Markets Data Volatility Heatmap Portfolio Calculator

YELP Deep Analytical Report

Yelp Inc. | Category: Equity Small Cap | Last Updated: 2026-03-24 | Data Range: 2012-03-01 → 2026-03-01 (169 months)
Quick Overview
Timeframe C-C DoR σ
(Historical)		 H-L DoR σ
(Historical)		 O-C DoR σ
(Historical)		 5Y ATRP
(Avg)		 Binomial IV
(Period)		 Yahoo IV
(Period)		 1σ Lower
(68.27%)		 1σ Upper 2σ Lower
(95.45%)		 2σ Upper
Daily 3.29% 2.65% 2.65% 2.99% 3.11% 3.15% 23.92 25.46 23.19 26.27
Weekly 6.86% 7.48% 7.01% 7.01% 6.86% 6.94% 23.04 26.43 21.52 28.31
Monthly 13.92% 17.01% 14.79% 14.82% 14.27% 14.45% 21.40 28.47 18.55 32.83
Quarterly 23.24% 29.33% 19.49% 24.20% 24.72% 25.02% 19.28 31.60 15.05 40.46
Annual — — — — 49.44% 50.05% 15.05 40.46 9.18 66.33
Option Time Horizon — — — — 18.66% 18.89% 20.48 29.74 16.99 35.84
Calculation Notes: Computed at 2026-03-23T16:37 UTC  |  Reference Contract: Call option expiring 2026-05-15 (52 days)  |  Spot Price (S): $24.68  |  Strike (K): $25.00 (first OTM call ≥ spot)  |  Observed Mid-Price: $1.7500 (Bid $1.6000 / Ask $1.9000)  |  Risk-Free Rate (r): 3.73% (1-Month CMT, US Treasury)  |  Dividend Yield (q): 0.00%  |  Binomial IV (Annual): 49.44% (CRR binomial tree, American, n=20 steps)  |  BS IV: 49.46% (European Black-Scholes)  |  Yahoo IV (Annual): 50.05% → period-scaled as σperiod = σannual·√h  |  Price bands: Upper = S·e+σ√h, Lower = S·e−σ√h
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.31. Further, an Excess Kurtosis of 14.81 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -9.80%290.82%0.82%
-9.80% to -7.34%210.59%1.42%
-7.34% to -4.88%822.32%3.74%
-4.88% to -2.41%3449.74%13.47%
-2.41% to 0.05%132737.56%51.03%
0.05% to 2.52%122834.76%85.79%
2.52% to 4.98%36910.44%96.24%
4.98% to 7.45%792.24%98.47%
7.45% to 9.91%220.62%99.09%
Greater than 9.91%320.91%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -3.23%3.34% 82.31%68.27%
±2σ -6.52%6.63% 95.92%95.45%
±3σ -9.80%9.91% 98.27%99.73%
Descriptive Statistics
Mean0.054%
Standard Error0.055%
Median0.000%
Mode0.000%
Standard Deviation3.286%
Sample Variance10.796%
Kurtosis14.81
Skewness0.31
Range54.268%
Minimum-26.598%
Maximum27.670%
Count3533
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 2.132% 1763 49.90% 1.064%
Negative -2.044% 1745 49.39% -1.010%
Zero 0.000% 25 0.71% 0.000%
Average True Range Percentage (ATRP)
Trading Days Horizon Average Daily True Range %
5 1 Week 2.62%
20 1 Month 3.43%
60 1 Quarter 3.57%
250 1 Year 2.90%
750 3 Years 2.65%
1,250 5 Years 2.99%
2,500 10 Years 3.46%
5,000 20 Years 4.01%
12,500 50 Years 4.01%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.19. Further, an Excess Kurtosis of 17.83 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -4.08%00.00%0.00%
-4.08% to -2.10%00.00%0.00%
-2.10% to -0.11%00.00%0.00%
-0.11% to 1.87%51814.66%14.66%
1.87% to 3.85%174549.38%64.04%
3.85% to 5.84%76221.56%85.60%
5.84% to 7.82%2858.06%93.66%
7.82% to 9.81%1073.03%96.69%
9.81% to 11.79%551.56%98.25%
Greater than 11.79%621.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 1.21%6.50% 87.75%68.27%
±2σ -1.44%9.15% 96.21%95.45%
±3σ -4.08%11.79% 98.25%99.73%
Descriptive Statistics
Mean3.855%
Standard Error0.045%
Median3.159%
Mode1.601%
Standard Deviation2.646%
Sample Variance7.003%
Kurtosis17.83
Skewness3.19
Range30.704%
Minimum0.638%
Maximum31.342%
Count3534
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 3.855% 3534 100.00% 3.855%
Negative 0.000% 0 0.00% 0.000%
