unstable

Bridgeway Capital Management: A Deeper Look at The Performance

unstable

Multi-factor investing is slowly becoming a more common investment strategy among professional investment management firms. These firms, more informally known as "quants," use statistical models to understand the common factors that drive performance in markets around the world. By structuring strategies that focus on these factors, managers can increase the expected return of their portfolios relative to traditional benchmarks.

We at IFA have been investing our clients' money this way since the founding of our firm, now 18 years ago. The earliest pioneer of multi-factor investing was Dimensional Fund Advisors. By following a passive and disciplined approach to structuring their strategies around the known dimensions of expected return, which include the market, size, relative-price, and profitability, they have been able to deliver excess returns over traditional benchmarks for their clients.

Investment management firm Bridgeway Capital Management also follows a quantitative approach to their own investment strategies. Their homepage even includes the tagline of, "statistically driven, evidence-based investing."

Founded in 1993 and based in Houston, TX, the firm currently manages $7.7 Billion in assets across 13 separate strategies that focus on the size and relative-price (value) premiums as well as attempt to capture the benefits of low volatility and momentum in separate strategies.

Today, we are going to take a deep dive into Bridgeway's performance to see how it stacks up against not only their Morningstar assigned benchmarks, but also their  excess return once we adjust for their exposure to the market, size, and relative-price factors that have been shown to be priced risk factors (also known as betas) in the market. We will conclude our analysis with a comparison to Dimensional and explain why not all multi-factor investing is the same. 

Fees & Expenses

Our analysis begins with an examination of the costs associated with the strategies. It should go without saying that if investors are paying a premium for investment management, then they should be receiving above average results consistently over time. The alternative would be to simply accept a market's return, less a significantly lower fee, via an index fund.

The costs we examine include expense ratios, front end (A), level (B) and deferred (C) loads, and 12b-1 fees. These are considered the "hard" costs that investors incur. Prospectuses, however, do not reflect the trading costs associated with mutual funds. Commissions and market impact costs are real costs associated with implementing a particular investment strategy and can vary depending on the frequency and size of the trades taken by portfolio managers. We can estimate the amount of cost associated with an investment strategy by looking at its annual turnover ratio. For example, a turnover ratio of 100% means that the portfolio manager turns over the entire portfolio in 1 year. This is considered an active approach and investors holding these funds in taxable accounts will likely incur a higher exposure to tax liabilities to short term and long term capital gains distributions relative to those incurred by passively managed funds.

The table below details the hard costs as well as the turnover ratio for all 9 strategies offered by Bridgeway that have at least 3 years of complete performance history. You can search this page for a symbol or name by using Control F in Windows or Command F on a Mac. Then click the link to see the Alpha Chart. Also remember that this is what is considered an in-sample test, the next level of analysis is to do an out-of-sample test ( for more information see here ).

Fund Name Ticker Turnover Ratio % Prospectus
Net Expense
Ratio
Global Category
Bridgeway Managed Volatility BRBPX 54.00 0.95 Long/Short Equity
Bridgeway Small-Cap Growth BRSGX 137.00 0.94 US Equity Small Cap
Bridgeway Small-Cap Momentum N BRSMX 184.00 0.91 US Equity Small Cap
Bridgeway Ultra-Small Company Market BRSIX 41.00 0.84 US Equity Small Cap
Bridgeway Omni Tax-Managed Sm-Cp Val N BOTSX 29.00 0.60 US Equity Small Cap
Bridgeway Small-Cap Value BRSVX 62.00 0.94 US Equity Small Cap
Bridgeway Omni Small-Cap Value N BOSVX 24.00 0.61 US Equity Small Cap
Bridgeway Ultra-Small Company BRUSX 101.00 1.27 US Equity Small Cap
Bridgeway Aggressive Investors 1 BRAGX 124.00 0.63 US Equity Mid Cap

Performance Analysis

The next question we address is whether investors can expect superior performance in exchange for the higher costs associated with Bridgeway's management. We compare each of the 3 strategies that have at least 3 years of performance history and against its current Morningstar assigned benchmark to see just how well each has delivered on their perceived value proposition. We have included relative return charts for each strategy at the bottom of this article. Here is what we found:

