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Cost of Capital John H. Cochrane University of Chicago GSB

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Standard approach Question: Should we invest, buy asset or company? Standard answer: Value = Expected Profit / Expected Return (Really, multiperiod version) ER? Use CAPM, ER = Rf + β E(Rm-Rf) Spend a lot of time on β, use 6% for E(Rm-Rf)

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Warning: Most people misunderstand “Expected.” Time Profit “Expected” “Risk” Time Profit Expected Risk What many people meanWhat the formula means This may explain high required-return hurdles.

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Warning 2: Valuation is very sensitive to growth, return assumptions. The cost of capital matters! P/D = 1/(r-g)

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Market Premium = 6%? My focus: using the CAPM for cost of capital Problem 1. We don’t know E(Rm-Rf)! 6% is very rough! Statistical uncertainty – large with 18% σ Economic uncertainty. 6% (0.5 Sharpe) is HUGE. No economic explanation for 6%. Did our grandparents really know 6%? Suggests true ex-ante premium is lower! T Yearsσ/√TInterval 58%-10% to 22% 204%-2% to 14% 502.5%1% to 11%

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Problem 2. Market Premium varies a lot through time. Returns are forecastable. Dividend (cashflow) growth is not forecastable. All variation in price / x is due to time-varying discount rate E(Rm-Rf). Your discount rate (cost of capital) should vary too; low cost when p/x is high! When p/x is high, it’s ok to invest in high p (high cost) projects

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Market premium varies a lot through time Forecasts made 5 (10) years ahead using D/P regression

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3. CAPM does not describe the cross-section of stocks.

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Multifactor models are replacing the CAPM Example: Fama-French model E(R i -R f ) = b i E(R m -R f ) + h i E(HML) + s i E(SMB)

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Use Dynamic Multifactor Models? Use multifactor models (e.g. FF) with time-varying betas and time-varying premiums? Note betas and premium vary over the life of the project as well as over time (when project is started). Technically complex but straightforward. Much theoretical literature is headed this way. Better answers? Problem 1: New premia just as uncertain and vary over time too! E t (R i -R f ) = b i E t (R m -R f ) + h i E t (HML) + s i E t (SMB) What’s E(HML), E(SMB)? Same statistical problem. Even less economic understanding of value/size premium. Less still of how they vary over time. More of them!

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Use Dynamic Multifactor Models? Problem 2: Lots of new “factors” and anomalies. FF fails on momentum, small growth (especially important here!), other anomalies. “Answer:” Many more factors! Momentum, small-growth, currencies, term premium, default premium, option returns and up/down betas……

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Answer guess 1: Comparables? Renewed use of comparables. (Keeping fallacies and pitfalls in mind.) E(Ri) = Rf + β E (Rm-Rf) Why not just measure the left hand side? Avg returns of similar firms? Old answers: 1.CAPM gives better measure. σ is lower (1/2) so σ √T is better. (Industry return may have been luck.) 2.Need to make β adjustments. This project may be low β though industry (comparable) is high β. 3.CAPM is “right” model.

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Comparables? New answers: 1.We don’t know (yet) that multifactor models give better predictions for ER going forward. 2.Challenge for MF is now to explain patterns already well described by characteristics (size, book/market, momentum, industry etc.) 3.Possible to be low β project with high ER characteristics, but how often does this really happen? 4.Much less confidence that MF models are “True” vs. “Descriptive.” Who really cares about covariance with SMB?

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Answer guess 2: Prices Why is the cost of capital different from the cost of tomatoes? Real question: If we issue stock for new investment or acquisition, will money raised = cost of investment? A: If new project is like your old projects, market / book ratio tells you the answer directly. Q theory: Invest whenever market / book > 1.

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