Portfolio Optimization

This portfolio optimizer tool supports the following portfolio optimization strategies:

Mean Variance Optimization – Find the optimal risk adjusted portfolio that lies on the efficient frontier
Conditional Value-at-Risk – Optimize the portfolio to minimize the expected tail loss
Risk Parity – Find the portfolio that equalizes the risk contribution of portfolio assets
Tracking Error – Find the portfolio that minimizes the tracking error against the selected benchmark
Information Ratio – Find the portfolio that maximizes the information ratio against the selected benchmark
Kelly Criterion – Finds the portfolio with the maximum expected geometric growth rate
Sortino Ratio – Find the portfolio that maximizes the Sortino ratio for the given minimum acceptable return
Omega Ratio – Find the portfolio that maximizes the Omega ratio for the given minimum acceptable return
Maximum Drawdown – Find the portfolio with the minimum worst case drawdown with optional minimum acceptable return

The optimization is based on the monthly return statistics of the selected portfolio assets for the given time period. The optimization result does not predict what allocation would perform best outside the given time period, and the actual performance of portfolios constructed using the optimized asset weights may vary from the given performance goal.

The required inputs for the optimization include the time range and the portfolio assets. Portfolio asset weights and constraints are optional. You can also use the Black-Litterman model based portfolio optimization, which allows the benchmark portfolio asset weights to be optimized based on investor's views.

