FINANCE
Valuation of the S&P500 Index with a Modified DDM
A short paper I wrote at Imperial College discussing a Gordon Growth Model with Dividends and Buybacks, dated 22 February 2021.
Note: This paper was written in conjuction with Cameron Brown, Joshua Mills, and Thomas Butler.
1 Introduction
This report values the S&P500 as of 21 February 2021. It comes at a difficult time, where the COVID-19 pandemic has shocked global markets resulting in significant share price declines during the initial months of the pandemic. Central banks slashed interest rates to encourage borrowing and boost the economy as further lockdowns led to increased market volatility. With many countries — bar China, now in recession and with significant blows to multiple sectors and employment — it may seem puzzling that the market conditions are following a similar trend to that seen in February 2020, when the market peaked before the COVID crash [1]. Many analysts are now identifying this trend as a bull market and warn of significant overshoot. In the following sections, we use the Dividend Discount Model (DDM) to determine whether there is merit to these concerns and make a mathematically supported argument for the market valuation. We explain our findings and also address the weaknesses and limitations of the model in question. Standard & Poor’s 500 Index (S&P500) is a market-capitalisation weighted index representing the 500 largest publicly-traded companies in the US. The S&P500 is generally preferred over other indices such as the Dow 30 as it covers 11 sectors from IT to healthcare and is therefore assumed to encapsulate conditions of the equity markets.
It should be noted that larger firms have a more significant impact on the overall performance of the S&P500; the 10 largest stocks listed on the index represent almost 30% of the value and most of these stocks lie in the technology sector. Regardless, this paper will continue with the assumption that the S&P500 is a better representative of market conditions.
2 Dividend Discount Model (DDM)
The price of a stock can be evaluated as the summation of the present values of the dividends it will pay in the future. This meaning is realised by the Dividend Discount Model presented in Equation (1) which calculates the current price of a stock, P_0 held for n years:
Div_i represents the dividend payment made after each year. The rate of return, r_E, is the expected return rate an investor can expect to achieve; usually, a threshold value that an investor requires to justify owning a stock. The number of years a stock can be held can theoretically be infinite, in which case Equation (1) can be taken to the limit of perpetuity:
When estimating the value of future dividends, a common assumption for developed companies is that the dividends will grow at a constant rate, g, per year. This assumption is known as the Gordon Growth Model and is given by:
The infinite series in Equation (3) can be simplified to:
During periods of supernormal growth, the assumption of a constant growth rate will not be appropriate. In these cases, the present value can be calculated individually using specific dividend predictions for each of the supernormal growth years until the market is assumed steady. The Gordon Growth Model can then be introduced for the remaining steady growth years to predict future payments from that point onwards.
The growth of dividends on the S&P500 is currently unsteady and consequently, dividends are evaluated in this assessment with varying growth rates for the first two years before assuming steady growth and utilising the Gordon Growth Model:
where
Companies can choose to purchase their own stock to reduce the number of available shares, this is commonly known as a buyback. This acts to boost demand and the price of their shares while also increasing the per-share earnings. The influence of buybacks on stock price is particularly pronounced in the S&P500 where they make up the majority of money given to the shareholders [2]. Assuming the growth of buybacks is equal to the growth rate of dividends, the present value of future payouts is raised by buybacks as demonstrated in Equation (7):
and when incorporated into Equation (5), produces a valuation equation of:
3 Valuation of the S&P500
The S&P500 Index is computed using Equation (9),
where the index divisor is manually adjusted every quarter based on specific corporate actions such as share buybacks and rights offerings. The divisor is applied to all index values to make the value more manageable and easier to track [3]. As of Q4 2020, the Index Divisor is at 8428.67×10^6 [4]. Reuters estimates 2021 buybacks to hit 651 billion in 2021 [5], which can be normalised with the Index Divisor as shown in Equation (10) to produce a value of B_2021 = $77.23.
To calculate the expected return, r_E, the Capital Asset Pricing Model (CAPM) was used. The model is an indication of the return an investor should expect when undertaking risk and is given by Equation (11) [6].
