This portfolio backtesting tool allows you to construct one or more portfolios based on the selected asset class level allocations in order to analyze and backtest portfolio returns, risk characteristics, drawdowns, and rolling returns. You can compare up to three different portfolios against the selected benchmark, and you can also specify any periodic contribution or withdrawal cashflows and the preferred portfolio rebalancing strategy.
You can also use the portfolio backtesting tool to build and compare portfolios based on specific mutual funds, ETFs, and stocks.
Portfolio Analysis Results (Jan 1978 - Jul 2022)
Note: The time period was constrained by the available data for Long Term Treasury [Jan 1978 - Jul 2022].
Trailing return and volatility are as of last full calendar month ending July 2022
Notes on results:
IMPORTANT: The projections or other information generated by Portfolio Visualizer regarding the likelihood of various investment outcomes are hypothetical in nature, do not reflect actual investment results and are not guarantees of future results. Results may vary with each use and over time.
The results do not constitute investment advice or recommendation, are provided solely for informational purposes, and are not an offer to buy or sell any securities. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. Past performance is not a guarantee of future results.
Asset allocation and diversification strategies do not guarantee a profit or protect against a loss.
Hypothetical returns do not reflect trading costs, transaction fees, commissions, or actual taxes due on investment returns.
The results are based on information from a variety of sources we consider reliable, but we do not represent that the information is accurate or complete.
Portfolio model information represents a blended portfolio consisting of the model's underlying positions and assigned weights provided by the user and rebalanced at the specified schedule. The results were constructed using net of fee mutual fund performance. Portfolio Visualizer does not provide preferential treatment to any specific security or investment.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
Compound annualized growth rate (CAGR) is the annualized geometric mean return of the portfolio. It is calculated from the portfolio start and end balance and is thus impacted by any cashflows.
The time-weighted rate of return (TWRR) is a measure of the compound rate of growth in a portfolio. This is calculated from the holding period returns (e.g. monthly returns), and TWRR will thus not be impacted by cashflows. If there are no external cashflows, TWRR will equal CAGR.
The money-weighted rate of return (MWRR) is the internal rate of return (IRR) taking into account cashflows. This is the discount rate at which the present value of cash inflows equals the present value of cash outflows.
Standard deviation (Stdev) is used to measure the dispersion of returns around the mean and is often used as a measure of risk. A higher standard deviation implies greater the dispersion of data points around the mean.
Sharpe Ratio is a measure of risk-adjusted performance of the portfolio, and it is calculated by dividing the mean monthly excess return of the portfolio over the risk-free rate by the standard deviation of excess return, and the displayed value is annualized.
Sortino Ratio is a measure of risk-adjusted return which is a modification of the Sharpe Ratio. While the latter is the ratio of average returns in excess of a risk-free rate divided by the standard deviation of those excess returns, the Sortino Ratio has the same denominator divided by the standard deviation of returns below the risk-free rate.
Treynor Ratio is a measure of risk-adjusted performance of the portfolio. It is similar to the Sharpe Ratio, but it uses portfolio beta (systematic risk) as the risk metric in the denominator.
Calmar Ratio is a measure of risk-adjusted performance of the portfolio. It is calculated as the annualized return over the past 36 months divided by the maximum drawdown over the past 36 months based on monthly returns.
Risk-free returns are calculated based on the Federal Reserve 3-Month Treasury Bill (secondary market) rates.
Downside deviation measures the downside volatility of the portfolio returns unlike standard deviation, which includes both upside and downside deviations. Downside deviation is calculated based on negative returns that hurt the portfolio performance.
Correlation measures to what degree the returns of the two assets move in relation to each other. Correlation coefficient is a numerical value between -1 and +1. If one variable goes up by a certain amount, the correlation coefficient indicates which way the other variable moves and by how much. Asset correlations are calculated based on monthly returns.
Skewness is a measure of the asymmetry of the probability distribution or returns from a normal Gaussian distribution shape about its mean. Negative skewness is associated with the left (typically negative returns) tail of the distribution extending further than the right tail; and positive skewness is associated with the right (typically positive returns) tail of the distribution extending further than the left tail.
Excess kurtosis is a measure of whether a data distribution is peaked or flat relative to a normal distribution. Distributions with high kurtosis tend to have a distinct peak near the mean, decline rather rapidly, and have heavy or fat tails.
