A reader requested evaluation of the Fosback Index and its Ned Davis variant. The creators of these indicators argue that a high (low) ratio of cash equivalents to assets among equity mutual funds indicates strong (weak) potential demand for stocks. The Investment Company Institute (ICI) surveys mutual fund managers monthly (with a lag of about a month) to measure the aggregate equity mutual fund liquidity ratio (LR). Only past year-end values of LR are readily available. Norman Fosback adjusts raw LR based on current interest rates, reasoning that mutual fund managers have more (less) incentive to hold cash when interest rates are high (low). We adjust the effect of interest rates via linear regression of annual LR against year-end yield of the 3-month U.S. Treasury bill (T-bill). We then define the difference between raw and adjusted values as Excess LR and relate this variable to annual returns of the Fidelity Fund (FFIDX) as a proxy for U.S. stock market total performance. Using year-end values of aggregate equity mutual fund LR from the 2015 Investment Company Fact Book, Table 15, year-end T-bill yield and annual returns for FFIDX during December 1984 through December 2014 ( 30 years), *we find that:*

The following chart relates year-end aggregate equity mutual fund LR to year-end T-bill yield over the available sample period. Results suggest a strong linear relationship, with R-squared statistic 0.62, meaning that variation in T-bill yield explains 62% of the variation in LR. The formula relating the two variables enables calculation of an adjusted LR for a given T-bill yield.

How do raw and adjusted LRs compare over time?

The next chart shows the trajectories of year-end raw equity mutual fund LR, T-bill yield and adjusted LR over the available sample period. Since T-bill yield generally declines, so do the measures of LR. The baseline value of adjusted LR (when T-bill yield is zero) is about 3.4%. There are times when raw LR compared to adjusted LR is “too high” or “too low.”

For another perspective, we plot the mismatch between raw and adjusted LR.

The next chart shows raw minus adjusted LR (Excess LR) by year over the available sample period. Results suggest that equity mutual funds in aggregate held too much cash in the early 1990s, not enough cash in the late 1990s and mid-2000s and too much cash at the end of 2008. After 2008, Excess LR is close to zero.

How does Excess LR relate to stock market performance?

The next chart summarizes correlations between annual Excess LR and annual FFIDX returns over the available sample period for various lead-lag relationships, ranging from FFIDX return leads Excess LR by four years (-4) to Excess LR leads FFIDX return by four years (4). Results suggest that:

- Negative correlations for years -3 through 0 suggest that a strong (weak) stock market tends to lower (raise) Excess LR.
- Positive correlations for lags 1 through 4 suggest that a high (low) Excess LR tends to precede a strong (weak) stock market the next few years.

The strongest indication is that Excess LR leads stock market return by two years.

A sample of 30 years is very small for this kind of analysis, so confidence in findings is low.

Do these findings support useful stock market timing?

The final chart tracks the cumulative values of $100,000 initial investments at the end of January 1985 in the S&P 500 Index for three scenarios:

- FFIDX: buy and hold FFIDX (FFIDX).
- Time FFDIX +1: hold FFIDX (T-bills) when Excess LR at prior year-end is positive (negative).
- Time FFIDX +2: hold FFIDX (T-bills) when Excess LR two years ago is positive (negative).

Calculations ignore any costs of exiting and re-entering FFIDX.

Results suggest that market timing based on Excess LR suppresses volatility and may improve performance. Compound annual growth rates are 9.4%, 7.8% and 10.4%, respectively, for the above three scenarios. Annual Sharpe ratios are about 0.43, 0.42 and 0.71. Time FFDIX +1 (Time FFIDX +2) is in the stock market about 59% (55%) of the time.

This test has the following weaknesses:

- As noted above, given data variability, the sample period is short for reliable inference.
- This test is in-sample, impounding look-ahead bias from the initial regression in the first chart above. An investor would not have been able to calculate Excess LR in real time. The sample is not long enough for out-of-sample testing.
- There is data snooping bias in selection of a two-year lag between Excess LR and market returns. In other words, a two-year lag may be lucky. Small samples amplify this bias.

In summary, *evidence from simple in-sample tests on a small sample supports some belief that the equity mutual fund liquidity ratio is useful for timing the U.S. stock market.*

Cautions regarding findings include:

- As noted, given the variability of data (especially annual returns), the sample is small for confident inference. Excluding a single extreme observation materially affects statistics.
- As noted, the market timing test is in-sample (impounding look-ahead bias), and the optimal lag between Excess LR and future stock market returns impound snooping bias.
- As noted, Excess LR has little to say about future stock market performance over the last six years.
- Some other way of adjusting raw liquidity ratio for interest rates may produce different results.

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