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Bad Beta, Good Beta. John Campbell and Tuomo Vuolteenaho Harvard University and NBER Presentation at Oxford Finance Summer Symposium 11/6/2004. RESEARCH AGENDA. High P/B – growth or glamour?.

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## Bad Beta, Good Beta

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**Bad Beta, Good Beta**John Campbell and Tuomo Vuolteenaho Harvard University and NBER Presentation at Oxford Finance Summer Symposium 11/6/2004**High P/B – growth or glamour?**• High P/B must in the long run forecast either high profitability (ROE) or low stock returns (or both) • If high P/B forecasts stock returns, this may be because high-P/B stocks are less risky or because they are overvalued (or both) • If high-P/B stocks' returns are less risky than low-P/B stocks', is this risk differential caused by differential risk in fundamentals or in mispricing (or both)?**Growth or glamour?**Does high P/B forecast high ROE or low returns? High ROE… …justifies high price Risk is caused by covariances in fundamentals Low stock returns… …caused by risk or mispricing? Risk… …is risk caused by fundamentals or mispricing? Valuation level caused by mispricing BBGB Risks caused by covariances in mispricing**The CAPM**• People have short investment horizons • The average investor holds the market • If an asset has a high return when the market performs poorly, then the asset is insurance • i.e., low or even negative market beta • If an asset performs poorly when the market performs poorly, then it is risky • i.e., high market beta • The average investor requires a high return to hold risky assets, and accepts a low return to hold insurance**Why does the market fall?**• Bad news about future cash flows: • wealth decreases and future investment opportunities remain constant • The discount rate or cost of capital applied to the market's cash flows increases • wealth decreases but future investment opportunities improve • To a long-horizon investor (with a constant relative risk aversion higher than unity), the first case is much worse news than the second • Suppose market portfolio of only corporate bonds: Would you rather have bonds defaulting or interest rates going up?**Intuition from Gordon model**D is dividend, P is price, k is discount rate, and g is dividend growth k (discount rate news) and/or g (cash-flow news) P**Merton's ICAPM idea**• We break the market return in two components: • We also break up the CAPM beta of a stock into two components: • cash-flow beta, βCF • discount-rate beta, βDR**Merton's ICAPM idea**• Intuitively, covariance or beta with the really bad market moves (market's cash-flow news) should have a higher risk premium than covariance or beta with the less bad market moves (market's discount-rate news) • Campbell's (1993) version of Merton's (1973) ICAPM predicts: • discount-rate-beta premium should equal the variance of the market return, and • cash-flow-beta premium should be γ times higher, where γ is the coefficient of relative risk aversion of a representative investor • This is because poor returns driven by increases in discount rates are partially compensated by improved prospects for future returns**Beta and cholesterol**• It used to be thought that heart attack risk could be measured by the overall level of cholesterol. Routine blood tests reported this level. • Now we know there are two types of cholesterol, HDL and LDL. One (“bad cholesterol”) strongly increases the risk of a heart attack, the other (“good cholesterol”) weakly reduces it. Routine blood tests now report the two levels separately. • Similarly, beta has two types, but in this case “good beta” is really “not so bad beta” as it does increase the risk premium. • We hope that routine risk analysis will in the future report both types of beta separately.**An illustration**The Empire Strikes Back Bad Beta Not so bad beta**Our paper's three steps**• Estimate the market's cash-flow and discount-rate news • Using the estimated series, measure the cash-flow and discount-rate betas for various assets • See how these betas explain average returns, and compare the premia to those predicted by the theory**Summary of results**• Value and small stocks have higher bad cash-flow betas than growth and large stocks explains the value and size premia • Growth stocks have negative CAPM alphas because their betas are predominantly of the good discount-rate variety explains the negative CAPM alphas of growth stocks • Sorting on past CAPM betas induces little spread in mean returns in the post-1963 sample, because the sort creates a spread only in the good discount-rate beta.**Risk vs. return 1963:7-2001:12**• E(Ri-Rrf) = var(rM)βi,DR +var(rM)βi,DR +ei • Vertical axis is the average realized return • Horizontal axis is the predicted average return • 's are selected ME-and-BE/ME-sorted portfolios • 's are beta-sorted portfolios**Some previous research**• The ICAPM theory: Merton (1973), Campbell (1993) • Decomposing the market's return: Campbell and Shiller (1988a, 1988b), Campbell (1991), Campbell and Ammer (1993) • Value spread predicts the market return: Eleswarapu and Reinganum (2001), Brennan, Xia, and Wang (2001) • Value stocks are more sensitive than growth stocks to market's cash-flow news: Liew and Vassalou (2000), Cohen, Polk, and Vuolteenaho (2002) • Cross-sectional tests of the ICAPM: Campbell (1996), Li (1997), Hodrick, Ng, and Sengmuller (1999), Lynch (1999), Chen (2000), Brennan, Xia, and Wang (2001), Ng (2002), Guo (2000), etc.