Autocorrelation In Vanguard Mutual Funds

by: Dane Van Domelen

When present, autocorrelation provides an excellent basis for trading strategies.

After stumbling upon autocorrelation in Vanguard’s high-yield mutual fund, I decided to test all 119 of Vanguard’s funds.

Of the 88 funds operating for the past 10 years, 11 exhibit substantial positive autocorrelation (Pearson r > 0.4).

Trading strategies are promising, but there are some logistical issues.

Autocorrelation: My Intuition is typically wrong

One of my first interests when I got into stock market analysis was the idea of autocorrelation. Intuitively, I thought there might be a tendency for investors to overreact to positive or negative news for a company. When Amazon (NASDAQ:AMZN) gains 15% after hours on a relatively minor earnings beat, for example, you get the feeling that a good portion of that surge is unwarranted, and might be given back in the coming week, months, or even on the next day.

Not really. Since its IPO in 1997, there is no correlation between AMZN gains on one day and the next (Pearson r = 0.007, p = 0.64).

What about the US stock market - maybe there's a tendency for overreactions there? It wouldn't even have to be overreactions. It could just be momentum, i.e. investors feeling increasingly emboldened by a string of positive gains.

Wrong again. The S&P 500 actually exhibits some anti-momentum. Since inception in 1993, there has been significant negative autocorrelation in SPY gains (Pearson r = -0.063, p < 0.001). That correlation corresponds to an R-squared value of 0.004, which means that only 0.4% of SPY's price movement is explained by the prior day's gain. As Bernie Sanders might say: It's not good enough!

In the scatterplot below, you can see the meager autocorrelation in AMZN and SPY. There's a lot of noise, and not much signal.

Figure 1. Autocorrelation in daily gains for AMZN and SPY.

Autocorrelation in Vanguard mutual funds

Recently, I stumbled upon evidence of potentially useful autocorrelation in Vanguard's high-yield mutual fund, VWEHX. Since inception in 1980, the Pearson correlation is a respectable 0.137 (p < 0.001), corresponding to an R-squared of 0.019.

That got me thinking, why not look at Vanguard's entire line-up of mutual funds, and see which funds exhibit the strongest and most consistent autocorrelation?

Of the 119 mutual funds listed on Vanguard's website (it says "126 matching funds" at the top of the page, but only 119 are listed), I decided to look at the subset of 88 funds that have been available for at least 10 years, going back to March 30, 2007.

The figure below shows the autocorrelation in each of these 88 funds over the past 10 years, sorted from most positive to most negative.

Figure 2. Autocorrelation in daily gains for 88 Vanguard mutual funds.

Of the 88 funds, autocorrelation was positive for 19 and negative for 69. The 11 left-most funds in the graph had surprisingly high autocorrelations, and are summarized in Table 1.

Table 1. Summary of 11 Vanguard funds with highest autocorrelation from March 30, 2007, to March 31, 2017.
Ticker Fund Autocorrelation
VNYTX Vanguard New York Long-Term Tax-Exempt Fund Investor Shares 0.455
VCITX Vanguard California Long-Term Tax-Exempt Fund Investor Shares 0.446
VWAHX Vanguard High-Yield Tax-Exempt Fund Investor Shares 0.437
VWEHX Vanguard High-Yield Corporate Fund Investor Shares 0.433
VWLTX Vanguard Long-Term Tax-Exempt Fund Investor Shares 0.431
VOHIX Vanguard Ohio Long-Term Tax-Exempt Fund 0.426
VCAIX Vanguard California Intermediate-Term Tax-Exempt Fund Investor Shares 0.420
VMATX Vanguard Massachusetts Tax-Exempt Fund 0.419
VPAIX Vanguard Pennsylvania Long-Term Tax-Exempt Fund Investor Shares 0.409
VWITX Vanguard Intermediate-Term Tax-Exempt Fund Investor Shares 0.408
VNJTX Vanguard New Jersey Long-Term Tax-Exempt Fund Investor Shares 0.404

Ten of the 11 are tax-exempt funds, including 7 state tax-exempt funds. The only non-tax-exempt fund is the high-yield fund VWEHX.