A drawdown refers to the decline in value of a single investment or an investment portfolio from a relative peak value to a relative trough. A maximum drawdown (Max Drawdown) is the maximum observed loss from a peak to a trough of a portfolio before a new peak is attained. Drawdown values are calculated based on monthly returns.
Value at Risk (VaR) measures the scale of loss at a given confidence level. If the 5% VaR is -3% the portfolio return is expected to be greater than -3% 95% of the time and less than -3% 5% of the time. Value at Risk can be calculated directly based on historical returns based on a given percentile or analytically based on the mean and standard deviation of the returns.
Conditional Value at Risk (CVaR) measures the scale of the expected loss once the specific Value at Risk (VaR) breakpoint has been breached, i.e., it calculates the average tail loss by taking a weighted average between the value at risk and losses exceeding the value at risk.
Beta is a measure of systematic risk and measures the volatility of a particular investment relative to the market or its benchmark. Alpha measures the active return of the investment compared to the market benchmark return. R-squared is the percentage of a portfolio's movements that can be explained by movements in the selected benchmark index.
Active return is the investment return minus the return of its benchmark. For periods longer than 12 months this is displayed as annualized value, i.e., annualized investment return minus annualized benchmark return.
Tracking error, also known as active risk, is the standard deviation of active return. This is displayed as annualized value based on the standard deviation of monthly active returns.
Information ratio is the active return divided by the tracking error. It measures whether the investment outperformed its benchmark consistently.
Gain/Loss ratio is a measure of downside risk, and it is calculated as the average positive return in up periods divided by the average negative return in down periods.
Upside Capture Ratio measures how well the fund performed relative to the benchmark when the market was up, and Downside Capture Ratio measures how well the fund performed relative to the benchmark when the market was down. An upside capture ratio greater than 100 would indicate that the fund outperformed its benchmark when the market was up, and a downside capture ratio below 100 would indicate that the fund lost less than its benchmark when the market was down. To calculate upside capture ratio a new series from the portfolio returns is constructed by dropping all time periods where the benchmark return is less than equal to zero. The up capture is then the quotient of the annualized return of the resulting manager series, divided by the annualized return of the resulting benchmark series. The downside capture ratio is calculated analogously.
All risk measures for the portfolio and portfolio assets are calculated based on monthly returns.
The annual results for 2022 are based on monthly returns from January to July.
