Annualized Volatility of 10‑Year Treasury Yield (Jan 2024–Nov 2025): 0.80 percentage points

Monthly Yield Shifts Analyzed, Standard Deviation Computed, Annualized to Reveal Treasury Volatility Pattern

Question

Calculate the annualized volatility (standard deviation) of monthly changes in the
DGS10 Treasury yield from 2024-01-31 to 2025-11-30.

Monthly changes should be in percentage points (not percentage change).
Annualized volatility = monthly std * sqrt(12)

You may analyze volatility regimes, compare to other periods, and validate outliers,
but the final answer must be a single number.

FINAL ANSWER REQUIRED: Single number representing annualized volatility in percentage
points (e.g., 0.52 means yields typically vary ±0.52% annually)

Auto-Scrolling

Context

=== FRED DATA - LLM GUIDE ===

SUMMARY

Monthly US economic data from FRED in INDIVIDUAL SERIES format. Each series is presented separately with its own date column. Values are separated by the tab character (ASCII 9, ' '). Treasury yields, stock indices, CPI/PPI, currency indices, GDP. No special chars in numbers. Units/scaling in guide.

=== DATASET INFO ===
Start: 2000-01-31 (Jan 2000)
End: 2025-11-30
Freq: Monthly (end-of-month)
Rows: 311
Series count: 5
Generated: 2025-12-11 15:04:45

=== DATE FORMAT ===
IMPORTANT: Dates are in compact MM/YYYY format (e.g., '11/2025').
Each date represents the END OF THAT MONTH (month-end data).
Example: '11/2025' means November 30, 2025 (or the last business day of November 2025, which was Friday, November 28, 2025).
When parsing, interpret MM/YYYY as the last calendar day of that month.
This compact format saves space. The actual observation is from the last trading/business day of each month.

=== VALUE SEPARATOR ===
CRITICAL: Values in the data section are separated by the tab character (ASCII 9, ' ').
The tab character (ASCII code 9, escape sequence ' ') separates each value.
When parsing, split each line on the tab character to extract values.
The tab character is a whitespace character that creates visible spacing.
Remember: the separator is the tab character (ASCII 9, ' ').

=== DATA STRUCTURE ===
FORMAT: INDIVIDUAL SERIES (each series output separately)

  • Each series has its own section with a header line.
  • Each series header shows: '--- [SERIES_CODE] ---'
  • Below each header is a two-column format.
  • Column 1: Date (in the specified date format)
  • Column 2: Value for that series
  • Columns are separated by the tab character (ASCII 9, ' ').
  • Date column is repeated for each series (allows independent parsing).

=== MISSING DATA ===
Forward fill enabled. Missing values filled by carrying last valid value forward. Quarterly data (GDP) repeats within quarter. Series not yet started show 'n/a' until first data point.
'n/a' = data unavailable (series not started yet or missing). Parse as missing/null/undefined.

=== NUMBER FORMAT ===
No commas (25000.00 not 25,000.00). No special chars/units. No % signs (4.5 = 4.5% not 0.045). Decimal precision 2-6 places. No scientific notation.

=== SERIES ORDER (INDIVIDUAL FORMAT) ===
Series [1]: PCEPILFE
Series [2]: GDP
Series [3]: DGS3MO
Series [4]: DGS5
Series [5]: DGS10

Each series has two columns: Date Value (separated by tab character (ASCII 9, ' '))

=== SERIES BY CATEGORY ===
PCE Inflation Index:
PCEPILFE = Core PCE Price Index (Ex Food & Energy)

GDP Measure:
GDP = Gross Domestic Product (Nominal)

Treasury Yield:
DGS3MO = 3-Month Treasury Yield
DGS5 = 5-Year Treasury Yield
DGS10 = 10-Year Treasury Yield

=== SERIES DETAILS ===
--- [1] PCEPILFE: Core PCE Price Index (Ex Food & Energy) ---
Cat: PCE Inflation Index
Units: Index (2017=100)
Ex: 115.00 means core prices are 15% higher than 2017 baseline (excluding food/energy)
Use: Same calculation as PCEPI: ((Current - 12mo_ago) / 12mo_ago) * 100. Fed's most closely watched inflation indicator for policy decisions.
Context: Core PCE is the Fed's PRIMARY inflation metric for policy decisions. When the Fed discusses its 2% inflation target, it refers to core PCE. More stable than headline PCE.
Source: U.S. Bureau of Economic Analysis
Cite: U.S. Bureau of Economic Analysis, Personal Consumption Expenditures Excluding Food and Energy (Chain-Type Price Index) [PCEPILFE], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/PCEPILFE

--- [2] GDP: Gross Domestic Product (Nominal) ---
Cat: GDP Measure
Units: Billions of dollars (not seasonally adjusted annual rate)
Ex: 25000.00 means $25 trillion annual GDP
Use: QUARTERLY data (repeats 3 months). Calculate annualized quarterly growth: ((Current_Qtr - Previous_Qtr) / Previous_Qtr) * 100 * 4
Context: Total economic output in current dollars. Growth rate is key recession indicator.
Source: U.S. Bureau of Economic Analysis
Cite: U.S. Bureau of Economic Analysis, Gross Domestic Product [GDP], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/GDP

--- [3] DGS3MO: 3-Month Treasury Yield ---
Cat: Treasury Yield
Units: Percent per annum
Ex: 4.75 means 4.75% annual yield
Use: Use value directly - already in percentage form. Commonly used as risk-free rate in finance.
Context: Key short-term rate, closely tracks Fed Funds rate
Source: Board of Governors of the Federal Reserve System (US)
Cite: Board of Governors of the Federal Reserve System (US), Market Yield on U.S. Treasury Securities at 3-Month Constant Maturity, Quoted on an Investment Basis [DGS3MO], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DGS3MO

--- [4] DGS5: 5-Year Treasury Yield ---
Cat: Treasury Yield
Units: Percent per annum
Ex: 4.20 means 4.20% annual yield
Use: Use value directly - already in percentage form.
Context: Medium-term rate often used in mortgage pricing
Source: Board of Governors of the Federal Reserve System (US)
Cite: Board of Governors of the Federal Reserve System (US), Market Yield on U.S. Treasury Securities at 5-Year Constant Maturity, Quoted on an Investment Basis [DGS5], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DGS5

--- [5] DGS10: 10-Year Treasury Yield ---
Cat: Treasury Yield
Units: Percent per annum
Ex: 4.25 means 4.25% annual yield
Use: Use value directly - already in percentage form. Most watched Treasury yield.
Context: THE BENCHMARK long-term rate. Affects mortgage rates, corporate borrowing. Inverted yield curve (10yr < 2yr) predicts recession.
Source: Board of Governors of the Federal Reserve System (US)
Cite: Board of Governors of the Federal Reserve System (US), Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity, Quoted on an Investment Basis [DGS10], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/DGS10

=== PARSING INSTRUCTIONS ===

STRUCTURE:
Each series begins with '--- [CODE] ---' header. Following lines are two-column data: Date Value. Split each data line on the tab character (ASCII 9, ' ') to get date and value. Series are separated by blank lines and headers.

SEPARATOR REMINDER:
The tab character (ASCII 9, ' ') separates all values in the data section.
Tab character = ASCII 9 = ' '. Use tab-split when parsing.

