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 (Mar 2010 - Dec 2020)

Note: The time period was constrained by the available data for ProShares UltraPro QQQ (TQQQ) [Mar 2010 - Dec 2020].

Portfolio optimization results with goal to maximize return subject to 22.25% targeted annual volatility. The possible range of expected annual portfolio returns for the given period is 33.58% to 73.16%. Refer to the efficient frontier section for additional details.

Portfolio Allocations

Maximum Return at 22.25% Volatility
Ticker	Name	Allocation
UPRO	ProShares UltraPro S&P500	40.09%
TQQQ	ProShares UltraPro QQQ	7.53%
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	52.38%
Save portfolio »

Maximum Sharpe Ratio Weights
Ticker	Name	Allocation
TQQQ	ProShares UltraPro QQQ	52.35%
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	47.65%
Save portfolio »

Portfolio Performance Summary

Portfolio performance statistics
Metric	Maximum Return at 22.25% Volatility	Maximum Sharpe Ratio Weights
Start Balance	$10,000	$10,000
End Balance	$212,084	$493,695
CAGR	32.57%	43.32%
Expected Return	35.72%	48.06%
Stdev	22.18%	26.33%
Best Year	76.65%	98.80%
Worst Year	-13.35%	-10.27%
Max. Drawdown	-20.03%	-26.10%
Sharpe Ratio (ex-ante)	1.59	1.80
Sharpe Ratio (ex-post)	1.37	1.49
Sortino Ratio	2.59	3.05
US Stock Market Correlation	0.53	0.62

Trailing Returns

Trailing Returns
Name	Annualized Return						Annualized Volatility
Name	3 Month	1 year	3 year	5 year	10 year	Full	3 year	5 year
Maximum Return at 22.25% Volatility	12.23%	52.27%	32.59%	31.93%	31.26%	32.57%	29.36%	25.07%
Maximum Sharpe Ratio Weights	15.01%	98.80%	51.36%	45.06%	41.44%	43.32%	34.24%	29.84%
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 2010 are based on full calendar months from March 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.

Efficient Frontier Assets
#	Asset	CAGR	Expected Return	Standard Deviation	Sharpe Ratio	Min. Weight	Max. Weight
1	ProShares UltraPro S&P500 (UPRO)	31.52%	45.19%	44.23%	1.009	0.00%	100.00%
2	ProShares UltraPro QQQ (TQQQ)	52.68%	73.17%	51.82%	1.401	0.00%	100.00%
3	Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)	15.79%	24.36%	39.42%	0.604	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 (0.56% annualized).

Asset Correlations

Efficient Frontier Asset Correlations
Name	Ticker	UPRO	TQQQ	TMF
ProShares UltraPro S&P500	UPRO	1.00	0.93	-0.45
ProShares UltraPro QQQ	TQQQ	0.93	1.00	-0.39
Direxion Daily 20+ Yr Trsy Bull 3X ETF	TMF	-0.45	-0.39	1.00
Based on monthly returns from Mar 2010 to Dec 2020

