The great rotation out of bonds into stocks appears to be slated for at least a step back over the next 10 months. Over the last 15 months, the yield on the 10-year Treasury bond has risen substantially and stocks also rose substantially. This is very consistent with the notion of the great rotation where people sell bonds and buy stocks. In the coming few months, the correlation between the monetary base and bond yields suggest bond yields will fall. The unusual correlation between the T-Bill yield and the T-Bond yield that only happens when the T-Bill yield is below about 0.5% also suggests bond yields will fall. It is a mathematical identity that if bond yields fall bond prices go up. Given the correlation between bond yields and stock prices over the last 10 years, a drop in bond yields also implies a headwind to stock prices, if not a drop.

The path to this conclusion started with a chart in a recent John Hussman article. The second chart in the article showed a correlation between the 3 month T-bill yield and the monetary base relative to GDP. I became curious whether there was a lead time in the correlation. I was a bit surprised to find the strongest correlation came with the T-Bill yield leading the monetary base by 3 months.

Each blue dot on the scatter plot above represents the T-Bill average yield for one month and the monetary base as a percent of GDP three months earlier. The yield in the chart is plotted on a logarithmic scale where a doubling from 0.1% to 0.2% is the same distance as a doubling from 10% to 20%. This allows the exponential best fit to be shown as a straight red line rather than the curved fit Hussman shows in his chart. The same data is plotted in a time-series format on the right of the chart where the T-Bill yield is in blue and the monetary base in red. The red monetary base scale is inverted to show that the yield gets lower as the monetary base becomes a bigger percent of GDP.

Given the three month lead time and the high correlation, it would seem the T-Bill has a strong influence on the monetary base or something else like the Fed has a big influence on both. I was hoping to find the opposite where the monetary base had a leading influence on T-Bill yields and could be used to predict a change in the yield. I then became curious if the relationship was the same for T-Bonds. It was not: the monetary base leads T-Bond yields by 9 months. Also it was a power fit rather than an exponential fit.

The T-Bond yield like the T-Bill yield above is plotted on a logarithmic scale, but the scatter plot still shows a curvilinear fit with the monetary base. To show this power fit on the time series plot (on the right in the chart above), I use a log scale for the T-Bond yield (black) and an inverted log scale (red) for the monetary base.

There are several observations worth noting. The previous historical low yield for the 10 year Treasury was in January 1941 at 1.95%. This low roughly lines up with the monetary base high (low on chart). The monthly average of the 10 year yield hit its all-time low of 1.53% in July 2012 and rose to 2.82% in September 2013. The timing of these moves is roughly aligned with declines (rise on the chart) in the monetary base. The rise of the monetary base to all-time highs now suggests the 10 year T-Bond yield will decline to at least June of 2014. Since the last point on the red monetary base line is at an all-time high (low on chart) the timing for a bottom in yields has not yet been indicated.

The 3 month lag with T-Bills and 9 month lead with T-Bonds launched a new inquiry. How could the difference in lead times be 12 months when the correlation between T-Bills and T-Bonds is strongest on a concurrent basis? I then wondered if it would be different if I compared the log of the two yields. On this basis, the highest correlation comes with the T-Bill yield leading 10 months.

*(click to enlarge*)

It appears that when the T-Bill yield is below about 0.5% (or perhaps it is the monetary base above 1.25% of GDP) that the relationship between T-Bill and T-Bond yields changes. This change shows up more easily using the log of the yields since it gives greater emphasis to yields at low levels. For example, the T-Bill yield move from 0.02% in September 2013 to 0.05% in October would move as much on the log scale as moving from 8% to 20%. With the 10 month lead time, that 0.02% September low suggests the long bond yield will trend down till about July 2014. Below is a look at the correlation since 2010.

The last point on the black line shows the average T-Bond yield for October at 2.62%. While the yield is up in November, it has remained below the September high. This correlation suggests the T-Bond will decline, but not fall below the low from last year, whereas the monetary base could be interpreted to indicate a new low will be made.

**Rising Yields Bad for Stocks?**

Sometimes a rising bond yield is good for stocks and sometime it's bad. The correlation flip-flops. The biggest indicator I have found of whether bond yields and stock prices are positively or negatively correlated is the level of the interest rate. When the 10-year yield is above 4.8%, the correlation tends to be negative where a rising yield is bad for stocks. When the yield is below 4.8%, a rising yield is likely to be good for stocks. Below is a chart showing the correlation coefficient of stocks and the 10-year T-Bond yield in black along with the bond yield in red.

