Stock Prices
March 20, 2025 · 1 min read · Page View:
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This is a tutorial for stock prices in the context of random processes.
SOME FUNDAMENTALS ON STOCKS AND INVESTMENTS #
- Return = [CashFlow+(Price1 - Price0)/Price0]
- Risk: Most investors are risk averse, thus prefer “Steady Eddie” to “Volatile Joe”. Investors demand higher return for stocks with volatile business performance.
FACTORS IMPACTING STOCK PRICES #
- Market: Liquidity, Supply/demand, Addition to/Removal from Stock Index, Investment ratings, Sentiment, Market Profitability.
- Corporate Activities: Profitability, Business prospects / growth, Improved Profitability (Sales/Costs), Competition (Business / Capital Market), Corporate Governance, Red Flag, Stability and predictability.
- MACRO FACTORS: General Economy/Business Environment, Government(Political/Legal/Economics), Overall Political Environment, Social Changes, Costs of Input, Business Prospects.
- INTEREST RATE
RANDOM WALK MODEL #
- In a random walk model, the series itself is not random, but its differences (the changes from one period to the next) are random.
- Mathematically, $X_{t}=X_{t - 1}+e_{t}$ or $X_{t}-X_{t - 1}=e_{t}$, where $x_{t}$ is the value in time period $t$, $x_{t - 1}$ is the value in time period $t - 1$, and $e_{t}$ is the value of the error term in time period $t$.
- Transforming a series (e.g., changing to first differences) can help forecast future trends. If a series follows a random walk, the original series may offer little insight, and analyzing the first-differenced series may be necessary.
INTEL CLOSING PRICES #
$H_{0}$: The series is random.
$H_{1}$: The series is not random.
Original series:
- Number of runs up and down = 76. Expected number of runs = 104.333. p-value = 1.16648E - 7. Since the p-value < 0.05, we can reject $H_{0}$. The original series for Intel Closing Prices is not random.
First-differenced series:
- Number of runs up and down = 99. Expected number of runs = 104.333. p-value = 0.357469. Since the p-value > 0.05, we cannot reject $H_{0}$. The first-differenced series for Intel Closing Prices is random.
Conclusion for Intel Closing Prices [6/16/97 - 6/12/00]: The series (Intel Closing Prices) is not random, but its differences are random. It follows a random walk model.
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