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

Efficient Frontier Assets
#	UPRO	TQQQ	TMF	Expected Return^*	Standard Deviation^*	Sharpe Ratio^*
1	46.04%	0.00%	53.96%	33.58%	21.83%	1.513
2	47.08%	0.31%	52.61%	33.94%	21.86%	1.527
3	45.68%	1.76%	52.56%	34.29%	21.92%	1.539
4	44.28%	3.20%	52.52%	34.65%	21.98%	1.551
5	42.88%	4.64%	52.47%	35.01%	22.04%	1.563
6	41.48%	6.09%	52.43%	35.36%	22.11%	1.574
7	40.09%	7.53%	52.38%	35.72%	22.18%	1.586
8	38.69%	8.97%	52.34%	36.08%	22.25%	1.597
9	37.29%	10.42%	52.29%	36.44%	22.33%	1.607
10	35.89%	11.86%	52.25%	36.80%	22.41%	1.617
11	34.49%	13.30%	52.20%	37.17%	22.49%	1.628
12	33.09%	14.75%	52.16%	37.53%	22.58%	1.637
13	31.70%	16.19%	52.11%	37.89%	22.67%	1.647
14	30.30%	17.63%	52.07%	38.26%	22.77%	1.656
15	28.90%	19.08%	52.02%	38.62%	22.86%	1.665
16	27.50%	20.52%	51.98%	38.99%	22.97%	1.674
17	26.10%	21.96%	51.93%	39.36%	23.07%	1.682
18	24.70%	23.41%	51.89%	39.73%	23.18%	1.690
19	23.31%	24.85%	51.84%	40.10%	23.29%	1.698
20	21.91%	26.29%	51.80%	40.47%	23.40%	1.706
21	20.51%	27.74%	51.75%	40.84%	23.52%	1.713
22	19.11%	29.18%	51.71%	41.21%	23.63%	1.720
23	17.71%	30.62%	51.66%	41.58%	23.76%	1.727
24	16.31%	32.07%	51.62%	41.96%	23.88%	1.734
25	14.92%	33.51%	51.57%	42.33%	24.01%	1.740
26	13.52%	34.95%	51.53%	42.71%	24.14%	1.746
27	12.12%	36.40%	51.48%	43.08%	24.27%	1.752
28	10.72%	37.84%	51.44%	43.46%	24.41%	1.758
29	9.32%	39.28%	51.39%	43.84%	24.55%	1.763
30	7.92%	40.73%	51.35%	44.22%	24.69%	1.769
31	6.53%	42.17%	51.30%	44.60%	24.83%	1.774
32	5.13%	43.61%	51.26%	44.98%	24.98%	1.779
33	3.73%	45.06%	51.21%	45.36%	25.13%	1.783
34	2.33%	46.50%	51.17%	45.75%	25.28%	1.788
35	0.93%	47.94%	51.12%	46.13%	25.43%	1.792
36	0.00%	49.17%	50.83%	46.51%	25.59%	1.796
37	0.00%	49.96%	50.04%	46.90%	25.75%	1.799
38	0.00%	50.76%	49.24%	47.29%	25.93%	1.802
39	0.00%	51.55%	48.45%	47.67%	26.13%	1.803
40	0.00%	52.35%	47.65%	48.06%	26.33%	1.804
41	0.00%	53.14%	46.86%	48.45%	26.55%	1.804
42	0.00%	53.94%	46.06%	48.84%	26.78%	1.803
43	0.00%	54.73%	45.27%	49.23%	27.02%	1.801
44	0.00%	55.52%	44.48%	49.63%	27.27%	1.799
45	0.00%	56.32%	43.68%	50.02%	27.54%	1.796
46	0.00%	57.11%	42.89%	50.41%	27.81%	1.793
47	0.00%	57.91%	42.09%	50.81%	28.10%	1.789
48	0.00%	58.70%	41.30%	51.21%	28.39%	1.784
49	0.00%	59.49%	40.51%	51.60%	28.70%	1.779
50	0.00%	60.29%	39.71%	52.00%	29.01%	1.773
51	0.00%	61.08%	38.92%	52.40%	29.33%	1.767
52	0.00%	61.88%	38.12%	52.80%	29.67%	1.761
53	0.00%	62.67%	37.33%	53.20%	30.01%	1.754
54	0.00%	63.47%	36.53%	53.60%	30.36%	1.747
55	0.00%	64.26%	35.74%	54.01%	30.71%	1.740
56	0.00%	65.05%	34.95%	54.41%	31.08%	1.733
57	0.00%	65.85%	34.15%	54.81%	31.45%	1.725
58	0.00%	66.64%	33.36%	55.22%	31.83%	1.717
59	0.00%	67.44%	32.56%	55.63%	32.22%	1.709
60	0.00%	68.23%	31.77%	56.03%	32.61%	1.701
61	0.00%	69.03%	30.97%	56.44%	33.01%	1.693
62	0.00%	69.82%	30.18%	56.85%	33.41%	1.685
63	0.00%	70.61%	29.39%	57.26%	33.83%	1.676
64	0.00%	71.41%	28.59%	57.67%	34.24%	1.668
65	0.00%	72.20%	27.80%	58.09%	34.67%	1.660
66	0.00%	73.00%	27.00%	58.50%	35.10%	1.651
67	0.00%	73.79%	26.21%	58.92%	35.53%	1.643
68	0.00%	74.58%	25.42%	59.33%	35.97%	1.634
69	0.00%	75.38%	24.62%	59.75%	36.41%	1.626
70	0.00%	76.17%	23.83%	60.17%	36.86%	1.617
71	0.00%	76.97%	23.03%	60.58%	37.31%	1.609
72	0.00%	77.76%	22.24%	61.00%	37.77%	1.600
73	0.00%	78.56%	21.44%	61.42%	38.23%	1.592
74	0.00%	79.35%	20.65%	61.85%	38.69%	1.584
75	0.00%	80.14%	19.86%	62.27%	39.16%	1.576
76	0.00%	80.94%	19.06%	62.69%	39.64%	1.568
77	0.00%	81.73%	18.27%	63.12%	40.11%	1.560
78	0.00%	82.53%	17.47%	63.54%	40.59%	1.552
79	0.00%	83.32%	16.68%	63.97%	41.07%	1.544
80	0.00%	84.12%	15.88%	64.40%	41.56%	1.536
81	0.00%	84.91%	15.09%	64.83%	42.05%	1.528
82	0.00%	85.70%	14.30%	65.25%	42.54%	1.521
83	0.00%	86.50%	13.50%	65.69%	43.04%	1.513
84	0.00%	87.29%	12.71%	66.12%	43.53%	1.506
85	0.00%	88.09%	11.91%	66.55%	44.04%	1.499
86	0.00%	88.88%	11.12%	66.98%	44.54%	1.491
87	0.00%	89.68%	10.32%	67.42%	45.04%	1.484
88	0.00%	90.47%	9.53%	67.85%	45.55%	1.477
89	0.00%	91.26%	8.74%	68.29%	46.06%	1.470
90	0.00%	92.06%	7.94%	68.73%	46.58%	1.464
91	0.00%	92.85%	7.15%	69.17%	47.09%	1.457
92	0.00%	93.65%	6.35%	69.61%	47.61%	1.450
93	0.00%	94.44%	5.56%	70.05%	48.13%	1.444
94	0.00%	95.23%	4.77%	70.49%	48.65%	1.438
95	0.00%	96.03%	3.97%	70.94%	49.17%	1.431
96	0.00%	96.82%	3.18%	71.38%	49.70%	1.425
97	0.00%	97.62%	2.38%	71.83%	50.23%	1.419
98	0.00%	98.41%	1.59%	72.27%	50.75%	1.413
99	0.00%	99.21%	0.79%	72.72%	51.28%	1.407
100	0.00%	100.00%	0.00%	73.17%	51.82%	1.401
^*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 (0.56% annualized).