  • 33% (3 funds) have underperformed their respective benchmarks since inception, having delivered a NEGATIVE relative return
  • 67% (6 funds) have outperformed their respective benchmarks since inception, having delivered a POSTIVE relative return
  • 0% (0 funds) have outperformed their respective benchmarks consistently enough since inception to provide 97.5% confidence that such outperformance will persist as opposed to being based on random outcomes

Based on the historical performance of their strategies, it seems that Bridgeway has done quite well in terms of delivering outperformance for their investors. 2 out of every 3 funds produced an average return above their benchmark. But there has been much variability around their relative return, leading all of their funds to have a statistically insignificant outperformance. In other words, we have a low degree of confidence that this outperformance will persist into the future. The inclusion of statistical significance is key to this exercise as it indicates which outcome is the most likely vs. random-chance.

Regression Analysis

How we define or choose or benchmark is extremely important, especially for funds that are targeting the known dimensions of expected return. If we relied solely on commercial indices assigned by Morningstar, then we may lead to the false conclusion that Bridgeway has a better set of rules. Because Morningstar is limited in terms of trying to fit the best commercial benchmark with each fund in existence, there is, of course, going to be some error in terms of matching up proper characteristics such as average market capitalization or average price-to-earnings ratio.

A better way of controlling for these possible discrepancies is to run multiple regressions where we account for the known dimensions (Betas) of expected return in the US (market, size, relative price, etc.). For example, if we were to look at all of the US-based strategies from Bridgeway that have been around for at least the last 10 years, we could run multiple regressions to see what their relative returns look like once we control for the multiple betas that we know are being systematically priced into the overall market. The chart below displays the average relative return and the standard deviation of that difference for the last 10 years ending 12/31/2016.

As you can see, for all Bridgeway strategies with at least 10 years of performance history, the entire relative return diminished once we controlled for risk exposure to factors. Not a single fund produced an excess return that was statistically significant at the 97.5% confidence level (green shaded area). Why is this important? It means that if we wanted to simply replicate their risk exposure, we could do so more cost-effectively through the use of other funds that capture those factors at a lower cost. With lower costs, we could have more confidence that we will experience a more desirable result.

Comparison with Dimensional

We have shown that Bridgeway's performance can be attributed to their overall exposure to the known dimensions of expected return. The last part of our analysis is to dissect their risk exposure in an attempt to highlight the difference in approaches to targeting risk premiums.

First, if we were to compare the 3-factor regressions of Bridgeway's Ultra-Small Company Fund (BRUSX) and Dimensional's Micro Cap (DFSCX) strategy over the 10-year period ending 12/31/2016, you will notice a trend. Dimensional's strategies have more relative-price (HML) exposure compared to that of Bridgeway. They have similar size exposure (SmB), but Bridgeway has significantly more sensitivity to the overall market (MKT-B).

Data Series Symbol Annualized Return α t(α) MKT-B SmB HmL Adj R�
Bridgeway Ultra-Small Company BRUSX 4.24 -0.36% -1.51 1.14 0.89 0.05 0.88
DFA US Micro Cap I DFSCX 7.63 0.00% 0.05 0.99 0.91 0.30 0.98

Over the last 10-years, the value premium within small-cap stocks has actually been negative, which should harm Dimensional's performance more since they have more exposure to the relative price factor. If we compared the performance of the Russell 2000 Growth Index to the Russell 2000 Value Index for the 10-year period ending 12/31/2016, you will see that small-cap growth stocks have outperformed small-cap value stocks by 1.50% per year.

Index 10-Year Return as of 12/31/2016
Russell 2000 Growth Index 7.76%
Russell 2000 Value Index 6.26%

The size premium (SmB) has actually been a wash over the last 10 years. The performance of the Russell 1000 Index and the Russell 2000 Index has almost been identical.

Index 10-Year Return as of 12/31/2016
Russell 1000 Index 7.08%
Russell 2000 Index 7.07%

Given these data points, we would expect Bridgeway's Ultra-Small Company Fund would have outperformed DFA's Micro Cap Fund. Surprisingly, DFA outperformed Bridgeway by 3.39% per year . How could this be?