Calculation of points on the black line is based on the previous 24 monthly changes in stock prices and T-Bond yields. The black vertical axis for the correlation coefficient or "R" goes from -1 to 1. If "R" were at 1.0, it would mean that in the previous 24 months each monthly change in the stock index goes the same direction as the change in bond yields and that the ratio of the changes were the same for all 24 months. An "R" of -1 would mean bond yields and stock prices moved in opposite directions by a constant proportion in each of the last 24 months. As "R" gets closer to zero, there would be an increasing mix of months that had both positive and negative correlations.

The last point on the black line plotted at October 2013 had an R of 0.42. So in the last 2 years, stocks prices and bond yields tended to move the same direction. If you squared the correlation coefficient, you would get the coefficient of determination or R-squared. The square of 0.42 is 0.18, so about 18% of the variation in stock prices the last two years appears to be explained by changes in bond yields.

Below is a look at the S&P 500 and the 10-year yield during the last 4 years. The 4 multi-month stock declines all came with declining yields. These declines are shaded in pink. The two biggest rises in yields, shaded in green, corresponded with significant stock advances.

**Low Interest Rates Imply Overvalued Stocks**

Interest rates are below the level that historically corresponds with the highest stock market values. Below is a scatter plot of the 10-year T-Bond yield and the PEses. Each point on the chart represents the 10 -year T-Bond yield and the valuation of the S&P 500 for a given month. The last month with full data, October, is highlighted in green.

In previous versions of this chart, I had plotted the optimal interest rate at 5.5% which is closer to the yield at the peak of the tech bubble in 2000. Since the correlation between stocks and bonds inverts around 4.8%, as noted above, I now think 4.8% is the optimal level for stock valuation and the tech bubble was even larger than I previously thought since it occurred while interest rates were above the optimal level.

October's PEses was 42.6; the best fit line suggests the 2.62% yield in October would normally have a PEses of 19.4. From this perspective, the market was about 54% overvalued in October. In contemplating this apparent overvaluation, I was curious if an elevated monetary base explained the difference. Here is the scatter plot with the two periods of an elevated monetary base: the one associated with the great recession is in orange, the one starting in the Great Depression in purple.

Most of the orange dots have a higher valuation than the historical norm for a given bond yield. A majority of the purple dots fall below the best fit line showing a lower valuation. On the basis of these two periods, an elevated monetary base resulting from aggressive Fed policy does not inherently keep stocks at elevated values.

Here is a time series chart with the PEses in blue and the estimate of PEses from the bond yield red fitted lines.

For the last couple of years, the percentage gap between the PEses estimated from bond yields and the actual PEses has been larger than any time in history. This could mean we are in a bigger bubble than the tech bubble in 2000.

**Conclusion**

The leading influences of the monetary base and the T-Bill yield suggest the long bond yield will decline during the next 8 to 10 months. Stocks appear to be priced as though the T-Bond yield was at its optimal level of 4.8%. Since bond yields and stock prices tend to be positively correlated when the yield is below 4.8%, the likely decline in bond yields would be a headwind for stocks.

Stocks (NYSEARCA:SPY) have averaged unusually high valuations since 1996 as measured by the PEses. I have been expecting a return to a valuation more consistent with the historical level. A falling bond yield could be part of the catalyst to reduce valuations. If a recession were to start in the next few months, the great rotation could go into full reverse where bond yields fell to new lows and the stock market took out its 2009 low.

As I write, the 10 year T-Bond yield is at 2.79%. This is up significantly from the average yield in October and could be an attractive entry point to buy bonds (NYSEARCA:TENZ), (NYSEARCA:TLH), (NYSEARCA:TLT), (NASDAQ:VGLT). This may also be an attractive time to lighten up in equities, especially if the S&P 500 fails to meaningfully penetrate 1800. While stock prices could push higher or remain elevated for some time, the downside in the next three years appears to vastly outweigh the upside.

**Disclosure: **I am short SPY. 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:** There is no guarantee analysis of historical data their trends and correlations enable accurate forecasts. The data presented is from sources believed to be reliable, but its accuracy cannot be guaranteed. Past performance does not indicate future results. This is not a recommendation to buy or sell specific securities. This is not an offer to manage money.