Daily returns of three funds

What it is good for

• Compare the volatility (standard deviation) of three return series.
• Show that returns have fatter tails than a normal distribution (kurtosis, Q–Q plot).
• Estimate a 95% or 99% one-day Value-at-Risk with empirical quantiles vs a normal approximation.
• Measure correlation between funds and see how it changes in turbulent periods.

Methods: standard deviation, kurtosis, Q–Q plot, empirical quantiles, normality tests, correlation matrix, rolling volatility.

Data quality notes

• Returns are in percent (1.0 = 1%), rounded to 3 decimals.
• Excess kurtosis is clearly positive for all funds; normal-based VaR underestimates tail risk.
• Row 513 (date in the third year) is a crash day: the growth fund's worst day.
• Volatility clusters, so consecutive days are not independent in their variability.
• No missing values.

Provenance and licence

A common market shock and fund-specific shocks are drawn from Student t distributions with 4–5 degrees of freedom scaled to unit variance (fat tails). Volatility follows a GARCH(1,1)-like recursion (α = 0.08, β = 0.90), so calm and turbulent periods cluster. Fund return = mean + daily volatility × (loading × market shock + idiosyncratic shock), with volatility scales 0.25% (income), 0.7% (balanced) and 1.4% (growth); the realised daily standard deviations in this sample are about 0.21%, 0.54% and 0.99% because volatility spends most days below its long-run average. On trading day 513 a crash of −2.1%, −5.6% and −9.2% is imposed. Trading days are Sunday–Thursday.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241009). It does not describe real people or organisations; any resemblance is coincidental.