Portfolio Type

Time Period

Start Year

First Month

End Year

Last Month

Optimization Goal

Targeted Annual Return

Targeted Annual Volatility

Targeted Tracking Error

Targeted Monthly CVaR

Robust Optimization

Use Historical Returns

Use Historical Volatility

Use Historical Correlations

Correlation Matrix

Browse…

Asset Constraints

Group Constraints

Compared Allocation

Benchmark

Benchmark Ticker

Portfolio Assets

Allocation

Expected Return

Volatility

Min. Weight

Max. Weight

Group

Select asset 1

Enter percentage allocation for asset 1 %

Expected return for asset 1 %

Expected volatility for asset 1 %

Minimum allocation for asset 1 %

Maximum allocation for asset 1 %

Group assignment for asset 1

Select asset 2

Enter percentage allocation for asset 2 %

Expected return for asset 2 %

Expected volatility for asset 2 %

Minimum allocation for asset 2 %

Maximum allocation for asset 2 %

Group assignment for asset 2

Select asset 3

Enter percentage allocation for asset 3 %

Expected return for asset 3 %

Expected volatility for asset 3 %

Minimum allocation for asset 3 %

Maximum allocation for asset 3 %

Group assignment for asset 3

Select asset 4

Enter percentage allocation for asset 4 %

Expected return for asset 4 %

Expected volatility for asset 4 %

Minimum allocation for asset 4 %

Maximum allocation for asset 4 %

Group assignment for asset 4

Select asset 5

Enter percentage allocation for asset 5 %

Expected return for asset 5 %

Expected volatility for asset 5 %

Minimum allocation for asset 5 %

Maximum allocation for asset 5 %

Group assignment for asset 5

Select asset 6

Enter percentage allocation for asset 6 %

Expected return for asset 6 %

Expected volatility for asset 6 %

Minimum allocation for asset 6 %

Maximum allocation for asset 6 %

Group assignment for asset 6

Select asset 7

Enter percentage allocation for asset 7 %

Expected return for asset 7 %

Expected volatility for asset 7 %

Minimum allocation for asset 7 %

Maximum allocation for asset 7 %

Group assignment for asset 7

Select asset 8

Enter percentage allocation for asset 8 %

Expected return for asset 8 %

Expected volatility for asset 8 %

Minimum allocation for asset 8 %

Maximum allocation for asset 8 %

Group assignment for asset 8

Select asset 9

Enter percentage allocation for asset 9 %

Expected return for asset 9 %

Expected volatility for asset 9 %

Minimum allocation for asset 9 %

Maximum allocation for asset 9 %

Group assignment for asset 9

Select asset 10

Enter percentage allocation for asset 10 %

Expected return for asset 10 %

Expected volatility for asset 10 %

Minimum allocation for asset 10 %

Maximum allocation for asset 10 %

Group assignment for asset 10

Total

Total allocation for portfolio %

Asset Groups

Min. Weight

Max. Weight

Full name for group A at index 1

Minimum allocation for group A at index 1 %

Maximum allocation for group A at index 1 %

Full name for group B at index 2

Minimum allocation for group B at index 2 %

Maximum allocation for group B at index 2 %

Full name for group C at index 3

Minimum allocation for group C at index 3 %

Maximum allocation for group C at index 3 %

Full name for group D at index 4

Minimum allocation for group D at index 4 %

Maximum allocation for group D at index 4 %

Full name for group E at index 5

Minimum allocation for group E at index 5 %

Maximum allocation for group E at index 5 %

Full name for group F at index 6

Minimum allocation for group F at index 6 %

Maximum allocation for group F at index 6 %

Portfolio Optimization Results (Sep 2011 - Dec 2020)

Note: The time period was constrained by the available data for iPath S&P 500 Dynamic VIX ETN (XVZ) [Sep 2011 - Dec 2020].

Portfolio optimization results with goal to minimize maximum drawdown subject to 20.00% targeted annual return. The possible range of expected annual portfolio returns for the given period is 19.39% to 48.12%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Minimum Maximum Drawdown
Ticker	Name	Allocation
UPRO	ProShares UltraPro S&P500	32.70%
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	30.57%
XVZ	iPath S&P 500 Dynamic VIX ETN	36.73%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
Metric	Minimum Maximum Drawdown
Start Balance	$10,000
End Balance	$49,938
CAGR	18.80%
Expected Return	20.00%
Stdev	14.50%
Best Year	78.51%
Worst Year	-12.06%
Max. Drawdown	-14.62%
Sharpe Ratio (ex-ante)	1.34
Sharpe Ratio (ex-post)	1.22
Sortino Ratio	2.44
US Stock Market Correlation	0.25

Trailing Returns

Trailing Returns
Name	Annualized Return					Annualized Volatility
Name	3 Month	1 year	3 year	5 year	Full	3 year	5 year
Minimum Maximum Drawdown	6.10%	78.51%	30.51%	25.02%	18.80%	19.53%	16.64%
Trailing annualized return and volatility are for full months ending in December 2020 excluding portfolio cashflows.

Notes on results:

Past performance is no guarantee of future results, which may vary. All use is subject to terms of service.
Investing involves risk, including possible loss of principal. The value of the investments and the income derived from them may fluctuate over time.
All portfolio returns presented are hypothetical and backtested. Hypothetical returns do not reflect trading costs, transaction fees, or taxes.
Portfolio optimization determines target weights for portfolio assets based on mathematical models that can use either historical or forecasted data as inputs. Optimization results are not guarantees of future performance.
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.
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.
The results are based on the total return of assets and assume that all received dividends and distributions are reinvested.
The annual results for 2011 are based on full calendar months from September to December
CAGR = Compound Annual Growth Rate
Stdev = Annualized standard deviation of monthly returns
Sharpe ratio is calculated and annualized from monthly excess returns over the risk free rate (3-month treasury bill)
Drawdowns are calculated based on monthly returns.
The backtested results assume monthly rebalancing of portfolio assets to match the specified allocation.
The results from the evolutionary algorithm for non-convex optimization may vary slightly between optimization runs depending on convergence to the global optimum.

Efficient Frontier Assets
#	Asset	CAGR	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	ProShares UltraPro S&P500 (UPRO)	34.85%	48.12%	42.99%	1.105	0.00%	100.00%
2	Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)	12.49%	20.50%	38.64%	0.514	0.00%	100.00%
3	iPath S&P 500 Dynamic VIX ETN (XVZ)	-4.63%	-1.17%	31.39%	-0.057	0.00%	100.00%
Results based on historical returns. Ex ante Sharpe Ratio calculated using 3-month treasury bill returns as the risk-free rate (0.63% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	UPRO	TMF	XVZ
ProShares UltraPro S&P500	UPRO	1.00	-0.38	-0.54
Direxion Daily 20+ Yr Trsy Bull 3X ETF	TMF	-0.38	1.00	0.15
iPath S&P 500 Dynamic VIX ETN	XVZ	-0.54	0.15	1.00
Based on monthly returns from Sep 2011 to Dec 2020

Note: You can hover over any of the data points on the chart for more information.

