What discount rate justifies pricing?
Rob Arnott, Feifei Li, and Geoffrey Warren tested whether differences in discount rates across companies justify pricing anomalies such as the value effect and size effect in their “Clairvoyant Discount Rates” paper published in the Journal of Portfolio Management, Fall 2013 issue. In other words, they calculated discount rates assuming that the net present value of a firm’s stock equals price. The goal is to determine which rate of return (clairvoyant discount rate or CDR) an investor was expecting if she knew that the future price in the holding period will be. Historical data was used starting from December 31, 1955 through December 31, 2011 and 10 year, 20 year, and 56 year holding periods were used.
A money weighted rate of return, or internal rate of return (IRR) was used to account for dividends the stock pays. An investor could either reinvest dividends into a risk free asset or market or spend dividends. The “Clairvoyant Discount Rates” paper also assumes that discount rates remain constant through holding periods. Individual stock returns as opposed to portfolio returns were used. Firms were classified in quintiles according to valuation (book to market ratio) and size (market cap).
Prices for growth stocks imply extremely low CDRs
The authors found that the most popular growth stocks imply a CDR that is below the comparable returns on bonds and even cash. Particularly, the CDR to justify stock prices for the 10-year holding period for the average growth quintile has averaged 3.98% whereas the comparable CDR for the average growth quintile has averaged 10.75%. The assumption is that investors can foresee 10 years of cash distributions and hence future prices in 10 years. For a 20 year holding period, investors required a 6.75% CDR for growth stocks and a 10.98% CDR for value stocks. For the 56 year holding period, investors forecasted a CDR of 5.01% for growth stocks and 8.37% for value stocks. It is striking to see that for the 56 year holding period, growth stocks return less than the one month T-bill and the 10 year Treasury bond (see chart below). This research provides more backing to the value effect, where value outperforms growth over the long term.
The authors point out that the CDRs come out to be lower than S&P 500 returns over comparable holding periods. The main reason for this finding is return dispersion of the stocks included in the study. Particularly, some growth stocks may generate a CDR below 0% while others may return 10%. The market index has a larger dispersion between CDRs; hence the average return is higher compared to a smaller group of stocks.
Source: Research Affiliates, based on data from Compustat and CRSP.
Size effect explained by more dispersed CDRs among small caps
At first glance, the well-documented size effect, where small cap stocks return more than large cap stocks, is absent from this study. However, when taking a deeper look, the authors find that the dispersion of returns for small cap stocks is much wider than for their large cap counterparts. Overall, small caps have the potential to outperform large caps thanks to a few outlier firms providing excess returns that compensate for the firms with lower CDRs.