Annual returns for the configured portfolios
Year	Inflation	Maximum Return at 22.25% Volatility		Maximum Sharpe Ratio Weights		ProShares UltraPro S&P500 (UPRO)	ProShares UltraPro QQQ (TQQQ)	Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)
Year	Inflation	Return	Balance	Return	Balance	ProShares UltraPro S&P500 (UPRO)	ProShares UltraPro QQQ (TQQQ)	Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)
2010	1.12%	39.64%	$13,964	54.08%	$15,408	40.92%	65.62%	10.27%
2011	2.96%	53.83%	$21,481	48.93%	$22,946	-11.88%	-8.05%	109.14%
2012	1.74%	27.76%	$27,444	34.42%	$30,844	46.80%	52.29%	0.60%
2013	1.50%	16.87%	$32,073	29.57%	$39,963	118.49%	139.73%	-39.01%
2014	0.76%	70.74%	$54,762	78.15%	$71,193	38.00%	57.09%	97.34%
2015	0.73%	-3.09%	$53,070	7.97%	$76,871	-5.24%	17.23%	-13.73%
2016	2.07%	16.12%	$61,623	10.40%	$84,866	30.79%	11.38%	-2.52%
2017	2.11%	47.66%	$90,991	67.75%	$142,364	71.37%	118.06%	22.73%
2018	1.91%	-13.35%	$78,844	-10.27%	$127,742	-25.15%	-19.80%	-11.01%
2019	2.29%	76.65%	$139,277	94.41%	$248,343	102.31%	133.83%	34.74%
2020	1.36%	52.27%	$212,084	98.80%	$493,695	10.08%	110.05%	41.60%
Annual return for 2010 is from 03/01/2010 to 12/31/2010

