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## Cost of Capital

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**Cost of Capital**John H. Cochrane University of Chicago GSB**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)**Warning: Most people misunderstand “Expected.”**What many people mean What the formula means • This may explain high required-return hurdles. Profit Profit Risk “Expected” Expected Risk “Risk” Time Time**Warning 2: Valuation is very sensitive to growth, return**assumptions. The cost of capital matters!P/D = 1/(r-g)**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!**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**Market premium varies a lot through time**Forecasts made 5 (10) years ahead using D/P regression**Multifactor models are replacing the CAPM**Example: Fama-French model E(Ri-Rf) = bi E(Rm-Rf) + hiE(HML) + si E(SMB)**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! Et(Ri-Rf) = bi Et(Rm-Rf) + hiEt(HML) + siEt(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!**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……**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: • CAPM gives better measure. σ is lower (1/2) so σ√T is better. (Industry return may have been luck.) • Need to make β adjustments. This project may be low β though industry (comparable) is high β. • CAPM is “right” model.**Comparables?**• New answers: • We don’t know (yet) that multifactor models give better predictions for ER going forward. • Challenge for MF is now to explain patterns already well described by characteristics (size, book/market, momentum, industry etc.) • Possible to be low β project with high ER characteristics, but how often does this really happen? • Much less confidence that MF models are “True” vs. “Descriptive.” Who really cares about covariance with SMB?**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.