In my last post (Beta Exposure) I had mentioned that there are three statistical sources of returns: alpha (Î±), beta (Î²), and epsilon (Îµ). Nonetheless, there are also three fundamental sources of returns: dividends, earnings growth, and changes in valuation multiples. It is always very important to understand where we are relative to history.

Historically, the S&P has delivered an 11.18% total nominal return. Earnings per share have grown by 5.83% peak-to-peak and dividends have averaged 4.22%. This means that an expansion of multiples has contributed an average of 1.13% to the total return. These have obviously fluctuated over time.

So where do we stand relative to history? Our peak-to-peak earnings growth measure is at the top of its 6% growth channel and has been for quite some time.

The dividend yield is currently 1.94%, remarkably low relative to history.

Investing is a claim on a stream of future cash flows to be delivered in the future discounted at a return that is sufficient for the amount of risk taken. Hence, the most fundamental valuation model is the dividend discount model.

We have reverse engineered the dividend discount model to approximate the required rate of return implied by the price. This was then used to calculate a fair value on the S&P relative to the required return. This is prepared throughout history using real dividends and price to remove fluctuations in inflation.

Dividends have historically grown (G) by 1.5% annually (REAL) and the equation to fit the data begins at a required real return of 7.5% and declines linearly by .002% as a function of time (monthly). The fit has a 91% correlation to historical data. Presently, in order to achieve an annualized real 4.1% return, the S&P would have to experience a 35% deterioration from current levels to a fair value of 1432.

Also, buybacks are taken into account in the dividend yield of the S&P 500 making adjustments unnecessary. In this case, the 1.5% annual growth is a reflection of growth in dividends *per-share*. Despite share buybacks, the dividend yield has continued to fall. Companies are paying out less in earnings as dividends and, consequently, companies are either inflating their earnings or share buybacks are being offset by option compensation or additional share issuance.

Finally, there is the price-to-earnings multiple.

Currently, trailing twelve-month valuations remain reasonable at 19. However, TTM P/E multiples are very noisy and, used in isolation, provide very poor forecasts of future returns. Nevertheless, in conjunction with other indicators, it can improve information about future returns.

We can add the logarithms of the TTM P/E multiples and profit margins and regress it against subsequent 10-year returns.

There is an 80% correlation with subsequent returns and, as implied by the model, should be ~3% nominal return moving forward. Currently, profit margins are exceedingly high, and despite a "reasonable" multiple of 19, it is above the historical average. Historically, the combination has offered lower than average expected returns.

Now let's put this all together. Currently, the TTM P/E stands at 19.16, which translates into an earnings yield of 5.22%. Companies have historically paid out 45% of their earnings but this number has continued to slide over time and currently stands at ~29%. However, I am going to assume 45%. Also, real earnings growth has averaged 1.5% but the annualized peak-to-peak earnings growth has ranged from 1%-3%. I am going to be optimistic and say 3% earnings growth moving forward. This translates into (.0522 * .45 + .03) = 5.35% real and 7.65% nominal returns (assuming 2.3% inflation rate). Mind you, this is assuming multiples and margins remain historically elevated, real earnings grow at the highest annualized peak-to-peak growth rate ever recorded, and the payout ratio reverts from 29% to 45%. These measures also need to be sustained over the long term. In my opinion, and based on over a century of data, this scenario is highly improbable.

Again, I reiterate my belief that returns moving forward should be low and long-term investors should plan accordingly. Recessionary and market crash conditions remain relatively subdued (Beta Exposure), however, current market conditions are ripe for the emergence of such signals and should be monitored closely.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.