PTC India Ltd: Share Price Target from 2025 to 2034
| Year | Projected Price (₹) |
|---|---|
| 2025 | 185.37 |
| 2026 | 214.42 |
| 2027 | 236.51 |
| 2028 | 208.60 |
| 2029 | 198.46 |
| 2030 | 180.99 |
| 2031 | 202.02 |
| 2032 | 179.29 |
| 2033 | 189.01 |
| 2034 | 163.27 |
How are the Share Price Targets for PTC India Ltd Calculated?
We calculate the share price targets for PTC India Ltd using the Geometric Fractional Brownian Motion (GFBM) model. This model incorporates historical price data and accounts for the "long memory" of stock prices by using the Hurst exponent, offering a more realistic projection by considering market persistence or anti-persistence. 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 (October 4, 2024).
33 valid data points from the historical price data in the period from August 21, 2024 to October 4, 2024 have been used for the calculations.
These returns measure the rate of return over the historical period under consideration.
Step 2: 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 October 4, 2024
For PTC India Ltd, the drift (average growth rate) is -0.14%.
This drift represents the average historical growth rate of the stock between August 21, 2024 and October 4, 2024.
Step 3: 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 2)
- n: Number of log returns (time intervals) between August 21, 2024 and October 4, 2024
For PTC India Ltd, the volatility (standard deviation of returns) is 2.57%.
The volatility shows the level of price variation between August 21, 2024 and October 4, 2024.
Step 4: 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 PTC India Ltd, the calculated Hurst exponent is 0.59, indicating persistent (trend-following) behavior.
Since H = 0.59, this indicates a tendency for the stock price to follow a trend. If the price increases, it is likely to continue rising, and if it decreases, it is likely to keep falling. This behavior is often called "trend-following."
Step 5: Project Future Share Prices Using the GFBM Formula
The future price of the stock is projected using the Geometric Fractional Brownian Motion (GFBM) model, which incorporates both the drift, volatility, and a memory effect through the Hurst exponent. 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 2)
- σ: Volatility (calculated in Step 3)
- 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.
Step 6: View the Projected Share Prices
The projected share prices for the next 10 years are calculated based on the GFBM model, which accounts for historical growth (drift), market volatility, memory effects (Hurst exponent), and random price fluctuations. These projections provide an estimate of future prices considering the stock's past performance and market conditions.
Conclusion
By using the Geometric Fractional Brownian Motion (GFBM) model, we provide a more realistic projection of share prices for PTC India Ltd over the next 10 years. This model considers historical performance, volatility, and market memory, offering a more 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.
