Phillip Guerra
June 12, 2016
Alt-Robo Portfolio Manager & Anesthesiologist with U.S. Anesthesia Partners

Here's an easy way you can use Statistics to improve your returns

How many investment companies or financial advisors use the power of Statistics to cross-validate their models? Most firms I can think of promote their backtests based on the same data available from Yahoo, Google, Ycharts, etc. So we end up wondering if their models are really just over-optimized, overfitted curves, and succumb to lookback bias. But hey this is the 21st century, and we have have the technology and the knowledge to do more.

Being trained in medicine, I can say this:  the equivalent in medicine of backtesting just using the one, original empirical data set that we all can get on Yahoo Finance, etc would merely be a "Case Report on one patient" - i.e. what physicians would consider the weakest of evidence . One patient a trend doth not make. Imagine if I started to administer a new drug on you or a new treatment algorithm that was based on the anecdotal results of just one, singular patient only .  Not cool.

As investors, we should probably take page from medicine's playbook and only use advisors that refer to studies using data from hundreds of patients  on both a retrospective and prospective basis to be able to say "I practice evidence-based investing."

So here's an easy way you can use Statistics to improve your risk-adjusted returns. Below, I show the formula to create new data sets for yourself that allow you to adjust the mean and the standard deviation of randomly-sampled, empirical data so you can apply bootstrap estimates to your own models and see if they have a shot at working in the future :

Figure 1. Formula to specify mean and standard deviation from a data set.
SD Mean Shift Formula
Where Zi = the adjusted sample and c1 = the desired variance and c2 = the desired mean while Xi, Xbar, and sigmaX are derived from the usual formulas of mean and SD.
 
Below, I randomly re-sample with replacement at a daily resolution the 20-yr empirical data set from 1996-2016 and apply the above formula to create 100 new, 20-yr data sets that intentionally have a worsened mean and SD as many finance pros believe may occur over the next 10 years. Then I apply the same quant models our firm uses for our clients today and run them 100 times over each new data set which yields these results:

Table 1. Results of bootstrapped estimates of Physician Capital Partner's portfolio metrics. 
Bootstrap Stats Active5710
 
To be sure, using Statistics does not guarantee success in the future; it only allows an investor to get an idea for the likelihood of success - which may or may not happen no matter what the p-values are.  

However at a minimum, we can at least get a better idea if the above results could have been simply due to chance alone (i.e. luck).  Here's how to read the statistical inference below: "Because the 99% confidence intervals of the mean Sharpe ratios do not overlap each other when comparing between 60/40 and 'Active5,7, or 10' (i.e. the name of our quant portfolios and their volatility targets at the 5%,7%, and 10% level), it is reasonable to conclude that the means are truly different when alpha level = 0.01." i.e. another way to say it: "It is unlikely that the observed differences are due to chance alone."
 
Table 2. Sharpe Ratios and their confidence intervals at the 99% level.
Bootstrap T-Test
 

Figure 2. Bootstrapped equity curves.
 
 
 
Figure 3. Histogram of return data from one, data set iteration.
Bootstrap Histogram of returns

Using:

1) Statistics derived from medicine's research methodology along with
2) offering liquid-alternative, quantitative investment strategies via
3) a low-fee, robo-advisor platform

...are the fundamental ways  how Physician Capital Partners differentiates itself from the crowd.
 
Physician Capital Partners is a low-fee, autonomous, liquid-alternative robo-advisor founded by a physician and CFA charterholder that offers high-performance, quantitative hedge fund strategies designed to protect and grow capital regardless of the direction of GDP and inflation. For family offices, institutions, non-profits, and individual investors who want an alternative asset with value, dynamic algorithms, and low equity correlation.

Loading PDF

Loading PDF

More from Phillip Guerra