- Vanguard's VISVX had a beta loading of 0.94, while DFA's DFSVX's loading on beta was 1.0. We should expect both to have betas of close to one, with DFSVX's slightly higher loading being explained by its owning smaller stocks, which tend to have higher betas. The slightly higher beta should contribute to higher returns, as beta's annual premium was 5.4 percent.
- Given the Morningstar data we examined, it shouldn't be a surprise that VISVX had a lower size-loading than did DFSVX—0.58 versus 0.82. The higher size-loading for DFSVX should contribute to higher returns, as the size premium was 5.4 percent.
- DFSVX also had a somewhat higher value loading, 0.65 versus 0.62 for VISVX. The slightly higher value-loading should make a small contribution to returns, as the value premium was 3.9 percent.
- It's typical that value funds will have negative loadings on the momentum premium. And that's the case here, as both funds had slightly negative loadings—DFSVX (-0.07) and VISVX (-0.10). The small negative loadings subtracted from both of their returns—a bit more from VISVX, in fact—as the momentum premium was 4.1 percent.
- The r-squareds were very high in both cases—0.93 for VISVX and 0.96 for DFSVX. That tells us that the model is doing a very good job of explaining the variability in the returns of the two funds.
As you should expect of a pure index fund, VISVX's alpha was slightly negative, at -0.01 percent per month, a bit less than its expense ratio of 0.22 percent. DFSVX's alpha was slightly positive, at 0.04 per month—and to generate its alpha, it had to overcome a higher expense ratio—0.52 percent.
The alpha might have been generated from the various screens DFA employs, or from its patient trading strategy. Or it might be a result of the fact that the value premium is actually largest in the smallest stocks, which DFSVX owns more of. Whatever the source, DFA's fund construction and implementation strategies added to returns beyond just the contribution from the higher loading factors.
Before moving on, it's important to note that some of the alpha is related to the greater securities-lending revenue DFSVX generates, which is mainly due to the fact that the smaller stocks it owns tend to command greater fees when they are lent out.
Relative to VISVX, in each case, DFSVX's returns benefited from its different factor loadings: The higher beta-loading contributed 0.32 percent to its returns (5.4 percent x .06); the higher size-loading contributed 1.30 percent (5.4 percent x .24); the higher value-loading contributed 0.12 percent (3.9 percent x 0.3); and the less negative momentum-loading contributed 0.12 percent (4.1 percent x 0.03).
The total relative benefit from the loadings on the four factors was 1.86 percent. The benefits of the higher loadings, along with the contribution from the alpha the fund generated, explain the difference in returns between the two funds.
Even though the two funds are both small-cap value funds, and both are "passively" managed, over the period 1999-2013, DFSVX returned 12.28 percent per annum, while VISVX returned 10.03 percent per annum. It's also important to note that, as you would expect from a fund owning much smaller and deeper value stocks, DFSVX experienced greater volatility—its annual standard deviation was 24.1 percent versus 19.7 percent for VISVX.
However, the higher returns more than compensated for the higher volatility, as the Sharpe ratio for DFSVX was 0.53 versus 0.49 for VISVX.
Until now, we've only looked at how the funds performed in isolation. However, as Harry Markowitz demonstrated, the right way to consider any investment is to consider how its addition impacts the risks and returns of the overall portfolio. Thus, we'll now turn our attention to how the addition of these two funds would have impacted the performance of a balanced portfolio.
Our base case is Portfolio A. Its holdings are 60 percent S&P 500/40 percent 5-year Treasury notes. Portfolio B keeps the same 60/40 allocation, but splits the equity portion equally: 30 percent S&P 500 and 30 percent DFSVX. Portfolio C splits the equity portion equally between the S&P 500 and VISVX. Portfolio D lowers the equity allocation to 50 percent, splitting it 30 percent S&P 500 and 20 percent DFSVX, while increasing the bond allocation to 50 percent 5-Year Treasury Notes.