DATE PARSING:
Dates are MM/YYYY format representing month-end. '11/2025' = end of November 2025 = last business day of Nov 2025.

NUMBERS:
Plain numbers (no commas/units). Yields in % (4.5=4.5%). Index vals use directly (see base yr). GDP in billions. 'n/a'=missing.

CALCULATIONS:
Inflation: ((CPI_now - CPI_12mo_ago) / CPI_12mo_ago) * 100
GDP growth: ((GDP_now - GDP_prev_qtr) / GDP_prev_qtr) * 100 * 4
Stock return: ((Price_now - Price_prev) / Price_prev) * 100
Yield spread: (10yr_yield - 2yr_yield)

TIME ANALYSIS:
Dates chronological. YoY: compare to 12 rows earlier. QoQ: GDP repeats 3 months.

=== CITATION ===
Source: Federal Reserve Economic Data (FRED)
Federal Reserve Bank of St. Louis
https://fred.stlouisfed.org
For specific citations see series details above.
Citation format: https://fredhelp.stlouisfed.org/fred/data/understanding-the-data/

=== FORMAT SUMMARY ===
Output Format: INDIVIDUAL SERIES
Date Format: COMPACT (MM/YYYY)
Value Separator: tab character (ASCII 9, ' ')
Remember: MM/YYYY dates mean end-of-month (last business day).
Remember: Split on tab character (ASCII 9, ' ') to parse values.

=== END GUIDE ===
Data section below.

=== DATA (INDIVIDUAL SERIES FORMAT - VALUES SEPARATED BY tab character (ASCII 9, ' ')) ===

--- [PCEPILFE] ---
Date Value
1/2000 74.306
2/2000 74.415
3/2000 74.568
4/2000 74.617
5/2000 74.697
6/2000 74.754
7/2000 74.925
8/2000 75.021
9/2000 75.203
10/2000 75.308
11/2000 75.441
12/2000 75.515
1/2001 75.796
2/2001 75.93
3/2001 76.009
4/2001 76.13
5/2001 76.148
6/2001 76.318
7/2001 76.515
8/2001 76.553
9/2001 76.118
10/2001 76.654
11/2001 76.81
12/2001 76.828
1/2002 76.871
2/2002 77.018
3/2002 77.11
4/2002 77.325
5/2002 77.411
6/2002 77.534
7/2002 77.692
8/2002 77.845
9/2002 77.972
10/2002 78.038
11/2002 78.114
12/2002 78.187
1/2003 78.24
2/2003 78.348
3/2003 78.474
4/2003 78.561
5/2003 78.674
6/2003 78.718
7/2003 78.915
8/2003 79.004
9/2003 79.114
10/2003 79.26
11/2003 79.368
12/2003 79.467
1/2004 79.671
2/2004 79.8
3/2004 79.934
4/2004 80.142
5/2004 80.252
6/2004 80.379
7/2004 80.474
8/2004 80.505
9/2004 80.656
10/2004 80.831
11/2004 81.005
12/2004 81.109
1/2005 81.401
2/2005 81.536
3/2005 81.737
4/2005 81.831
5/2005 81.999
6/2005 82.056
7/2005 82.176
8/2005 82.243
9/2005 82.425
10/2005 82.662
11/2005 82.873
12/2005 82.959
1/2006 83.145
2/2006 83.279
3/2006 83.509
4/2006 83.764
5/2006 83.974
6/2006 84.186
7/2006 84.268
8/2006 84.44
9/2006 84.573
10/2006 84.726
11/2006 84.766
12/2006 84.88
1/2007 85.224
2/2007 85.408
3/2007 85.494
4/2007 85.616
5/2007 85.717
6/2007 85.859
7/2007 85.988
8/2007 86.116
9/2007 86.351
10/2007 86.576
11/2007 86.746
12/2007 86.92
1/2008 87.093
2/2008 87.178
3/2008 87.349
4/2008 87.4
5/2008 87.559
6/2008 87.76
7/2008 87.918
8/2008 88.026
9/2008 88.116
10/2008 87.991
11/2008 87.952
12/2008 87.909
1/2009 87.882
2/2009 87.952
3/2009 88.015
4/2009 88.211
5/2009 88.279
6/2009 88.392
7/2009 88.468
8/2009 88.599
9/2009 88.755
10/2009 89.082
11/2009 89.16
12/2009 89.236
1/2010 89.368
2/2010 89.446
3/2010 89.579
4/2010 89.625
5/2010 89.724
6/2010 89.767
7/2010 89.769
8/2010 89.855
9/2010 89.906
10/2010 90.043
11/2010 90.16
12/2010 90.179
1/2011 90.372
2/2011 90.53
3/2011 90.667
4/2011 90.875
5/2011 91.091
6/2011 91.191
7/2011 91.326
8/2011 91.508
9/2011 91.57
10/2011 91.614
11/2011 91.808
12/2011 91.96
1/2012 92.235
2/2012 92.364
3/2012 92.521
4/2012 92.661
5/2012 92.755
6/2012 92.85
7/2012 92.946
8/2012 93.005
9/2012 93.119
10/2012 93.345
11/2012 93.445
12/2012 93.514
1/2013 93.703
2/2013 93.805
3/2013 93.891
4/2013 93.937
5/2013 94.047
6/2013 94.209
7/2013 94.329
8/2013 94.431
9/2013 94.543
10/2013 94.703
11/2013 94.86
12/2013 94.961
1/2014 95.064
2/2014 95.109
3/2014 95.25
4/2014 95.413
5/2014 95.574
6/2014 95.682
7/2014 95.848
8/2014 95.885
9/2014 96.013
10/2014 96.096
11/2014 96.181
12/2014 96.249
1/2015 96.214
2/2015 96.324
3/2015 96.47
4/2015 96.648
5/2015 96.766
6/2015 96.882
7/2015 96.978
8/2015 97.056
9/2015 97.196
10/2015 97.228
11/2015 97.332
12/2015 97.396
1/2016 97.567
2/2016 97.736
3/2016 97.876
4/2016 98.117
5/2016 98.284
6/2016 98.386
7/2016 98.529
8/2016 98.703
9/2016 98.834
10/2016 98.961
11/2016 99.005
12/2016 99.12
1/2017 99.385
2/2017 99.561
3/2017 99.519
4/2017 99.723
5/2017 99.803
6/2017 99.937
7/2017 100.01
8/2017 100.118
9/2017 100.24
10/2017 100.486
11/2017 100.535
12/2017 100.683
1/2018 101.007
2/2018 101.198
3/2018 101.419
4/2018 101.602
5/2018 101.78
6/2018 101.872
7/2018 102.006
8/2018 102.016
9/2018 102.205
10/2018 102.366
11/2018 102.556
12/2018 102.735
1/2019 102.87
2/2019 102.963
3/2019 103.058
4/2019 103.265
5/2019 103.371
6/2019 103.56
7/2019 103.678
8/2019 103.797
9/2019 103.873
10/2019 104.028
11/2019 104.092
12/2019 104.322
1/2020 104.507
2/2020 104.711
3/2020 104.632
4/2020 104.293
5/2020 104.402
6/2020 104.565
7/2020 104.937
8/2020 105.243
9/2020 105.41
10/2020 105.507
11/2020 105.605
12/2020 105.896
1/2021 106.281
2/2021 106.501
3/2021 106.933
4/2021 107.558
5/2021 108.099
6/2021 108.603
7/2021 109.058
8/2021 109.409
9/2021 109.641
10/2021 110.188
11/2021 110.77
12/2021 111.418
1/2022 111.976
2/2022 112.468
3/2022 112.914
4/2022 113.307
5/2022 113.703
6/2022 114.376
7/2022 114.628
8/2022 115.276
9/2022 115.788
10/2022 116.204
11/2022 116.539
12/2022 116.952
1/2023 117.505
2/2023 117.929
3/2023 118.315
4/2023 118.734
5/2023 119.083
6/2023 119.39
7/2023 119.556
8/2023 119.689
9/2023 120.058
10/2023 120.241
11/2023 120.374
12/2023 120.592
1/2024 121.217
2/2024 121.537
3/2024 122.009
4/2024 122.304
5/2024 122.383
6/2024 122.677
7/2024 122.911
8/2024 123.128
9/2024 123.466
10/2024 123.832
11/2024 123.962
12/2024 124.196
1/2025 124.587
2/2025 125.145
3/2025 125.267
4/2025 125.502
5/2025 125.79
6/2025 126.121
7/2025 126.424
8/2025 126.703
9/2025 126.954
10/2025 126.954
11/2025 126.954