The results assume annual rebalancing of portfolio assets to match the specified allocation.
Annual returns for the configured portfolios
Year
Inflation
Permanent Portfolio
Golden Butterfly
22/33/44 Gold/SCV/10yrT
US Stock Market
Short Term Treasury
Long Term Treasury
Gold
US Small Cap Value
10-year Treasury
Return
Balance
Return
Balance
Return
Balance
1978
9.02%
11.82%
$11,182
13.30%
$11,330
14.16%
$11,416
8.45%
3.35%
-1.55%
37.01%
19.25%
-0.74%
1979
13.29%
39.19%
$15,564
38.92%
$15,739
41.14%
$16,112
24.25%
8.08%
-2.10%
126.55%
37.80%
1.83%
1980
12.52%
13.04%
$17,593
15.58%
$18,192
11.26%
$17,927
33.15%
8.81%
-4.99%
15.19%
25.77%
-1.29%
1981
8.92%
-5.46%
$16,633
-1.23%
$17,969
0.38%
$17,996
-4.15%
14.26%
0.65%
-32.60%
15.69%
5.28%
1982
3.83%
26.17%
$20,985
28.31%
$23,055
33.26%
$23,982
20.50%
22.12%
47.10%
14.94%
36.87%
39.57%
1983
3.79%
3.26%
$21,670
11.13%
$25,622
11.51%
$26,741
22.66%
8.00%
-1.29%
-16.31%
42.61%
2.30%
1984
3.95%
3.26%
$22,378
3.75%
$26,583
4.31%
$27,893
2.19%
14.01%
16.24%
-19.38%
5.69%
14.87%
1985
3.80%
22.00%
$27,301
25.09%
$33,253
27.11%
$35,456
31.27%
13.83%
36.90%
6.00%
37.46%
29.85%
1986
1.10%
18.69%
$32,403
17.75%
$39,155
18.39%
$41,978
14.57%
10.35%
30.87%
18.96%
13.99%
21.35%
1987
4.43%
7.25%
$34,752
5.10%
$41,151
3.05%
$43,258
2.61%
4.78%
-2.92%
24.53%
-3.51%
-2.64%
1988
4.42%
4.22%
$36,219
9.18%
$44,927
9.32%
$47,288
17.32%
5.67%
9.15%
-15.26%
29.00%
6.90%
1989
4.65%
13.67%
$41,171
14.78%
$51,567
13.74%
$53,787
28.12%
11.48%
17.93%
-2.84%
19.21%
17.84%
1990
6.11%
1.63%
$41,841
-2.51%
$50,274
-3.50%
$51,902
-6.08%
9.92%
5.78%
-3.11%
-19.05%
7.70%
1991
3.06%
13.19%
$47,360
19.14%
$59,898
20.80%
$62,699
32.39%
11.49%
17.43%
-8.56%
42.96%
18.91%
1992
2.90%
4.38%
$49,435
9.15%
$65,380
11.31%
$69,789
9.11%
6.75%
7.41%
-5.73%
28.23%
7.23%
1993
2.75%
12.85%
$55,786
14.50%
$74,858
16.69%
$81,436
10.62%
6.31%
16.78%
17.68%
21.10%
12.97%
1994
2.67%
-2.46%
$54,412
-1.98%
$73,373
-3.74%
$78,393
-0.17%
-0.48%
-7.04%
-2.17%
-0.07%
-7.19%
1995
2.54%
19.74%
$65,154
21.86%
$89,410
21.72%
$95,418
35.79%
12.11%
30.09%
0.98%
30.32%
25.55%
1996
3.32%
4.88%
$68,332
8.18%
$96,727
6.05%
$101,196
20.96%
4.39%
-1.26%
-4.59%
21.41%
-0.00%
1997
1.70%
7.50%
$73,456
13.09%
$109,386
12.37%
$113,713
30.99%
6.51%
13.90%
-21.41%
35.44%
11.97%
1998
1.61%
10.71%
$81,325
8.03%
$118,175
5.52%
$119,993
23.26%
7.36%
13.05%
-0.83%
-2.68%
14.64%
1999
2.68%
4.46%
$84,955
4.24%
$123,187
-2.23%
$117,318
23.81%
1.85%
-8.66%
0.85%
3.35%
-7.83%
2000
3.39%
3.13%
$87,618
6.88%
$131,666
13.80%
$133,504
-10.57%
8.83%
19.72%
-5.44%
21.88%
17.28%
2001
1.55%
0.47%
$88,031
3.12%
$135,769
7.12%
$143,003
-10.97%
7.80%
4.31%
0.75%
13.70%
5.40%
2002
2.38%
7.33%
$94,481
3.02%
$139,871
7.89%
$154,289
-20.96%
8.02%
16.67%
25.57%
-14.20%
15.45%
2003
1.88%
14.08%
$107,779
18.70%
$166,025
16.72%
$180,082
31.35%
2.38%
2.68%
19.89%
37.19%
0.15%
2004
3.26%
6.33%
$114,600
9.77%
$182,251
10.82%
$199,563
12.52%
1.03%
7.12%
4.65%
23.55%
4.50%
2005
3.42%
8.03%
$123,801
7.64%
$196,171
7.27%
$214,068
5.98%
1.77%
6.61%
17.76%
6.07%
3.01%
2006
2.54%
10.89%
$137,285
