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.

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.

Bootstrap Active5,7,10 (1-50)

Bootstrap Active5,7,10 (51-100)

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.

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