Equity Valuation Based on GDP Growth 2.0

This is based on my post Equity Valuation Based on GDP Growth with a slight twist.

As I've outlined previously, over the long run equity valuation and earnings both grow at roughly the pace as nominal GDP. If earnings (for example) grew faster, then earnings would eventually become larger than the entire economy, which is not possible.

With that in mind, here goes...

The below chart shows:

• Blue: the S&P index (pulled via Irrational Exuberance)
• Yellow: the value ending in 2011 equal to that of the S&P 500 index, then brought back in time by the nominal GDP growth rate (GDP data is available at the Bureau of Economic Analysis)

This is an attempt to compare historical S&P 500 valuation (relative to the size of the US economy), relative to the current valuation level. For example... if the S&P 500 (blue) is below the nominal GDP line (yellow), then the S&P 500 was cheaper then (on this relative measure) than it is now. It also means when the lines cross, valuation levels were equal to today.

The relevance: The chart below shows the relative valuation for each year from 1929 through 2001 (in December 2011 terms), then shows the subsequent 10 year forward change in the S&P 500 (note this does not include dividends).

This chart shows that if this valuation metric can forecast the future (I am not saying it will, but it seems useful), then equity markets may be a decent buy here. At relative value zero (i.e. today's measure) the trend-line goes through 0% on the x-axis at roughly 7.5% annualized (before dividends).

Source: Irrational Exuberance / Bureau of Economic Analysis

Model Building / Data Mining

Yesterday, I outlined findings of a model that allocates to the S&P 500 when the VIX is below 20 and to cash when above 20. This post will expand on that post to build a model that outperforms the S&P, with less volatility, over the 1993-2011 time frame. The post is less about how great the model is (that is to be determined), as much as just how easy it is to use simple data mining techniques to build models that look GREAT using historical data (i.e. buyer beware of all these new funds / models coming out).

The Model

When analyzing the original model, we saw that the S&P 500 actually performed quite well on average (albeit with huge swings at times) at both low (VIX below 17.5) and high (VIX above 25 levels). Thus, a simple model would allocate to stocks when the VIX is below 17.5 or above 25 and cash when it is not. But, let's see if we can data mine improve on that further. When stocks do poorly, bonds (especially government bonds) tend to do very well (i.e. they become negatively correlated). Using Fidelity's Government Income Fund 'FGOVX' (I am not vouching for this fund, it was simply the first I found with daily returns going back to 1993), we compare returns of government bonds within each volatility "bucket" relative to what we found for the S&P 500.

As can be seen above, in each of the 17.5 to 25 VIX "buckets", government bonds outperformed (on average). This is just what we were looking for.

To the model's results... in 'daily rebalancing' we allocate on a daily basis to the S&P 500 (ETF SPY) when VIX is below 17.5 or above 25 and to government bonds (fund FGOVX) when it is not (monthly is simply on a monthly basis). This rotation strategy had excess returns over SPY's 7.7% annualized return since 1993 of almost 3% on a daily basis and 1.7% on a monthly basis annualized (excluding transaction costs) with volatility reduced around 3% over that time frame.

Model Results (January 1993 - December 2011)

So is this legit model building or data mining? I believe it may be both (if a potential legit model, it needs further testing across markets and time frames), but in no way am I confident this performance can be replicated on a going forward basis.

Source: VIX, SPY, FGOVX

Emerging Market Rotation Strategy

Along with taking a deeper look at macro trends / releases to try to figure out this whole economy thing (in these all-too-interesting times), I spend quite a bit of my time creating (long-term oriented) trading models. The goal? To better allocate my investments by taking away some of my emotion.

The following model I will walk through is a simple model (available for download here) based on my friend Meb Faber's (of World Beta blog and Cambria Investment Management) Timing Model.

What is it...

It is an Emerging Market "EM" timing model that allocates between two EM sectors... fixed income and equities. As a way of background, since 1999 (I could only pull data for both indices as of December 1998 - due to the methodology below, the start of the model is 10 months later), both EM fixed income and equities have had very similar returns, but have had VERY different ways of getting there (see chart below). At a high level, EM equity tends to outperform when both are trending higher, but EM fixed income outperforms when EM beta struggles.

With that in mind... what is the model? On an end-of-month basis:

• If EM Equity Total Return index > 10-Month moving average, allocate to EM Equities
• If EM Equity Total Return index < 10-Month moving average, allocate to EM Fixed Income

The result? Over this time frame, the rotation strategy has significantly outperformed both EM fixed income and equities with volatility and drawdown levels right between the two (note that a 50/50 blend had returns of around 10.7% with slightly less volatility than the rotation strategy).

If anyone can pull data for EM indices going back further in time, please send my way as I'd like to see how this performs over the longer term.

Source: MSCI, JP Morgan, World Beta

Model: Download here

The Predictive Power of "Stocks as Bonds"

My recent post Corporate Profits, Economic Growth, and Equity Valuation outlined that equity performance can be quite volatile, but over the long-run tends to mean revert back to its underlying factor... economic growth.

Which brings me to a model created by the great Eddy Elfenbein (of Crossing Wall Street), which I initially came across in his post What if the Stock Market Were a Bond, back in October 2010. Eddy's explanation of that concept:

I took all of the historical market performance of the S&P 500 (including dividends) and invented a hypothetical long-term bond that matched the market’s monthly gains step-for-step.

I assumed that it’s a bond of infinite maturity and pays a fixed coupon each month.

The result, which starts December 1925, is the following (reproduced) chart.

Crossing Wall Street Model for Stocks (12/1925 - 8/2011)

While I expected a strong relationship between the above chart with forward equity returns (the model is driven by equity performance, but accounts for the market being rich / cheap to its long-term trend and normalizes returns using backward and forward looking performance), I was surprised by how closely it tied (data was pulled from Irrational Exuberance).

Crossing Wall Street Model vs Ten Year Forward Equity Returns

Same Chart, but a Change in Scale to the Right Hand Side

The likely question is how well this model will predict the future as it shows a 12%+ annualized ten year forward return. My initial thought is don't read too much into the model for predictive power UNLESS the underlying factors that drove the last 85 years of equity performance are expected to continue (and at the same level). In addition, Eddy lays out one more issue:

There’s one hitch, though. I have to choose a starting yield-to-maturity for the beginning of the data series in December 1925. So this isn’t a completely kosher experiment because the starting point is based on my guess.

This issue can be seen in the below model which goes back further... all the way to 1871. Rather than predict a forward ten year equity return of more than 12+%, the model predicts returns of less than 5% (due to lower equity returns between 1871 and 1925).

Source: Irrational Exuberance / Crossing Wall Street