PayPal (PYPL)

PayPal Tail Risk

Tail-risk stats use daily return distributions rather than simple end-point returns. They show how ugly the left tail has been, how severe the worst 5% of days were, and whether returns were skewed toward outsized upside or downside shocks.

The histogram shows the shape of PayPal's daily log returns over the 5Y window. Bars left of the 5% VaR marker are the worst 5% of days; the ES marker is the average loss inside that tail. Skew and excess kurtosis describe whether the distribution is symmetric around zero and whether extreme days are more common than a Normal distribution predicts.

PYPL daily return distribution (5Y)

PYPL daily return distribution (5Y)

Log-return histogram with Value-at-Risk and Expected Shortfall markers at the 5% left tail.

Days Download PNG

PYPL 5Y

VaR

-4.01%

ES

-6.71%

Skew

-1.61

Excess kurtosis

15.14

Days

1254

±2σ days

29 / 23

worst-5% daily return and the average loss inside it

Formula $\displaystyle \mathrm{VaR}_{5\%} = Q_{0.05}(R),\quad \mathrm{ES}_{5\%} = \mathbb{E}[R \mid R \le \mathrm{VaR}_{5\%}]$

Less negative daily VaR and Expected Shortfall values mean the left tail was less violent. Skew and excess kurtosis help distinguish between steady compounding and a path dominated by occasional extreme moves.