Efficient Frontier Assets
#	UPRO	TMF	XVZ	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	35.03%	23.21%	41.77%	19.39%	14.12%	1.329
2	35.43%	23.49%	41.08%	19.66%	14.13%	1.347
3	35.84%	23.77%	40.39%	19.92%	14.14%	1.364
4	36.24%	24.05%	39.70%	20.18%	14.16%	1.381
5	36.65%	24.34%	39.02%	20.45%	14.19%	1.397
6	37.05%	24.62%	38.33%	20.71%	14.22%	1.413
7	37.46%	24.90%	37.64%	20.98%	14.26%	1.427
8	37.86%	25.18%	36.95%	21.24%	14.31%	1.441
9	38.27%	25.47%	36.26%	21.51%	14.37%	1.454
10	38.67%	25.75%	35.58%	21.78%	14.43%	1.466
11	39.08%	26.03%	34.89%	22.04%	14.50%	1.477
12	39.49%	26.31%	34.20%	22.31%	14.58%	1.487
13	39.89%	26.60%	33.51%	22.58%	14.66%	1.497
14	40.30%	26.88%	32.83%	22.85%	14.76%	1.506
15	40.70%	27.16%	32.14%	23.12%	14.85%	1.514
16	41.11%	27.44%	31.45%	23.39%	14.96%	1.522
17	41.51%	27.73%	30.76%	23.66%	15.07%	1.528
18	41.92%	28.01%	30.08%	23.93%	15.19%	1.534
19	42.32%	28.29%	29.39%	24.20%	15.31%	1.540
20	42.73%	28.57%	28.70%	24.48%	15.44%	1.544
21	43.13%	28.85%	28.01%	24.75%	15.58%	1.549
22	43.54%	29.14%	27.32%	25.02%	15.72%	1.552
23	43.94%	29.42%	26.64%	25.30%	15.87%	1.555
24	44.35%	29.70%	25.95%	25.57%	16.02%	1.557
25	44.75%	29.98%	25.26%	25.85%	16.18%	1.559
26	45.16%	30.27%	24.57%	26.12%	16.34%	1.560
27	45.56%	30.55%	23.89%	26.40%	16.51%	1.561
28	45.97%	30.83%	23.20%	26.67%	16.68%	1.562
29	46.38%	31.11%	22.51%	26.95%	16.85%	1.562
30	46.78%	31.40%	21.82%	27.23%	17.04%	1.562
31	47.19%	31.68%	21.14%	27.51%	17.22%	1.561
32	47.59%	31.96%	20.45%	27.79%	17.41%	1.560
33	48.00%	32.24%	19.76%	28.07%	17.61%	1.559
34	48.40%	32.53%	19.07%	28.35%	17.80%	1.557
35	48.81%	32.81%	18.39%	28.63%	18.01%	1.555
36	49.21%	33.09%	17.70%	28.91%	18.21%	1.553
37	49.62%	33.37%	17.01%	29.19%	18.42%	1.551
38	50.02%	33.65%	16.32%	29.47%	18.63%	1.548
39	50.43%	33.94%	15.63%	29.76%	18.85%	1.545
40	50.83%	34.22%	14.95%	30.04%	19.07%	1.543
41	51.24%	34.50%	14.26%	30.32%	19.29%	1.539
42	51.64%	34.78%	13.57%	30.61%	19.52%	1.536
43	52.05%	35.07%	12.88%	30.89%	19.74%	1.533
44	52.45%	35.35%	12.20%	31.18%	19.97%	1.530
45	52.86%	35.63%	11.51%	31.46%	20.21%	1.526
46	53.27%	35.91%	10.82%	31.75%	20.44%	1.522
47	53.67%	36.20%	10.13%	32.04%	20.68%	1.519
48	54.08%	36.48%	9.45%	32.33%	20.92%	1.515
49	54.48%	36.76%	8.76%	32.62%	21.17%	1.511
50	54.89%	37.04%	8.07%	32.90%	21.41%	1.507
51	55.29%	37.33%	7.38%	33.19%	21.66%	1.504
52	55.70%	37.61%	6.69%	33.49%	21.91%	1.500
53	56.10%	37.89%	6.01%	33.78%	22.16%	1.496
54	56.51%	38.17%	5.32%	34.07%	22.42%	1.492
55	56.91%	38.45%	4.63%	34.36%	22.67%	1.488
56	57.32%	38.74%	3.94%	34.65%	22.93%	1.484
57	57.72%	39.02%	3.26%	34.95%	23.19%	1.480
58	58.13%	39.30%	2.57%	35.24%	23.45%	1.476
59	58.53%	39.58%	1.88%	35.53%	23.72%	1.472
60	58.94%	39.87%	1.19%	35.83%	23.98%	1.468
61	59.35%	40.15%	0.51%	36.12%	24.25%	1.464
62	59.92%	40.08%	0.00%	36.42%	24.51%	1.460
63	60.98%	39.02%	0.00%	36.72%	24.80%	1.456
64	62.03%	37.97%	0.00%	37.02%	25.09%	1.450
65	63.09%	36.91%	0.00%	37.31%	25.41%	1.444
66	64.14%	35.86%	0.00%	37.61%	25.74%	1.437
67	65.20%	34.80%	0.00%	37.91%	26.09%	1.429
68	66.25%	33.75%	0.00%	38.21%	26.45%	1.421
69	67.30%	32.70%	0.00%	38.51%	26.83%	1.412
70	68.36%	31.64%	0.00%	38.81%	27.22%	1.403
71	69.41%	30.59%	0.00%	39.11%	27.62%	1.394
72	70.47%	29.53%	0.00%	39.42%	28.03%	1.384
73	71.52%	28.48%	0.00%	39.72%	28.46%	1.374
74	72.58%	27.42%	0.00%	40.02%	28.90%	1.363
75	73.63%	26.37%	0.00%	40.33%	29.35%	1.353
76	74.69%	25.31%	0.00%	40.63%	29.81%	1.342
77	75.74%	24.26%	0.00%	40.94%	30.28%	1.331
78	76.80%	23.20%	0.00%	41.24%	30.76%	1.321
79	77.85%	22.15%	0.00%	41.55%	31.24%	1.310
80	78.91%	21.09%	0.00%	41.85%	31.74%	1.299
81	79.96%	20.04%	0.00%	42.16%	32.25%	1.288
82	81.02%	18.98%	0.00%	42.47%	32.76%	1.277
83	82.07%	17.93%	0.00%	42.78%	33.28%	1.267
84	83.13%	16.87%	0.00%	43.09%	33.81%	1.256
85	84.18%	15.82%	0.00%	43.40%	34.34%	1.246
86	85.23%	14.77%	0.00%	43.71%	34.88%	1.235
87	86.29%	13.71%	0.00%	44.02%	35.43%	1.225
88	87.34%	12.66%	0.00%	44.33%	35.98%	1.215
89	88.40%	11.60%	0.00%	44.65%	36.54%	1.205
90	89.45%	10.55%	0.00%	44.96%	37.10%	1.195
91	90.51%	9.49%	0.00%	45.27%	37.67%	1.185
92	91.56%	8.44%	0.00%	45.59%	38.25%	1.176
93	92.62%	7.38%	0.00%	45.90%	38.82%	1.166
94	93.67%	6.33%	0.00%	46.22%	39.41%	1.157
95	94.73%	5.27%	0.00%	46.53%	39.99%	1.148
96	95.78%	4.22%	0.00%	46.85%	40.59%	1.139
97	96.84%	3.16%	0.00%	47.17%	41.18%	1.130
98	97.89%	2.11%	0.00%	47.49%	41.78%	1.122
99	98.95%	1.05%	0.00%	47.81%	42.38%	1.113
100	100.00%	0.00%	0.00%	48.12%	42.99%	1.105
^*Ex-ante values shown for portfolio return and volatility. Ex ante Sharpe Ratio calculated using historical 3-month treasury bill returns as the risk-free rate (0.63% annualized).

