The S&P 500 Index (SPX) contains the 500 large market cap companies listed on the US stock exchanges. As of Nov 16, 2020, Information Technology, Consumer Discretionary, Health Care and Communication Services constitutes 64% of the index. The top six largest market cap companies on SPX as of mid November are Apple, Microsoft, Amazon, Alphabet (Google) and Facebook. Energy and Real Estate companies represent only 4% of the index given the ripple effect of the pandemic on the public equities, punishing low growth, asset intensive companies with higher net debt burden and low dividend yield while rewarding high growth companies with low net debt, low dividend yield, high P/B and P/E ratios. The sector weights of S&P 500 Index as of November 16, 2020 are displayed in the following graph and table.

### Valuation of the Index

The valuation of SPX is built upon the main pillars of valuation of its cashflows, growth and risk. The cash flows represent cash flows to common shareholders of companies which include dividends and buybacks. The growth of these cashflows is represented by the growth rate of the dividends and buybacks during the high growth period, prior to reaching the terminal year; in terminal year, the growth is then represented by the terminal growth rate which is capped by the risk-free rate. The standard proxy for the risk-free rate is the 10-year treasury yields in the mature markets such as United States. Finally, the risk of these cashflows is represented by the cost of equity. Cost of equity is determined by the relative risk of the stocks with respect to the overall market, measured by beta, and the market equity risk premiums (ERP) over and above the risk-free rates (r_f). Since the S&P500 is a proxy for the entire US developed, mature market, the beta in this case is 1. Hence:

In order to forecast buybacks and dividends of SPX, consider the forecast of the earnings of SPX for a period of 5 years (which is the high growth term) prior to bringing the valuation to a close in the terminal year. As many analysts forecast SPX earnings for a period of two to three years forward under either a bottom up or a top down approach, in this analysis, we will use the average of the bottom up forecasts sourced from Refinitiv as well as the top down estimates of earnings provided by Yardeni Research for 2020 and 2021.

Considering the YoY growth rate of the earnings provided by the analysts, and knowing that this growth rate will eventually be capped and reach the risk-free rate in the terminal year, the compounded growth rate of the earnings during the 5 year high growth period is calculated to be 3.7%. Since the earning estimates and current low interest rate environment has already included the impact of COVID-19, the adjustment of this growth rate for the impact of pandemic is no longer required; however, since the pandemic has severely impacted the earnings in 2020 and 2021, we can control for the impact of COVID-19 on the forecast of future earnings through integration of a scalar, which represents the earning loss recouped by the end of the fifth year (2024F). If this scalar is set to 100%, it means all the earning lost in 2020 due to the pandemic is recouped by 2024, and if this scalar is set to 80%, it means only 80% of the earning loss is recouped by 2024. This scalar is used in calculation of the earnings in the final year prior to the terminal year, in 2024 using the following formula:

The terminal year earnings is the earnings in 2024 grown at the terminal growth rate, in this case, the risk-free rate of 0.89% as of Nov 16, 2020.

Dividends and buybacks are determined by calculating the dividend and buyback payout ratio through out the forecast period and applying the ratio to the earnings in the corresponding years to get the cashflows to equity holders. Given the Dividend + Buyback and Earnings Per Share levels of the index in 2019, the 2019 payout ratio stands at 89.75%. The best approach to arrive at a continuous payout ratio throughout the forecast period is to find the term year payout ratio given proxies for term growth rate and term return on equity (ROE) of the index, using the following:

And derive the payout ratio for the term year. In this analysis, the term payout ratio is 94% given a 15.08% ROE and 0.89% growth rate. The payout ratio during the high growth phase of the forecast is then the gradual increases from 89.75% to 94% in the term year.

Terminal value is defined as the

The Dividends and buybacks throughout the forecast period is discounted at cost of equity of 5.91% to arrive at the intrinsic value of the index of 3,228.88. Given the current level of the index at 3,585.15, the index is overvalued slightly, by about 10%.

### Is US S&P 500 Index overvalued?

Given the current level of the index at 3,585.15, and the intrinsic value of the index at 3,228.88 based on the inputs, the index is overvalued, slightly, by 10%. It is always best to not only consider the point estimates and expected values, but to consider the distribution of the results and valuation in the decision-making process.