Zero 0.000% 0 0.00% 0.000%
Open-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.42. Further, an Excess Kurtosis of 7.47 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -7.93%210.59%0.59%
-7.93% to -5.94%330.93%1.53%
-5.94% to -3.95%1173.31%4.84%
-3.95% to -1.96%41011.60%16.44%
-1.96% to 0.03%121634.41%50.85%
0.03% to 2.02%115532.68%83.53%
2.02% to 4.01%40611.49%95.02%
4.01% to 6.00%992.80%97.82%
6.00% to 7.99%471.33%99.15%
Greater than 7.99%300.85%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -2.62%2.68% 78.52%68.27%
±2σ -5.28%5.34% 94.91%95.45%
±3σ -7.93%7.99% 98.56%99.73%
Descriptive Statistics
Mean0.029%
Standard Error0.045%
Median-0.025%
Mode0.000%
Standard Deviation2.654%
Sample Variance7.045%
Kurtosis7.47
Skewness0.42
Range41.662%
Minimum-21.726%
Maximum19.936%
Count3534
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 1.883% 1745 49.38% 0.930%
Negative -1.799% 1769 50.06% -0.901%
Zero 0.000% 20 0.57% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.34. Further, an Excess Kurtosis of 4.90 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -20.32%81.09%1.09%
-20.32% to -15.18%81.09%2.18%
-15.18% to -10.03%273.68%5.87%
-10.03% to -4.89%689.28%15.14%
-4.89% to 0.26%25735.06%50.20%
0.26% to 5.40%25034.11%84.31%
5.40% to 10.55%8010.91%95.23%
10.55% to 15.69%212.86%98.09%
15.69% to 20.84%30.41%98.50%
Greater than 20.84%111.50%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.60%7.12% 80.22%68.27%
±2σ -13.46%13.98% 94.41%95.45%
±3σ -20.32%20.84% 97.41%99.73%
Descriptive Statistics
Mean0.257%
Standard Error0.253%
Median0.212%
Mode-2.554%
Standard Deviation6.860%
Sample Variance47.065%
Kurtosis4.90
Skewness0.34
Range76.714%
Minimum-33.030%
Maximum43.684%
Count733
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 4.719% 386 52.66% 2.485%
Negative -4.707% 347 47.34% -2.228%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Weeks Horizon Average Weekly True Range %
4 1 Month 9.25%
12 1 Quarter 9.16%
52 1 Year 7.18%
156 3 Years 6.39%
260 5 Years 7.01%
520 10 Years 8.18%
1,040 20 Years 9.44%
2,600 50 Years 9.44%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.61. Further, an Excess Kurtosis of 9.02 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -12.34%00.00%0.00%
-12.34% to -6.73%00.00%0.00%
-6.73% to -1.12%00.00%0.00%
-1.12% to 4.48%9512.94%12.94%
4.48% to 10.09%38953.00%65.94%
10.09% to 15.70%15220.71%86.65%
15.70% to 21.30%415.59%92.23%
21.30% to 26.91%233.13%95.37%
26.91% to 32.52%141.91%97.28%
Greater than 32.52%202.72%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 2.61%17.57% 88.96%68.27%
±2σ -4.86%25.04% 95.23%95.45%
±3σ -12.34%32.52% 97.28%99.73%
Descriptive Statistics
Mean10.089%
Standard Error0.276%
Median7.996%
Mode6.085%
Standard Deviation7.476%
Sample Variance55.892%
Kurtosis9.02
Skewness2.61
Range57.134%
Minimum2.236%
Maximum59.370%
Count734
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.089% 734 100.00% 10.089%
Negative 0.000% 0 0.00% 0.000%
Zero 0.000% 0 0.00% 0.000%
Open-to-Close Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.22. Further, an Excess Kurtosis of 7.74 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -20.75%30.41%0.41%
-20.75% to -15.49%81.09%1.50%
-15.49% to -10.23%172.32%3.81%
-10.23% to -4.97%8811.99%15.80%
-4.97% to 0.28%28138.28%54.09%
0.28% to 5.54%24032.70%86.78%
5.54% to 10.80%557.49%94.28%
10.80% to 16.05%212.86%97.14%
16.05% to 21.31%101.36%98.50%