Annual returns for the configured portfolios
Year	Inflation	Minimum Maximum Drawdown Return	Minimum Maximum Drawdown Balance	ProShares UltraPro S&P500 (UPRO)	Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)	iPath S&P 500 Dynamic VIX ETN (XVZ)
2011	-0.39%	16.79%	$11,679	3.97%	41.41%	-3.00%
2012	1.74%	9.26%	$12,760	46.80%	0.60%	-18.59%
2013	1.50%	2.77%	$13,113	118.49%	-39.01%	-26.74%
2014	0.76%	30.95%	$17,171	38.00%	97.34%	-15.57%
2015	0.73%	-4.77%	$16,352	-5.24%	-13.73%	-9.44%
2016	2.07%	14.94%	$18,796	30.79%	-2.52%	7.37%
2017	2.11%	19.53%	$22,466	71.37%	22.73%	-17.16%
2018	1.91%	-12.06%	$19,757	-25.15%	-11.01%	-9.62%
2019	2.29%	41.59%	$27,974	102.31%	34.74%	-6.79%
2020	1.36%	78.51%	$49,938	10.08%	41.60%	93.79%
Annual return for 2011 is from 09/01/2011 to 12/31/2011

Monthly returns for the configured portfolios
Year	Month	Minimum Maximum Drawdown Return	ProShares UltraPro S&P500 (UPRO)	Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)	iPath S&P 500 Dynamic VIX ETN (XVZ)
2011	9	8.88%	-20.69%	41.35%	8.18%
2011	10	2.19%	32.61%	-12.87%	-12.35%
2011	11	1.76%	-3.35%	4.89%	3.71%
2011	12	3.14%	2.30%	9.46%	-1.36%
2012	1	4.38%	13.90%	-1.50%	0.80%
2012	2	2.88%	13.24%	-7.95%	2.68%
2012	3	-1.36%	9.29%	-13.02%	-1.13%
2012	4	2.59%	-2.38%	14.37%	-2.80%
2012	5	3.80%	-17.35%	28.90%	1.74%
2012	6	1.79%	11.47%	-5.78%	-0.52%
2012	7	3.67%	3.52%	11.43%	-2.66%
2012	8	1.11%	6.53%	-4.61%	1.04%
2012	9	-2.07%	7.52%	-7.87%	-5.77%
2012	10	-4.72%	-5.96%	-2.13%	-5.77%
2012	11	0.28%	1.01%	3.90%	-3.40%
2012	12	-2.99%	2.82%	-7.80%	-4.14%
2013	1	-1.23%	15.39%	-9.58%	-9.08%
2013	2	1.25%	3.56%	3.39%	-2.58%
2013	3	3.31%	11.03%	-1.77%	0.66%
2013	4	4.19%	5.45%	14.25%	-5.31%
2013	5	-2.57%	6.80%	-19.65%	3.29%
2013	6	-2.49%	-5.23%	-10.33%	6.48%
2013	7	1.00%	16.41%	-7.41%	-5.73%
2013	8	-4.32%	-9.21%	-4.47%	0.15%
2013	9	2.20%	9.60%	1.53%	-3.84%
2013	10	3.06%	13.76%	4.12%	-7.34%
2013	11	0.30%	8.87%	-8.19%	-0.28%
2013	12	-1.56%	7.54%	-6.01%	-5.94%
2014	1	2.85%	-10.72%	19.47%	1.10%
2014	2	2.78%	13.65%	1.63%	-5.95%
2014	3	0.37%	2.15%	1.76%	-2.37%
2014	4	1.38%	1.65%	5.96%	-2.68%
2014	5	5.26%	6.62%	8.79%	1.12%
2014	6	0.58%	6.22%	-1.00%	-3.14%
2014	7	-1.23%	-4.44%	1.61%	-0.75%
2014	8	8.70%	11.95%	14.42%	1.05%
2014	9	-2.43%	-4.44%	-6.65%	2.87%
2014	10	2.23%	6.03%	8.06%	-6.01%
2014	11	6.10%	8.34%	9.08%	1.62%
2014	12	1.20%	-1.54%	9.38%	-3.16%
2015	1	6.41%	-9.47%	31.01%	0.07%