12.56%
$220,814
12.30%
$240,392
15.51%
3.77%
1.74%
22.55%
19.24%
2.19%
2007
4.08%
13.27%
$155,500
9.20%
$241,128
9.06%
$262,163
5.49%
7.89%
9.24%
30.45%
-7.07%
10.42%
2008
0.09%
-0.73%
$154,363
-7.00%
$224,260
-0.25%
$261,496
-37.04%
6.68%
22.51%
4.92%
-32.05%
20.53%
2009
2.72%
10.53%
$170,614
14.49%
$256,753
10.72%
$289,527
28.70%
1.44%
-12.06%
24.03%
30.34%
-10.17%
2010
1.50%
14.48%
$195,322
16.55%
$299,243
18.19%
$342,203
17.09%
2.63%
8.93%
29.27%
24.82%
7.92%
2011
2.96%
10.52%
$215,861
7.58%
$321,926
8.04%
$369,719
0.96%
2.26%
29.28%
9.57%
-4.16%
16.24%
2012
1.74%
6.75%
$230,436
9.11%
$351,267
8.81%
$402,282
16.25%
0.69%
3.46%
6.60%
18.56%
2.73%
2013
1.50%
-2.03%
$225,767
5.66%
$371,150
1.93%
$410,029
33.35%
-0.10%
-13.03%
-28.33%
36.41%
-8.57%
2014
0.76%
9.06%
$246,216
9.32%
$405,757
7.73%
$441,737
12.43%
0.71%
25.27%
-2.19%
10.39%
10.63%
2015
0.73%
-2.87%
$239,161
-3.25%
$392,581
-3.42%
$426,639
0.29%
0.45%
-1.54%
-10.67%
-4.77%
1.12%
2016
2.07%
5.69%
$252,777
9.48%
$429,815
10.35%
$470,809
12.53%
1.00%
1.21%
8.03%
24.65%
1.00%
2017
2.11%
10.71%
$279,854
10.90%
$476,681
7.75%
$507,281
21.05%
0.40%
8.59%
12.81%
11.67%
2.39%
2018
1.91%
-1.94%
$274,433
-4.02%
$457,530
-4.05%
$486,717
-5.26%
1.35%
-1.90%
-1.94%
-12.34%
0.99%
2019
2.29%
16.56%
$319,867
17.77%
$538,818
15.00%
$559,741
30.65%
3.59%
14.13%
17.86%
22.61%
8.03%
2020
1.36%
16.98%
$374,191
14.73%
$618,194
11.85%
$626,078
20.87%
3.96%
18.29%
24.81%
5.72%
10.01%
2021
7.04%
3.96%
$389,015
8.76%
$672,352
6.81%
$668,743
25.59%
-0.87%
-4.73%
-4.15%
27.96%
-3.33%
2022
6.28%
-9.91%
$350,446
-9.39%
$609,216
-6.85%
$622,946
-14.05%
-2.64%
-18.96%
-4.01%
-7.29%
-7.91%
Annual return for 2022 is from 01/01/2022 to 07/31/2022
Portfolio return and risk metrics
Metric
Permanent Portfolio
Golden Butterfly
22/33/44 Gold/SCV/10yrT
Arithmetic Mean (monthly)
0.69%
0.80%
0.80%
Arithmetic Mean (annualized)
8.60%
10.03%
10.10%
Geometric Mean (monthly)
0.67%
0.77%
0.78%
Geometric Mean (annualized)
8.30%
9.66%
9.71%
Standard Deviation (monthly)
2.16%
2.40%
2.44%
Standard Deviation (annualized)
7.48%
8.33%
8.45%
Downside Deviation (monthly)
1.15%
1.38%
1.37%
Maximum Drawdown
-13.38%
-16.64%
-15.18%
Stock Market Correlation
0.57
0.79
0.66
Beta(*)
0.27
0.42
0.36
Alpha (annualized)
4.94%
4.42%
5.25%
R2
32.27%
62.49%
43.95%
Sharpe Ratio
0.54
0.64
0.64
Sortino Ratio
0.85
0.98
1.00
Treynor Ratio (%)
14.69
12.59
14.97
Calmar Ratio
0.41
0.47
0.49
Active Return
-3.25%
-1.90%
-1.85%
Tracking Error
12.84%
10.28%
11.76%
Information Ratio
-0.25
-0.19
-0.16
Skewness
0.17
-0.39
-0.24
Excess Kurtosis
2.61
2.74
2.45
Historical Value-at-Risk (5%)
-2.37%
-2.72%
-2.79%
Analytical Value-at-Risk (5%)
-2.86%
-3.15%
-3.21%
Conditional Value-at-Risk (5%)
-3.78%
-4.72%
-4.80%
Upside Capture Ratio (%)
35.55
49.28
44.70
Downside Capture Ratio (%)
16.08
32.49
24.11
Safe Withdrawal Rate
5.89%
7.46%
7.80%
Perpetual Withdrawal Rate
4.43%
5.62%
5.67%
Positive Periods
341 out of 535 (63.74%)
353 out of 535 (65.98%)
344 out of 535 (64.30%)
Gain/Loss Ratio
1.35
1.24
1.33
* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.
