % change in DLF stock closing price is negative whereas that of Gold ETF is positive; which means that 50% of the time, we can expect ETF to appreciate in value and DLF to depreciate. 5. The box plot also contrasts the variation in the % change in both investments; the DLF stock varies over a...