Monthly returns for the configured portfolios
Year	Month	Maximum Return at 22.25% Volatility Return	Maximum Sharpe Ratio Weights Return	ProShares UltraPro S&P500 (UPRO)	ProShares UltraPro QQQ (TQQQ)	Direxion Daily 20+ Yr Trsy Bull 3X ETF (TMF)
2010	3	5.90%	9.66%	18.90%	24.58%	-6.73%
2010	4	7.31%	7.94%	4.08%	6.09%	9.96%
2010	5	-2.74%	-4.08%	-24.15%	-22.85%	16.54%
2010	6	0.70%	-1.91%	-16.58%	-18.88%	16.73%
2010	7	8.09%	9.55%	21.17%	21.80%	-3.90%
2010	8	7.05%	4.45%	-13.46%	-15.12%	25.94%
2010	9	9.72%	18.28%	27.94%	43.14%	-9.02%
2010	10	-1.05%	3.77%	11.44%	19.55%	-13.57%
2010	11	-3.60%	-3.62%	-0.82%	-1.43%	-6.03%
2010	12	3.59%	2.21%	21.36%	14.81%	-11.63%
2011	1	-1.69%	-0.29%	6.56%	8.01%	-9.40%
2011	2	7.20%	6.92%	10.39%	9.14%	4.49%
2011	3	-0.79%	-1.49%	-0.80%	-2.35%	-0.55%
2011	4	7.59%	7.62%	8.73%	8.58%	6.57%
2011	5	3.52%	2.68%	-3.93%	-4.31%	10.36%
2011	6	-6.76%	-7.19%	-5.87%	-7.01%	-7.39%
2011	7	4.73%	8.64%	-6.39%	4.43%	13.28%
2011	8	4.40%	2.80%	-21.09%	-19.54%	27.34%
2011	9	12.29%	12.21%	-20.69%	-14.31%	41.35%
2011	10	8.70%	10.38%	32.61%	31.54%	-12.87%
2011	11	0.45%	-2.98%	-3.35%	-10.15%	4.89%
2011	12	5.66%	3.03%	2.30%	-2.83%	9.46%
2012	1	6.81%	13.35%	13.90%	26.86%	-1.50%
2012	2	2.66%	6.75%	13.24%	20.14%	-7.95%
2012	3	-1.93%	1.89%	9.29%	15.46%	-13.02%
2012	4	6.25%	4.60%	-2.38%	-4.30%	14.37%
2012	5	6.65%	3.07%	-17.35%	-20.45%	28.90%
2012	6	2.31%	2.37%	11.47%	9.79%	-5.78%
2012	7	7.57%	6.64%	3.52%	2.28%	11.43%
2012	8	1.41%	6.23%	6.53%	16.09%	-4.61%
2012	9	-0.95%	-2.63%	7.52%	2.14%	-7.87%
2012	10	-4.68%	-9.20%	-5.96%	-15.63%	-2.13%
2012	11	2.69%	3.53%	1.01%	3.19%	3.90%
2012	12	-3.10%	-4.73%	2.82%	-1.93%	-7.80%
2013	1	1.73%	-0.56%	15.39%	7.65%	-9.58%
2013	2	3.25%	1.92%	3.56%	0.59%	3.39%
2013	3	4.16%	3.73%	11.03%	8.74%	-1.77%
2013	4	10.17%	10.42%	5.45%	6.94%	14.25%
2013	5	-6.76%	-3.76%	6.80%	10.71%	-19.65%
2013	6	-8.11%	-9.12%	-5.23%	-8.02%	-10.33%
2013	7	4.21%	7.01%	16.41%	20.14%	-7.41%
2013	8	-6.16%	-3.02%	-9.21%	-1.69%	-4.47%
2013	9	5.77%	8.54%	9.60%	14.91%	1.53%
2013	10	8.78%	9.66%	13.76%	14.70%	4.12%
2013	11	0.04%	1.51%	8.87%	10.34%	-8.19%
2013	12	0.54%	1.77%	7.54%	8.86%	-6.01%
2014	1	5.43%	5.95%	-10.72%	-6.36%	19.47%
2014	2	7.49%	8.84%	13.65%	15.40%	1.63%
2014	3	1.15%	-3.54%	2.15%	-8.37%	1.76%
2014	4	3.63%	1.77%	1.65%	-2.03%	5.96%
2014	5	8.28%	11.26%	6.62%	13.50%	8.79%
2014	6	2.68%	4.47%	6.22%	9.46%	-1.00%
2014	7	-0.71%	2.36%	-4.44%	3.05%	1.61%
2014	8	13.51%	14.97%	11.95%	15.47%	14.42%
2014	9	-5.47%	-4.62%	-4.44%	-2.78%	-6.65%
2014	10	7.14%	7.28%	6.03%	6.58%	8.06%
2014	11	9.18%	11.81%	8.34%	14.30%	9.08%
2014	12	3.73%	0.54%	-1.54%	-7.51%	9.38%
2015	1	11.92%	11.14%	-9.47%	-6.95%	31.01%
2015	2	-0.64%	3.39%	17.48%	22.74%	-17.87%
2015	3	-1.33%	-2.68%	-5.28%	-7.46%	2.57%
2015	4	-3.97%	-2.21%	2.59%	5.16%	-10.30%
