Using a few main factors, we can derive the intrinsic value of the S&P 500 (SPY) or back out growth expectations and/or risk tolerance in the market.

We need the following:

- Current value of the index

- Earnings yield

- Dividend yield

- Cash payout ratio (i.e., what percent of earnings are paid back to shareholders)

- Expected earnings growth rate

- Current risk-free rate

- Equity risk premium (i.e., how much more yield do investors expect out of stocks versus a safe asset)

- Long-run economic growth expectations

- Long-run inflation expectations

The earnings yield of the index is approximately 4.06%. Dividend yield around 1.91%. The earnings yield is up about 15-20 bps from last month from growth in Q2 earnings relative to Q1.

Cash payout ratio can be assumed at about 80%. Historically it’s trended at about 75% but a dearth of viable investments and low earnings relative to historical norms has pushed this higher in recent years to help keep shareholders onboard.

The expected earnings growth rate should be somewhat higher than the nominal long-run growth rate given equities are leveraged investments. Namely, corporations have debt and they use this extra capital to invest in certain initiatives to grow their earnings. If companies are leveraged at 50% debt and 50% equity, then one might expect earnings growth to be approximately twice that of nominal economic growth, at least in the short-term.

Currently non-financial debt as a percentage of total market value of US equities is

The risk-free rate is debatable. Many use the 10-year US Treasury as a convenient safe benchmark, which is fine. One can also use the rate of return on cash, which also makes sense mainly because people invest their money to earn a return in excess of whatever interest they could get on cash. This is what I’m personally using in this exercise wherein I use the 3-month Treasury as a proxy. It’s currently trading at 1.08%.

The equity risk premium (ERP) is something that can be sensitized over a range. This reflects a discount rate or a returns expectation in the market. If the ERP is 6%, for example, then this assumes investors expect a 6% return above that of cash.

For long-run growth expectations I use 1.8%, which accords with the US Federal Reserve’s expectations and

**Valuation**

If we run these assumptions over an ERP (i.e., nominal returns expectations over cash) range of 5.0%-7.0%, then we get valuations going from 1,890 to 3,410 for an intrinsic value.

At 5.5%-6.5%, a range of __2,130 to 2,850__.

Below represents a pricing curve based on various required rates of return. Investors with higher returns expectations will price the index lower than those with lower returns expectations.

A 6% ERP (or 7% nominal returns expectations) would place the value of the index __at 2,440__.

If we were to back out a value based on the current mark of the index, we’d get an ERP of 5.95%, or **7.03% **forward nominal returns expectations.

This comes to about **5.2% in real terms** using 10-year breakeven inflation expectations.

If we were to reduce earnings growth expectations to simply nominal growth, then we’d get a slightly lower ERP of 5.81%, or **6.89% **in nominal returns expectations (or 5.0%-5.1% in real terms).

The following graph shows valuation levels of the S&P 500 at various risk premiums – i.e., expected returns above that of cash. Year-over-year earnings growth is set equal to the 3.6% assumed long-run level.

**Conclusion**

Since February 5, 1971 – the first day the S&P 500, Dow Jones, and NASDAQ traded simultaneously – stocks have averaged about 7.2% in real terms.

(*Source: measuringworth.com*)

This means stocks are overvalued if we’re going purely in terms of returns of the past, mostly as a coordinated central bank effort to price up equities in order to create a wealth effect.

Investors currently should expect annualized forward returns of about 200-220 bps below this.

In the end, the long-term growth rate of the economy dictates everything. If we expect growth and inflation to average 1.8% each over an indefinite period of time (i.e., 3.6% nominal GDP), we’re looking at low rates of return. If we take this 3.6% nominal growth rates and assume 2% in dividends, this gives us just 5.6% in nominal forward returns. So it’s quite safe to say we’re looking at anywhere from 5.5%-7.0% forward nominal returns (approximately 3.5%-4.0% in real returns).