# Inferential analysis to compare the performance of stocks listed in the BSE (2011-2020)

Annualized average return refers to the return earned by investors by investing in a particular stock. On the other hand, market return defines the return earning capacity of investors from all the stocks traded in the stock market. With the availability of a higher annualized average return over a market return, investors have the opportunity to earn a return higher than the possibility of earning in the market. Comparison of these returns enables investors to understand the return-generating capacity and the performance of stocks.

The comparison of stock performance is done descriptively wherein the nature of the dataset is known. But this comparison is influenced by the presence of volatility, therefore its results may be biased. Therefore a statistical comparison of the performance of the stocks is crucial. The previous article assessed the performance of stocks during the global financial crisis.

It was seen that despite the presence of high risk, growth stocks are the most effective investment instrument. However, major changes in the investment and behaviour of stocks take place post-crisis (April 1, 2010 – March 31, 2015) and during stock market crashes (April 1, 2015 – March 31, 2020). Furthermore, as investors value historical movement, past performance needs to be analyzed for at least 20 years (April 1, 2000 – March 31, 2020). Thus, this article examines the performance of 303 BSE 500 listed companies for the specified period and identifies the most efficient source of investment during and post a financial crisis.

## Analyzing the performance of stocks by comparing the annual average return with the market return

The performance of the growth stocks for the period April 1, 2010, to March 31, 2015, is represented in the table below.

Growth stocks | Income stocks | Value stocks | |
---|---|---|---|

Pearson correlation | 0.946 | 0.922 | 0.999 |

t Stat | 1.715 | 0.673 | -1.958 |

P(T<=t) two-tail | 0.161 | 0.538 | 0.122 |

t Critical two-tail | 2.776 | 2.776 | 2.776 |

The table above represents the findings of Pearson’s correlation and t-test. Its findings are represented below:

### Pearson correlation findings

**Growth stocks:**Pearson correlation value of 0.946 is greater than the required value of 0.5. Thus, there is a strong positive correlation between the average return and market return for growth stocks.**Income stocks:**Pearson correlation value of 0.922 is more than 0.5 showing a strong positive correlation but compared to growth stocks it is less. Thus, the income stocks’ linkage between average return and the market return is less than the growth stocks.**Value stocks:**Pearson correlation value of 0.999 is greater than 0.5. Not only is it higher than the required value, but is also higher than the values of growth stocks and income stocks. Hence, value stocks have the highest influence of variability on returns with a possibility to improve the undervalued stocks. Therefore, they can earn more returns for investors in comparison to income and growth stocks.

### T-test findings

A comparison of the stock performance was done using a t-test. The above table shows that:

**Growth stocks**: with the t-stat value of 1.715 which is less than the critical value of 2.776, the null hypothesis of no significant difference in the performance of stocks is not rejected. The P-value of growth stocks depicts a similar result with a value of 0.161 which is greater than 0.01, 0.05, or 0.10.**Income stocks:**In the case of income stocks, the t stat value is 0.673 which is also smaller than the critical value of 2.776. Thus, the null hypothesis of no significant difference is not rejected. Its p-value is also higher than the significance level i.e. 0.538 > 0.01, 0.05, or 0.10, thus there is not much significant difference in the performance.**Value stocks:**Value stocks further with an absolute t stat value of 1.958 is less than the critical value of t i.e. 2.776. Even the p-value is 0.122 which is greater than the significance value of 0.01, 0.05, or 0.10. Hence, the null hypothesis of value stocks is not rejected showing that there is no significant difference in the performance of stocks.

Hence, correlation and t-tests show that value stocks perform better than other stocks. For the given period, investors of value stocks have a better opportunity to earn profit and thus, having more valuation of stocks, there is an improvement in stocks. Furthermore, growth stocks also have return generation for the investor but compared to value stocks, the presence of higher risk reduces the possibility of return. Thus, value and growth stocks for the period outperform income stocks in the return-generating capacity.

## Analyzing the performance o stocks by comparing the annual average return with the market return

The examination of the performance of stocks for the period April 1, 2015, to March 31, 2020, is shown in below table

Growth stocks | Income stocks | Value stocks | |
---|---|---|---|

Pearson correlation | 0.914 | 0.938 | 0.886 |

t Stat | 0.503 | 0.633 | -0.211 |

P(T<=t) two-tail | 0.642 | 0.561 | 0.843 |

t Critical two-tail | 2.776 | 2.776 | 2.776 |

Analysis of the results shown in Table 2 is represented below sub-sections.

### Pearson correlation findings

**Growth stocks**: With the Pearson coefficient value of 0.914, the growth stocks have a higher correlation as compared to the required value of 0.5. This states that there is the presence of a strong positive linkage between the market and annual average return for the period April 1, 2015, to March 31, 2020.**Income stocks:**The Pearson value of 0.938 is greater than the required value of 0.5 and even higher than the growth stock’s Pearson correlation. Thus, income stocks’ performance is better than growth stocks for the current period.**Value stocks:**The Pearson correlation is 0.886 which is higher than the required level of moderate relationship i.e. 0.5 but still less than the growth and income stocks value. Hence, the value stocks are undervalued in the market-leading to lower performance.

