Pair Trading Lab: Analysis VKQ vs VMO

From:

2025-05-13

To:

2026-05-12

HQ Analysis of VKQ / VMO

Symbol	Title	Sector	Industry	M.Cap.[M]	Div Yield	Last Close	AvgVol 200d
VKQ	Invesco Municipal Trust	Financial Services	Asset Management	542	0	9.79	209738
VMO	Invesco Municipal Opportunity Trust	Financial Services	Asset Management	658	0	9.82	258469

Orthogonal Spread Analysis

Here we apply an orthogonal regression (also known as total least squares) to both price series. We are interested in some key statistical properties (like β, ...) and in analysing orthogonal residuals:

TLS: VKQ^*(t) = β * VMO^*(t) + α

Regression coefficient α:

0.162722

Regression coefficient β:

0.983408

Standard Deviation (σ):

0.036123

ADF test of residuals (p-value):

0.0015

95% confidence: residuals don't contain a unit root

99% confidence: residuals don't contain a unit root

Mean Reversion Coefficient (MRC):

-0.252351

Half-life:

2.75

Skewness:

-0.2480

Kurtosis:

-0.3411

Doornik-Hansen normality test (p-value):

0.0782

Normality test failed at 95% confidence

Shapiro-Wilk normality test (p-value):

0.0838

Normality test failed at 95% confidence

Cointegration Analysis

In this section, Engle-Granger cointegration test is performed using OLS regression method in both directions. Residuals of the regression are plotted and analyzed further:

VKQ / VMO

VMO / VKQ

Profit Analysis

Profit analysis is a set of backtests performed using multiple pair trading models over significant portion of parameter space. Backtest results are displayed in a form of scatter plot. In addition, you can see aggregated statistics in the left panel. All backtests are performed using 100% margin (leverage 1:1). This is the profit analysis where backtested strategies are allowed to open both long and short positions:

VKQ / VMO

VMO / VKQ

This is the profit analysis where backtested strategies are allowed to open long positions only:

VKQ / VMO

VMO / VKQ

This is the profit analysis where backtested strategies are allowed to open short positions only:

VKQ / VMO

VMO / VKQ

Profit Analysis (Inverted!)

This profit analysis has been performed using strategies with inverted signals and transformed prices. Mostly useful for trading pairs composed of an inverse ETF in order to stay market-neutral (more info). "even" means that the first leg is both inverted and transformed, "odd" means that the first leg is transformed but the second leg is inverted.

Backtested strategies have been allowed to open both long and short positions:

This is the profit analysis where backtested strategies are allowed to open long positions only:

This is the profit analysis where backtested strategies are allowed to open short positions only:

Disclaimer: Backtested, simulated or hypothetical performance results have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. There are numerous factors related to the stock market in general and to the implementation of any stock market timing program, which cannot be fully accounted for in the preparation of hypothetical performance results. The backtested results listed here do not take into consideration slippage, fees, taxes, or dividends and interest earned on cash positions. These factors would affect actual trading results. Simulated, backtested or hypothetical stock trading systems in general are also subject to the fact that they are designed with the benefit of hindsight. Backtested performance does not represent actual performance and should not be interpreted as an indication of such performance. No representation is being made that you will or is likely to achieve profits or losses similar to these being shown. This site provides impersonal educational stock trading information, and therefore, no consideration can or is made toward your financial circumstances. All material presented within is not to be regarded as investment advice, but for general informational purposes only.

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Orthogonal Spread Analysis

Cointegration Analysis

Profit Analysis

Profit Analysis (Inverted!)