Tata Consultancy Services Ltd: Share Price Target from 2025 to 2034
Predicted Share Price for Tata Consultancy Services Ltd for Tomorrow (2024-11-23): 4,091.37
| Year | Projected Price (₹) |
|---|---|
| 2025 | 3,052.24 |
| 2026 | 2,482.69 |
| 2027 | 2,508.24 |
| 2028 | 2,241.73 |
| 2029 | 2,077.84 |
| 2030 | 1,905.25 |
| 2031 | 1,751.28 |
| 2032 | 1,417.94 |
| 2033 | 1,139.57 |
| 2034 | 977.06 |
How are the Share Price Targets for Tata Consultancy Services Ltd Calculated?
We calculate the share price targets for Tata Consultancy Services Ltd using a combined approach of Geometric Fractional Brownian Motion (GFBM) and the Exponential Moving Average (EMA) for trend analysis. This hybrid model incorporates historical price data, memory effects through the Hurst exponent, and dynamic regime shifts based on the stock's trends. Below are the detailed steps of how these projections are calculated.
Step 1: Calculate the Log Returns
The log returns measure the relative change in stock prices over time. It is calculated as follows:
\[ \text{Log Return} = \ln \left( \frac{S_{i}}{S_{i-1}} \right) \]
Where:
- Si: Stock price at time i
- Si-1: Stock price at time i-1
The log returns are calculated for each consecutive pair of stock prices between the start date (August 21, 2024) and the end date (November 21, 2024).
53 valid data points from the historical price data in the period from August 21, 2024 to November 21, 2024 have been used for the calculations.
These returns measure the rate of return over the historical period under consideration.
Step 2: Calculate the Exponential Moving Average (EMA)
The EMA is a weighted average of past prices that gives more importance to recent prices. It is calculated as follows:
\[ EMA = \alpha \times P_{t} + (1 - \alpha) \times EMA_{t-1} \]
Where:
- α: Smoothing factor \(\frac{2}{n+1}\)
- Pt: Current stock price at time t
- EMAt-1: EMA from the previous time step
The EMA helps identify the trend in stock prices. If the stock price is above the EMA, the stock is considered to be in an upward trend, and if below, it is in a downward trend.
Step 3: Calculate the Drift (Average Growth Rate)
The drift is the average rate at which the stock price grows over time. It is calculated as the mean of the log returns:
\[ \mu = \frac{1}{n} \sum_{i=1}^{n} \ln \left( \frac{S_{i}}{S_{i-1}} \right) \]
Where:
- μ: Drift (average growth rate)
- n: Number of log returns (time intervals) between August 21, 2024 and November 21, 2024
For Tata Consultancy Services Ltd, the drift (average growth rate) is -0.21%.
This drift represents the average historical growth rate of the stock between August 21, 2024 and November 21, 2024.
Step 4: Calculate the Volatility
The volatility measures the extent of price fluctuations. It is calculated as the standard deviation of the log returns:
\[ \sigma = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} \left( \ln \left( \frac{S_{i}}{S_{i-1}} \right) - \mu \right)^2 } \]
Where:
- σ: Volatility (standard deviation of log returns)
- μ: Drift (calculated in Step 3)
- n: Number of log returns (time intervals) between August 21, 2024 and November 21, 2024
For Tata Consultancy Services Ltd, the volatility (standard deviation of returns) is 1.13%.
The volatility shows the level of price variation between August 21, 2024 and November 21, 2024.
Step 5: Calculate the Hurst Exponent
The Hurst exponent measures the "memory" or persistence of the stock price movement. It is calculated as follows:
\[ H = \frac{\log(R/S)}{\log(n)} \]
Where:
- R/S: Rescaled range (calculated from cumulative deviations and standard deviation)
- n: Number of time intervals between the start and end dates
The Hurst exponent provides insight into the market behavior:
- H > 0.5: Persistent behavior (trend-following) The market shows long-term trends, where past movements are likely to continue in the same direction.
- H = 0.5: Random behavior (similar to Brownian motion) The market behaves randomly, and past price movements do not provide any indication of future price movements.
- H < 0.5: Anti-persistent behavior (mean-reverting) The market shows mean-reverting behavior, where extreme movements are followed by corrections in the opposite direction.
For Tata Consultancy Services Ltd, the calculated Hurst exponent is 0.46, indicating mean-reverting (anti-persistent) behavior.
Step 6: Project Future Share Prices Using GFBM and EMA
The future price of the stock is projected using a combined model of Geometric Fractional Brownian Motion (GFBM) and Exponential Moving Average (EMA) for trend-based regime switching. The GFBM formula incorporates both the drift, volatility, and a memory effect through the Hurst exponent, while the EMA dynamically shifts the regime based on the stock's price trend. The GFBM formula is:
\[ S(t) = S(0) \times e^{\left(\mu - \frac{\sigma^2}{2}\right)t + \sigma W_H(t)} \]
Where:
- S(t): Projected stock price at time t
- S(0): Current stock price (most recent price from historical data)
- μ: Drift (average growth rate from Step 3)
- : Volatility (calculated in Step 4)
- WH(t): Fractional Wiener process incorporating the Hurst exponent
The fractional Wiener process introduces both randomness and memory into the model, simulating market fluctuations with persistence or anti-persistence based on the Hurst exponent. The EMA is used to switch between high-volatility and low-volatility regimes based on the stock's trend.
Step 7: Predicting Tomorrow's Stock Price for Tata Consultancy Services Ltd
The predicted price for tomorrow is derived using the Geometric Brownian Motion (GBM) formula, which incorporates the drift (average growth rate), volatility (price fluctuations), and a random factor to simulate possible market movements. The formula used is:
\[ S(t+1) = S(t) \times e^{\left(\mu - \frac{\sigma^2}{2}\right) + \sigma \times Z} \]
Where:
- S(t+1): Projected stock price for tomorrow
- S(t): Today's stock price (the most recent price from historical data)
- : Drift (average growth rate)
- : Volatility (price fluctuation)
- Z: A random variable sampled from a normal distribution to introduce market randomness
This method allows us to estimate the potential price of Tata Consultancy Services Ltd for tomorrow, factoring in both the historical growth and expected volatility.
Step 8: View the Projected Share Prices
The projected share prices for the next 10 years are calculated based on the combined GFBM and EMA model, which accounts for historical growth (drift), market volatility, memory effects (Hurst exponent), random price fluctuations, and trend-based regime shifts. These projections provide an estimate of future prices considering the stock's past performance and market conditions.
Conclusion
By using a hybrid approach of Geometric Fractional Brownian Motion (GFBM) and Exponential Moving Average (EMA), we provide a more realistic projection of share prices for Tata Consultancy Services Ltd over the next 10 years. This model considers historical performance, volatility, market memory, and current price trends, offering an accurate outlook for future stock price movements.
Disclaimer
The projected stock prices are provided for informational purposes only and do not constitute investment advice or recommendations. Past performance of securities is not indicative of future results. Getaka Financial Services is not responsible for any investment decisions made on the basis of this information. Investors are advised to seek independent financial advice from a SEBI-registered investment advisor before making any investment decisions. Investments in the securities market are subject to market risks. Please read all associated offer documents and terms carefully before investing.
