Using a few main factors, we can derive the intrinsic value of the S&P 500 (SPX) or back out growth expectations and/or risk tolerance in the market. What This Is and What It Isn’t Valuations have virtually nothing to do with market direction. Later on in this post, I show that forward long-run stock returns are less than past stock returns. This, however, means nothing in terms of what the future direction of the market might be in the short- or intermediate-term. That is driven by liquidity, as controlled by central banks (which is covered in posts like this), and not market levels. Valuation is closer to an indication of risk level. For example, equities (particularly tech stocks) were already very expensive in 1998, got even more expensive throughout 1999, but the valuations themselves said nothing about market direction, but rather market risk levels. The levels in 1998 and 1999 indicated a high level of risk. So when the NASDAQ peaked at obscenely expensive levels in March 2000, the peak-to-trough drawdown came to 81%, a figure generally only seen in economic depressions. More typical bear markets see 30%-35% drawdowns given valuations rarely rise to nosebleed levels. So buying equities at high valuations – which you can express in various forms (e.g., P/E, P/B, forward expected returns) – doesn’t mean one can’t make good returns in the short- or intermediate-term. It simply means that one's risk/reward is skewed to the downside. The converse is true for buying equities (or any financial asset) at low valuations. Nuts and Bolts With that said, to perform this exercise 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 3.79% on a trailing-twelve-months basis Dividend yield around 1.75%. Normally the latter figure tends to hover at around 2%, but the market has gone up faster than companies are willing to increase their dividends (dividends are essentially the portion of earnings that management believes are “guaranteed”). 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. In terms of a long-run growth rate, financial assets can’t perform beyond their earnings growth indefinitely. Accordingly, we should expect stocks to yield at about the long-run growth rate of the economy – approximately 3.5%-4% – using some combination of 1.7%-2.0% growth and 1.7%-2.0% inflation. 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 simply holding the funds in a savings account or similar where money can be withdrawn at any point. 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 1.45% as of the time of writing. 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 5.5%, for example, then this assumes investors expect a 5.5% return above that of cash. At a 1.45% return on cash, that’s approximately 7% in nominal returns, or about 5% in real terms assuming 2% inflation. For long-run growth expectations I use 1.8%, which accords with the US Federal Reserve’s expectations and 1.8% for inflation over the next ten years (though the 10-year breakeven – i.e., expected inflation average over the next 10 years – are near 52-week highs at around 2.0% currently). Valuation If we run these assumptions over an ERP (i.e., nominal returns expectations over cash) range of 5.0%-7.0% (6.45%-8.45% forward nominal returns expectations), then we get valuations going from 1,750 to 2,970 for an intrinsic value. At 5.5%-6.5% (6.95%-7.95% forward nominal returns expectations), a range of 1,950 to 2,530. The graph a few paragraphs 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 7.4%-7.5% nominal returns expectations) would place the value of the index at 2,200. If one were to require 7% nominal forward returns, that would put its value at 2,490 (again assuming 1.8% growth and 1.8% inflation long-term). If we were to back out a value based on the current mark of the index by adjusting the equity risk premium, we’d get an ERP of 5.23% – 35 bps lower than last month (due to the impact of a Fed rate hike and anticipation of further hikes in 2018) – or 6.68% forward nominal returns expectations. This comes to about 4.67% in real terms using 10-year breakeven inflation expectations, down 32 bps from last month. 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 (combination of 1.8% real growth and 1.8% inflation). Notice how we’re already to the very left of the curve based on present valuations, indicating that the return over cash isn’t much more than 5% per year over the long-run with stocks priced where they are currently. The graph below shows valuation levels of the S&P 500 using 7% forward nominal returns expectations and forward long-run nominal growth ranging from 3.00%-4.50%, at 25-bp increments. Bearish projections of long-run economic activity would discount the S&P’s fair value back to 2,120. 2% growth and 2% inflation would put it at 2,830. Bullish expectations of 2.25% growth and 2.25% inflation would estimate its fair value about 23% higher at 3,390. Conclusion Since February 5, 1971 – the first day the S&P 500, Dow Jones, and NASDAQ traded simultaneously – stocks in the S&P and Dow have averaged 7.4% annual returns in real terms. The tech-heavy NASDAQ has returned yielded an extra 213 bps annually due to the higher risks associated with these companies. (Source: measuringworth.com) At 4.68% expected forward real returns forward, this means stocks are overvalued purely going by the 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 real returns of about 2.7% below this. In the end, the long-term growth rate of the economy dictates everything. If we expect growth and inflation to average 2% each over an indefinite period of time (i.e., 4% nominal GDP), we’re looking at low rates of return. If we take this 4% nominal growth rates and assume 2% in dividends, this gives us just 6% in nominal forward returns with interest rates being the factor that could push this number up or down. So it’s fairly safe to say we’re looking at anywhere from 5.5%-7.0% forward nominal returns (approximately 3.5%-5.0% in real returns).