Greater than 21.31%111.50%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -6.73%7.29% 80.11%68.27%
±2σ -13.74%14.30% 94.41%95.45%
±3σ -20.75%21.31% 98.09%99.73%
Descriptive Statistics
Mean0.283%
Standard Error0.259%
Median-0.090%
Mode-4.102%
Standard Deviation7.010%
Sample Variance49.136%
Kurtosis7.74
Skewness1.22
Range83.977%
Minimum-29.282%
Maximum54.695%
Count734
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 5.169% 355 48.37% 2.500%
Negative -4.316% 377 51.36% -2.217%
Zero 0.000% 2 0.27% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of 0.41. Further, an Excess Kurtosis of 2.30 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -40.84%10.60%0.60%
-40.84% to -30.41%10.60%1.19%
-30.41% to -19.97%84.76%5.95%
-19.97% to -9.53%2414.29%20.24%
-9.53% to 0.91%5432.14%52.38%
0.91% to 11.35%4929.17%81.55%
11.35% to 21.78%1810.71%92.26%
21.78% to 32.22%105.95%98.21%
32.22% to 42.66%21.19%99.40%
Greater than 42.66%10.60%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -13.01%14.82% 75.60%68.27%
±2σ -26.93%28.74% 95.83%95.45%
±3σ -40.84%42.66% 98.81%99.73%
Descriptive Statistics
Mean0.908%
Standard Error1.074%
Median0.450%
Mode-42.341%
Standard Deviation13.917%
Sample Variance193.696%
Kurtosis2.30
Skewness0.41
Range104.720%
Minimum-42.341%
Maximum62.379%
Count168
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 10.893% 86 51.19% 5.576%
Negative -9.564% 82 48.81% -4.668%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Months Horizon Average Monthly True Range %
3 1 Quarter 19.29%
12 1 Year 14.77%
36 3 Years 13.84%
60 5 Years 14.82%
120 10 Years 17.67%
240 20 Years 20.42%
600 50 Years 20.42%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 3.24. Further, an Excess Kurtosis of 18.03 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -27.15%00.00%0.00%
-27.15% to -14.40%00.00%0.00%
-14.40% to -1.64%00.00%0.00%
-1.64% to 11.12%2414.20%14.20%
11.12% to 23.87%8147.93%62.13%
23.87% to 36.62%3822.49%84.62%
36.62% to 49.38%148.28%92.90%
49.38% to 62.14%63.55%96.45%
62.14% to 74.89%31.78%98.22%
Greater than 74.89%31.78%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 6.86%40.88% 88.76%68.27%
±2σ -10.14%57.88% 96.45%95.45%
±3σ -27.15%74.89% 98.22%99.73%
Descriptive Statistics
Mean23.870%
Standard Error1.308%
Median18.894%
Mode13.912%
Standard Deviation17.007%
Sample Variance289.253%
Kurtosis18.03
Skewness3.24
Range144.831%
Minimum4.665%
Maximum149.496%
Count169
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 23.870% 169 100.00% 23.870%
Negative 0.000% 0 0.00% 0.000%
Zero 0.000% 0 0.00% 0.000%
Open-to-Close Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.30. Further, an Excess Kurtosis of 4.76 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -43.31%00.00%0.00%
-43.31% to -32.21%10.59%0.59%
-32.21% to -21.11%52.96%3.55%
-21.11% to -10.02%2414.20%17.75%
-10.02% to 1.08%6538.46%56.21%
1.08% to 12.17%4727.81%84.02%
12.17% to 23.27%158.88%92.90%
23.27% to 34.36%84.73%97.63%
34.36% to 45.46%21.18%98.82%
Greater than 45.46%21.18%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -13.72%15.87% 77.51%68.27%
±2σ -28.51%30.66% 96.45%95.45%
±3σ -43.31%45.46% 98.82%99.73%
Descriptive Statistics
Mean1.076%
Standard Error1.138%
Median-0.689%
Mode-38.103%
Standard Deviation14.794%
Sample Variance218.872%
Kurtosis4.76
Skewness1.30
Range112.424%
Minimum-38.103%
Maximum74.321%
Count169
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 12.418% 78 46.15% 5.731%
Negative -8.646% 91 53.85% -4.656%
