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  MAPE – A Critical Comparison
P/E ratio for stock market valuation is affected by interest rates, inflation and monetary policies
Purpose
With US equity market indexes at an all-time high, it’s controversial over whether stocks are over-valued, fair market, or under-valued. The most commonly-used measure of the value of a share or market, Cyclically-Adjusted Price-Earnings (CAPE), was popularized by Yale University professor Robert Shiller; awarded the Nobel Prize for Economic Sciences in 2013.
 
Two divisions formed, the Shillerites and non-Shillerites, argued that CAPE did not take into account the effect of interest rates; especially the post 2008 monetary policy shift that influenced movements in interest rates. An argument could be made that CAPE is adjusted for inflation, and since the Federal Reserve Monetary Policy has an important influence on inflation, the effect of interest rates directly influenced inflation, respective the CAPE calculation.

MAPE, or the Monetary-Adjusted Price-Earnings ratio described here, builds on the widely accepted CAPE algorithm. MAPE is constructed by amending the CAPE ratio with three variables for inflation, long-term interest rate shifts, and foreign exchanges values. MAPE's intent is to correct the CAPE measure of stock market valuation affected by the interest rates and inflation.
MAPE Methodology
MAPE is a valuation measure generally applied to broad equity indices by using adjusted per-share earnings over a 10-year period with current levels for the equity indices.

The MAPE ratio is calculated by taking the annual Earnings Per Share (EPS) of an equity index such as the S&P 500 for the past 10 years. The MAPE algorithm adjusts these earnings for shifts in inflation using the CPI for long-term interest rate changes using the yield on 10 year Treasuries, and for foreign exchanges fluctuations using the Trade-Weighted Dollar Index. When we take the average of these adjusted EPS figures over the 10-year period and divide the current level of the S&P 500 by the 10-year average adjusted EPS number, it yields the MAPE ratio as follows:

MAPE = P /  Avg10y { E  *  [ CPI / Avg2y(CPI)  /  (10yT / Avg5y(10yT))  /  (TW$ / Avg1y(TW$)) ] ​}​​
Where:
  • P is the current indices value;
  • Avg10y is the 10 year average; Avg5y is the 5 year average; Avg2y is the 2 year average; Avg1y is the 12 month average;
  • E is the indices annual EPS;
  • 10yT is the yield on 10 year Treasuries;
  • TW$ is the Trade-Weighted Dollar Index
Observations
The figure below depicts the plots for Professor Shiller’s CAPE ratio and the new MAPE ratio. This comparative analysis yields several stark observations regarding market values during the years indicated.
  1. Managing Director

  1. In the early 1980’s interest rates climbed at an exorbitant rate in a short period of time from 8% to 15%. It happened literally overnight. The plot above shows that the high inflation era was characterized by substantial market undervaluation as the CAPE ratio languished below the MAPE ratio. This continued until 1994 when both ratios converged and simultaneously the MAPE and CAPE indices exhibited similar movements indicating the market adjusted itself to the inflation of the earlier years establishing a new “Fair” value. 
  2. MAPE and CAPE 1994 convergence is followed by a period with large P/E expansion that spiked above 45. From early 1994 till beginning of 2010, both ratios indicated similar market valuation. The figure above shows a shift from a state of undervaluation to valuation exceeding the previous high;
  3. Both ratios signaled the 2000 “dot-com” crash and the more recent 2008 financial crisis;
  4. From 2004 till 2006, the CAPE-MAPE divergence indicated a slight market overvalue. This “light” overvalue points to the fact that the central bank monetary policy was not a significant cause of the financial crisis; a statement that reflects Former Federal Reserve Chairman Alan Greenspan's conclusions.
  5. In early 2010, after QE1 concluded, MAPE and CAPE started to diverge again. In this case, the difference between the MAPE-CAPE indices can be viewed as a measure of market overvaluation as compared to the level of interest rates.
      

The information these two methods yield when overlaid, offer similar outputs for most of the historical data when equity markets are subject to traditional monetary policies.  When equity markets are subject to a shift in Federal Reserve policies, the changes in financial conditions affect economic activity or equity valuations as indicated in this comparison.

Of note is that the comparison between the MAPE-CAPE graphs illustrates the P/E valuation divergence subject to the monetary policy shift. However, there are other factors that affect market valuation and are emphasized by the behavior of investors. The results plotted in the figure above reinforce the effect of irrational investing relevant to 2000 and 2008 which was also prevalent for that period of time.
Conclusion
Between late 2008 and October 2014 the Federal Reserve undertook nontraditional monetary policy measures to provide additional support to the economy. The primary purpose of these purchases was to help improve economy-wide demand in an attempt to influence overall financial conditions.  The P/E divergence characterized by the MAPE-CAPE plots indicates that instead, the monetary policies may have distorted asset classes valuations.  This would lead the analyst to derive today that investors are being deceived by low interest rates and low inflationary environment into believing that stock markets are cheap!

Ultimately, comparing MAPE-CAPE ratios highlights market valuation is being corrupted by interest rates. This comparison simply rationalizes the need for a meter that forecasts future valuation movements. Further development of convergence-divergence indices between MAPE and CAPE indicators can be used to determine improvements of traditional P/E ratio accuracy in signaling market tops or bottoms as a result of expected monetary policy effects.

Going forward, the return on stock market valuation could be influenced by a shift when these two ratios, which would gradually converge due to normalization of the asset value, hopefully beforehand, rather than after a market correction.

One last thought: Was it necessary for a non-traditional monetary policy beyond QE1?  
Disclaimer​​
Any opinions, views, news, research, analyses, prices or other information contained on this website is provided as general market commentary and are not intended to constitute investment advice. Angler Analytics LTD will not accept liability for any loss or damage, including without limitation to, any loss of profit, which may arise directly or indirectly from use of or reliance on such information.

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