Dr. Raj, the data scientist, models a stock’s daily return as a random variable with a mean of 0.4% and standard deviation of 1.2%. If he observes 5 consecutive trading days, what is the expected total return over the period, assuming returns are independent?

["Modeling Daily Stock Returns: Expected Total Return Over 5 Trading Days", "In financial data science, modeling stock returns as random variables is essential for risk assessment, portfolio optimization, and algorithmic trading strategies. Dr. Raj, a data scientist specializing in quantitative finance, models the daily return of a particular stock as a random variable with a known mean and volatility. His model assumes returns are independent and identically distributed (i.i.d.) over time.", "### Understanding the Model", "Dr. Raj specifies that the daily return of the stock has:", "- Mean (expected daily return): 0.4%\n- Standard deviation: 1.2%", "Since returns are independent across days, the total return over a period is the sum of daily returns. This property is key in computing expected aggregate performance.", "### Center of Expectation: Daily Mean Return", "The expected return in a single trading day is 0.4%. This expected value represents the average gain (or loss) one could expect per day under Dr. Raj’s model.", "### Extending to Multiple Days", "For independent daily returns, the expected total return over 5 consecutive trading days is simply the sum of the daily expected returns:", "[\n\ ext{Expected Total Return} = 5 \ imes \ ext{Expected Daily Return}\n]", "[\n= 5 \ imes 0.4% = 2.0%\n]", "Note: The standard deviation of 1.2% influences the variance and risk (i.e., how much returns typically deviate from the mean), but it does not affect the expected total return under linear additivity.", "### Conclusion", "Assuming independence and linearity, Dr. Raj’s model predicts that over 5 trading days, the expected total return is 2.0%, reflecting a positive average performance despite daily volatility.", "---", "This insight underscores a fundamental principle in financial modeling: the expected return over multiple independent periods accumulates linearly from the daily mean—regardless of the volatility of individual day returns.", "For more insights into modeling financial data, visit Dr. Raj’s Data Science Finance Blog."]