The equity risk premium is approximated with the S&P Equity Risk Premium Index, which shows a 10-year return of 5.81% [7]. Taking 52-week treasury bond interest of 6% (as of 12 February 2021) [8], and β = 1 since the S&P500 is used as a benchmark for market risk, the required return on equity an investor should expect is r_E = 11.81%. This value is corroborated by the value retrieved from Bloomberg terminal, which places r_E at 10.65%. Moving forward, calculations involving return on equity will use 10.65% for a more conservative approach.
As described in Section 2, Equation (8) may be used to estimate the present value with two years of supernormal growth, followed by steady growth modelled by the Gordon Growth Model.
A 20 year average for a dividend growth rate of g= 7.05% was calculated from S&P500 quarterly data, shown in Section 7 of the S&P500 Earnings and Estimates Report [9]. The historical average is used for the Gordon Growth Model since this represents a region of steady growth. Future dividend projections were found from the Bloomberg Terminal: D_2021 = $63.88, D_2022 = $67.88 and the 2022 buybacks were extrapolated from the 2021 data using the 21–22 dividend growth rate to produce: B_2022 = $82.07. Using these values, the valuation of the S&P500 comes to $3879.525. The Bloomberg Terminal puts the current price at $3934.83 at the time of writing.
4 Strengths and Weaknesses of DDM
4.1 Strengths
The DDM is particularly suited to evaluating companies that retain stable and regular growth rates. These companies typically tend to be much larger and more mature; therefore by nature, are more likely to be listed on the S&P500. The index is made from 505 stocks from the largest companies in the US; thus, even if there are a few companies that do not see steady growth, their effect on the overall behaviour of the index is minimal. This is what makes a DDM more suited to evaluating an index than to an individual firm. Furthermore, the data and time required to carry out a DDM is significantly less than that required to perform a discounted cash flow (DCF). The latter requires an analysis of the predicted future cash flows for every single company listed on the index which is clearly labour intensive for an index containing over 500 firms. Finally, because the DDM does not take into account the condition of the market, firms of differing sizes and industries can be compared against one another.
4.2 Weaknesses
One of the main limitations of a DDM is the fact it can only be used to value mature companies that regularly pay out dividends to their shareholders. This means that applying the model to fast-growing firms is difficult and a great deal of error may be induced when trying to predict the growth rate of dividends. By using the model we are assuming steady growth rates, which is not necessarily applicable for all companies listed on the index. Within the S&P500, several companies have never paid out dividends, Facebook and Google being prime examples. As of November 2019, 78 of the 505 companies listed on the index did not pay regular dividends to their shareholders[10]. This means that when evaluating the index using the DDM, these 78 companies are completely neglected and the results are not wholly representative of the performance of the entire index. The problem is intensified when one considers that the S&P500 is proportionally represented by its constituents and therefore, tech giants like Facebook and Google who sit in the top 10 places of the index are not being considered by the DDM. The issue has also been exacerbated with the onset of coronavirus, with over 40 companies suspending payouts [11]. A second disadvantage of the DDM is that the model assumes that the earnings of firms on the index are proportional to the dividends paid out by these firms. A company’s performance and worth have purely been evaluated by its dividend payout. In fact, some companies will pay out regular dividends regardless of their performance, and may even borrow money to ensure dividends are paid out regularly to their shareholders. This deceives the DDM and inflates the actual value of certain firms; in such scenarios, a Discounted Cash Flow model (DCF) may triumph instead. Finally, the DDM model is extremely sensitive to the growth rate of dividends, g, and the rate of return on equity, r_E. When discounting a future dividend payout, the model divides the future dividend by (r_E−g)^N where N is the number of years in the future in which the dividend is paid. Clearly small changes to the growth rate or the return on equity have a great effect on the discounting of future dividend payments.
An example of this effect is shown in Figure (1), which uses data from Section 3; an exponential increase in current valuation is seen with an increase in growth rate. The equity cost of capital is dependent on the risk-free rate determined by interest rates on government bonds and also by an Equity Risk Premium (ERP) which varies drastically between firms and is highly dependent on many factors such as the company’s maturity. Furthermore, the ERP is extremely dependent on macroeconomic uncertainty and not just the risk associated with an individual firm [12].