Zero 0.000% 0 0.00% 0.000%
Close-to-Close Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 1.24. Further, an Excess Kurtosis of 1.11 proves the distribution possesses Fat Tails (Higher Outlier Risk).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -67.30%00.00%0.00%
-67.30% to -49.87%00.00%0.00%
-49.87% to -32.44%11.79%1.79%
-32.44% to -15.00%916.07%17.86%
-15.00% to 2.43%2748.21%66.07%
2.43% to 19.86%814.29%80.36%
19.86% to 37.30%58.93%89.29%
37.30% to 54.73%35.36%94.64%
54.73% to 72.16%35.36%100.00%
Greater than 72.16%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -20.82%25.67% 78.57%68.27%
±2σ -44.06%48.92% 91.07%95.45%
±3σ -67.30%72.16% 100.00%99.73%
Descriptive Statistics
Mean2.429%
Standard Error3.106%
Median-5.642%
Mode-32.978%
Standard Deviation23.244%
Sample Variance540.277%
Kurtosis1.11
Skewness1.24
Range98.662%
Minimum-32.978%
Maximum65.684%
Count56
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 24.817% 22 39.29% 9.750%
Negative -12.057% 34 60.71% -7.320%
Zero 0.000% 0 0.00% 0.000%
Average True Range Percentage (ATRP)
Quarters Horizon Average Quarterly True Range %
4 1 Year 22.16%
12 3 Years 23.72%
20 5 Years 24.20%
40 10 Years 30.74%
80 20 Years 35.91%
200 50 Years 35.91%
High-to-Low Returns
Gram-Charlier Analysis: Data reveals Highly Right Skewed (Extreme Positive Tail Risk) with a Skewness factor of 2.39. Further, an Excess Kurtosis of 8.61 proves the distribution possesses Extreme Fat Tails (Frequent Outliers, Leptokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -42.54%00.00%0.00%
-42.54% to -20.54%00.00%0.00%
-20.54% to 1.46%00.00%0.00%
1.46% to 23.46%1017.54%17.54%
23.46% to 45.46%2442.11%59.65%
45.46% to 67.46%1322.81%82.46%
67.46% to 89.45%610.53%92.98%
89.45% to 111.45%23.51%96.49%
111.45% to 133.45%11.75%98.25%
Greater than 133.45%11.75%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ 16.12%74.79% 87.72%68.27%
±2σ -13.21%104.12% 96.49%95.45%
±3σ -42.54%133.45% 98.25%99.73%
Descriptive Statistics
Mean45.457%
Standard Error3.885%
Median35.818%
Mode12.807%
Standard Deviation29.332%
Sample Variance860.369%
Kurtosis8.61
Skewness2.39
Range173.151%
Minimum12.807%
Maximum185.958%
Count57
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 45.457% 57 100.00% 45.457%
Negative 0.000% 0 0.00% 0.000%
Zero 0.000% 0 0.00% 0.000%
Open-to-Close Returns
Gram-Charlier Analysis: Data reveals Fairly Symmetrical with a Skewness factor of -0.13. Further, an Excess Kurtosis of 0.09 proves the distribution possesses Normal Tails (Mesokurtic).
Bin Distribution Over Raw Range
Bin / RangeFrequencyProbCum. Prob
Less than -56.11%00.00%0.00%
-56.11% to -41.49%00.00%0.00%
-41.49% to -26.88%58.77%8.77%
-26.88% to -12.26%915.79%24.56%
-12.26% to 2.35%1017.54%42.11%
2.35% to 16.97%2238.60%80.70%
16.97% to 31.59%712.28%92.98%
31.59% to 46.20%23.51%96.49%
46.20% to 60.82%23.51%100.00%
Greater than 60.82%00.00%100.00%
Standard Deviation Interval Analysis
SDLower BndUpper Bnd Actual %Normal %
±1σ -17.13%21.84% 73.68%68.27%
±2σ -36.62%41.33% 92.98%95.45%
±3σ -56.11%60.82% 100.00%99.73%
Descriptive Statistics
Mean2.355%
Standard Error2.581%
Median5.949%
Mode-39.337%
Standard Deviation19.489%
Sample Variance379.830%
Kurtosis0.09
Skewness-0.13
Range88.239%
Minimum-39.337%
Maximum48.902%
Count57
Frequency Breakdown
CategoryAvg ReturnCountProbabilityFreq Adj Return
Positive 14.609% 35 61.40% 8.971%
Negative -17.140% 22 38.60% -6.615%
Zero 0.000% 0 0.00% 0.000%