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Stock Market Performance Perspectives

| | Posted in: Equity Premium

How different are stock market performance metrics for:

  • Capital gains only, capital gains plus dividends accrued as cash (spent or saved), and capital gains plus dividends reinvested in the stock market?
  • Nominal versus real returns?
  • Simple return-to-risk calculations versus Sharpe ratio?

Using quarterly S&P 500 Index levels and dividends, quarterly U.S. Consumer Price Index (CPI) data (all items) and monthly 3-month U.S. Treasury bill (T-bill) yield as the risk-free rate/return on cash during the first quarter of 1988 through the second quarter of 2021, we find that:

The following chart compares cumulative nominal performances of the S&P 500 Index over the sample period for four perspectives:

  1. Capital Gains Only – based on quarterly index levels.
  2. Total Return with Cash Dividends – capital gain plus dividends accrued as cash, with zero return on cash (for example, if spent quarterly as earned).
  3. Total Return with Saved Dividends – capital gain plus dividends accrued as cash, with the risk-free rate as return on cash.
  4. Total Return with Reinvested Dividends – capital gains with dividends reinvested in the index each quarter as earned.

Respective compound annual growth rates (CAGR) are 8.9%, 9.5%, 9.6% and 10.7%. Accruing cash dividends (spent or saved) appears to reduce volatility by excluding a growing part of holdings from market volatility.

How do real returns differ from nominal returns, and how do arithmetic average annual returns differ from CAGRs?

The next chart compares nominal and real arithmetic annual average returns and CAGRs for the S&P 500 Index, without and with dividends, over the available sample period. Real returns derive from quarterly adjustments to returns for inflation. Annual returns range from 6.2% CAGR for real capital gains only to 11.8% nominal arithmetic average annual return for capital gains plus reinvested dividends.

Choosing one of these alternatives for benchmarking depends on investor views on buy-and-hold as an alternative investment, treatment of dividends and expected inflation. Arithmetic average annual return (CAGR) may be more appropriate as a short-term (long-term) benchmark.

How do these differences translate to simple risk-adjusted performances?

The final chart compares simple risk adjustment measures (nominal and real arithmetic average annual returns divided by standard deviation of annual returns, and Sharpe ratio) for the S&P 500 Index without and with dividends over the available sample period. The risk-free rate used in calculating Sharpe ratios is an annual average of daily T-bill yield.

Saving dividends generates the highest risk-adjusted performances by small margins.

Since inflation rate and T-bill yield are related, average annual real return-to-volatility ratios and Sharp ratios are similar.

In summary, evidence suggests that some investors may prefer to save (rather than reinvest) dividends and that this scenario is the most conservative risk-adjusted benchmark.

Cautions regarding findings include:

  • The available sample period is not long and may not be representative of future investment environments regarding equity returns and inflation.
  • Investors may be able to achieve a higher return than the risk-free rate on saved dividends via term commitments. Such a boost may extend the risk-adjusted performance lead for saved dividends, but may also increase annual marked-to-market volatility.
  • Dividend reinvestment ignores any costs/imprecision of investing dividends and may overstate performance.
  • The above performance statistics assume a tame stock market return distribution for a quarterly measurement frequency. To the extent that the actual distribution is wild, these statistics lose meaning as expectations.

See also “Components of U.S. Stock Market Returns by Decade”.

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