2015	2	-0.09%	17.48%	-17.87%	-0.93%
2015	3	-0.17%	-5.28%	2.57%	2.11%
2015	4	-1.82%	2.59%	-10.30%	1.31%
2015	5	-1.71%	3.43%	-7.91%	-1.13%
2015	6	-5.95%	-6.21%	-12.49%	-0.28%
2015	7	3.38%	6.17%	13.40%	-7.45%
2015	8	-2.95%	-18.87%	-2.75%	11.05%
2015	9	-1.46%	-8.64%	5.10%	-0.54%
2015	10	5.44%	26.79%	-1.73%	-7.61%
2015	11	-0.80%	0.81%	-2.71%	-0.64%
2015	12	-4.40%	-6.06%	-2.41%	-4.57%
2016	1	1.95%	-15.38%	17.74%	4.23%
2016	2	2.43%	-1.68%	8.71%	0.86%
2016	3	5.89%	21.50%	-0.64%	-2.58%
2016	4	0.70%	0.81%	-2.39%	3.18%
2016	5	3.01%	4.65%	1.86%	2.50%
2016	6	6.25%	-0.20%	21.23%	-0.47%
2016	7	6.42%	11.13%	6.07%	2.52%
2016	8	-0.05%	0.11%	-3.58%	2.74%
2016	9	-2.21%	-0.54%	-4.78%	-1.57%
2016	10	-6.66%	-5.62%	-13.32%	-2.05%
2016	11	-4.91%	11.05%	-23.91%	-3.29%
2016	12	2.17%	5.96%	-0.99%	1.43%
2017	1	1.63%	5.14%	1.49%	-1.37%
2017	2	5.40%	11.91%	4.41%	0.44%
2017	3	-1.45%	-0.22%	-2.35%	-1.79%
2017	4	-0.30%	2.77%	4.43%	-6.98%
2017	5	2.34%	3.70%	5.17%	-1.23%
2017	6	-0.08%	1.51%	1.98%	-3.22%
2017	7	0.61%	5.87%	-2.43%	-1.53%
2017	8	1.81%	0.21%	10.13%	-3.68%
2017	9	0.51%	5.69%	-7.29%	2.40%
2017	10	1.56%	6.83%	-0.53%	-1.40%
2017	11	4.41%	8.87%	1.73%	2.66%
2017	12	1.72%	3.45%	5.04%	-2.59%
2018	1	1.98%	18.22%	-9.77%	-2.70%
2018	2	-11.81%	-13.53%	-9.57%	-12.14%
2018	3	0.99%	-8.69%	8.44%	3.42%
2018	4	-4.14%	-0.14%	-6.71%	-5.57%
2018	5	3.07%	6.46%	5.27%	-1.78%
2018	6	1.15%	1.29%	1.49%	0.74%
2018	7	1.24%	10.73%	-4.70%	-2.27%
2018	8	5.15%	9.09%	3.36%	3.12%
2018	9	-2.34%	1.20%	-8.77%	-0.13%
2018	10	-7.74%	-20.78%	-9.11%	5.02%
2018	11	2.64%	4.28%	4.76%	-0.57%
2018	12	-1.60%	-26.25%	17.93%	4.10%
2019	1	4.51%	23.89%	0.41%	-9.34%
2019	2	-0.21%	9.28%	-4.52%	-5.07%
2019	3	7.22%	4.85%	17.00%	1.18%
2019	4	2.62%	11.81%	-6.56%	2.07%
2019	5	0.12%	-18.89%	21.11%	-0.41%
2019	6	6.94%	21.37%	1.90%	-1.72%
2019	7	1.51%	3.80%	0.32%	0.46%
2019	8	8.30%	-6.62%	35.11%	-0.74%
2019	9	0.03%	5.30%	-9.07%	2.91%
2019	10	1.50%	5.70%	-4.11%	2.43%
2019	11	4.20%	10.73%	-2.01%	3.54%
2019	12	-0.90%	8.38%	-10.05%	-1.55%
2020	1	6.14%	-0.91%	23.80%	-2.28%
2020	2	0.34%	-23.04%	17.91%	6.53%
2020	3	19.12%	-48.13%	11.91%	85.01%
2020	4	12.83%	37.17%	2.68%	-0.40%
2020	5	2.78%	13.38%	-6.48%	1.04%
2020	6	1.41%	3.23%	0.54%	0.52%
2020	7	11.12%	17.70%	13.13%	3.58%
2020	8	3.69%	22.05%	-14.89%	2.82%
2020	9	-2.13%	-12.26%	2.15%	3.32%
2020	10	-5.13%	-8.48%	-10.35%	2.20%
2020	11	8.11%	35.20%	4.24%	-12.78%
2020	12	3.45%	11.14%	-2.32%	1.41%

