# Excess Implied Return (EIR) 1. Dan Gode and James Ohlson

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2 Excess Implied Return (EIR) 2 EIR deals with the first three points via the computation of implied return (IR). EIR deals with the last point by subtracting required return computed using CAPM from IR. Compared to PEG, EIR requires more inputs, computations, and concepts. We next spell out the inputs and the computations of EIR. 2. Our screen: Excess Implied Return (EIR) EIR is motivated by the idea that an investment is attractive if its implied excess return exceeds the return that one should require based on its risk. We measure the latter using CAPM. EIR is computed in three steps described below Step 1: Infer implied return (IR) Our measure of the implied return is the discount rate (r e ) inferred from the current stock price and earnings forecasts. Such reverse engineering requires the following inputs: Firm-specific inputs: P 0 : Current stock price per share e 1 and e 2 : Analyst forecasts of earnings per share for Y1 and Y2. d 1 : Analyst forecast of dividends per share for Y1. If this is not available, then d 1 is approximated by current dividend payout times e 1. g: Terminal growth rate in residual change in earnings. Common input for all firms: r L : forward earnings yield or forward E/P ratio in the very long run. Historical data suggests r L to be about 6%. We set g = r e r L to capture the idea that growth and risk go together. Since r L is the same for all firms, a high g implies a high r e, and vice versa. We then use the following Ohlson-Juettner (OJ) valuation formula (developed later) to solve for the discount rate that relates current stock price to future earnings forecasts. Implied return (IR) or r e = (e 2 - e 1 )/e 1 + r L (r L P 0 /e 1 +1 d 1 /e 1 ) 2.2. Step 2: Compute required return using CAPM (RR) We infer the required return based on risk using CAPM. Most CAPM implementations use historical realized return or surveys to set the market risk premium. Our spreadsheet allows this approach. However, we believe that the computation of implied risk premium for the market portfolio should be the same as that for individual stocks. Therefore, we use the IR formula to estimate the implied risk premium for the market portfolio. This step requires the following inputs: r f : risk free rate used to derive market risk premium [yield on 10-year government bonds] β: company s beta mp 0 : Price of the market portfolio (S&P index) per share me 1 and me 2 : Analyst forecasts of earnings per share for the market portfolio (S&P index) for Y1 and Y2 md 1 : Analyst forecast of dividends per share for the market portfolio (S&P index) for Y1 r L : forward earnings yield or forward E/P ratio in the very long run described above February 19, 2012 Visit for updates. 2

4 Excess Implied Return (EIR) 4 P 0 = e 1 + e 2 e 1 r e (e 1 d 1 ) r e r e (r e g) One can now infer r e as follows: r e = A + SQRT ( A 2 + e 1 * ( e 2 e 1 - g) ) P 0 e 1 where A = 1 ( g + d 1 ) 2 P 0 To infer r e using the above formula requires some value of g, the growth rate of the residual change in earnings. The spreadsheet allows for three possibilities. Out of these three, the third one which captures the idea that growth comes with risk is the most reasonable. This case, described in Assumption III below, provides our main measure of implied returns Assumption I: g = short-term growth in earnings, (e 2 -e 1 )/e 1 Given the restriction g = (e 2 -e 1 )/e 1, reverse engineering the OJ formula implies: r e = g + d 1 P 0 This familiar expression shows that the growth rate plus dividend yield determines the discount factor. It serves as benchmark when, effectively, short and long term growth are the same Assumption II: g = long-run GDP growth One can assume that, in the long run, all firms will grow at the long-run GDP growth rate of about 3%. If g is set equal to zero and there are no dividends, then PEG and r e have a one-to-one relation. More generally, one can expect PEG and r e to rank firms similarly Assumption III: g = r e r L to capture the idea that growth comes with risk This case gives the formula discussed initially. Recall that r L is the forward earnings yield in the long run. Setting g = r e r L in the OJ derivation, one obtains: P 0 = e 1 + e 2 e 1 r e (e 1 d 1 ) r e r e r L This leads to the previously stated implied return formula: r e = (e 2 - e 1 )/e 1 + r L (r L P 0 /e d 1 /e 1 ) As a benchmark, if P 0 /e 1 = 1/r L and the payout is zero, then r e is the simple average of EPS growth and r L Why EIR can deviate from zero Besides mispricing, EIR can deviate from zero for the following reasons: Analyst forecasts available on public web sites may be stale and subject to potential biases. Thus, the forecast can differ markedly from the market s true but unobservable expectations. Consider a firm that announces bad news that lowers the analyst forecasts and the stock price. Suppose it takes a few days for the analyst forecasts to be updated on public web sites. In those few days, the price will appear abnormally low relative to publicly available analyst forecasts and the EIR will appear to be high. If February 19, 2012 Visit for updates. 4

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