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Research 
Research document 
June 2013 
Correlation and Volatility 
1 
Jcarlos López Moraleja
Functional Data Analisys 
2 
Implied Volatility 
Absolute 
Volatility 
Relative Volatility 
Correlation 
• Delta 1 
• Delta hedge 
Long 
Future 
• Long to neutral Volatility 
• Hedge first loss PS ATM 
• Short Volatility 
• Tactical Volatility Short Put 
• Short Volatility 
• Strategic Trade Short Call 
• Long Volatility 
• Black Swan 
Long Put 
OTM 
• Short of Volatility 
• Strategic hedging 
Long 
Butterfly 
Risk Matrix 
Based on a dynamic process of risk 
management decisions developed from a 
quantitative Model 
Dynamic and Systematic decision making 
supported by the model's interpretations of 
market absolute and relative volatility
Returns for Volatility Levels 
3 
200% 
150% 
100% 
50% 
0% 
-50% 
-100% 
-150% 
-200% 
12.2 
13.5 
14.8 
16.3 
18.0 
19.9 
21.9 
24.2 
26.6 
29.4 
32.4 
35.7 
39.3 
43.4 
47.8 
52.7 
58.1 
64.1 
70.7 
77.9 
85.9 
94.7 
Negative Returns 
Positive Returns
Rate of return Vs Volatility distribution 
4 
50.0% 
40.0% 
30.0% 
20.0% 
10.0% 
0.0% 
-10.0% 
-20.0% 
-30.0% 
-40.0% 
-50.0% 
-60.0% 
Return distribution Dj EuroStoxx 50 based 
on Volatility level 
>0 <0 UP DOWN NET Net UP/Down 
12.2 6% -1.3% 11 5 4.6% 6 
12.8 20% -3.7% 34 12 16.1% 22 
13.5 23% -9.2% 47 33 13.8% 14 
14.1 25% -14.4% 49 40 10.2% 9 
14.8 41% -23.3% 61 43 17.2% 18 
15.6 44% -23.5% 68 45 20.8% 23 
16.3 46% -32.2% 81 73 14.1% 8 
17.2 50% -42.8% 80 75 7.0% 5 
18.0 58% -41.4% 91 70 16.9% 21 
18.9 69% -40.1% 99 59 29.1% 40 
19.9 74% -54.4% 80 77 19.9% 3 
20.9 82% -80.8% 107 109 1.0% -2 
21.9 115% -78.8% 132 106 36.4% 26 
23.0 95% -119.1% 119 138 -24.0% -19 
24.2 108% -118.9% 113 129 -11.2% -16 
25.4 139% -117.1% 137 124 22.3% 13 
26.6 142% -112.0% 122 110 30.0% 12 
28.0 158% -138.4% 131 119 19.1% 12 
29.4 121% -148.2% 102 118 -27.4% -16 
30.8 77% -108.8% 55 78 -31.6% -23 
32.4 66% -83.3% 51 63 -17.6% -12 
34.0 35% -56.4% 30 42 -21.7% -12 
35.7 54% -57.2% 27 28 -2.9% -1 
37.5 54% -54.6% 31 34 -0.2% -3 
39.3 70% -37.7% 35 37 32.0% -2 
41.3 46% -94.9% 30 48 -49.1% -18 
43.4 78% -47.2% 42 26 31.0% 16 
45.5 67% -74.9% 31 41 -7.8% -10 
47.8 69% -72.7% 28 35 -3.6% -7 
50.2 49% -81.5% 18 31 -32.0% -13 
52.7 50% -75.7% 21 28 -25.5% -7 
55.4 23% -36.8% 7 13 -14.0% -6 
58.1 23% -49.7% 9 17 -26.7% -8 
61.0 8% -38.1% 3 11 -30.0% -8 
64.1 15% -20.5% 5 6 -5.6% -1 
67.3 12% -14.1% 3 4 -2.0% -1 
70.7 0% -4.0% 0 1 -4.0% -1 
74.2 5% -5.8% 1 2 -0.3% -1 
77.9 8% -6.7% 2 2 1.5% 0 
81.8 0% -8.2% 0 1 -8.2% -1 
