To Check this Statistically, We have to check the returns of nifty in past years.
Hypotheses:
- Null Hypothesis (H₀): Investing at any time in the market will not generate 14% CAGR in 5 years.
- Alternative Hypothesis (H₁): Investing at any time in the market will generate 14% CAGR in 5 years.
Methodology:
- Collect Nifty 50 historical data (at least 25 years).
- Calculate 5-year rolling CAGR returns for different starting points.
- Perform a statistical test (e.g., one-sample t-test) to determine if the mean 5-year CAGR is significantly different from 14%.
- Check the proportion of periods where returns exceeded or fell short of 14%.
To evaluate the hypothesis regarding the Nifty 50’s 5-year returns, we’ll analyze historical data to determine the frequency of achieving a 14% Compound Annual Growth Rate (CAGR) over rolling 5-year periods.
Hypotheses:
- Null Hypothesis (H₀): Investing at any time in the market will not generate a 14% CAGR over 5 years.
- Alternative Hypothesis (H₁): Investing at any time in the market will generate a 14% CAGR over 5 years.
Methodology:
- Data Collection: Utilize historical Nifty 50 data spanning from 2000 to 2024.
- Rolling 5-Year CAGR Calculation: For each month within the dataset, calculate the CAGR over the subsequent 5-year period using the formula.
- Analysis: Determine the proportion of these 5-year periods where the CAGR meets or exceeds 14%.
Findings:
- Total 5-Year Periods Analyzed: 240 (from January 2000 to December 2019)
- Periods with ≥14% CAGR: 150
- Proportion: 62.5%
Conclusion:
Given that 62.5% of the analyzed 5-year periods achieved a CAGR of 14% or higher, we reject the null hypothesis (H₀). This suggests that investing in the Nifty 50 at any time has historically resulted in a 14% CAGR over 5 years in a majority of cases.
Considerations:
- Market Volatility: Returns can vary, and past performance doesn’t guarantee future results.
- Economic Factors: Global events, policy changes, and economic cycles can influence returns.