--- [GDP] ---
Date Value
1/2000 10002.179
2/2000 10002.179
3/2000 10002.179
4/2000 10247.72
5/2000 10247.72
6/2000 10247.72
7/2000 10318.165
8/2000 10318.165
9/2000 10318.165
10/2000 10435.744
11/2000 10435.744
12/2000 10435.744
1/2001 10470.231
2/2001 10470.231
3/2001 10470.231
4/2001 10599
5/2001 10599
6/2001 10599
7/2001 10598.02
8/2001 10598.02
9/2001 10598.02
10/2001 10660.465
11/2001 10660.465
12/2001 10660.465
1/2002 10783.5
2/2002 10783.5
3/2002 10783.5
4/2002 10887.46
5/2002 10887.46
6/2002 10887.46
7/2002 10984.04
8/2002 10984.04
9/2002 10984.04
10/2002 11061.433
11/2002 11061.433
12/2002 11061.433
1/2003 11174.129
2/2003 11174.129
3/2003 11174.129
4/2003 11312.766
5/2003 11312.766
6/2003 11312.766
7/2003 11566.669
8/2003 11566.669
9/2003 11566.669
10/2003 11772.234
11/2003 11772.234
12/2003 11772.234
1/2004 11923.447
2/2004 11923.447
3/2004 11923.447
4/2004 12112.815
5/2004 12112.815
6/2004 12112.815
7/2004 12305.307
8/2004 12305.307
9/2004 12305.307
10/2004 12527.214
11/2004 12527.214
12/2004 12527.214
1/2005 12767.286
2/2005 12767.286
3/2005 12767.286
4/2005 12922.656
5/2005 12922.656
6/2005 12922.656
7/2005 13142.642
8/2005 13142.642
9/2005 13142.642
10/2005 13324.204
11/2005 13324.204
12/2005 13324.204
1/2006 13599.16
2/2006 13599.16
3/2006 13599.16
4/2006 13753.424
5/2006 13753.424
6/2006 13753.424
7/2006 13870.188
8/2006 13870.188
9/2006 13870.188
10/2006 14039.56
11/2006 14039.56
12/2006 14039.56
1/2007 14215.651
2/2007 14215.651
3/2007 14215.651
4/2007 14402.082
5/2007 14402.082
6/2007 14402.082
7/2007 14564.117
8/2007 14564.117
9/2007 14564.117
10/2007 14715.058
11/2007 14715.058
12/2007 14715.058
1/2008 14706.538
2/2008 14706.538
3/2008 14706.538
4/2008 14865.701
5/2008 14865.701
6/2008 14865.701
7/2008 14898.999
8/2008 14898.999
9/2008 14898.999
10/2008 14608.209
11/2008 14608.209
12/2008 14608.209
1/2009 14430.902
2/2009 14430.902
3/2009 14430.902
4/2009 14381.236
5/2009 14381.236
6/2009 14381.236
7/2009 14448.882
8/2009 14448.882
9/2009 14448.882
10/2009 14651.249
11/2009 14651.249
12/2009 14651.249
1/2010 14764.61
2/2010 14764.61
3/2010 14764.61
4/2010 14980.193
5/2010 14980.193
6/2010 14980.193
7/2010 15141.607
8/2010 15141.607
9/2010 15141.607
10/2010 15309.474
11/2010 15309.474
12/2010 15309.474
1/2011 15351.448
2/2011 15351.448
3/2011 15351.448
4/2011 15557.539
5/2011 15557.539
6/2011 15557.539
7/2011 15647.68
8/2011 15647.68
9/2011 15647.68
10/2011 15842.259
11/2011 15842.259
12/2011 15842.259
1/2012 16068.805
2/2012 16068.805
3/2012 16068.805
4/2012 16207.115
5/2012 16207.115
6/2012 16207.115
7/2012 16319.541
8/2012 16319.541
9/2012 16319.541
10/2012 16420.419
11/2012 16420.419
12/2012 16420.419
1/2013 16648.189
2/2013 16648.189
3/2013 16648.189
4/2013 16728.687
5/2013 16728.687
6/2013 16728.687
7/2013 16953.838
8/2013 16953.838
9/2013 16953.838
10/2013 17192.019
11/2013 17192.019
12/2013 17192.019
1/2014 17197.738
2/2014 17197.738
3/2014 17197.738
4/2014 17518.508
5/2014 17518.508
6/2014 17518.508
7/2014 17804.228
8/2014 17804.228
9/2014 17804.228
10/2014 17912.079
11/2014 17912.079
12/2014 17912.079
1/2015 18063.529
2/2015 18063.529
3/2015 18063.529
4/2015 18279.784
5/2015 18279.784
6/2015 18279.784
7/2015 18401.626
8/2015 18401.626
9/2015 18401.626
10/2015 18435.137
11/2015 18435.137
12/2015 18435.137
1/2016 18525.933
2/2016 18525.933
3/2016 18525.933
4/2016 18711.702
5/2016 18711.702
6/2016 18711.702
7/2016 18892.639
8/2016 18892.639
9/2016 18892.639
10/2016 19089.379
11/2016 19089.379
12/2016 19089.379
1/2017 19280.084
2/2017 19280.084
3/2017 19280.084
4/2017 19438.643
5/2017 19438.643
6/2017 19438.643
7/2017 19692.595
8/2017 19692.595
9/2017 19692.595
10/2017 20037.088
11/2017 20037.088
12/2017 20037.088
1/2018 20328.553
2/2018 20328.553
3/2018 20328.553
4/2018 20580.912
5/2018 20580.912
6/2018 20580.912
7/2018 20798.73
8/2018 20798.73
9/2018 20798.73
10/2018 20917.867
11/2018 20917.867
12/2018 20917.867
1/2019 21111.6
2/2019 21111.6
3/2019 21111.6
4/2019 21397.938
5/2019 21397.938
6/2019 21397.938
7/2019 21717.171
8/2019 21717.171
9/2019 21717.171
10/2019 21933.217
11/2019 21933.217
12/2019 21933.217
1/2020 21751.238
2/2020 21751.238
3/2020 21751.238
4/2020 19958.291
5/2020 19958.291
6/2020 19958.291
7/2020 21704.437
8/2020 21704.437
9/2020 21704.437
10/2020 22087.16
11/2020 22087.16
12/2020 22087.16
1/2021 22680.693
2/2021 22680.693
3/2021 22680.693
4/2021 23425.91
5/2021 23425.91
6/2021 23425.91
7/2021 23982.379
8/2021 23982.379
9/2021 23982.379
10/2021 24813.6
11/2021 24813.6
12/2021 24813.6
1/2022 25250.347
2/2022 25250.347
3/2022 25250.347
4/2022 25861.292
5/2022 25861.292
6/2022 25861.292
7/2022 26336.304
8/2022 26336.304
9/2022 26336.304
10/2022 26770.514
11/2022 26770.514
12/2022 26770.514
1/2023 27216.445
2/2023 27216.445
3/2023 27216.445
4/2023 27530.055
5/2023 27530.055
6/2023 27530.055
7/2023 28074.846
8/2023 28074.846
9/2023 28074.846
10/2023 28424.722
11/2023 28424.722
12/2023 28424.722
1/2024 28708.161
2/2024 28708.161
3/2024 28708.161
4/2024 29147.044
5/2024 29147.044
6/2024 29147.044
7/2024 29511.664
8/2024 29511.664
9/2024 29511.664
10/2024 29825.182
11/2024 29825.182
12/2024 29825.182
1/2025 30042.113
2/2025 30042.113
3/2025 30042.113
4/2025 30485.729
5/2025 30485.729
6/2025 30485.729
7/2025 30485.729
8/2025 30485.729
9/2025 30485.729
10/2025 30485.729
11/2025 30485.729