2015	5	-2.29%	-0.45%	3.43%	6.35%	-7.91%
2015	6	-9.61%	-9.96%	-6.21%	-7.65%	-12.49%
2015	7	10.50%	13.38%	6.17%	13.35%	13.40%
2015	8	-10.60%	-12.45%	-18.87%	-21.28%	-2.75%
2015	9	-1.40%	-1.83%	-8.64%	-8.13%	5.10%
2015	10	12.63%	18.66%	26.79%	37.23%	-1.73%
2015	11	-1.00%	-0.61%	0.81%	1.31%	-2.71%
2015	12	-4.12%	-4.17%	-6.06%	-5.77%	-2.41%
2016	1	1.54%	-2.61%	-15.38%	-21.13%	17.74%
2016	2	3.43%	0.99%	-1.68%	-6.04%	8.71%
2016	3	9.86%	10.67%	21.50%	20.97%	-0.64%
2016	4	-1.65%	-6.15%	0.81%	-9.56%	-2.39%
2016	5	3.80%	7.61%	4.65%	12.84%	1.86%
2016	6	10.45%	6.02%	-0.20%	-7.83%	21.23%
2016	7	9.34%	14.68%	11.13%	22.52%	6.07%
2016	8	-1.61%	-0.14%	0.11%	2.99%	-3.58%
2016	9	-2.28%	0.76%	-0.54%	5.80%	-4.78%
2016	10	-9.58%	-8.76%	-5.62%	-4.61%	-13.32%
2016	11	-8.01%	-10.82%	11.05%	1.10%	-23.91%
2016	12	2.07%	0.89%	5.96%	2.60%	-0.99%
2017	1	4.03%	8.96%	5.14%	15.76%	1.49%
2017	2	8.09%	9.11%	11.91%	13.39%	4.41%
2017	3	-0.89%	1.83%	-0.22%	5.64%	-2.35%
2017	4	4.04%	6.34%	2.77%	8.07%	4.43%
2017	5	5.05%	8.45%	3.70%	11.43%	5.17%
2017	6	1.04%	-3.28%	1.51%	-8.07%	1.98%
2017	7	2.02%	5.42%	5.87%	12.56%	-2.43%
2017	8	5.77%	7.46%	0.21%	5.04%	10.13%
2017	9	-1.62%	-4.02%	5.69%	-1.06%	-7.29%
2017	10	3.50%	6.94%	6.83%	13.74%	-0.53%
2017	11	4.88%	3.71%	8.87%	5.50%	1.73%
2017	12	4.11%	3.02%	3.45%	1.18%	5.04%
2018	1	4.27%	9.85%	18.22%	27.70%	-9.77%
2018	2	-10.90%	-7.79%	-13.53%	-6.16%	-9.57%
2018	3	-0.07%	-3.00%	-8.69%	-13.42%	8.44%
2018	4	-3.60%	-3.42%	-0.14%	-0.42%	-6.71%
2018	5	6.63%	11.41%	6.46%	17.00%	5.27%
2018	6	1.46%	1.85%	1.29%	2.18%	1.49%
2018	7	2.41%	1.72%	10.73%	7.56%	-4.70%
2018	8	6.74%	10.86%	9.09%	17.69%	3.36%
2018	9	-4.23%	-5.02%	1.20%	-1.60%	-8.77%
2018	10	-15.11%	-18.27%	-20.78%	-26.61%	-9.11%
2018	11	3.99%	0.74%	4.28%	-2.91%	4.76%
2018	12	-3.15%	-5.51%	-26.25%	-26.84%	17.93%
2019	1	11.82%	14.29%	23.89%	26.92%	0.41%
2019	2	2.00%	2.33%	9.28%	8.57%	-4.52%
2019	3	11.68%	13.88%	4.85%	11.05%	17.00%
2019	4	2.55%	5.59%	11.81%	16.64%	-6.56%
2019	5	1.68%	-2.51%	-18.89%	-24.01%	21.11%
2019	6	11.30%	12.95%	21.37%	23.00%	1.90%
2019	7	2.16%	3.40%	3.80%	6.20%	0.32%
2019	8	15.15%	12.65%	-6.62%	-7.79%	35.11%
2019	9	-2.49%	-3.34%	5.30%	1.88%	-9.07%
2019	10	1.07%	4.55%	5.70%	12.43%	-4.11%
2019	11	4.17%	5.43%	10.73%	12.20%	-2.01%
2019	12	-1.05%	1.17%	8.38%	11.37%	-10.05%
2020	1	12.72%	15.63%	-0.91%	8.19%	23.80%
2020	2	-1.19%	-0.77%	-23.04%	-17.77%	17.91%
2020	3	-15.93%	-14.28%	-48.13%	-38.13%	11.91%
2020	4	19.80%	25.60%	37.17%	46.45%	2.68%
2020	5	3.37%	6.67%	13.38%	18.63%	-6.48%
2020	6	2.94%	9.67%	3.23%	17.98%	0.54%
2020	7	15.65%	17.91%	17.70%	22.25%	13.13%
2020	8	3.68%	11.31%	22.05%	35.17%	-14.89%
2020	9	-5.21%	-8.86%	-12.26%	-18.88%	2.15%
2020	10	-9.60%	-10.31%	-8.48%	-10.28%	-10.35%
2020	11	18.93%	20.10%	35.20%	34.54%	4.24%
2020	12	4.38%	6.77%	11.14%	15.05%	-2.32%

