Glossary
Total Return
The total performance achieved by holding a stock over a given period. It combines price performance and dividend income, assuming dividends are reinvested.
The given period can be 1 day, 1 year or a period between any two dates.
Total Return is an index that is rebased to 100 on the initial date. It is often shown alongside its annualised performance.
In Bogle’s framework (¹), Total Return is broken down into two terms; ACE does the same, the split being exact:
Cost of Equity
Some synonyms of Cost of Equity: intrinsic profitability, steady-state yield
The intrinsic rate of profitability of a stock — what a stock fundamentally yields by virtue of its activity and assets, independently of valuation changes. The term “Cost” comes from the perspective of the chief financial officer; symmetrically, it is the yield an investor can reasonably expect.
Although the Cost of Equity is considered “not directly observable”, the standard Gordon formula can provide a useful proxy, albeit blind to the impact of debt and cash, and difficult to implement over a period shorter than a year.
ACE makes it calculable and readable on a daily basis.
Cost of Equity with Gordon
Following the standard Gordon-Shapiro formula, as adopted by Jack Bogle (see (i) and ACE):
Simple and meaningful, but blind to the use of debt and cash.
Dividend yield is theoretically equal to the Dividend at end of year divided by Price at beginning of the year. This creates unnecessary technicalities we won’t detail here, as ACE naturally addresses them through its cash management approach.
Cost of Equity with ACE
ACE generalises Gordon’s formula, moving from an annual to a daily calculation and integrating the use of debt and cash:
where Shareholder Yield = Dividends + Buybacks (net of issuances) + ΔCash – ΔDebt, relative to price and annualised.
Unlike standard Gordon, ACE takes into account debt and cash movements. For example, if a company borrows in order to increase its distribution, the Shareholder Yield — and consequently the Cost of Equity — remains unchanged.
Investment Return
Some synonyms of Investment Return: Cost of Equity running over time, Wealth Creation.
The component of Total Return attributable to the stock’s intrinsic profitability.
Investment Return is the cumulative Cost of Equity over time. It represents genuine wealth creation, independently of valuation changes.
Mathematically, each day:
Investment Return index = previous day’s index × (1 + Cost of Equity / 365)
Earnings Estimates
The consensus forecast of a company’s earnings for the coming fiscal years, as continuously updated by financial analysts.
Using daily Earnings Estimates rather than delayed quarterly or yearly accounting publications, provides a much more timely picture of a company’s momentum.
Profit
Profit is a common term that does not have a single, precise definition; it refers to the residual income remaining after costs and expenses are deducted from revenues.
In ACE’s formalism:
This definition captures what the entire enterprise generates for both shareholders and debt holders, in consistency with the use of Enterprise Value (= Market Value + Debt – Cash). Earnings Estimates are used for the Earnings component.
PE ratio
The Price Earnings ratio is the price of a share divided by its earnings.
In ACE’s framework, the PE uses Earnings Estimates (consensus forecast) rather than trailing earnings. The ACE counterpart to the PE ratio is the EV-to-Profit ratio.
EV-to-Profit ratio
ACE’s valuation indicator — the counterpart of Gordon’s PE ratio, integrating debt and cash:
where Enterprise Value = Market Value + Debt – Cash, and Profit = Earnings + Interest.
Unlike the PE ratio, the EV-to-Profit ratio is not distorted by changes in debt. For example, if a company takes on debt in order to distribute more dividends or buybacks, this has no impact on shareholder wealth (ignoring the negative tax effect). According to Modigliani and common sense (see Didactic story), Enterprise Value should remain stable; therefore, the Price should fall by the amount of debt increase.
This would make the stock appear cheaper to PE followers. However, this would be a false signal as nothing has changed in reality.
Another example relates to growth opportunities financed through internal cash flow or increased debt. While it is harder to demonstrate, the distortion in PE ratios can be even more misleading.
The ACE model does not suggest that using debt is a bad idea – it simply shows that the PE is distorted in many cases.
Speculative Return
The component of Total Return attributable to the stock’s changes in valuation.
The Speculative Return is the cumulated effect of the changes in the chosen ratio.
Speculative Return with Gordon
With the standard Gordon model, the corresponding ratio is PE ratio.
The Gordon Speculative Return is the cumulated effect of the changes in the PE. To second-order accuracy, it equals the effect of the difference between final PE and the initial PE.
This leads to an interesting property:
if PE does not change in a year, the Total Return will be Dividend Yield + Earnings Growth,
i.e. standard Gordon formula (see ACE, end of Summary).
Speculative Return with ACE
With ACE model, the corresponding ratio is EV-to-Profit ratio.
The ACE Speculative Return is the cumulated effect of the changes in the EV-to-Profit ratio.
The same logic applies:
if the EV-to-Profit ratio remains unchanged for a given period, the Speculative Return will be zero (to second-order accuracy²). In this case, the Total Return will equal the Investment Return, i.e. the cumulative of running ACE Cost of Equity (see above).
¹Occam’s Razor Redux: Establishing Reasonable Expectations for Financial Market Returns
JOHN C. BOGLE AND MICHAEL W. NOLAN THE JOURNAL OF PORTFOLIO MANAGEMENT FALL 2015
²The accuracy of the ACE outputs is not affected by second-order terms, which are mastered and checked.