As I said earlier, I'm looking for strong, but also consistent, autocorrelation. So let's look at these funds' autocorrelations over the entire 10-year period, using a 50-day moving window. For simplicity, I'll include just two of the state tax-exempt funds, California long-term and Massachusetts.

Figure 3. 50-day autocorrelation over time for select Vanguard mutual funds, using data from March 30, 2007, to March 31, 2017. This is really promising, as all of the funds exhibit autocorrelation very consistently over time. For example, VCITX's autocorrelation was positive 98.8% of the time.

I don't really have any experience with tax-exempt bond funds, so I would tend to favor the one non-tax-exempt fund, VWEHX. This high-yield bond fund was the one that tipped me off on autocorrelation to begin with.

So let's take a closer look at VWEHX. In the autocorrelation scatterplot below, you can see that there is a definite linear association between one day's gain and the next.

Figure 4. Autocorrelation in daily gains for VWEHX.

For one final visual, let's try to improve the signal-to-noise ratio here and look at how the average VWEHX daily gain varies across quantiles of the prior day's gain. (The quantiles are deciles, but there are 7 rather than 10 groups because 0% gains were very common.) As you can see below, there is a clear tendency for VWEHX to average stronger growth following days of positive growth.

Figure 5. Mean +/- 95% CI for VWEHX

Where autocorrelation comes from...

I don't really know what the source of autocorrelation is for VWEHX and certain tax-exempt Vanguard mutual funds. I initially thought it could be an artifact of the timing of dividend distributions, but I would expect that to result in negative autocorrelation, not positive.

One possibility is simply that the dividend yield of these funds fluctuates over time. When the yield is relatively higher, there will tend to be days of higher growth clustered together, which could show up in positive correlation. But that effect would likely occur for all bond funds, not just 11 of 88.

Overall, my sense is that there's something about the tax-exempt mutual funds that makes them exhibit considerable positive autocorrelation. Maybe Seeking Alpha commenters can shed light on this. Whatever the source of autocorrelation is, hopefully it's a truly predictive indicator, and not just an artifact of how these funds operate.

...and what we can do with it

An obvious strategy would be to hold these funds following days of positive growth. For example, over the past 10 years, if you had held VWEHX only following days of positive growth, and held cash otherwise, you would have enjoyed annualized growth of 13.5%, more than double VWEHX's buy-and-hold rate of 6.2%.

But there are a few problems. First, these are mutual funds, so the net asset value is posted after hours each trading day. Once you find out whether a fund had positive or negative growth for a given day, the best you can do is submit a buy order that will be executed at the end of the next trading day. In other words, you completely miss the trading day where you expect a boost from autocorrelation.

Interestingly, there is still considerable autocorrelation when you look at gains shifted by 2 days rather than 1. For VWEHX, the 1-day autocorrelation over the past 10 years is 0.433, and the 2-day autocorrelation is 0.281. So a strategy where you submit a buy order following a loss, and realize the change 2 days later, could still be profitable. But even then, Vanguard's frequent trading policy for its mutual funds might get in the way of implementing this strategy.

One potential solution would be to trade the corresponding ETF for VWEHX or the various tax-exempt funds that exhibit autocorrelation. Unfortunately, ETF versions of these 11 funds do not exist. There is one tax-exempt ETF, Vanguard Tax-Exempt Bond ETF (NYSEARCA:VTEB), but it has not exhibited autocorrelation since inception in Aug. 2015 (Pearson r = -0.076, p = 0.13).

In closing, here are some of my current thoughts on autocorrelation-based strategies, which I plan to explore further in future articles:

  1. Develop trading strategy with Vanguard mutual funds based on 2-day autocorrelation, using all 11 funds with high autocorrelation to get around the frequent trading policy.
  2. Look at month to month rather than day to day autocorrelation, to get around Vanguard's policy, but also to limit trading frequency and associated costs in general.
  3. See whether autocorrelation is present in high-yield and tax-exempt funds/ETFs in general, or is unique to Vanguard's mutual funds.
  4. Identify one or more ETFs, in any area, that exhibits strong and consistent autocorrelation.

Disclosure: I am/we are long VWEHX. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

Additional disclosure: The author used Yahoo Finance to obtain historical stock prices and used R (including the "quantmod", "stocks", and "dvmisc" packages) to analyze the data and generate figures. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.