# Testing the Equity Mutual Fund Liquidity Ratio

March 31, 2014 • **Posted in** Mutual/Hedge Funds, Sentiment Indicators

A reader requested an 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 to measure the aggregate mutual fund liquidity ratio. However, only the most recent survey results and past year-end values of the liquidity ratio are publicly available. Monthly values are available with a lag of about one month. Norman Fosback adjusts the raw liquidity ratio 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 raw liquidity ratio from ICI for interest rates by debiting the contemporaneous 13-week U.S. Treasury bill (T-bill) yield. Using January and February closes of the S&P 500 index and year-end values of the equity mutual fund liquidity ratio and T-bill yield during December 1984 through February 2014 ( about 30 years), *we find that:*

The following chart summarizes year-end equity mutual fund raw and adjusted liquidity ratios over the entire sample period. It shows that the raw liquidity ratio has been relatively low in recent years, and the adjusted liquidity ratio (ALR) has sometimes been negative since the mid-1990s. The average year-end ALR is 2.5% over the sample period. It appears the fund managers allow ALR to drift toward zero during extended bull markets (or, alternatively, bear markets shock managers into maintaining a higher cash reserve).

To measure the power of ALR to predict stock returns, we use a linear regression.

Since ICI measures the liquidity ratio monthly, we first consider monthly returns. Since there is a one-month lag in reporting, we test the power of year-end ALR to predict the S&P 500 Index return for the ensuing February (end of January to end of February).

The following scatter plot relates S&P 500 Index February return to preceding year-end ALR during 1985 through 2014. The Pearson correlation for this relationship is 0.22 and the R-squared statistic 0.05, indicating that ALR explains 5% of the variation in February returns.

Does the same result hold for an annual rather than monthly horizon?

The next scatter plot relates S&P 500 Index end of January-to-end of January annual return to preceding year-end ALR during 1985 through 2014. The Pearson correlation for this relationship is 0.23 and the R-squared statistic is again 0.05, indicating that ALR explains 5% of the variation in annual returns. Results suggest that ALR changes slowly over time.

Does this tendency translate into a useful market timing strategy?

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 four scenarios:

- Hold the index (T-bills) when the prior year-end ALR is above 3% (ALR > 3%).
- Hold the index (T-bills) when the prior year-end ALR is above 2% (ALR > 2%).
- Hold the index (T-bills) when the prior year-end ALR is above 1% (ALR > 1%).
- Buy and hold the S&P 500 Index.

Calculations ignore dividends and (infrequent) trading frictions, both to the disadvantage of buy-and-hold.

The value of the timing strategy is extremely sensitive to the ALR threshold. Moreover, an investor operating in real time (truly out-of-sample) may have had great difficulty deciding what threshold to use early in the sample period.

In summary, *evidence from simple tests on a small sample supports little 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 very small for confident inference. Excluding a single extreme observation materially affects statistics. The sample is too small to test for non-linearity in the relationship between ALR and future returns. A full set of monthly inputs may be illuminating.
- As noted, excluding dividends and trading frictions from the market timing test puts the buy-and-hold benchmark at a disadvantage.
- Some other way of adjusting raw liquidity ratio for interest rates may produce different results.

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