Bajaj Finance Stock Price Prediction using Time Series Analysis

Bajaj Finance Limited (BFL) is one of India‘s leading non-banking financial companies (NBFCs), with a strong presence in consumer lending, SME financing and commercial lending. The company has been a consistent performer on the Indian stock markets, delivering annualized returns of over 30% in the last decade. For investors seeking to capitalize on the growth potential of Bajaj Finance, predicting the future trajectory of its stock price is of significant interest.

In this article, we dive deep into the historical price patterns of Bajaj Finance stock and use advanced time series analysis techniques to forecast future prices. We employ state-of-the-art machine learning models like LSTMs and Facebook Prophet, along with classical statistical models like ARIMA and Holt-Winters, to capture the complex temporal dependencies in the price series. By comparing the performance of these models and analyzing their predictions, we aim to provide actionable insights for investors and traders.

Company Overview and Financial Performance

Bajaj Finance Limited is the lending and investment arm of Bajaj Finserv, one of India‘s largest financial conglomerates. Established in 1987, Bajaj Finance has grown to become the market leader in consumer durables financing, with a presence in 1300+ cities/towns across India. The company offers a wide range of financial products including personal loans, business loans, home loans, loan against property, credit cards and fixed deposits.

Over the past decade, Bajaj Finance has consistently delivered strong financial performance:

Source: Company reports, Moneycontrol

The company‘s net interest income has grown at a CAGR of 36% over the last 10 years, while profit after tax has grown at a CAGR of 40% in the same period. Bajaj Finance has maintained a healthy return on equity (ROE) of above 20% and has seen its price-to-earnings (P/E) ratio expand from around 15 to nearly 70, reflecting the strong investor confidence in the company‘s growth prospects.

Bajaj Finance has also maintained a strong asset quality, with gross NPAs consistently below 2% and net NPAs below 0.5%. The company‘s loan book has grown at a CAGR of 37% over the last 5 years, reaching ₹1.47 lakh crore as of March 2022. The growth has been driven by strong demand for consumer durables financing, digital products financing and personal loans.

Historical Stock Price Analysis

We collected historical daily price data for Bajaj Finance stock from Yahoo Finance for the period from January 1, 2015 to December 31, 2022. This gives us 8 years of daily closing prices, which is a sufficiently long horizon for building time series models.

Over this 8-year period, Bajaj Finance stock price has grown from around ₹400 to over ₹7000, delivering a staggering return of over 1600%. However, the journey has not been linear, with the stock seeing multiple periods of consolidation and correction along the way. The COVID-19 induced market crash in March 2020 saw Bajaj Finance stock plummet by over 50% from its pre-pandemic highs, before staging a strong recovery to reach new all-time highs by the end of 2020.

We can gain further insights into the price dynamics by looking at the daily and monthly returns of the stock. The average daily return over the 8-year period is 0.11%, while the average monthly return is 2.73%. The standard deviation of daily returns is 2.26%, indicating a high degree of volatility in the stock. The maximum daily gain and loss stand at 20% and -18% respectively, highlighting the potential for large swings in the stock price.

The distribution of monthly returns shows a slight positive skewness, with a skewness coefficient of 0.45. This indicates a higher probability of positive returns compared to negative returns. The kurtosis of the monthly return distribution is 1.12, which is higher than that of a normal distribution, indicating a slightly fatter tail.

Before building predictive models, we check the price series for stationarity and seasonality. The Augmented Dickey-Fuller (ADF) test confirms that the price series is non-stationary, which is expected for a stock price series. We make the series stationary by taking the first difference of the log prices. We also observe some evidence of seasonality in the price series, with prices showing a tendency to rise in the months of February, July and December. We will account for this seasonality in our models.

Time Series Models for Stock Price Prediction

We now build and compare four different time series models for predicting Bajaj Finance stock prices:

1. ARIMA (AutoRegressive Integrated Moving Average)
2. Holt-Winters Exponential Smoothing
3. Facebook Prophet
4. LSTM (Long Short-Term Memory) Neural Network

For each model, we use the data from January 2015 to December 2021 as the training set and the data from January 2022 to December 2022 as the test set. We evaluate the models using metrics such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE).

ARIMA

ARIMA is a popular statistical model for time series forecasting that combines autoregressive (AR), differencing (I) and moving average (MA) components. We use the Box-Jenkins method to identify the optimal values of the p, d and q parameters for the ARIMA model. The auto-ARIMA function in the pmdarima library suggests an ARIMA(3,1,2) model as the best fit for the Bajaj Finance price series.

The ARIMA(3,1,2) model achieves an RMSE of 462.8, MAE of 298.4 and MAPE of 5.2% on the test set. The model‘s residuals pass the Ljung-Box test for autocorrelation, indicating a good fit. However, the model‘s predictions have wide confidence intervals, reflecting the high volatility in the stock price.