### Simulation of S&P 500 Index valuation and vistribution of the values

In the context of investment analysis, we can not only arrive at the expected value of the index level via the intrinsic valuation process, but we can also integrate more statistics into decision making by applying Monte Carlo simulations. Given the distribution of the input variables such as ERP, terminal ROE, percentage of losses recouped by 2024 and any other variable deemed appropriate for simulation purposes, one can arrive at the distribution of the implied valuation. Hence, instead of point estimates, we can come up with the distribution of values and the likelihood of over and under valuation of the index.

It is important to consider the historical values of input variables to determine the correct distribution of the inputs. In this analysis, considering the historical values of the implied ERP since 2008, we chose a log normal distribution (mean: 5.1%, stdev: 0.6%), and given the historical index ROE levels since 2001, we used a normal distribution (mean: 15.05%, stdev: 2.19%) to describe these variables. Consequently, we arrived at the distribution of the intrinsic value of the index (mean: 3,208.53, stdev:374), representing the 50th percentile of the data. The distribution as well as the deciles of the valuation along with % of over and undervaluation are displayed below. At 3,585 current level of the index on Nov 16, 2020, the index is overvalued by about 11% given the Monte Carlo simulation results.

### Can the stock market behavior and its rebound in 2020Q2 and 2020Q3 be a predictive measure of the future performance improvement of the economy?

SPX along with many other equity indices in the US and worldwide took a hard hit during the first quarter of 2020 bottoming on March 23rd. As displayed below, SPX hit 2,237 on Mar 23rd, 2020, since when it has gradually recouped all its YTD losses.

The economy, however, has not rebounded as quickly as the stock markets and many remain unemployed.

The following graph displays the S&P500 quarterly (QoQ) returns and US Domestic Real GDP quarterly growth rate percentage (YoY). Please note, GDP is cyclical and seasonal and hence YoY percentage change is considered in the analysis. At the first glance, the data looks noisy and there seems to be no relationship between GDP YoY growth rate and the stock market returns.

However, the correlation of S&P 500 quarterly return data (as a proxy of US stock market returns) and GDP YoY growth rate in future quarters seems to display an interesting pattern. As we shift the GDP growth rate by one, two, three, four and more quarters ahead, the correlation of the stock returns and future GDP growth turns more positive, peaking at 27% with a four quarters shift. Consequently, the GDP growth rate lags the stock market growth and rebound by about four quarters, pointing to the fact that the stock markets have recouped all losses YTD while the GDP and the economy is still struggling. It is expected for GDP and the economy to take one year (or four quarters) prior to reaching similar performance levels as that of the the stock markets. As displayed, in the following table, the correlation of S&P500 quarterly returns and US Stocks Quarterly Returns with the Real GDP YoY % Change is maximized once we look four quarter ahead.

Even though markets can be inefficient, they have no egos and hence markets can be a humble predictor and extraordinarily platforms for relaying messages with respect to the future movement of the economy.

Note:

Many wonder why the term growth rate is capped at risk-free rate. Embedded in the risk-free rate is an expected inflation and expected real growth rate. "Embedded in the nominal growth rate of the economy is an expected inflation and expected real growth rate. Over the long term, in steady state, the risk-free rate is a good proxy of the nominal growth rate. " by Aswath Damodaran, Kerschner Family Chair in Finance Education, NYU Stern Professor.

In the model, if we change the term growth rate to 2% instead of 0.9% which is the current low risk-free rate, the valuation stays still very similar and bounded. What one hand gives us, the other takes away and the reason is that the mid-term (2020-2024) growth rates is built based on an interpolation of the growth rates from 2021 up until the term year. One would have to consider how the risk-free rate can also change through out the forecast period as risk-free rate is also a component of cost of equity. Once the risk-free rate increases to its long term average or if it mean reverts to the long term average, cost of equity also increases; hence, since the discount rate of the cash flows increases, the present value of those cashflows that are grown at a higher growth rate also stays bounded and similar to the original valuation under a term growth rate of 0.9%

Sources: