In this blog and overall, I have been an advocate of common sense investing, investing in low-cost diversified three-fund portfolio with small-cap value tilt, as I detailed in this blog post as well. This already suggests, in addition to the well-known and commonly adopted 3-fund portfolio (commonly adopted by reasonable investors only), adding small-cap-value tilt increases returns. As I read new books, I thought maybe we really can do even better by changing asset allocation. And by this, I’m not talking about invest-in-bitcoin craziness or invest-in-next-unicorn mania, I’m talking about still sticking to investing basics, using low-cost diversified funds, but tilting it towards small-cap-value funds.
Of course, giving it the benefit of doubt, I still needed to test these claims. In this post, I will go through several suggestions in this book and other articles, back-test them, and see if they really end up with higher returns, measure their risk, and see if it is really worth changing asset allocation.
Why Tilt Towards Small-Cap-Value?
- Based on Fama and French 3-factor model, small-cap stocks outperform large-cap stocks in the long run, and value stocks outperform growth stocks. Combining these two premiums (size premium and value premium), small-cap-value stocks results in higher returns in the long term.
- Based on Paul Merriman’s book First Time Investor, between 1926-2011, S&P500 index (a proxy for large-cap stock fund, which has a performance similar to US total stock fund), has returned 9.3%, where US small-cap-value fund returned 14.4%.
- Based on William Bernstein’s book The Intelligent Asset Allocator, between 1926-1998, small-cap stocks (not value) returned 12.18%, as opposed to 11.2% return of large-cap stocks. Moreover, investing in value stocks results in higher returns, referred to as value premium.
All these findings combined, we are off to our investigation into SCV impact on portfolios.
Assumptions
First off, let’s go remind some assumptions for readers who may not have read the previous posts:
- It is correct that past returns are not an indicator of future returns, for the short-term. But, for the long-term, the confidence interval around the return (a proxy for the risk of investment) decreases. Therefore, when back-testing a portfolio in this post, we will post results of the longest time frame we can (the historical length of different funds vary.). As a good rule of thumb, returns for more than 20 years (and ideally 30 years) of a fund are reliable, and have low standard deviation.
- This post will go through many alternative portfolios, which may or may not perform better than a 3-fund portfolio, or even if it does, the extra returns may not be worth the new portfolio complexity. We will go through this later in the post.
- In all back-tests below, dividends and distributions are re-invested, and returns are not adjusted for inflation.
- We are always rebalancing portfolios annually, that is a constant across all portfolios.
Experiment 1: Small-Cap-Value or not to Small-Cap-Value
Let’s test our proposal to use 3-fund portfolio plus small-cap-value first. The baseline will be 3-fund portfolio, and treatment will be 3-fund portfolio + SCV.
- Baseline: 3-fund portfolio:
- VTSAX: 60%
- VTIAX: 30%
- VBTLX: 10%
- Treatment: 3-fund portfolio + SCV:
- VTSAX: 40%
- VTIAX: 20%
- VBTLX: 10%
- VSIAX: 30%
Before running the back-test, here are a couple of notes:
- Treatment portfolio has kept VTSAX : VTIAX allocation proportional to baseline portfolio (60:30 vs. 40:20), in order to reserve 30% to VSIAX (Small-cap-value fund). Bond allocation (VBTLX) is the same for both portfolios, 10%.
- When we run the back-test below, the first thing to point out is that, the cumulative set of funds in baseline / treatment portfolios only have 8 years of history, which is way below 20 years, which is assumed to be the duration of a fund for its returns to have low standard deviation, and hence be more reliable. We will keep this in mind.