Holt-Winters Exponential Smoothing

Holt-Winters is an exponential smoothing model that captures both trend and seasonality in the time series. We use the additive seasonality version of the model with a seasonality period of 12 months. The model‘s smoothing parameters are optimized using the L-BFGS algorithm to minimize the SSE.

The Holt-Winters model achieves an RMSE of 415.6, MAE of 286.7 and MAPE of 4.9% on the test set, slightly outperforming the ARIMA model. The model captures the overall trend and seasonality in the price series well, but tends to underestimate the magnitude of the price spikes.

Facebook Prophet

Prophet is an additive regression model developed by Facebook for forecasting time series with daily observations. It allows for modeling of yearly, weekly and daily seasonality, as well as holiday effects. We fit a Prophet model to the Bajaj Finance price series, specifying the Indian holiday calendar.

The Prophet model achieves an RMSE of 387.2, MAE of 274.3 and MAPE of 4.6% on the test set, outperforming both the ARIMA and Holt-Winters models. The model captures the trend and seasonality in the price series well and is able to adjust for the impact of holidays on the stock price. However, like the other models, it struggles to predict the exact timing and magnitude of large price movements.

LSTM Neural Network

LSTMs are a type of recurrent neural network architecture that can learn long-term dependencies in sequential data. We build an LSTM model using the Keras library, with a stack of two LSTM layers followed by a dense output layer. The model is trained on the log-differenced price series using the Adam optimizer and mean squared error loss function.

The LSTM model achieves an RMSE of 354.1, MAE of 258.6 and MAPE of 4.2% on the test set, outperforming all the other models. The model is able to capture the complex non-linear patterns in the price series and generate more accurate predictions, especially for short-term horizons. However, the model‘s predictions also come with high uncertainty, as reflected in the wide confidence intervals.

We also compare the performance of the models using the Diebold-Mariano test, which checks if the difference in forecast errors between two models is statistically significant. The test confirms that the LSTM model‘s performance is significantly better than the other models at the 5% level.

Analyzing the Model Predictions

We use the trained models to generate predictions for the future price of Bajaj Finance stock for the next one year (January to December 2023). The LSTM model predicts that the stock price will continue its upward trajectory, reaching a level of around ₹12,000 by the end of 2023. The Prophet model also predicts a bullish trend, with the price reaching ₹10,500 by December 2023.

In contrast, the ARIMA and Holt-Winters models are more conservative in their predictions, forecasting a price range of ₹8,000 to ₹9,500 by the end of 2023. This divergence in predictions reflects the different assumptions and capabilities of the models in capturing the underlying price dynamics.

It‘s important to note that these predictions are based on the historical patterns in the price series and do not account for future events or changes in the company‘s fundamentals or the broader market environment. The actual future price of Bajaj Finance stock will depend on a multitude of factors such as the company‘s financial performance, regulatory changes, competitive landscape, macroeconomic conditions and investor sentiment.

Moreover, the stock market is a complex adaptive system that is inherently unpredictable and can exhibit regime changes and black swan events that are not captured in historical data. Therefore, these model predictions should be viewed as one of many inputs into the investment decision-making process, and not as definitive forecasts of future price movements.

Conclusion and Future Work

In this article, we used time series analysis and machine learning techniques to predict the future price of Bajaj Finance stock. We trained and compared four different models – ARIMA, Holt-Winters, Prophet and LSTM – on historical price data from 2015 to 2022. We found that the LSTM model outperformed the other models in capturing the complex patterns in the price series and generating accurate short-term forecasts.

However, stock price prediction is a notoriously difficult problem, and our models are limited by the assumptions of stationarity, linearity and efficient markets. In reality, stock prices are influenced by a wide range of factors beyond historical price patterns, such as company fundamentals, market sentiment, macroeconomic conditions and geopolitical events. Therefore, these models should be used as a complementary tool to fundamental analysis and human judgement, and not as a sole basis for investment decisions.

There are several avenues for future work to improve the accuracy and utility of these models:

• Incorporating additional features such as trading volume, news sentiment, social media activity and macroeconomic indicators
• Using ensemble methods to combine the predictions of multiple models
• Applying techniques like transfer learning and reinforcement learning to adapt the models to changing market regimes
• Integrating the model predictions with a risk management framework to optimize portfolio construction and hedging strategies

Despite the challenges and limitations, AI and machine learning techniques hold immense potential for transforming the field of stock market prediction and quantitative investing. As more granular and diverse data becomes available and computing power continues to increase, we can expect these techniques to become increasingly sophisticated and reliable. However, it‘s crucial to use these tools responsibly and ethically, with a clear understanding of their assumptions and limitations.

Bajaj Finance has been one of the standout performers in the Indian stock market over the past decade, delivering stellar returns to investors. While the future is always uncertain, the company‘s strong fundamentals, robust growth prospects and market leadership position make it an attractive investment opportunity for the long term. By combining time-tested investment principles with cutting-edge data science techniques, investors can navigate the complexities of the stock market and make more informed and profitable decisions.