5 Factors Affecting Valuation
Arguments exist for certain markets being undervalued, such as the airline market. The presence of technology that filters the air, as well as the use of masks, have increased trust amongst passengers. As a result, jet fuel prices are expected to increase. Furthermore, several commodities such as copper and silver have been deemed undervalued due to their increasing demand for use in renewable energy [13]. However, our simple valuation suggests that the market is slightly overvalued overall. For the rest of this assessment we note the Gordon Growth Model:
While this equation may be ineffective to value a single company as mentioned previously, it allows us to understand qualitatively, why the market may be over or undervalued. r_E, or return on equity, indicates the risk involved in holding stock and it can be expressed as the risk-free interest rate combined with the equity risk premium. Currently, the interest rates in the US are at an all-time low, and spending and earnings have increased as companies are more likely to debt-finance new projects. Additionally, with lower returns, investors have become less interested in treasury bonds and are filling more of their portfolios with equity. As the interest rate drops, the return on equity falls too. These recent factors have led to a surge in the equity market. The dividends issued by a company have a complicated relationship with the company’s performance, many companies will abstain from paying out dividends to retain earnings and grow and changes in dividend policy are often indicative of the company’s health. If analysts under-predict dividend yield due to the concern over the company’s health and overlook the fact that the company is predicted to grow significantly, they may in turn under-predict the value of the market considerably.
6 References
[1] Michael Santoli. A look at the state of the stock market one year since its pre-Covid peak. 2021. URL: https://www.cnbc.com/2021/02/13/a-look-at-the-state-of-the-stock-market-once-year-since-its-pre-covid-peak.html
[2] The Bank’s response to climate change — Bank of England. URL: https://www.bankofengland.co.uk/quarterly-bulletin/2017/q2/the-banks-response-to-climate-change
[3] Standard & Poor’s 500 Index Calculation. 2020. URL: https://www.cftech.com/the-brainbank-archive/finance/138-standard-poor-s-500-index-calculation
[4] Standard & Poor’s 500 Index Divisor. 2020. URL: https://ycharts.com/indicators/sp_500_divisor#:~:text=S%5C%26P%5C%20500%5C%20Divisor%5C%20is%5C%20at,1.76%5C%25%5C%20from%5C%20one%5C%20year%5C%20ago
[5] U.S. corporate buybacks are on the rise, lifting investor hopes. 2020. URL: https://www.reuters.com/article/us-usa-stocks-buybacks-idUSKBN29U18R
[6] Capital Asset Pricing Model (CAPM). 2020. URL: https://www.investopedia.com/terms/c/capm.asp
[7] S&P U.S. Equity Risk Premium Index. 2020. URL: https://www.spglobal.com/spdji/en/indices/strategy/sp-us-equity-risk-premium-index/#overview
[8] Daily Treasury Bill Rates Data. 2020. URL: https://www.treasury.gov/resource-center/data-chart-center/interest-rates/pages/TextView.aspx?data=billrates
[9] Howard Silverblatt. S&P500 Earnings and Estimates Report. S&P 500 Index, 2020
[10] 78 Stocks in the SP 500 Don’t Pay a Dividend. Here Are Some That Should. 2019. URL: https://www.barrons.com/articles/78-stocks-in-the-s-p-500-dont-pay-a-dividend-here-are-some-that-should-51573233301
[11] Despite the Pandemic, SP 500 Dividends Hit Another Record in 2020. 2020. URL: https://www.barrons.com/articles/s-p-500-dividends-hit-another-record-in-2020-51609357661
[12] Bank of England. An improved model for understanding equity prices. 2017.
[13] Are Commodities Setting Up for a 2021 Bull Market? — US Global Investors. 2020. URL: https://www.usfunds.com/investor-library/frank-talk-a-ceo-blog-by-frank-holmes/commodities-setting-up-for-a-2021-bull-market/#.YDKd_ZP7TOQ
