Equity and Fixed Income

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1 Equity and Fixed Income Juliusz Jabłecki Quantitative Finance Dept. Faculty of Economic Sciences University of Warsaw and Head of Monetary Policy Analysis Team Economic Institute, National Bank of Poland 1

2 Lecture 2: Approaches to equity valuation Total market capitalization of global equity markets is ca. USD 55 tn (65% world GDP) with some 46 ths listings. Equity markets have changed a lot over the past century. Source: Credit Suisse Global Investment Returns Yearbook

3 From an investment point of view equities form one of the main asset classes Source: Credit Suisse Global Investment Returns Yearbook 2013 There are several approaches to valuing equity. In what follows we first describe basic rules of thumb, before introducing the Bloomberg Discounted Dividend Model (DDM) and the JP Morgan fair value model for equities. 3

4 Heuristic #1: Price-to-earnings ratio is a gauge of overconfidence. Stocks with low P/E are attractive. Investors who buy stocks with low PE ratios think they re getting a bargain. Generally, they believe that when a stock s PE ratio is high, investors have unrealistic expectations for the earnings growth of that stock. High hopes, the low PE investor reasons, are usually dashed, along with the price of the stock. Conversely, they believe the prices of low PE stocks are unduly discounted and, when earnings recover, the price of the stock will follow. Source: J. O Shaughnessy, What Works on Wall Street, 2005 The strategy of selecting low P/E stocks hasn t performed spectacularly well... 4

5 Heuristic #2: Look at price-to-book ratio which is not susceptible to earnings manipulation...investors who buy stocks with low price-to-book ratios believe they are getting stocks at a price close to their liquidating value, and that they will be rewarded for not paying high prices for assets. Over the long haul, buying low P/B stocks has actually performed reasonably well... Source: J. O Shaughnessy, What Works on Wall Street,

6 There is no fundamental theoretical reason why we should care about these heuristics other than that others might as well... 6

7 We now look at a simple, yet powerful valuation model. DDM is based on a simple idea that stock price should be equal to the present value of forecasted dividends: P V = D 1 (1 + r) + D 2 (1 + r) = i=1 D i (1 + r) i DDM looks deceptively simple. In fact, there are some obvious problems with applying it in practice: we don t know future earnings: E 1, E 2,... we don t know future payout ratios, and hence, dividends D 1, D 2,... we don t know which discount rate r to apply A useful starting point is to assume e.g. constant dividend or dividend growing at a constant rate. But how sensible is that? Practitioners have a way of using DDM and it is worth looking at how they do it. 7

8 Implementation step 1: determine the discount rate using CAPM Each investor demands compensation for investing in a (risky) stock S instead of a risk-free bond r s = r f (risk-free rate) + Π(equity risk premium) = = r f + β (r M r f ) = = r f + cov(r M, r S ) (r var(r M ) M r s ) The knowns in this equation are: 8

9 the risk-free rate which can be approximated e.g. by 10Y US Treasury bond yield; the beta which can be found by regressing stock s return on the market index (S&P 500) But how to determine r M? We could simply calculate historical average return on S&P 500, but that would be backward-looking. Instead, Bloomberg uses a forward-looking approach: find out analysts expectations of dividends for all companies in the market calculate capitalization-weighted dividend return one would obtain by holding the market use market prices of all stocks to find out capitalizationweighted price of the market find out r M as implied by expected dividends and current prices 9

10 This is how the market risk premium has behaved in the US: Beta for Apple 0.9 Apple risk premium 0.9 ( ) = 6.7% Implementation step 2: determine model stages and companies growth rates In FY1, FY2 dividend forecasts are readily available for most tickets. 10

11 From that point on, Bloomberg assumes each company develops in three stages: growth, transition and mature. The length of the growth and transition periods depends on whether the equity is classified as explosive growth, high growth, average growth, or slow/mature growth. 11

12 Growth stage: varies from 3Y to 9Y; during the first year of the growth stage, if there is an explicit EPS forecast for FY3, use that forecast; if there is no explicit forecast for FY3, the EPS in FY3 is set as FY2 (1 + long-term growth rate); during the remaining years of the growth stage earnings per share (EPS) grow at the long-term growth rate. Transition stage: following the growth stage, the model assumes that the earnings growth rate for the firm approaches the rate that applies to the general market for all mature issues.the model applies the same linear increase or decrease to the payout ratio to arrive at the mature stage payout ratio, which defaults to 45%. Mature stage: After the transition stage, the model assumes that all issues have the same earnings growth rate and payout rate. The payout rate defaults to 45%. The mature growth rate equals: retention rate r M 12

13 Example: Assume that a U.S. equity has per share earnings estimates of $0.50 in the first year and $1.00 in the second year with an indicated annual dividend of $0.10. Also assume that the firm has an annual growth rate of 15% and that its growth and transition stages are each two years. The firm s current payout ratio is then 20% as a result of its current annual dividend and first year earnings of $0.50 per share (0.10/0.50 = 20%). Assume that the current 10-year Treasury bond rate is 6% and that the equity risk premium is 4%. Theoretical value of the equity equals $

14 The second model we analyze is the JP Morgan Fair Value Model for Equities. The model assumes that the equity price is equal to the expected future cash flows (i.e. dividends) discounted to the present using an equity discount rate (EDR): P = i ke 0 (1 + g) i (1 + EDR) i, where E 0 denotes current earnings, g is earnings growth rate and k the payout ratio. To implement the model, k, g and EDR need to be specified. dividend payout ratio is assumed to equal the long-term average for S&P 500, k = 50%; earnings are assumed to grow accoring to a two-stage model; the first stage lasts 5 years over which g is estimated using a backward-looking econometric model (as analysts forecasts were found to be systematically over-optimistic); in the second stage g reverts to the long-run average since 1950s of g LT = 2.2% 14

15 15

16 With these assumptions: P = ke 0 EDR g LT (1 + g LT + 5(g E g LT )) Given market price, implied EDR can be determined: Market price implied EDR econometric model 16

17 17

18 The EDR model has worked reasonably well in practice... The full model is parameterized as follows 18

19 These coefficients may be already outdated. We will try to see how the model performs using current data. 19

20 Exam-like problems 1. Determine the formula for the price of a stock in DDM assuming: (a) constant dividend; (b) dividend growing at a constant rate g; (c) what condition does g and r have to satisfy for the discounted dividend series to converge (and hence for price to exist). 2. The stock market is composed of three companies A, B, and C, each with a share of 1/3 in total capitalization. Analysts expect A to pay a perpetual dividend of 10; B to pay a divided of 3 next year and to grow by 5% forever; C to pay a dividend of 2 and grow by 8% forever. The market prices of stocks A, B, C are 100, 105 and 110 respectively. Find the implied market rate of return. 3. Assume that a U.S. equity has per share earnings estimates of $0.50 in the first year and $1.00 in the second year with 20

21 an indicated annual dividend of $0.10. Also assume that the firm has an annual growth rate of 15% and that its growth and transition stages are each two years. The firm s current payout ratio is then 20% as a result of its current annual dividend and first year earnings of $0.50 per share (0.10/0.50 = 20%). Assume that the current 10-year Treasury bond rate is 6% and that the equity risk premium is 4%. Calculate the theoretical value of the equity using the Bloomberg dividend discount model. 21

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