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# Mathematics 101: The Cheap Money Printing Machine And CAPE

Like many other bloggers and pundits, I have amply pontificated on the relative attractiveness of the stock market. For years, cash and gold hoarding bears have clung to the distorted, money-losing Shiller CAPE P/E ratio (see CAPE Smells Like B.S.), which has incorrectly signaled investors to stay out of stocks and miss trillions of dollars in price appreciation. Apparently, the ironclad Shiller CAPE device has been temporarily neutralized by the Federal Reserve’s artificially cheapening money printing press policies, just like Superman’s strength being stripped by the nullifying powers of kryptonite. The money printing logic seems so elegantly sound, I felt compelled to encapsulate this powerful relationship in an equation:

Interests Rate Cuts + Printing Press On = Stocks Go Higher

Wow, amazing…this is arithmetic any investor (or 3rd grader) could appreciate! Fortunately for me, I have a child in elementary school, so I became emboldened to share my new found silver bullet equation. I initially received a few raised eyebrows from my child when I introduced the phrase “Quantitative Easing” but it didn’t take long before she realized Rate Cuts + QE = Fat Piggy Bank.

After the intensive tutorial, I felt so very proud. With a smile on my face, I gave myself a big pat on the back, until I heard my child say, “Daddy, after looking at this squiggly S&P 500 line from 2007-2014, can you help my brain understand because I have some questions.”

Here is the subsequent conversation:

Child: “Daddy, if the Federal Reserve is so powerful and you should “not fight the Fed,” how come stock prices went down by -58% from 2007 – 2009, even though the Fed cut rates from 5.25% to 0%?”

Me: “Uhhhh….”

Child: “Daddy, if stock prices went down so much after massive rate cuts, does that mean stock prices will go up when the Fed increases rates?”

Me: “Uhhhh….”

Child: “Daddy, if Quantitative Easing is good for stock prices, how come after the QE1 announcement in November 2008, stock prices continued to go down -25%?”

Me: “Uhhhh….”

Child: “Daddy, if QE makes stocks go up, how come stock prices are at all-time record highs after the Fed has cut QE by -\$70 billion per month and is completely stopping QE by 100% next month?”

Me: “Uhhhh….”

Child: “Daddy, everyone is scared of rate increases but when the Fed increased interest rates by 250 basis points in 1994, didn’t stock prices stay flat for the year?”

What started as a confident conversation about my bullet-proof mathematical equation ended up with me sweating bullets.

Math 101A: Low Interest Rates = Higher Asset Prices

As my previous conversation highlights, the relationship between rate cuts and monetary policy may not be as clear cut as skeptics would like you to believe. Although I enjoy the widely covered Shiller CAPE discussions on market valuations, somehow the media outlets fail to make the all-important connection between interest rates and P/E ratios.

One way of framing the situation is by asking a simple question:

Would you rather have \$100 today or \$110 a year from now?

The short answer is…”it depends.” All else equal, the level of interest rates will ultimately determine your decision. If interest rates are offering 20%, a rational person would select the \$100 today, invest the money at 20%, and then have \$120 a year from now. On the other hand, if interest rates were 0.5%, a rational person would instead select the option of receiving \$110 a year from now because collecting a \$100 today and investing at 0.5% would only produce \$100.50 a year from now.

The same time-value-of-money principle applies to any asset, whether you are referring to gold, cars, houses, private businesses, stocks, or other assets. The mathematical fact is, all else equal, a rational person will always pay more for an asset when interest rates are low, and pay less when interest rates are high. As the 200-year interest chart below shows, current long-term interest rates are near all-time lows.

The peak in interest rates during the early 1980s correlated with a single digit P/E ratio (~8x). The current P/E ratio is deservedly higher (~16x), but it is dramatically lower than the 30x+ P/E ratio realized in the 2000 year timeframe. If none of this discussion makes sense, consider the simple Rule of 20 (see also The Rule of 20 Can Make You Plenty), which states as a simple rule-of-thumb, the average market P/E ratio should be equal to 20 minus the level inflation. With inflation currently averaging about 2%, the Rule of 20 implies an equilibrium of ~18x. If you assume this P/E multiple and factor in a 7-8% earnings growth rate, you could legitimately argue for 20% appreciation in the market to S&P 2,400 over a 12-month period. It’s true, a spike in interest rates, combined with a deceleration in earnings would justify a contraction in stock prices, but even under this scenario, current index values are nowhere near the bubble levels of 2000.

After six long years, the QE train is finally grinding to a halt, and a return towards Fed policy normalcy could be rapidly approaching. Many investors and skeptical bears have tried to rationalize the tripling in the market from early 2009 as solely due to the cheap Fed money printing machine. Unfortunately, history and mathematics don’t support that assertion. If you don’t believe me, perhaps a child may be able to explain it to you better.

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DISCLOSURE: Sidoxia Capital Management (SCM) and some of its clients own a range of positions in certain exchange traded fund positions, but at the time of publishing SCM had no direct position in any other security referenced in this article. No information accessed through the Investing Caffeine (IC) website constitutes investment, financial, legal, tax or other advice nor is to be relied on in making an investment or other decision. Please read disclosure language on IC Contact page.

Mathematics 101: The Cheap Money Printing Machine by Wade W. Slome, CFA, CFP, Investing Caffeine