85.9 0% 0.0% 0 0 0.0% 0 
90.2 0% -6.2% 0 1 -6.2% -1 
94.7 0% 0.0% 0 0 0.0% 0
Volatility frequency data 
5 
1998- 
2014 
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 
4129 130 256 255 254 253 253 259 257 255 253 256 255 257 257 257 253 170 Tot % Tot 
5% 
10.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
10.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
11.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
11.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 
12.2 15 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 15.0 0% 
12.8 45 0 0 0 0 0 0 1 42 1 0 0 0 0 0 0 0 1 45.0 1% 
13.4 76 0 0 0 0 0 0 6 54 10 0 0 0 0 0 0 0 6 76.0 2% 
14.1 89 0 0 0 0 0 0 4 39 28 11 0 0 0 0 0 1 6 89.0 2% 
14.8 100 0 0 0 0 0 0 6 31 43 9 0 0 0 0 0 5 6 100.0 2% 
15.5 113 0 0 0 0 0 0 9 29 38 10 0 0 0 0 0 14 13 113.0 3% 
16.3 154 0 0 0 0 0 0 22 18 39 20 0 0 0 0 3 29 23 154.0 4% 
17.1 154 0 0 0 0 0 0 26 16 20 22 0 0 0 0 8 29 33 154.0 4% 
18.0 165 0 0 0 0 0 0 30 9 13 32 0 0 0 0 12 36 34 166.0 4% 
18.9 157 0 0 0 0 0 0 47 4 13 30 2 0 4 3 6 35 14 158.0 4% 
19.8 148 0 1 9 8 2 2 30 0 9 22 6 0 4 10 5 28 12 148.0 4% 
20.8 215 0 10 25 18 3 7 25 0 13 24 8 0 18 22 11 23 8 215.0 5% 
21.8 236 4 19 11 26 6 10 13 0 9 8 25 0 21 24 21 30 8 235.0 6% 
22.9 262 5 23 24 26 9 13 14 0 8 8 20 1 30 32 31 15 3 262.0 6% 
24.1 236 10 33 15 19 8 10 8 0 3 9 26 10 25 22 30 5 3 236.0 6% 
25.3 257 4 31 26 18 30 17 4 0 6 15 24 14 28 13 26 1 0 257.0 6% 
26.5 233 4 26 30 19 15 26 8 0 0 15 11 28 23 5 21 2 0 233.0 6% 
27.9 265 6 31 36 26 20 29 1 0 2 8 14 39 22 8 23 0 0 265.0 6% 
29.3 218 9 19 40 23 16 19 4 0 0 5 14 15 25 8 21 0 0 218.0 5% 
30.7 138 11 12 21 13 4 13 0 0 0 1 10 16 17 7 13 0 0 138.0 3% 
32.3 118 3 15 13 5 3 14 1 0 0 2 11 22 8 9 12 0 0 118.0 3% 
33.9 74 4 6 4 5 0 16 0 0 0 1 10 13 6 1 8 0 0 74.0 2% 
35.6 53 8 2 1 4 6 4 0 0 0 1 3 5 8 7 4 0 0 53.0 1% 
37.3 66 17 7 0 3 9 1 0 0 0 0 2 10 4 11 2 0 0 66.0 2% 
39.2 70 9 13 0 7 10 3 0 0 0 0 3 9 3 13 0 0 0 70.0 2% 
41.2 76 4 6 0 10 9 7 0 0 0 0 6 14 2 18 0 0 0 76.0 2% 
43.2 70 7 2 0 7 7 8 0 0 0 0 5 18 4 12 0 0 0 70.0 2% 
45.4 74 3 0 0 5 13 21 0 0 0 0 2 18 2 10 0 0 0 74.0 2% 
47.6 63 5 0 0 6 15 18 0 0 0 0 1 6 1 11 0 0 0 63.0 2% 
50.0 50 4 0 0 1 15 6 0 0 0 0 4 9 2 9 0 0 0 50.0 1% 
52.5 50 6 0 0 3 23 7 0 0 0 0 6 4 0 1 0 0 0 50.0 1% 
55.2 21 3 0 0 1 4 2 0 0 0 0 7 3 0 1 0 0 0 21.0 1% 
57.9 25 3 0 0 1 14 0 0 0 0 0 6 1 0 0 0 0 0 25.0 1% 
60.8 15 1 0 0 0 8 0 0 0 0 0 6 0 0 0 0 0 0 15.0 0% 
63.9 10 0 0 0 0 4 0 0 0 0 0 6 0 0 0 0 0 0 10.0 0% 
67.0 8 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 8.0 0% 