Due to the existence of high volatility and the BSE market crash of 2015, 2016, 2018, and 2020 the growth stock performance has also degraded. But the income stocks due to their capability of overcoming the volatility impact provided investors with the opportunity of having a steady income.

### T-test findings

Assessment of the performance of stocks on the t-test basis is shown below

**Growth stocks:**The t-stat value of 0.503 is less than the critical value of 2.776. Even the p-value of the stocks is higher than the significance level i.e. 0.503 > 0.01, 0.05 or 0.10. Thus, the null hypothesis for the growth stocks having no significant difference in the performance of the market and stock is not rejected.**Income stocks:**The t-stat value is 0.633 which is also less than the critical value of 2.776 showing non-rejection of the null hypothesis. The P-value of 0.561 is also higher than the significance level of 0.01, 0.05, or 0.10. Hence, there is no significant difference in income stock’s performance for the current period.**Value stocks:**The absolute t-stat value of 0.211 is less than 2.776. The p-value is also higher than the significance values of 0.01, 0.05, or 0.10; therefore the null hypothesis is not rejected.

For all three stocks, there is no difference in the performance of their returns and the market returns. However, a comparison of Pearson correlation and t stat shows that income stocks have performed better than any other stock. Due to higher volatility in the market, income stocks have created an opportunity for better returns for the investors while growth and value stocks have not derived benefits from their investment.

## Analyzing the performance of stocks by comparing the annual average return with the market return

In order to compare the altogether performance of stocks, the examination of the period April 1, 2000, to March 31, 2020, was done.

Growth stocks | Income stocks | Value stocks | |
---|---|---|---|

Pearson correlation | 0.954 | 0.878 | 0.907 |

t Stat | 3.083 | 1.080 | 1.009 |

P(T<=t) two-tail | 0.006 | 0.294 | 0.325 |

t Critical two-tail | 2.093 | 2.093 | 2.093 |

### Pearson correlation findings

**Growth stocks:**Pearson correlation value is 0.954 which is higher than the required value of a moderate relationship i.e. 0.5. Thus, growth stocks have a strong positive linkage between the annual average return and the market return for the current period.**Income stocks:**The value of the Pearson correlation is 0.878 which is greater than 0.5. This shows that a strong positive relationship between the annual average return and the market return is present. But this linkage is weaker than the relationship that exists in growth stocks’ average return.**Value Stocks:**Pearson correlation value of 0.907 also depict the strong positive linkage between annual average return and market return. This high and strong relationship shows that the performance of value stocks has raised the value of undervalued stocks in comparison to income stocks. But still, with the higher Pearson correlation, growth stocks are the most sustainable source of earnings.

### T-test findings

Comparison of performance for the growth, income, and value stocks is further done by t-test. The results are depicted in above table 3.

**Growth stocks:**The t-stat value of 3.083 is greater than the critical value of 2.093. Therefore the null hypothesis of no significant difference in the performance of stocks is rejected. Herein, the p-value of growth stocks is also 0.006 which is less than 0.01, 0.05, and 0.10. Thus, growth stocks do have a difference in the performance of stocks due to different mean values of annualized average return and market return.**Income stocks:**the t-stat value of 1.080 is less than the critical value of t i.e. 2.093. Even the p-value of stocks is 0.294 which is greater than 0.01, 0.05, and 0.10. Thus, the null hypothesis of no significant difference in the performance of stocks is not rejected.**Value stocks:**the t-stat value of 1.009 is also less than the critical value of 2.093. The P-value of the stock is 0.325 > 0.01, 0.05 or 0.10. Thus, the null hypothesis of no significant difference in the performance of stocks is not rejected.

Hence, growth stocks have outperformed all other stocks. With the presence of high volatility in the market and the risk, the investors of growth stocks got the opportunity to earn benefits higher than the market return value. For the period April 1, 2000, to March 31, 2020, even in presence of the global financial crisis, crude oil plunge, and BSE crashes; growth stocks had the highest return and the income stocks only covered the volatility just provided a low steady income.

## The benefit of higher return with the risk of bearing volatility in the market

Growth stocks being the provider of sustainable returns at the risk of higher volatility tend to provide the highest return compared to income and value stocks. Herein, as for the different time intervals in the period April 1, 2000, to March 31, 2020, the growth stocks had the strongest linkage between the annual average returns and the market return while income stocks had the lowest. With a strong relationship and the higher t stat value, the performance of annual average return and market return was different. This advantage to the investor of growth stocks provides them with the benefit to gain returns higher than the market rate. Thus, though the investors have to bear the risk of volatility, growth stocks are the optimal source of earning a higher return.

The performance of stocks varies with time and events. In order to effectively predict the behaviour of a stock, it is essential that the investor assesses the influence of different time periods on the movement of stocks. Thus, the next article examines the performance of stocks in presence of short-term movements.

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