When Bridgeway targets risk factors, they do so in a very concentrated way. Their current holdings indicate just over 100 different securities. This concentration comes with additional risk, most of which is idiosyncratic (firm-specific risk), which is not expected to compensate investors with an additional return. This explains why Bridgeway is much more sensitive to the overall market (MKT-B). 

On the other hand, Dimensional takes a much more diversified approach, which increases the reliability of capturing the premiums they are seeking in the marketplace. We have written on this topic before in our article Targeting Premiums & Diversification . The DFA U.S. Micro Cap Fund currently holds 1,546 different companies. This diversification has worked well for investors in terms of capturing the risk premiums both Bridgeway and Dimensional are seeking in their strategies.

We can do a similar analysis between the Bridgeway Small Cap Value Fund and the DFA Small Cap Value Fund over the 10-year period ending 12/31/2016. The regression results are below. We see that DFA has outperformed by 1.35% per year ; although, DFA should have been penalized for their increased exposure to the relative-price factor, which didn't provide a positive premium over this time. 

Data Series Symbol Annualized Return α t(α) MKT-B SmB HmL Adj R�
Bridgeway Small-Cap Value BRSVX 5.47 -0.20% -1.03 1.10 0.67 0.14 0.89
DFA US Small Cap Value I DFSVX 6.82 -0.05% -0.76 1.06 0.85 0.48 0.99

Omni Funds

(The following was taken from the Bridgeway website) "The Bridgeway Omni Small-Cap Value Fund uses a market capitalization weighted approach to invest in a broad and diverse group of small-cap stocks that Bridgeway Capital Management determines to be value stocks. This approach is sometimes referred to as "passive, asset-class investing." Use of the term "omni" in the name refers to the fact that the Fund intends to provide risk and return characteristics similar to investing in a basket of stocks in a specific asset class. The Fund is designed to be an excellent complement to core strategies used by advisors with a long-term evidence-based investing approach.

The Fund uses a market capitalization weighted approach to invest in a broad and diverse group of small-cap stocks that Bridgeway determines to be value stocks. For investment purposes, "small-cap stocks" are defined as companies that have a market capitalization generally in the lowest 15% of total market capitalization or smaller than the 1000th largest U.S. company, whichever results in the higher capitalization. "Value stocks" are those that Bridgeway determines are priced cheaply relative to some financial measures of worth, such as the ratio of price to book value, price to earnings, price to sales, or price to cash flow. This approach is sometimes referred to as "passive, asset-class investing." Use of the term "Omni" in the name refers to the fact that the Fund intends to provide risk and return characteristics similar to investing in a basket of stocks in a specific asset class. This strategy is designed to complement core strategies used by advisors who favor a long-term passive investment approach."

Based on this description, 5 years of data is not enough to evaluate the expected return of this fund.  To do this, you would need long-term historical returns for the factors embedded in the fund. Our analysis is just comparing live data with the Morningstar benchmarks. 

Conclusion

Although the vast majority of strategies offered by Bridgeway have outperformed their Morningstar assigned benchmark, this entire excess return can be explained once we control for the known dimensions of expected return. Further, it is important to note that not all multi-factor investing is created equal. Bridgeway takes a more concentrated approach while Dimensional takes a more diversified approach. As we have shown, the diversified approach increases the reliability of capturing the premiums that both are seeking as the concentration is likely to increase the overall risk of a strategy without additional expected return. 

Here are the individual charts for the Bridgeway funds we analyzed using actual returns and Morningstar assigned benchmarks.

 

 

 

 

 

 

 

 

 


 

Here is a calculator to determine the t-stat. Don't trust an alpha or average return without one.

 

The Figure below shows the formula to calculate the number of years needed for a t-stat of 2. We first determine the excess return over a benchmark (the alpha) then determine the regularity of the excess returns by calculating the standard deviation of those returns. Based on these two numbers, we can then calculate how many years we need (sample size) to support the manager's claim of skill.