70.4 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.0 0% 
73.9 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2.0 0% 
77.6 5 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 5.0 0% 
81.5 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.0 0% 
85.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0% 
89.9 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.0 0% 
94.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0% 
Rº -6.8% -1.9% 46.7% -2.7% -20.2% -37.3% 15.7% 6.9% 21.3% 15.1% 6.8% -44.4% 21.1% -5.8% -17.1% 13.8% 17.6% 2.4%
The risk structure of correlation and volatility 
6 
300 
250 
200 
150 
100 
50 
0 
Correlation Vs Volatility 
11 
14 
16 
18 
20 
22 
24 
26 
28 
30 
32 
34 
36 
38 
40 
42 
44 
46 
48 
50 
100 
Correlation General Data: 
Nº data: 4,129 
Daily Correlation -0.73 
Nº of days positive correlation: 852 
% of days positive correlation: 34% 
Rolling correlation based on number of data : 
Days; 22 18 15 10 5 
Min. Correlation: -0.97 -0.98 -0.98 -0.99 -1.00 
Max. Correlation: -0.12 0.06 0.35 0.67 0.87 
Average Correlation: -0.78 -0.78 -0.77 -0.77 -0.75 
Data Analisys, Correlation and Volatility: 
*Volatility for correlation below -0.78 
Volatility: 0 10-26 26 - 100 
Nº Days Above Aver. Corr.: 2,444.00 1,493.00 951.00 
% Correl. Below -0.78: 59.5% 36% 23% 
Min. Vol: 11.72 
Max. Vol: 87.51 
Average Volatility: 26.352475 
% over total 2444: 61.1% 38.9%

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Correlation and volatility DJ EuroStoxx50 Oct 2014

  • 1. Research Research document June 2013 Correlation and Volatility 1 Jcarlos López Moraleja
  • 2. Functional Data Analisys 2 Implied Volatility Absolute Volatility Relative Volatility Correlation • Delta 1 • Delta hedge Long Future • Long to neutral Volatility • Hedge first loss PS ATM • Short Volatility • Tactical Volatility Short Put • Short Volatility • Strategic Trade Short Call • Long Volatility • Black Swan Long Put OTM • Short of Volatility • Strategic hedging Long Butterfly Risk Matrix Based on a dynamic process of risk management decisions developed from a quantitative Model Dynamic and Systematic decision making supported by the model's interpretations of market absolute and relative volatility
  • 3. Returns for Volatility Levels 3 200% 150% 100% 50% 0% -50% -100% -150% -200% 12.2 13.5 14.8 16.3 18.0 19.9 21.9 24.2 26.6 29.4 32.4 35.7 39.3 43.4 47.8 52.7 58.1 64.1 70.7 77.9 85.9 94.7 Negative Returns Positive Returns