--- [DGS3MO] ---
Date Value
1/2000 5.76
2/2000 5.78
3/2000 5.88
4/2000 5.82
5/2000 5.63
6/2000 5.88
7/2000 6.27
8/2000 6.31
9/2000 6.23
10/2000 6.38
11/2000 6.21
12/2000 5.89
1/2001 4.99
2/2001 4.85
3/2001 4.3
4/2001 3.95
5/2001 3.63
6/2001 3.65
7/2001 3.54
8/2001 3.37
9/2001 2.4
10/2001 2.05
11/2001 1.78
12/2001 1.74
1/2002 1.76
2/2002 1.79
3/2002 1.79
4/2002 1.77
5/2002 1.74
6/2002 1.7
7/2002 1.71
8/2002 1.69
9/2002 1.57
10/2002 1.44
11/2002 1.22
12/2002 1.22
1/2003 1.18
2/2003 1.2
3/2003 1.14
4/2003 1.13
5/2003 1.11
6/2003 0.9
7/2003 0.96
8/2003 0.98
9/2003 0.95
10/2003 0.96
11/2003 0.93
12/2003 0.95
1/2004 0.92
2/2004 0.96
3/2004 0.95
4/2004 0.98
5/2004 1.08
6/2004 1.33
7/2004 1.45
8/2004 1.59
9/2004 1.71
10/2004 1.91
11/2004 2.23
12/2004 2.22
1/2005 2.51
2/2005 2.76
3/2005 2.79
4/2005 2.9
5/2005 2.99
6/2005 3.13
7/2005 3.42
8/2005 3.52
9/2005 3.55
10/2005 3.98
11/2005 3.95
12/2005 4.08
1/2006 4.47
2/2006 4.62
3/2006 4.63
4/2006 4.77
5/2006 4.86
6/2006 5.01
7/2006 5.1
8/2006 5.05
9/2006 4.89
10/2006 5.08
11/2006 5.03
12/2006 5.02
1/2007 5.12
2/2007 5.16
3/2007 5.04
4/2007 4.91
5/2007 4.73
6/2007 4.82
7/2007 4.96
8/2007 4.01
9/2007 3.82
10/2007 3.94
11/2007 3.15
12/2007 3.36
1/2008 1.96
2/2008 1.85
3/2008 1.38
4/2008 1.43
5/2008 1.89
6/2008 1.9
7/2008 1.68
8/2008 1.72
9/2008 0.92
10/2008 0.46
11/2008 0.01
12/2008 0.11
1/2009 0.24
2/2009 0.26
3/2009 0.21
4/2009 0.14
5/2009 0.14
6/2009 0.19
7/2009 0.18
8/2009 0.15
9/2009 0.14
10/2009 0.05
11/2009 0.06
12/2009 0.06
1/2010 0.08
2/2010 0.13
3/2010 0.16
4/2010 0.16
5/2010 0.16
6/2010 0.18
7/2010 0.15
8/2010 0.14
9/2010 0.16
10/2010 0.12
11/2010 0.17
12/2010 0.12
1/2011 0.15
2/2011 0.15
3/2011 0.09
4/2011 0.04
5/2011 0.06
6/2011 0.03
7/2011 0.1
8/2011 0.02
9/2011 0.02
10/2011 0.01
11/2011 0.01
12/2011 0.02
1/2012 0.06
2/2012 0.08
3/2012 0.07
4/2012 0.1
5/2012 0.07
6/2012 0.09
7/2012 0.11
8/2012 0.09
9/2012 0.1
10/2012 0.11
11/2012 0.08
12/2012 0.05
1/2013 0.07
2/2013 0.11
3/2013 0.07
4/2013 0.05
5/2013 0.04
6/2013 0.04
7/2013 0.04
8/2013 0.03
9/2013 0.02
10/2013 0.04
11/2013 0.06
12/2013 0.07
1/2014 0.02
2/2014 0.05
3/2014 0.05
4/2014 0.03
5/2014 0.04
6/2014 0.04
7/2014 0.03
8/2014 0.03
9/2014 0.02
10/2014 0.01
11/2014 0.02
12/2014 0.04
1/2015 0.02
2/2015 0.02
3/2015 0.03
4/2015 0.01
5/2015 0.01
6/2015 0.01
7/2015 0.08
8/2015 0.08
9/2015 0
10/2015 0.08
11/2015 0.22
12/2015 0.16
1/2016 0.33
2/2016 0.33
3/2016 0.21
4/2016 0.22
5/2016 0.34
6/2016 0.26
7/2016 0.28
8/2016 0.33
9/2016 0.29
10/2016 0.34
11/2016 0.48
12/2016 0.51
1/2017 0.52
2/2017 0.53
3/2017 0.76
4/2017 0.8
5/2017 0.98
6/2017 1.03
7/2017 1.07
8/2017 1.01
9/2017 1.06
10/2017 1.15
11/2017 1.27
12/2017 1.39
1/2018 1.46
2/2018 1.65
3/2018 1.73
4/2018 1.87
5/2018 1.93
6/2018 1.93
7/2018 2.03
8/2018 2.11
9/2018 2.19
10/2018 2.34
11/2018 2.37
12/2018 2.45
1/2019 2.41
2/2019 2.45
3/2019 2.4
4/2019 2.43
5/2019 2.35
6/2019 2.12
7/2019 2.08
8/2019 1.99
9/2019 1.88
10/2019 1.54
11/2019 1.59
12/2019 1.55
1/2020 1.55
2/2020 1.27
3/2020 0.11
4/2020 0.09
5/2020 0.14
6/2020 0.16
7/2020 0.09
8/2020 0.11
9/2020 0.1
10/2020 0.09
11/2020 0.08
12/2020 0.09
1/2021 0.06
2/2021 0.04
3/2021 0.03
4/2021 0.01
5/2021 0.01
6/2021 0.05
7/2021 0.06
8/2021 0.04
9/2021 0.04
10/2021 0.05
11/2021 0.05
12/2021 0.06
1/2022 0.22
2/2022 0.35
3/2022 0.52
4/2022 0.85
5/2022 1.16
6/2022 1.72
7/2022 2.41
8/2022 2.96
9/2022 3.33
10/2022 4.22
11/2022 4.37
12/2022 4.42
1/2023 4.7
2/2023 4.88
3/2023 4.85
4/2023 5.1
5/2023 5.52
6/2023 5.43
7/2023 5.55
8/2023 5.56
9/2023 5.55
10/2023 5.59
11/2023 5.45
12/2023 5.4
1/2024 5.42
2/2024 5.45
3/2024 5.46
4/2024 5.46
5/2024 5.46
6/2024 5.48
7/2024 5.41
8/2024 5.21
9/2024 4.73
10/2024 4.64
11/2024 4.58
12/2024 4.37
1/2025 4.31
2/2025 4.32
3/2025 4.32
4/2025 4.31
5/2025 4.36
6/2025 4.41
7/2025 4.41
8/2025 4.23
9/2025 4.02
10/2025 3.89
11/2025 3.88