**Paper's three empirical steps**• Estimate the market's cash-flow and discount-rate news • Using the estimated series, measure the cash-flow and discount-rate betas for various assets • See how these betas explain average returns, and compare the premia to those predicted by the theory**Idea of news identification**• If an asset’s return is unexpectedly high, • its expected cash flows must have increased (i.e., cash-flow news must have been positive), and/or • future expected returns decreased (i.e., discount-rate news must have been negative) • The objective is to empirically split the market return into these two components • We use the Campbell-Shiller log-linear present-value model and a VAR to do just that**Defining news terms**• Cash-flow news: Change in discounted sum of current and future expected dividend growth rates • Discount-rate news: Change in discounted sum of future expected returns • Set the discount coefficient ρto .95 annualized**VAR implementation**• Assume that a VAR model generates returns • One can then compute unexpected returns and discount-rate news • Cash-flow news can be taken as a residual**VAR state variables**• Excess market return • log return on CRSP VW minus log return on three-month T-bills • TERM yield spread (in percentage points) • Yield on ten-year taxable T-bonds minus yield on short-term taxable T-notes • Smoothed P/E • Log S&P 500 price index minus log 10-year trailing moving average of S&P 500's aggregate earnings • Small-stock value spread • Log(BE/ME) of small-value Fama-French 2-by-3 portfolio minus log(BE/ME) of small-growth portoflio**Logic behind state variables**• TERM yield spread • High TERM yield spread forecasts high returns on long-term bonds • Since stocks are long-term assets, expected stock returns should also be high • Predicted coefficient positive • Smoothed P/E • Ten-year trailing moving average controls for cash-flow-generating ability of the stocks in S&P 500 • Holding cash-flow-generating ability constant, higher price must mean lower future stock returns • Predicted coefficient negative**Logic behind state variables**• Small-stock value spread • If the ICAPM is to explain the value effect, value minus growth stock returns must be correlated with changes in discount rates, so a moving average of these returns should be a proxy for the level of the discount rate • Growth stocks have a longer "duration," thus their values should be especially dependent on discount rates • Imperfect-capital-markets story: High discount rates = SEO market is closed. Maybe small growth stocks require financing simply to survive? • Small growth stocks sensitive to "irrational exuberance?" • All these phenomena likely to be more extreme for small stocks • Predicted coefficient negative**VAR state-variable data**VS PE TY**Summary of the market's news**• At monthly frequency, market's discount-rate news are about twice as volatile as cash-flow news (5% per month vs. 2.5% per month) • Correlation between the news terms is low (.11) • An interpretation of the VAR: • Negative cash-flow news corresponds to a profit recession • Positive discount-rate news corresponds to a valuation recession • A drop in stock prices that is accompanied by a drop in the P/E, higher TERM yield spread, and a shrinking value spread are signs of a valuation recession**Paper's three empirical steps**• Estimate the market's cash-flow and discount-rate news • Using the estimated series, measure the cash-flow and discount-rate betas for various assets • See how these betas explain average returns, and compare the premia to those predicted by the theory**Defining betas**• We use fitted values of VAR news to estimate betas on various portfolios • The denominator is equal to variance of unexpected market return • We include a lag to alleviate infrequent-trading problems, sluggish reaction of small stocks to new information, etc.**Test assets**• We measure the cash-flow and discount-rate betas on Fama-French 25 ME-and-BE/ME-sorted portfolios • We also create risk-sorted portfolios by sorting stocks on pre-estimated regression loadings on • market return, • change in term-yield spread, and • change in the small-stock value spread • Data ranges: • Full period, 1929:1-2001:12 • Early subsample, 1929:1-1963:6 • Modern subsample, 1963:7-2001:12**Beta evolution**βCF Value minus growth Small minus big βDR**Paper's three empirical steps**• Estimate the market's cash-flow and discount-rate news • Using the estimated series, measure the cash-flow and discount-rate betas for various assets • See how these betas explain average returns, and compare the premia to those predicted by the theory**Epstein-Zin objective function**• We assume that long-horizon investor has Epstein-Zin (1989, 1991) preferences • If the elasticity of intertemporal substitution () approaches 1, the optimal consumption-wealth ratio approaches a constant (=1-)**Epstein-Zin risk premia**• Suppose that the investor follows an optimal portfolio strategy, denoted by p • Campbell (1993) shows that the approximate optimality of portfolio strategy p requires that the following first-order conditions are satisfied:**Substituting out consumption**Discount-rate news NDR**Asset pricing model**• Recognizing that unexpected return equals cash-flow news minus discount-rate news allows us to rewrite the first-order condition: Premium on cash-flow beta Premium on discount-rate beta**Implementation**• Set the reference portfolio to the CRSP value-weight index portfolio • Use an unconditional betas and mean returns • Use average simple returns on the left hand side • Include a lag in beta estimation One free parameter Plug in the market's historical variance**Test assets**• 25 Fama-French ME-and-BE/ME-sorted portfolios • Value vs. growth • Small caps vs. large caps • 20 risk-sorted portfolios formed on betas w/r • market return, • change in term-yield spread, and • change in the small-stock value spread • Data ranges: • Full period, 1929:1-2001:12 • Early subsample, 1929:1-1963:6 • Modern subsample, 1963:7-2001:12**Post-1963, ICAPM beats CAPM**R2 = 47.4% R2 = - 61.6%**Critical issues**• The following steps are critical for the empirical success of our model: • Inclusion of the small-stock value-spread variable in the VAR state vector • Inclusion of at least one lagged month at the beta-estimation stage • ρ = δ value between .941/12 and .961/12 • Exclusion of momentum portfolios from the asset-pricing test**Conclusions**• Merton's ICAPM predicts that, if investors are conservative, • "bad" cash-flow beta (covariance of a firm's stock return with the market's cash-flow news) should have a high premium • "good" discount-rate beta (covariance of a firm's stock return with the market's discount-rate news) should have a very small premium

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