Portfolio return and risk metrics
Metric	Maximum Return at 22.25% Volatility	Maximum Sharpe Ratio Weights
Arithmetic Mean (monthly)	2.58%	3.32%
Arithmetic Mean (annualized)	35.72%	48.06%
Geometric Mean (monthly)	2.38%	3.04%
Geometric Mean (annualized)	32.57%	43.32%
Volatility (monthly)	6.40%	7.60%
Volatility (annualized)	22.18%	26.33%
Downside Deviation (monthly)	3.37%	3.70%
Max. Drawdown	-20.03%	-26.10%
US Market Correlation	0.53	0.62
Beta^(*)	0.80	1.12
Alpha (annualized)	19.41%	23.77%
R²	27.88%	38.73%
Sharpe Ratio	1.37	1.49
Sortino Ratio	2.59	3.05
Treynor Ratio (%)	38.07	35.22
Calmar Ratio	1.74	1.97
Active Return	18.35%	29.10%
Tracking Error	19.07%	20.68%
Information Ratio	0.96	1.41
Skewness	-0.16	-0.02
Excess Kurtosis	0.49	0.13
Historical Value-at-Risk (5%)	-8.92%	-9.16%
Analytical Value-at-Risk (5%)	-7.91%	-9.13%
Conditional Value-at-Risk (5%)	-11.62%	-12.18%
Upside Capture Ratio (%)	123.46	177.44
Downside Capture Ratio (%)	30.25	56.81
Safe Withdrawal Rate	34.15%	41.83%
Perpetual Withdrawal Rate	22.97%	28.67%
Positive Periods	87 out of 130 (66.92%)	87 out of 130 (66.92%)
Gain/Loss Ratio	1.38	1.48
^* US stock market is used as the benchmark for calculations. Value-at-risk metrics are based on monthly values.