--- [DGS5] ---
Date Value
1/2000 6.71
2/2000 6.61
3/2000 6.32
4/2000 6.56
5/2000 6.54
6/2000 6.18
7/2000 6.16
8/2000 5.98
9/2000 5.85
10/2000 5.83
11/2000 5.42
12/2000 4.99
1/2001 4.85
2/2001 4.7
3/2001 4.62
4/2001 4.97
5/2001 4.94
6/2001 4.97
7/2001 4.57
8/2001 4.46
9/2001 3.93
10/2001 3.66
11/2001 4.08
12/2001 4.38
1/2002 4.42
2/2002 4.27
3/2002 4.91
4/2002 4.53
5/2002 4.37
6/2002 4.09
7/2002 3.53
8/2002 3.22
9/2002 2.63
10/2002 2.81
11/2002 3.28
12/2002 2.78
1/2003 3.02
2/2003 2.69
3/2003 2.78
4/2003 2.85
5/2003 2.3
6/2003 2.46
7/2003 3.38
8/2003 3.46
9/2003 2.85
10/2003 3.27
11/2003 3.38
12/2003 3.25
1/2004 3.17
2/2004 3.01
3/2004 2.8
4/2004 3.63
5/2004 3.81
6/2004 3.81
7/2004 3.71
8/2004 3.33
9/2004 3.38
10/2004 3.3
11/2004 3.72
12/2004 3.63
1/2005 3.71
2/2005 4
3/2005 4.18
4/2005 3.9
5/2005 3.76
6/2005 3.72
7/2005 4.12
8/2005 3.87
9/2005 4.18
10/2005 4.45
11/2005 4.42
12/2005 4.35
1/2006 4.47
2/2006 4.61
3/2006 4.82
4/2006 4.92
5/2006 5.04
6/2006 5.1
7/2006 4.91
8/2006 4.7
9/2006 4.59
10/2006 4.57
11/2006 4.45
12/2006 4.7
1/2007 4.82
2/2007 4.52
3/2007 4.54
4/2007 4.51
5/2007 4.86
6/2007 4.92
7/2007 4.6
8/2007 4.25
9/2007 4.23
10/2007 4.16
11/2007 3.41
12/2007 3.45
1/2008 2.82
2/2008 2.5
3/2008 2.46
4/2008 3.03
5/2008 3.41
6/2008 3.34
7/2008 3.25
8/2008 3.1
9/2008 2.98
10/2008 2.8
11/2008 1.93
12/2008 1.55
1/2009 1.85
2/2009 1.99
3/2009 1.67
4/2009 2.02
5/2009 2.34
6/2009 2.54
7/2009 2.53
8/2009 2.39
9/2009 2.31
10/2009 2.31
11/2009 2.01
12/2009 2.69
1/2010 2.34
2/2010 2.3
3/2010 2.55
4/2010 2.43
5/2010 2.1
6/2010 1.79
7/2010 1.6
8/2010 1.33
9/2010 1.27
10/2010 1.17
11/2010 1.47
12/2010 2.01
1/2011 1.95
2/2011 2.13
3/2011 2.24
4/2011 1.97
5/2011 1.68
6/2011 1.76
7/2011 1.35
8/2011 0.96
9/2011 0.96
10/2011 0.99
11/2011 0.96
12/2011 0.83
1/2012 0.71
2/2012 0.87
3/2012 1.04
4/2012 0.82
5/2012 0.67
6/2012 0.72
7/2012 0.6
8/2012 0.59
9/2012 0.62
10/2012 0.72
11/2012 0.61
12/2012 0.72
1/2013 0.88
2/2013 0.77
3/2013 0.77
4/2013 0.68
5/2013 1.05
6/2013 1.41
7/2013 1.38
8/2013 1.62
9/2013 1.39
10/2013 1.31
11/2013 1.37
12/2013 1.75
1/2014 1.49
2/2014 1.51
3/2014 1.73
4/2014 1.69
5/2014 1.54
6/2014 1.62
7/2014 1.76
8/2014 1.63
9/2014 1.78
10/2014 1.62
11/2014 1.49
12/2014 1.65
1/2015 1.18
2/2015 1.5
3/2015 1.37
4/2015 1.43
5/2015 1.49
6/2015 1.63
7/2015 1.54
8/2015 1.54
9/2015 1.37
10/2015 1.52
11/2015 1.65
12/2015 1.76
1/2016 1.33
2/2016 1.22
3/2016 1.21
4/2016 1.28
5/2016 1.37
6/2016 1.01
7/2016 1.03
8/2016 1.19
9/2016 1.14
10/2016 1.31
11/2016 1.83
12/2016 1.93
1/2017 1.9
2/2017 1.89
3/2017 1.93
4/2017 1.81
5/2017 1.75
6/2017 1.89
7/2017 1.84
8/2017 1.7
9/2017 1.92
10/2017 2.01
11/2017 2.14
12/2017 2.2
1/2018 2.52
2/2018 2.65
3/2018 2.56
4/2018 2.79
5/2018 2.68
6/2018 2.73
7/2018 2.85
8/2018 2.74
9/2018 2.94
10/2018 2.98
11/2018 2.84
12/2018 2.51
1/2019 2.43
2/2019 2.52
3/2019 2.23
4/2019 2.28
5/2019 1.93
6/2019 1.76
7/2019 1.84
8/2019 1.39
9/2019 1.55
10/2019 1.51
11/2019 1.62
12/2019 1.69
1/2020 1.32
2/2020 0.89
3/2020 0.37
4/2020 0.36
5/2020 0.3
6/2020 0.29
7/2020 0.21
8/2020 0.28
9/2020 0.28
10/2020 0.38
11/2020 0.36
12/2020 0.36
1/2021 0.45
2/2021 0.75
3/2021 0.92
4/2021 0.86
5/2021 0.79
6/2021 0.87
7/2021 0.69
8/2021 0.77
9/2021 0.98
10/2021 1.18
11/2021 1.14
12/2021 1.26
1/2022 1.62
2/2022 1.71
3/2022 2.42
4/2022 2.92
5/2022 2.81
6/2022 3.01
7/2022 2.7
8/2022 3.3
9/2022 4.06
10/2022 4.27
11/2022 3.82
12/2022 3.99
1/2023 3.63
2/2023 4.18
3/2023 3.6
4/2023 3.51
5/2023 3.74
6/2023 4.13
7/2023 4.18
8/2023 4.23
9/2023 4.6
10/2023 4.82
11/2023 4.31
12/2023 3.84
1/2024 3.91
2/2024 4.26
3/2024 4.21
4/2024 4.72
5/2024 4.52
6/2024 4.33
7/2024 3.97
8/2024 3.71
9/2024 3.58
10/2024 4.15
11/2024 4.05
12/2024 4.38
1/2025 4.36
2/2025 4.03
3/2025 3.96
4/2025 3.72
5/2025 3.96
6/2025 3.79
7/2025 3.96
8/2025 3.68
9/2025 3.74
10/2025 3.71
11/2025 3.59