Drawdowns for Historical Market Stress Periods
Drawdowns for Historical Market Stress Periods
Stress Period
Start
End
Permanent Portfolio
Golden Butterfly
22/33/44 Gold/SCV/10yrT
Black Monday Period
Sep 1987
Nov 1987
-5.57%
-10.93%
-8.77%
Asian Crisis
Jul 1997
Jan 1998
-1.81%
-1.80%
-1.57%
Russian Debt Default
Jul 1998
Oct 1998
-5.06%
-8.79%
-7.83%
Dotcom Crash
Mar 2000
Oct 2002
-4.58%
-6.84%
-5.96%
Subprime Crisis
Nov 2007
Mar 2009
-13.38%
-16.64%
-13.83%
COVID-19 Start
Jan 2020
Mar 2020
-1.48%
-7.38%
-7.32%
Drawdowns for Permanent Portfolio
Drawdowns for Permanent Portfolio (worst 10)
Rank
Start
End
Length
Recovery By
Recovery Time
Underwater Period
Drawdown
1
Mar 2008
Oct 2008
8 months
Sep 2009
11 months
1 year 7 months
-13.38%
2
Feb 1980
Mar 1980
2 months
Jun 1980
3 months
5 months
-12.53%
3
Dec 1980
Sep 1981
10 months
Aug 1982
11 months
1 year 9 months
-12.25%
4
Jan 2022
Jun 2022
6 months
-11.79%
5
Aug 2016
Dec 2016
5 months
Aug 2017
8 months
1 year 1 month
-6.95%
6
Oct 2012
Jun 2013
9 months
Feb 2014
8 months
1 year 5 months
-6.75%
7
Feb 2015
Dec 2015
11 months
Apr 2016
4 months
1 year 3 months
-6.49%
8
May 1983
May 1984
1 year 1 month
Oct 1984
5 months
1 year 6 months
-5.95%
9
Sep 1987
Nov 1987
3 months
Oct 1988
11 months
1 year 2 months
-5.57%
10
Oct 1978
Nov 1978
2 months
Jan 1979
2 months
4 months
-5.36%
Worst 10 drawdowns included above
Drawdowns for Golden Butterfly
Drawdowns for Golden Butterfly (worst 10)
Rank
Start
End
Length
Recovery By
Recovery Time
Underwater Period
Drawdown
1
Mar 2008
Feb 2009
1 year
Sep 2009
7 months
1 year 7 months
-16.64%
2
Feb 1980
Mar 1980
2 months
Jun 1980
3 months
5 months
-13.73%
3
Jan 2022
Jun 2022
6 months
-12.54%
4
Sep 1987
Nov 1987
3 months
Jan 1989
1 year 2 months
1 year 5 months
-10.93%
5
May 1998
Aug 1998
4 months
Dec 1998
4 months
8 months
-9.44%
6
Dec 1980
Sep 1981
10 months
Nov 1981
2 months
1 year
-9.09%
7
Jan 1990
Oct 1990
10 months
Feb 1991
4 months
1 year 2 months
-7.94%
8
Dec 1981
Mar 1982
4 months
Aug 1982
5 months
9 months
-7.77%
9
Oct 1978
Nov 1978
2 months
Jan 1979
2 months
4 months
-7.41%
10
Feb 2020
Mar 2020
2 months
May 2020
2 months
4 months
-7.38%
Worst 10 drawdowns included above
Drawdowns for 22/33/44 Gold/SCV/10yrT
Drawdowns for 22/33/44 Gold/SCV/10yrT (worst 10)
Rank
Start
End
Length
Recovery By
Recovery Time
Underwater Period
Drawdown
1
Feb 1980
Mar 1980
2 months
Jun 1980
3 months
5 months
-15.18%
2
Mar 2008
Oct 2008
8 months
Aug 2009
10 months
1 year 6 months
-13.83%
3
Jan 2022
Jun 2022
6 months
-10.20%
4
Dec 1989
Oct 1990
11 months
Feb 1991
4 months
1 year 3 months
-9.34%
5
Jun 1981
Sep 1981
4 months
Nov 1981
2 months
6 months
-9.17%
6
May 1998
Aug 1998
4 months
Jun 2000
1 year 10 months
2 years 2 months
-9.12%
7
Sep 1987
Oct 1987
2 months
Jun 1988
8 months
10 months
-8.77%
8
Oct 1978
Nov 1978