Portfolio return and risk metrics
Metric	Minimum Maximum Drawdown
Arithmetic Mean (monthly)	1.53%
Arithmetic Mean (annualized)	20.00%
Geometric Mean (monthly)	1.45%
Geometric Mean (annualized)	18.80%
Volatility (monthly)	4.19%
Volatility (annualized)	14.50%
Downside Deviation (monthly)	2.08%
Max. Drawdown	-14.62%
US Market Correlation	0.25
Beta^(*)	0.25
Alpha (annualized)	14.58%
R²	6.14%
Sharpe Ratio	1.22
Sortino Ratio	2.44
Treynor Ratio (%)	70.58
Calmar Ratio	2.09
Active Return	3.81%
Tracking Error	17.66%
Information Ratio	0.22
Skewness	0.51
Excess Kurtosis	2.95
Historical Value-at-Risk (5%)	-4.80%
Analytical Value-at-Risk (5%)	-5.32%
Conditional Value-at-Risk (5%)	-7.03%
Upside Capture Ratio (%)	63.99
Downside Capture Ratio (%)	3.07
Safe Withdrawal Rate	16.89%
Perpetual Withdrawal Rate	13.66%
Positive Periods	76 out of 112 (67.86%)
Gain/Loss Ratio	1.30
^* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Minimum Maximum Drawdown