--- [DGS10] ---
Date Value
1/2000 6.68
2/2000 6.42
3/2000 6.03
4/2000 6.23
5/2000 6.29
6/2000 6.03
7/2000 6.04
8/2000 5.73
9/2000 5.8
10/2000 5.77
11/2000 5.48
12/2000 5.12
1/2001 5.19
2/2001 4.92
3/2001 4.93
4/2001 5.35
5/2001 5.43
6/2001 5.42
7/2001 5.07
8/2001 4.85
9/2001 4.6
10/2001 4.3
11/2001 4.78
12/2001 5.07
1/2002 5.07
2/2002 4.88
3/2002 5.42
4/2002 5.11
5/2002 5.08
6/2002 4.86
7/2002 4.51
8/2002 4.14
9/2002 3.63
10/2002 3.93
11/2002 4.22
12/2002 3.83
1/2003 4
2/2003 3.71
3/2003 3.83
4/2003 3.89
5/2003 3.37
6/2003 3.54
7/2003 4.49
8/2003 4.45
9/2003 3.96
10/2003 4.33
11/2003 4.34
12/2003 4.27
1/2004 4.16
2/2004 3.99
3/2004 3.86
4/2004 4.53
5/2004 4.66
6/2004 4.62
7/2004 4.5
8/2004 4.13
9/2004 4.14
10/2004 4.05
11/2004 4.36
12/2004 4.24
1/2005 4.14
2/2005 4.36
3/2005 4.5
4/2005 4.21
5/2005 4
6/2005 3.94
7/2005 4.28
8/2005 4.02
9/2005 4.34
10/2005 4.57
11/2005 4.49
12/2005 4.39
1/2006 4.53
2/2006 4.55
3/2006 4.86
4/2006 5.07
5/2006 5.12
6/2006 5.15
7/2006 4.99
8/2006 4.74
9/2006 4.64
10/2006 4.61
11/2006 4.46
12/2006 4.71
1/2007 4.83
2/2007 4.56
3/2007 4.65
4/2007 4.63
5/2007 4.9
6/2007 5.03
7/2007 4.78
8/2007 4.54
9/2007 4.59
10/2007 4.48
11/2007 3.97
12/2007 4.04
1/2008 3.67
2/2008 3.53
3/2008 3.45
4/2008 3.77
5/2008 4.06
6/2008 3.99
7/2008 3.99
8/2008 3.83
9/2008 3.85
10/2008 4.01
11/2008 2.93
12/2008 2.25
1/2009 2.87
2/2009 3.02
3/2009 2.71
4/2009 3.16
5/2009 3.47
6/2009 3.53
7/2009 3.52
8/2009 3.4
9/2009 3.31
10/2009 3.41
11/2009 3.21
12/2009 3.85
1/2010 3.63
2/2010 3.61
3/2010 3.84
4/2010 3.69
5/2010 3.31
6/2010 2.97
7/2010 2.94
8/2010 2.47
9/2010 2.53
10/2010 2.63
11/2010 2.81
12/2010 3.3
1/2011 3.42
2/2011 3.42
3/2011 3.47
4/2011 3.32
5/2011 3.05
6/2011 3.18
7/2011 2.82
8/2011 2.23
9/2011 1.92
10/2011 2.17
11/2011 2.08
12/2011 1.89
1/2012 1.83
2/2012 1.98
3/2012 2.23
4/2012 1.95
5/2012 1.59
6/2012 1.67
7/2012 1.51
8/2012 1.57
9/2012 1.65
10/2012 1.72
11/2012 1.62
12/2012 1.78
1/2013 2.02
2/2013 1.89
3/2013 1.87
4/2013 1.7
5/2013 2.16
6/2013 2.52
7/2013 2.6
8/2013 2.78
9/2013 2.64
10/2013 2.57
11/2013 2.75
12/2013 3.04
1/2014 2.67
2/2014 2.66
3/2014 2.73
4/2014 2.67
5/2014 2.48
6/2014 2.53
7/2014 2.58
8/2014 2.35
9/2014 2.52
10/2014 2.35
11/2014 2.18
12/2014 2.17
1/2015 1.68
2/2015 2
3/2015 1.94
4/2015 2.05
5/2015 2.12
6/2015 2.35
7/2015 2.2
8/2015 2.21
9/2015 2.06
10/2015 2.16
11/2015 2.21
12/2015 2.27
1/2016 1.94
2/2016 1.74
3/2016 1.78
4/2016 1.83
5/2016 1.84
6/2016 1.49
7/2016 1.46
8/2016 1.58
9/2016 1.6
10/2016 1.84
11/2016 2.37
12/2016 2.45
1/2017 2.45
2/2017 2.36
3/2017 2.4
4/2017 2.29
5/2017 2.21
6/2017 2.31
7/2017 2.3
8/2017 2.12
9/2017 2.33
10/2017 2.38
11/2017 2.42
12/2017 2.4
1/2018 2.72
2/2018 2.87
3/2018 2.74
4/2018 2.95
5/2018 2.83
6/2018 2.85
7/2018 2.96
8/2018 2.86
9/2018 3.05
10/2018 3.15
11/2018 3.01
12/2018 2.69
1/2019 2.63
2/2019 2.73
3/2019 2.41
4/2019 2.51
5/2019 2.14
6/2019 2
7/2019 2.02
8/2019 1.5
9/2019 1.68
10/2019 1.69
11/2019 1.78
12/2019 1.92
1/2020 1.51
2/2020 1.13
3/2020 0.7
4/2020 0.64
5/2020 0.65
6/2020 0.66
7/2020 0.55
8/2020 0.72
9/2020 0.69
10/2020 0.88
11/2020 0.84
12/2020 0.93
1/2021 1.11
2/2021 1.44
3/2021 1.74
4/2021 1.65
5/2021 1.58
6/2021 1.45
7/2021 1.24
8/2021 1.3
9/2021 1.52
10/2021 1.55
11/2021 1.43
12/2021 1.52
1/2022 1.79
2/2022 1.83
3/2022 2.32
4/2022 2.89
5/2022 2.85
6/2022 2.98
7/2022 2.67
8/2022 3.15
9/2022 3.83
10/2022 4.1
11/2022 3.68
12/2022 3.88
1/2023 3.52
2/2023 3.92
3/2023 3.48
4/2023 3.44
5/2023 3.64
6/2023 3.81
7/2023 3.97
8/2023 4.09
9/2023 4.59
10/2023 4.88
11/2023 4.37
12/2023 3.88
1/2024 3.99
2/2024 4.25
3/2024 4.2
4/2024 4.69
5/2024 4.51
6/2024 4.36
7/2024 4.09
8/2024 3.91
9/2024 3.81
10/2024 4.28
11/2024 4.18
12/2024 4.58
1/2025 4.58
2/2025 4.24
3/2025 4.23
4/2025 4.17
5/2025 4.41
6/2025 4.24
7/2025 4.37
8/2025 4.23
9/2025 4.16
10/2025 4.11
11/2025 4.02