2 months
Feb 1979
3 months
5 months
-8.19%
9
Oct 1979
Oct 1979
1 month
Dec 1979
2 months
3 months
-7.56%
10
Feb 2020
Mar 2020
2 months
Jun 2020
3 months
5 months
-7.32%
Worst 10 drawdowns included above
Portfolio Assets
Performance statistics for portfolio components
Name
CAGR
Stdev
Best Year
Worst Year
Max Drawdown
Sharpe Ratio
Sortino Ratio
Market Correlation
US Stock Market
11.56%
15.51%
35.79%
-37.04%
-50.89%
0.51
0.74
1.00
Short Term Treasury
5.58%
3.09%
22.12%
-2.64%
-4.26%
0.43
0.70
0.05
Long Term Treasury
7.71%
11.22%
47.10%
-18.96%
-29.66%
0.34
0.54
0.04
Gold
5.28%
18.59%
126.55%
-32.60%
-61.78%
0.14
0.22
0.05
US Small Cap Value
14.08%
17.95%
42.96%
-32.05%
-56.13%
0.59
0.84
0.89
10-year Treasury
6.89%
8.31%
39.57%
-10.17%
-15.76%
0.34
0.52
0.03
Portfolio Asset Performance
Performance of portfolio assets
Name
Total Return
Annualized Return
3 Month
Year To Date
1 year
3 year
5 year
10 year
US Stock Market
-0.04%
-14.05%
-7.86%
12.31%
11.99%
13.29%
Short Term Treasury
0.49%
-2.64%
-3.38%
0.46%
0.96%
0.79%
Long Term Treasury
-0.91%
-18.96%
-19.34%
-2.02%
1.11%
1.45%
Gold
-7.24%
-4.01%
-3.37%
7.20%
6.33%
0.48%
US Small Cap Value
0.27%
-7.29%
-1.98%
9.71%
7.82%
11.43%
10-year Treasury
2.70%
-7.91%
-9.63%
-0.28%
1.24%
1.05%
Trailing returns as of last calendar month ending July 2022
Monthly Correlations
Correlations for the portfolio assets
Name
US Stock Market
Short Term Treasury
Long Term Treasury
Gold
US Small Cap Value
10-year Treasury
Permanent Portfolio
Golden Butterfly
22/33/44 Gold/SCV/10yrT
US Stock Market
1.00
0.05
0.04
0.05
0.89
0.03
0.57
0.79
0.66
Short Term Treasury
0.05
1.00
0.71
0.09
0.05
0.83
0.45
0.35
0.45
Long Term Treasury
0.04
0.71
1.00
0.07
-0.02
0.94
0.52
0.37
0.44
Gold
0.05
0.09
0.07
1.00
0.04
0.08
0.71
0.52
0.56
US Small Cap Value
0.89
0.05
-0.02
0.04
1.00
-0.01
0.48
0.78
0.72
10-year Treasury
0.03
0.83
0.94
0.08
-0.01
1.00
0.51
0.36
0.47
Portfolio Return Decomposition
Portfolio return decomposition
Name
Permanent Portfolio
Golden Butterfly
22/33/44 Gold/SCV/10yrT
US Stock Market
$153,628
$187,455
Short Term Treasury
$36,707
$42,046
Long Term Treasury
$73,268
$87,240
Gold
$76,843
$96,671
$115,983
US Small Cap Value
$185,803
$332,549
10-year Treasury
$164,414
Return attribution decomposes portfolio gains into its constituent parts and identifies the contribution to returns by each of the assets.
Portfolio Risk Decomposition
Portfolio risk decomposition
Name
Permanent Portfolio
Golden Butterfly
22/33/44 Gold/SCV/10yrT
US Stock Market
30.22%
29.85%
Short Term Treasury
4.79%
2.61%
Long Term Treasury
19.89%
9.99%
Gold
45.10%
23.64%
27.60%
US Small Cap Value
33.91%
51.03%
10-year Treasury
21.37%
Risk attribution decomposes portfolio risk into its constituent parts and identifies the contribution to overall volatility by each of the assets.