Estimating S&P 500 Likely Range of Play

The purpose of this note is to estimate the S&P 500 likely range of play using the implied risk premium model developed by Prof Aswath Damodaran. In this note, I will use this model to estimate the likely S&P 500 Index value. The distribution of this value will emanate using the Monte Carlo simulations. While running the simulations I will tweak the inputs using triangular distribution and display outputs for such input tweaks.

Implied Risk Premium Model

The model is simple and takes in the following inputs:- a) Dividends and BuyBacks of S&P500 for the last 12 months; b) Likely growth rate for the future; c) Expected Returns for Stocks; d) 10 Year T Bond Rate = Risk-Free Rate. The S&P500 Index value will be just a simple discount of these future cash flows using the discount factor which is nothing but the expected returns for stocks for the future. Note that while estimating the cashflows, it is assumed that dividends and buybacks will grow at the estimated rate for 5 years, and after that, the growth rate will get aligned to that of the T-Bond rate — indicating a mature economy.

The maths and the formulas used in the model are derived in the following workings.

Figure 1 — Implied Risk Premium Model Formula

Estimating S&P Ranges

Using the above model we can estimate the possible values of S&P500 and their respective probabilities. While using the model we will not use static values as inputs, but these will be range-bound using a triangular input distribution function for which we lay out the min, max, and the most likely values. These values can be tweaked to see the impact on the output distribution function of the S&P500. This distribution function will be plotted by using the Monte Carlo simulation.

Option 1 — The Base Case

The inputs used for the base case are given in the following table.

Figure 2 — Inputs (Input — Option1)

The output for the base case is described in the following chart.

Figure 3 — S&P500 (Output — Option1)

Note that the most likely expected value for S&500 has emanated as 3902 for the base case. The Index is currently trading at 3924.

Option 2 — Increased Growth Rate

In this simulation, the growth rate is increased by 1% for all three metrics- min, max, and most likely. The inputs are listed in the following table.

Figure 4 — S&P500 (Input — Option2)

The output for option2 is described in the following chart.

Figure 5 — S&P500 (Output — Option2)

Note that the most likely expected value for S&500 has emanated as 4075 for option2. The Index is currently trading at 3924.

Option 3 — Increased Equity Risk Premium

In this model, the growth rates are brought down at par with the base case (Option1), but ERP is increased by 1% across all metrics. The inputs are listed in the following table.

Figure 6 — S&P500 (Input — Option3)

The output for option3 is described in the following chart.

Figure 7 — S&P500 (Output — Option3)

Note that the most likely expected value for S&500 is estimated as 3247 for option2. The Index is currently trading at 3924. Hence, in this option, the index will dive down by 17% from the current value.

Option 4 — Increased Growth Rate

In this option, we will hold the ERP same as Option3 but will drive up the growth rate by 1% across all metrics. The inputs to the model are listed in the following table.

Figure 8— S&P500 (Input — Option4)

The output for the option4 is described in the following chart.

Figure 9— S&P500 (Output — Option4)

Note that the most likely expected value for S&500 has emanated as 3388 for option2. The Index is currently trading at 3924. Hence, in this option, the index will dive down marginally from the current value.

Conclusion

It is clear from the above that the increased expected return for stocks is deadly as it will drive down the index dramatically. Why? As the Expected Return (ERP+T Bond Rate) is used to discount the cashflows to arrive at the PV. Hence, the higher the discounting factor, the lower will be the S&P500 index. As inflation increases, it drives up the T Bond yield rate, which in turn drives up the Expected Returns. Therefore, even if the growth becomes high due to increased inflation, then also the likely output on S&P500 is not satisfactory. Another dampener is the increased short-term rates by central banks — which slows the economy and the growth rates. Hence, at the peak of the crisis, we will see a double whammy — a slower growth rate, and increased expected return for stocks. Also, as the ERP is more driven by human perception (driven by surprises and changed external factors), and therefore any increase in the ERP (influenced by these factors) can drive the index down significantly. Hence, the task before the Central banks is really difficult. It has to walk the tightrope — manage the perception of investors and manage liquidity with the objective of containing inflation. While we are in the midst of this storm, the S&P Index is likely to remain subdued and might fall to an uncomfortable level and we all should be mentally prepared for that event — and have faith that as the inflation is contained, the ERP will return back to normal and so will be the S&P500.

(Views expressed are of my own and do not reflect that of my employer)

PS: Find the list of other relevant articles in the embedded link.