=== END DATA ===

Auto-Scrolling

Summary Output

The annualized volatility of the monthly changes in the 10‑Year Treasury yield (DGS10) from 2024‑01‑31 to 2025‑11‑30 is 0.80 percentage points per year (rounded to two decimal places).
Auto-Scrolling

Final Answer

0.80
Auto-Scrolling

Focused Answer

Numeric Value
0.80
Analysis Process
Question

Calculate the annualized volatility (standard deviation) of monthly changes in the
DGS10 Treasury yield from 2024-01-31 to 2025-11-30.

Monthly changes should be in percentage points (not percentage change).
Annualized volatility = monthly std * sqrt(12)

You may analyze volatility regimes, compare to other periods, and validate outliers,
but the final answer must be a single number.

FINAL ANSWER REQUIRED: Single number representing annualized volatility in percentage
points (e.g., 0.52 means yields typically vary ±0.52% annually)

Iteration 1
Complexity Analysis
Complexity moderate
Key Challenges
  • Accurately parsing the tab‑delimited series and handling 'n/a' entries
  • Ensuring the correct date window is used for the volatility calculation
  • Applying the proper annualization factor without unit conversion errors
Auto-Scrolling
Problem Dimensions
1. Data Extraction
Description: Identify and parse the monthly DGS10 Treasury yield values for the period 2024-01-31 to 2025-11-30 from the provided context.
Strategy: Search the context for the DGS10 block, extract the relevant rows, and clean the series before any calculations.
Components:
• Locate the DGS10 series in the context• Parse each line on tab delimiter• Convert 'n/a' to null and forward‑fill missing values• Ensure dates are month‑end and aligned

2. Volatility Computation
Description: Calculate the standard deviation of month‑over‑month changes in DGS10 (in percentage points) and annualize it.
Strategy: Apply standard statistical formulas after the cleaned series is available; verify units remain in percentage points.
Components:
• Compute monthly changes as simple differences (Δ = Y_t – Y_{t‑1})• Calculate the sample standard deviation of these changes• Multiply by sqrt(12) to obtain annualized volatility

3. Result Validation
Description: Confirm that the derived volatility is based on the correct data range and methodology.
Strategy: Perform logical checks and, if needed, a quick manual spot‑check of a few values.
Components:
• Check that only months from Jan 2024 through Nov 2025 are included• Validate that the monthly change definition matches the requirement (percentage‑point difference, not percent change)• Cross‑check the annualization factor
Strategy Establish the foundational data extraction for DGS10, compute the monthly‑change standard deviation, and produce the annualized volatility figure.
Candidate Plans (3 Generated)

Plan 1

Tasks

1a
knowledge
Extract the DGS10 monthly yield values from the provided context for the period 2024-01-31 to 2025-11-30, parsing tab‑delimited lines, converting 'n/a' to null, and forward‑filling missing values.
1b
python
Calculate the annualized volatility of monthly changes in the DGS10 series using the extracted data: compute month‑over‑month differences in percentage points, find the sample standard deviation of these differences, and multiply by sqrt(12).
1c
reasoning
Evaluate the result from the Python calculation: verify correct date range, confirm monthly changes were simple differences in percentage points, and ensure the sqrt(12) annualization factor was applied.

Performance Metrics

Overall
0.85
Evaluation: This plan received an overall quality score of 0.85 based on effectiveness, task independence, and completeness.

Plan 2

Tasks

1a
knowledge
Research standard practice for annualizing monthly volatility of yield series, documenting the formula and any assumptions about sample vs population standard deviation.
1b
python
Using the methodology from the research, compute the annualized volatility of DGS10 monthly changes (2024‑01‑31 to 2025‑11‑30) by calculating month‑over‑month differences, applying pandas .std(ddof=1) for sample standard deviation, and scaling by sqrt(12).
1c
reasoning
Cross‑validate the computed volatility: check that the data extraction matched the required window, that forward‑filled values were used appropriately, and that the final number is expressed in percentage points.

Performance Metrics

Overall
0.70
Evaluation: This plan received an overall quality score of 0.70 based on effectiveness, task independence, and completeness.

Plan 3

Tasks

1a
reasoning
Break down the problem: identify required inputs (DGS10 yields for 2024‑01‑31 to 2025‑11‑30), define monthly change as Δ = Y_t – Y_{t‑1} in percentage points, and outline the steps to compute standard deviation and annualize it.
1b
python
Execute the outlined steps: parse the DGS10 series from the context, compute monthly differences, calculate the sample standard deviation of those differences, and multiply by sqrt(12) to obtain annualized volatility.
1c
knowledge
Validate the Python output against known statistical conventions for volatility calculation and confirm the result is reasonable given recent DGS10 movements.

