DATA 621 Blog 3 Variance and Risk in Personal Finance:

Variance

Variance measures how spread out values are around the mean. In finance, variability is often associated with risk. Two investments may have the same average return but very different levels of volatility.

Understanding variance helps individuals evaluate consistency and uncertainty in outcomes, rather than focusing only on averages.

R Example

# Monthly returns for two investments
investment_A <- c(2, 3, 2, 3, 2, 3, 2, 3)
investment_B <- c(-5, 10, -4, 12, -6, 11, -3, 13)

mean(investment_A)
## [1] 2.5
mean(investment_B)
## [1] 3.5

Compare Variance

var(investment_A)
## [1] 0.2857143
var(investment_B)
## [1] 74.57143

Visualization

boxplot(investment_A, investment_B,
        names = c("Investment A", "Investment B"),
        main = "Monthly Return Comparison",
        ylab = "Percent Return")

Interpretation

Although both investments have similar average returns, Investment B shows much higher variance. This indicates greater risk and less predictable outcomes.

Conclusion

Variance provides essential context when evaluating financial decisions. Looking beyond averages allows for better assessment of risk and stability in everyday investing choices.