In this back-test, both portfolios start with $100K, and have no regular contribution, but they have annual rebalancing. Start / end balance, annualized return and standard deviation of both portfolios are shown in the table below. Full details are available here.
| Metric | Baseline: 3-fund | Treatment: 3-fund + SCV |
| Start Balance | $100,000 | $100,000 |
| End Balance | $323,548 | $323,941 |
| Annualized Return | 12.46% | 12.47% |
| Standard Deviation | 11.90% | 12.79% |
Annual returns of both portfolios, based on data from January 2012 – December 2021, 10 years in total, are similar: 12.46% vs. 12.47%. So, we didn’t get the small-cap-value premium yet. This may be because:
- This 10-year history has not seen a single recession (assuming the Covid recession between March-July 2020 was a short one, resulting in 20% downturn.)
- 10 years is not a long term in personal finance, when calculating annual returns. We need longer time horizons.
What happens in the longer term? For this, we will compare the same two portfolios, with one tweak: Instead of using specific funds (which limits the time period and hence our data), we will use asset classes:
- Baseline: 3-fund portfolio:
- US stock market: 60%
- International stock market: 30%
- US bond market: 10%
- Treatment: 3-fund portfolio + SCV:
- US stock market: 40%
- International stock market: 20%
- US bond market: 10%
- US small cap value: 30%
Comparison of these two portfolios are available here. Start / end balance, annualized return and standard deviation of both portfolios are shown in the table below, and growth of both portfolios over time are shown in the figure below. Notice that, this time, we go from 1986 to December 2021, a time period of 35 years.
| Metric | Baseline: 3-fund | Treatment: 3-fund + SCV |
| Start Balance | $100,000 | $100,000 |
| End Balance | $2,234,758 | $2,903,992 |
| Annualized Return | 9.28% | 10.10% |
| Standard Deviation | 13.50% | 13.94% |
As you see in the table and figure above, this time it is different: Based on the data from 1986 to December 2021, the second fund with 3-fund portfolio + SCV fund tilt returns 10.10% annual returns, compared to 9.28% of 3-fund portfolio. Over 35 years, this results in 30% increase in the end balance ($2,903,992 / $2,234,758 = 1.2994). Now, with 35 years of data, we do see the small-cap-value premium.
Experiment 2: What about mid-cap-value?
Next, we experiment with 3-fund portfolio (baseline) vs. baseline plus Small-cap-value tilt vs. baseline plus Mid-cap-value tilt:
- Baseline: 3-fund portfolio:
- US stock market: 60%
- International stock market: 30%
- US bond market: 10%
- Treatment: 3-fund portfolio + SCV:
- US stock market: 40%
- International stock market: 20%
- US bond market: 10%
- US small cap value: 30%
- Treatment: 3-fund portfolio + MCV:
- US stock market: 40%
- International stock market: 20%
- US bond market: 10%
- US mid cap value: 30%
Comparison of these three portfolios are available here. Start / end balance, annualized return and standard deviation of both portfolios are shown in the table below, and growth of both portfolios over time are shown in the figure below. Notice that, this time, we go from 1987 to December 2021, a time period of 34 years.
| Metric | P1: 3-fund | P2: 3-fund + SCV | P3: 3-fund + MCV |
| Start Balance | $100,000 | $100,000 | $100,000 |
| End Balance | $2,234,758 | $2,903,992 | $2,850,316 |
| Annualized Return | 9.28% | 10.10% | 10.04% |
| Standard Deviation | 13.50% | 13.94% | 13.54% |
Based on the table and figure above, 3-fund portfolio + mid-cap-value returns 10.04%, whereas 3-fund portfolio + small-cap-value returns 10.10%, using the data from 1987 to December 2021. The difference in annual returns is 0.06%. Over 34 years, this results in 1.8831% increase in the end balance ($2,903,992 / $2,850,316 = 1.018831). Maybe there is not much difference between MCV and SCV. This could be because most of the small-cap-value premium might be coming from the common denominator of MCV and SCV: the V, value premium.
One more observation in the experiment result above: 3rd portfolio with MCV tilt is has returns that is 0.06% below the 2nd portfolio with SCV tilt. But, take a look at the standard deviation: 3rd portfolio’s std (with MCV), 13.54% is very close to the std of 1st portfolio (3-fund portfolio), 13.50%. And 2nd portfolio (with SCV) has the highest std, 13.94%.