  • 4. Rate of return Vs Volatility distribution 4 50.0% 40.0% 30.0% 20.0% 10.0% 0.0% -10.0% -20.0% -30.0% -40.0% -50.0% -60.0% Return distribution Dj EuroStoxx 50 based on Volatility level >0 <0 UP DOWN NET Net UP/Down 12.2 6% -1.3% 11 5 4.6% 6 12.8 20% -3.7% 34 12 16.1% 22 13.5 23% -9.2% 47 33 13.8% 14 14.1 25% -14.4% 49 40 10.2% 9 14.8 41% -23.3% 61 43 17.2% 18 15.6 44% -23.5% 68 45 20.8% 23 16.3 46% -32.2% 81 73 14.1% 8 17.2 50% -42.8% 80 75 7.0% 5 18.0 58% -41.4% 91 70 16.9% 21 18.9 69% -40.1% 99 59 29.1% 40 19.9 74% -54.4% 80 77 19.9% 3 20.9 82% -80.8% 107 109 1.0% -2 21.9 115% -78.8% 132 106 36.4% 26 23.0 95% -119.1% 119 138 -24.0% -19 24.2 108% -118.9% 113 129 -11.2% -16 25.4 139% -117.1% 137 124 22.3% 13 26.6 142% -112.0% 122 110 30.0% 12 28.0 158% -138.4% 131 119 19.1% 12 29.4 121% -148.2% 102 118 -27.4% -16 30.8 77% -108.8% 55 78 -31.6% -23 32.4 66% -83.3% 51 63 -17.6% -12 34.0 35% -56.4% 30 42 -21.7% -12 35.7 54% -57.2% 27 28 -2.9% -1 37.5 54% -54.6% 31 34 -0.2% -3 39.3 70% -37.7% 35 37 32.0% -2 41.3 46% -94.9% 30 48 -49.1% -18 43.4 78% -47.2% 42 26 31.0% 16 45.5 67% -74.9% 31 41 -7.8% -10 47.8 69% -72.7% 28 35 -3.6% -7 50.2 49% -81.5% 18 31 -32.0% -13 52.7 50% -75.7% 21 28 -25.5% -7 55.4 23% -36.8% 7 13 -14.0% -6 58.1 23% -49.7% 9 17 -26.7% -8 61.0 8% -38.1% 3 11 -30.0% -8 64.1 15% -20.5% 5 6 -5.6% -1 67.3 12% -14.1% 3 4 -2.0% -1 70.7 0% -4.0% 0 1 -4.0% -1 74.2 5% -5.8% 1 2 -0.3% -1 77.9 8% -6.7% 2 2 1.5% 0 81.8 0% -8.2% 0 1 -8.2% -1 85.9 0% 0.0% 0 0 0.0% 0 90.2 0% -6.2% 0 1 -6.2% -1 94.7 0% 0.0% 0 0 0.0% 0
  • 5. Volatility frequency data 5 1998- 2014 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 4129 130 256 255 254 253 253 259 257 255 253 256 255 257 257 257 253 170 Tot % Tot 5% 10.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11.0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12.2 15 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 15.0 0% 12.8 45 0 0 0 0 0 0 1 42 1 0 0 0 0 0 0 0 1 45.0 1% 13.4 76 0 0 0 0 0 0 6 54 10 0 0 0 0 0 0 0 6 76.0 2% 14.1 89 0 0 0 0 0 0 4 39 28 11 0 0 0 0 0 1 6 89.0 2% 14.8 100 0 0 0 0 0 0 6 31 43 9 0 0 0 0 0 5 6 100.0 2% 15.5 113 0 0 0 0 0 0 9 29 38 10 0 0 0 0 0 14 13 113.0 3% 16.3 154 0 0 0 0 0 0 22 18 39 20 0 0 0 0 3 29 23 154.0 4% 17.1 154 0 0 0 0 0 0 26 16 20 22 0 0 0 0 8 29 33 154.0 4% 18.0 165 0 0 0 0 0 0 30 9 13 32 0 0 0 0 12 36 34 166.0 4% 18.9 157 0 0 0 0 0 0 47 4 13 30 2 0 4 3 6 35 14 158.0 4% 19.8 148 0 1 9 8 2 2 30 0 9 22 6 0 4 10 5 28 12 148.0 4% 20.8 215 0 10 25 18 3 7 25 0 13 24 8 0 18 22 11 23 8 215.0 5% 21.8 236 4 19 11 26 6 10 13 0 9 8 25 0 21 24 21 30 8 235.0 6% 22.9 262 5 23 24 26 9 13 14 0 8 8 20 1 30 32 31 15 3 262.0 6% 24.1 236 10 33 15 19 