Drawdowns for Minimum Maximum Drawdown
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Feb 2018	Oct 2018	9 months	Jun 2019	8 months	1 year 5 months	-14.62%
2	Aug 2016	Nov 2016	4 months	Nov 2017	1 year	1 year 4 months	-13.25%
3	Feb 2015	Dec 2015	11 months	May 2016	5 months	1 year 4 months	-10.50%
4	Sep 2012	Jan 2013	5 months	Apr 2014	1 year 3 months	1 year 8 months	-10.34%
5	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-7.16%
6	Sep 2014	Sep 2014	1 month	Nov 2014	2 months	3 months	-2.43%
7	Mar 2012	Mar 2012	1 month	Apr 2012	1 month	2 months	-1.36%
8	Jul 2014	Jul 2014	1 month	Aug 2014	1 month	2 months	-1.23%
9	Dec 2019	Dec 2019	1 month	Jan 2020	1 month	2 months	-0.90%

Portfolio Assets

Performance statistics for portfolio components
Ticker	Name	CAGR	Stdev	Best Year	Worst Year	Max. Drawdown	Sharpe Ratio	Sortino Ratio	US Mkt Correlation
UPRO	ProShares UltraPro S&P500	34.85%	42.99%	118.49%	-25.15%	-60.44%	0.91	1.45	0.99
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	12.49%	38.64%	97.34%	-39.01%	-49.74%	0.47	0.88	-0.39
XVZ	iPath S&P 500 Dynamic VIX ETN	-4.63%	31.39%	93.79%	-26.74%	-71.71%	-0.06	-0.15	-0.50

Monthly Correlations

Correlations for the portfolio assets
Ticker	Name	UPRO	TMF	XVZ	Minimum Maximum Drawdown
UPRO	ProShares UltraPro S&P500	1.00	-0.38	-0.54	0.24
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	-0.38	1.00	0.15	0.56
XVZ	iPath S&P 500 Dynamic VIX ETN	-0.54	0.15	1.00	0.39

Portfolio Risk Decomposition

Portfolio risk decomposition
Ticker	Name	Minimum Maximum Drawdown
UPRO	ProShares UltraPro S&P500	22.79%
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	45.83%
XVZ	iPath S&P 500 Dynamic VIX ETN	31.37%

Annual Asset Returns

Rolling returns summary
Roll Period	Average	High	Low
1 year	17.71%	88.22%	-12.06%
3 years	12.58%	32.39%	3.01%
5 years	12.05%	25.02%	7.33%
7 years	12.84%	21.07%	7.35%