Performance Metrics

Overall
0.65
Evaluation: This plan received an overall quality score of 0.65 based on effectiveness, task independence, and completeness.
Selected Plan
Task Tool Query
1a knowledge Extract the DGS10 monthly yield values from the provided context for the period 2024-01-31 to 2025-11-30, parsing tab‑delimited lines, converting 'n/a' to null, and forward‑filling missing values.
1b python Calculate the annualized volatility of monthly changes in the DGS10 series using the extracted data: compute month‑over‑month differences in percentage points, find the sample standard deviation of these differences, and multiply by sqrt(12).
1c reasoning Evaluate the result from the Python calculation: verify correct date range, confirm monthly changes were simple differences in percentage points, and ensure the sqrt(12) annualization factor was applied.
Task 1a
Tool knowledge
Query Extract the DGS10 monthly yield values from the provided context for the period 2024-01-31 to 2025-11-30, parsing tab‑delimited lines, converting 'n/a' to null, and forward‑filling missing values.
Result
[{"date":"2024-01-31","yield":3.99},{"date":"2024-02-29","yield":4.25},{"date":"2024-03-31","yield":4.2},{"date":"2024-04-30","yield":4.69},{"date":"2024-05-31","yield":4.51},{"date":"2024-06-30","yield":4.36},{"date":"2024-07-31","yield":4.09},{"date":"2024-08-31","yield":3.91},{"date":"2024-09-30","yield":3.81},{"date":"2024-10-31","yield":4.28},{"date":"2024-11-30","yield":4.18},{"date":"2024-12-31","yield":4.58},{"date":"2025-01-31","yield":4.58},{"date":"2025-02-28","yield":4.24},{"date":"2025-03-31","yield":4.23},{"date":"2025-04-30","yield":4.17},{"date":"2025-05-31","yield":4.41},{"date":"2025-06-30","yield":4.24},{"date":"2025-07-31","yield":4.37},{"date":"2025-08-31","yield":4.23},{"date":"2025-09-30","yield":4.16},{"date":"2025-10-31","yield":4.11},{"date":"2025-11-30","yield":4.02}]
Auto-Scrolling
Task 1b
Tool python
Query Calculate the annualized volatility of monthly changes in the DGS10 series using the extracted data: compute month‑over‑month differences in percentage points, find the sample standard deviation of these differences, and multiply by sqrt(12).
Methodology
Extracted Data
Summary: FORM B - Time series of monthly DGS10 Treasury yields. Extracted from analysis history task 0a (knowledge_retriever) which parsed the tab‑delimited data section for dates 2024‑01‑31 through 2025‑11‑30 and forward‑filled missing values. Only the 'yield' column is needed for volatility calculation; dates are retained for reference but not required for the computation. Access in Python via the variable 'dgs10_yields' as a list of floats representing percentage points for each month.
Values:
  • dgs10 yields = [3.99, 4.25, 4.20, 4.69, 4.51, 4.36, 4.09, 3.91, 3.81, 4.28, 4.18, 4.58, 4.58, 4.24, 4.23, 4.17, 4.41, 4.24, 4.37, 4.23, 4.16, 4.11, 4.02] # DGS10 yields (percent points) from 2024-01-31 to 2025-11-30
Suggested Approach
Approach: Compute month-over-month changes in DGS10 yields, calculate their sample standard deviation, and annualize by multiplying with sqrt(12)
Methods:
  • difference calculation
  • sample standard deviation
  • annualization
Formulas: monthly_changes = np.diff(dgs10_series), monthly_std = np.std(monthly_changes, ddof=1), annualized_volatility = monthly_std * np.sqrt(12)
Process: 5 steps — 1. Extract the DGS10 monthly yield series for the period 2024-01-31 to 2025-11-30 as a list of...
Data Transform: Requirements: 1 item
Libraries: numpy, pandas
Recommended Functions: numpy.diff, numpy.std, numpy.sqrt, pandas.Series.diff
Code
import numpy as np

# Data: DGS10 monthly yields (percentage points) from 2024-01-31 to 2025-11-30
dgs10_yields = [
    3.99,  # 2024-01-31
    4.25,  # 2024-02-29
    4.20,  # 2024-03-31
    4.69,  # 2024-04-30
    4.51,  # 2024-05-31
    4.36,  # 2024-06-30
    4.09,  # 2024-07-31
    3.91,  # 2024-08-31
    3.81,  # 2024-09-30
    4.28,  # 2024-10-31
    4.18,  # 2024-11-30
    4.58,  # 2024-12-31
    4.58,  # 2025-01-31
    4.24,  # 2025-02-28
    4.23,  # 2025-03-31
    4.17,  # 2025-04-30
    4.41,  # 2025-05-31
    4.24,  # 2025-06-30
    4.37,  # 2025-07-31
    4.23,  # 2025-08-31
    4.16,  # 2025-09-30
    4.11,  # 2025-10-31
    4.02   # 2025-11-30
]

# Convert list to NumPy array for vectorized operations
yields_array = np.array(dgs10_yields)

# Compute month‑over‑month changes (difference in percentage points)
monthly_changes = np.diff(yields_array)

# Sample standard deviation of monthly changes (unbiased estimator, ddof=1)
monthly_std = np.std(monthly_changes, ddof=1)

# Annualize volatility: multiply by sqrt(12)
annualized_volatility = monthly_std * np.sqrt(12)

# Output the result as a single float
print(annualized_volatility)
Auto-Scrolling
Result 0.8032288735949572
Task 1c
Tool reasoning
Query Evaluate the result from the Python calculation: verify correct date range, confirm monthly changes were simple differences in percentage points, and ensure the sqrt(12) annualization factor was applied.
Result
The knowledge‑retrieval step (task 0a) returned 23 monthly DGS10 yields covering 2024‑01‑31 through 2025‑11‑30, matching the required date range. The Python step (task 0b) used these 23 values to compute month‑over‑month differences, producing 22 change observations (Δ_i = yield_i – yield_{i‑1}). The code applied numpy.diff, then calculated the sample standard deviation with ddof=1, which is the unbiased estimator for a finite sample. Finally the result was multiplied by sqrt(12) to annualize the monthly volatility, as prescribed by the formula annualized_volatility = σ_month * √12. The printed output was 0.8032288735949572. Since the input series, difference definition, ddof setting, and √12 factor all align with the problem statement, the reported figure is consistent with the correct calculation. Therefore the value 0.8032288735949572 correctly represents the annualized volatility (in percentage‑points per year) of the DGS10 monthly changes for the period 2024‑01‑31 to 2025‑11‑30.
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Iteration Evaluation
Decision Analysis Complete
Decision Status
Analysis Complete
Quality Assessment
All tasks succeeded, producing a correct and verified numeric result.
Decision Rationale
The primary query has been fully answered with a validated annualized volatility value, and no further gaps remain. Additional iterations would not improve the final answer.
Synthesis
Result
The annualized volatility of the monthly changes in the 10‑Year Treasury yield (DGS10) from 2024‑01‑31 to 2025‑11‑30 is 0.80 percentage points per year (rounded to two decimal places).
Auto-Scrolling
Key Findings
  • The DGS10 series for the period contains 23 monthly observations, yielding 22 month‑over‑month changes.
  • The sample standard deviation of these changes is 0.2316 percentage points; annualizing with √12 gives 0.8033 percentage points.
  • The calculation follows the required methodology: simple differences in percentage points, unbiased (ddof=1) standard deviation, and sqrt(12) scaling.
Auto-Scrolling
Final Answer
Result 0.80
Answer Type float
Focused Answer
Answer Type Numeric Value
Selected Answer 0.80
Cost & Token Estimates Disclaimer
The token counts and cost figures presented below are estimates only and are provided for informational purposes. Actual values may differ due to infrastructure costs not reflected in API pricing, processing delays in token accounting, model pricing changes, calculation variances, or other factors. These estimates should not be relied upon for billing or financial decisions. For authoritative usage and cost information, please consult your official Groq API dashboard at console.groq.com, noting that final data typically appears after a delay of 15 minutes or more.
Token Usage Summary
Model openai/gpt-oss-120b
API Calls Made 22
Token Breakdown
Input Tokens 238,755
Cached Tokens 80,896
Output Tokens 9,507
Reasoning Tokens 1,748
Total Tokens 248,262
Cost Breakdown
Token Costs
Input Cost $0.0237
Cached Cost $0.0061
Output Cost $0.0057
Reasoning Cost $0.0010
Total Estimated Cost $0.0355

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