Let’s now compare SCV tilt, MCV tilt, and V tilt. The first portfolio has 30% in SCV, 2nd portfolio has 30% in MCV, and 3rd portfolio has 30% in V (Value). Comparison results are here, along with the summary of results in the table and figure below.
| Metric | P1: 3-fund + SCV | P2: 3-fund + MCV | P3: 3-fund + V |
| Start Balance | $100,000 | $100,000 | $100,000 |
| End Balance | $2,903,992 | $2,850,316 | $2,735,923 |
| Annualized Return | 10.10% | 10.04% | 9.92% |
| Standard Deviation | 13.94% | 13.54% | 13.52% |
The results suggest that the returns of these 3 portfolios are very close: 1st portfolio with SCV tilt returns 10.10%, 2nd portfolio with MCV tilt returns 10.04%, 3rd portfolio with V tilt returns 9.92%, all significantly higher compared to baseline 3-fund portfolio return from the previous experiment, which is 9.28%.
Experiment 3: Asset Allocation for SCV
Now that we back-tested and showed the value of SCV, we now want to know how much to allocate to SCV in our portfolio. To simplify calculations, we will make the following assumptions in the coming experiments:
- We will replace 3-fund portfolio with US stock market, which is essentially the 3-fund portfolio with 100% allocated to US stock market, and none allocated to International stock market and US total bond fund. With this change, we will create SCV tilt with US stock market as the baseline, with increasing allocation to US smal-cap-value fund.
- We will experiment with extremes first (0% vs. 100% in SCV), and then find a middle ground.
First we compare 100% US total market vs. 100% SCV. Comparison results are here.
| Metric | P1: US stock market | P2: US SCV |
| Start Balance | $100,000 | $100,000 |
| End Balance | $17,857,238 | $70,436,739 |
| Annualized Return | 10.93% | 14.01% |
| Standard Deviation | 15.57% | 18.25% |
Summary of results show significant difference between returns of US stock market and US SCV between 1972-2021, a period of 47 years. US SCV return is 14.01% compared to 10.93% of US stock market, more than 300 basis points higher. Over 47 years, this difference in annual growth rate results in around 4x higher end balance ($70,436,739 / $17,857,238 = 3.9444). If the investor is young enough, it makes sense to invest in SCV. But some may be more risk averse, so, we will try a mix of US stock market and US SCV in the next experiment:
- Portfolio 1: 75/25 – US stock market / US SCV
- Portfolio 2: 50/50 – US stock market / US SCV
- Portfolio 3: 25/75 – US stock market / US SCV
Comparison of these portfolios are here, along with the summary of results in the table and figure below.
| Metric | P1: 75/25 US / US SCV | P2: 50/50 US / US SCV | P1: 25/75 US / US SCV |
| Start Balance | $100,000 | $100,000 | $100,000 |
| End Balance | $26,711,507 | $38,352,223 | $52,960,595 |
| Annualized Return | 11.82% | 12.63% | 13.37% |
| Standard Deviation | 15.86% | 16.43% | 17.24% |
Summary of results show significant difference between returns of these portfolios, as US / US SCV ratio moves from 75/25 to 50/50 to 25/75: returns are 11.82%, 12.63%, 13.37% respectively.
That is to say, depending on the risk you need to / have the ability to take, increased US SCV allocation results in significant returns over the long term.
Conclusion
There is academic evidence from different articles and books that SCV tilt on 3-fund portfolio results in higher returns. As we have shown in our experiments, in the short term, the premium with SCV tilt may not be visible, e.g. in time periods of bull market. But in the long term, as the standard deviation of portfolios decrease and annual return rate values have smaller confidence interval, experiments show that SCV tilt results in more than 300 basis points compared to US stock market, with increased risk. Depending on the risk profile of the investor, SCV allocation in a portfolio results in significant end balance increase in the long term, more than 4x in 47 years. While many don’t observe SCV premium in their short investing history, the patient investor will benefit from the SCV premium in the long term.