Drawdowns for Maximum Return at 22.25% Volatility

Drawdowns for Maximum Return at 22.25% Volatility (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Aug 2016	Nov 2016	4 months	Jun 2017	7 months	11 months	-20.03%
2	Feb 2015	Sep 2015	8 months	May 2016	8 months	1 year 4 months	-19.01%
3	Sep 2018	Oct 2018	2 months	Mar 2019	5 months	7 months	-18.70%
4	Feb 2020	Mar 2020	2 months	May 2020	2 months	4 months	-16.93%
5	May 2013	Aug 2013	4 months	Jan 2014	5 months	9 months	-16.21%
6	Sep 2020	Oct 2020	2 months	Nov 2020	1 month	3 months	-14.31%
7	Feb 2018	Apr 2018	3 months	Aug 2018	4 months	7 months	-14.17%
8	Jun 2011	Jun 2011	1 month	Aug 2011	2 months	3 months	-6.76%
9	Sep 2012	Dec 2012	4 months	Mar 2013	3 months	7 months	-6.05%
10	Sep 2014	Sep 2014	1 month	Oct 2014	1 month	2 months	-5.47%
Worst 10 drawdowns included above

Drawdowns for Maximum Sharpe Ratio Weights

Drawdowns for Maximum Sharpe Ratio Weights (worst 10)
Rank	Start	End	Length	Recovery By	Recovery Time	Underwater Period	Drawdown
1	Sep 2018	Dec 2018	4 months	Apr 2019	4 months	8 months	-26.10%
2	Oct 2016	Nov 2016	2 months	Apr 2017	5 months	7 months	-18.63%
3	Sep 2020	Oct 2020	2 months	Dec 2020	2 months	4 months	-18.26%
4	Mar 2015	Sep 2015	7 months	Mar 2016	6 months	1 year 1 month	-16.87%
5	Feb 2020	Mar 2020	2 months	Apr 2020	1 month	3 months	-14.94%
6	Feb 2018	Apr 2018	3 months	Aug 2018	4 months	7 months	-13.62%
7	Sep 2012	Jan 2013	5 months	Apr 2013	3 months	8 months	-13.29%
8	May 2013	Jun 2013	2 months	Oct 2013	4 months	6 months	-12.54%
9	Jun 2011	Jun 2011	1 month	Jul 2011	1 month	2 months	-7.19%
10	Apr 2016	Apr 2016	1 month	May 2016	1 month	2 months	-6.15%
Worst 10 drawdowns included above

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	31.52%	44.23%	118.49%	-25.15%	-60.44%	0.84	1.34	0.99
TQQQ	ProShares UltraPro QQQ	52.68%	51.82%	139.73%	-19.80%	-49.12%	1.07	1.95	0.92
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	15.79%	39.42%	109.14%	-39.01%	-49.74%	0.54	1.04	-0.46

Monthly Correlations

Correlations for the portfolio assets
Ticker	Name	UPRO	TQQQ	TMF	Maximum Return at 22.25% Volatility	Maximum Sharpe Ratio Weights
UPRO	ProShares UltraPro S&P500	1.00	0.93	-0.45	0.54	0.64
TQQQ	ProShares UltraPro QQQ	0.93	1.00	-0.39	0.56	0.75
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	-0.45	-0.39	1.00	0.50	0.31

Portfolio Risk Decomposition

Portfolio risk decomposition
Ticker	Name	Maximum Return at 22.25% Volatility	Maximum Sharpe Ratio Weights
UPRO	ProShares UltraPro S&P500	43.42%
TQQQ	ProShares UltraPro QQQ	9.81%	77.61%
TMF	Direxion Daily 20+ Yr Trsy Bull 3X ETF	46.78%	22.39%

Annual Asset Returns

Rolling returns summary
Roll Period	Maximum Return at 22.25% Volatility			Maximum Sharpe Ratio Weights
Roll Period	Average	High	Low	Average	High	Low
1 year	32.63%	81.38%	-13.35%	43.04%	106.88%	-10.27%
3 years	27.41%	42.77%	11.55%	35.70%	53.66%	18.45%
5 years	26.73%	43.52%	16.76%	34.94%	52.25%	25.13%
7 years	27.13%	32.56%	20.41%	35.65%	46.51%	27.18%
10 years	30.53%	31.94%	28.44%	40.18%	43.47%	36.39%