8 10 8 0 3 9 26 10 25 22 30 5 3 236.0 6% 25.3 257 4 31 26 18 30 17 4 0 6 15 24 14 28 13 26 1 0 257.0 6% 26.5 233 4 26 30 19 15 26 8 0 0 15 11 28 23 5 21 2 0 233.0 6% 27.9 265 6 31 36 26 20 29 1 0 2 8 14 39 22 8 23 0 0 265.0 6% 29.3 218 9 19 40 23 16 19 4 0 0 5 14 15 25 8 21 0 0 218.0 5% 30.7 138 11 12 21 13 4 13 0 0 0 1 10 16 17 7 13 0 0 138.0 3% 32.3 118 3 15 13 5 3 14 1 0 0 2 11 22 8 9 12 0 0 118.0 3% 33.9 74 4 6 4 5 0 16 0 0 0 1 10 13 6 1 8 0 0 74.0 2% 35.6 53 8 2 1 4 6 4 0 0 0 1 3 5 8 7 4 0 0 53.0 1% 37.3 66 17 7 0 3 9 1 0 0 0 0 2 10 4 11 2 0 0 66.0 2% 39.2 70 9 13 0 7 10 3 0 0 0 0 3 9 3 13 0 0 0 70.0 2% 41.2 76 4 6 0 10 9 7 0 0 0 0 6 14 2 18 0 0 0 76.0 2% 43.2 70 7 2 0 7 7 8 0 0 0 0 5 18 4 12 0 0 0 70.0 2% 45.4 74 3 0 0 5 13 21 0 0 0 0 2 18 2 10 0 0 0 74.0 2% 47.6 63 5 0 0 6 15 18 0 0 0 0 1 6 1 11 0 0 0 63.0 2% 50.0 50 4 0 0 1 15 6 0 0 0 0 4 9 2 9 0 0 0 50.0 1% 52.5 50 6 0 0 3 23 7 0 0 0 0 6 4 0 1 0 0 0 50.0 1% 55.2 21 3 0 0 1 4 2 0 0 0 0 7 3 0 1 0 0 0 21.0 1% 57.9 25 3 0 0 1 14 0 0 0 0 0 6 1 0 0 0 0 0 25.0 1% 60.8 15 1 0 0 0 8 0 0 0 0 0 6 0 0 0 0 0 0 15.0 0% 63.9 10 0 0 0 0 4 0 0 0 0 0 6 0 0 0 0 0 0 10.0 0% 67.0 8 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 8.0 0% 70.4 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.0 0% 73.9 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2.0 0% 77.6 5 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 5.0 0% 81.5 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.0 0% 85.6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0% 89.9 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1.0 0% 94.3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.0 0% Rº -6.8% -1.9% 46.7% -2.7% -20.2% -37.3% 15.7% 6.9% 21.3% 15.1% 6.8% -44.4% 21.1% -5.8% -17.1% 13.8% 17.6% 2.4%
  • 6. The risk structure of correlation and volatility 6 300 250 200 150 100 50 0 Correlation Vs Volatility 11 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 100 Correlation General Data: Nº data: 4,129 Daily Correlation -0.73 Nº of days positive correlation: 852 % of days positive correlation: 34% Rolling correlation based on number of data : Days; 22 18 15 10 5 Min. Correlation: -0.97 -0.98 -0.98 -0.99 -1.00 Max. Correlation: -0.12 0.06 0.35 0.67 0.87 Average Correlation: -0.78 -0.78 -0.77 -0.77 -0.75 Data Analisys, Correlation and Volatility: *Volatility for correlation below -0.78 Volatility: 0 10-26 26 - 100 Nº Days Above Aver. Corr.: 2,444.00 1,493.00 951.00 % Correl. Below -0.78: 59.5% 36% 23% Min. Vol: 11.72 Max. Vol: 87.51 Average Volatility: 26.352475 % over total 2444: 61.1% 38.9%