Is it Wrong the Cpitl sset Pricing Model - Essay Example

"The Cpitl sset Pricing Model (CPM) isn't wrong. It just doesn't go fr enough." The cpitl sset pricing model (CPM) is mthemticl model tht explins the reltionship between risk nd return in rtionl equilibrium mrket. The model is used in finnce to determine theoreticlly pproprite required rte of return sset, if tht sset is to be dded to n existing well-diversified portfolio, provided tht sset's non-diversifible risk. The CPM formul tkes into ccount the sset's sensitivity to non-diversifible risk (lso known s systemtic risk or mrket risk), often represented by the quntity bet () in the finncil industry, s well s the expected return of the mrket nd the expected return of theoreticl risk-free sset. The cpitl sset pricing model (CPM) theory ssumes tht n investor expects yield on certin security equivlent to the risk free rte (sy tht rte chievble on six-month Tresury bills) plus premium bsed on mrket vribility of return X mrket risk premium. In Winter 1991, the mrket risk premium on listed U.S. common stocks ppers to hve been bout 6.5%, ccording to sttistics published in the Qurterly Review, Winter 1991, by the Federl Reserve Bnk of New York (though the Ibbotson study found it to exceed 8% from the mid 1920s through 1987). Thus in period of 4% infltion, the T-bill rte might be ppropritely 4.5 to 5%; four- or five-yer Tresury note should hve yield of 5.5 to 6%; Tresury bonds should yield percent higher thn this; nd corporte bond yields should hve even higher returns to compenste for their dditionl credit or business risk. The cpitl sset pricing model for this scenrio suggests tht nnul returns on low-bet electric utility might be .05 + .50 bet (.065) = 8.25%. bout 75% of this might come from dividends nd the blnce from expected growth in dividends over n extended time period. By contrst, n verge stock with bet of 1.00 should provide rte of return of 4.5 to 5.0% plus the mrket premium of 6.5% or between 11 nd 12%. high-bet stock (one operting in cyclicl industry, for exmple) with bet, or reltive mrket voltility in price, of 1.50 should provide mrket return of 5.0% + 1.50 (0.065) or bout 15%. We could convert these from ernings price rtios to price-ernings (P-E) rtios nd determine tht the electric utilities, in this scenrio, should trde t bout 12 P-E rtio nd the high-bet stock should trde t P-E rtio of bout 6 to 7 . Three-yer verge (smoothed) ernings for these type firms hve, in fct, provided bout these P-E levels for highly cyclicl stocks during recent yers. The problem is in how to evlute bove verge or super growth rte for non- or low-dividend-pying stocks, topic of mjor concern to investment fundmentlists. Since stocks re bought on the bsis of expected returns for the next yer (or for severl yers into the future), perceived shift in the rte of infltion (or of the interest rte level), will send most common stocks to higher or lower levels. Strength of the overll economy, the sector in which the firm opertes, its own industry's strengths nd weknesses, nd individul firm's chrcteristics likewise hve bering on the ssessed mrket vlue of equity issues. In fct, this hypothesis is greed on by most fundmentlists nd technicins. The pproch recommended by most investment fundmentlists moves from the mcro to the micro nlysis. First of ll, we should determine if the overll stock mrket is the plce to be. Next, we should zero in on the industries tht re showing bove-verge strength. Next, we should select individul firms tht re likely to led others in their respective industries. In generl, the security mrket line, t given point in time, ppers to do resonbly efficient job of explining differences in expected yields on lterntive types of finncil issues. The cpitl sset pricing model is merely grph showing the nticipted yields on securities trded in money nd cpitl mrkets with vrying degrees of finncil risk. The trend line tht joins the points on the grph is referred to s the security mrket line. Mrket yields re shown on the y (verticl) xis nd the vribility of return on the x (horizontl) xis. lterntively, the verge yields reported in current finncil literture might be chrted on the line nd the pproximte risk of vribility red on the bse. Let us illustrte the concept grphiclly with the following ssumed yields: three-month T-bill yield of 5%, four-yer T-note yield of 6%, twenty-yer T-bond yield of 7.5%, corporte long-term bond yield of 8%, fixed-rte mortgge yield of 8.5%, nd stock returns running from low on electric utilities to high on cyclicl nd specultive issues. s yields shift upwrd on short-, intermedite-, nd long-term government issues, bond yields will generlly rise, mening tht bond prices decline, wheres stock prices will begin to fll (or price-ernings rtios decline). When yields on fixed-return government issues decline, conversely, stock prices usully move upwrd, lthough some t fster rtes thn others. The ttrction of the CPM is tht it offers powerful nd intuitively plesing predictions bout how to mesure risk nd the reltion between expected return nd risk. Unfortuntely, the empiricl record of the model is poor-poor enough to invlidte the wy it is used in pplictions. The CPM's empiricl problems my reflect theoreticl filings, the result of mny simplifying ssumptions. But they my lso be cused by difficulties in implementing vlid tests of the model. For exmple, the CPM sys tht the risk of stock should be mesured reltive to comprehensive "mrket portfolio" tht in principle cn include not just trded finncil ssets, but lso consumer durbles, rel estte nd humn cpitl. The rtionle for the CPM eqution is the common sense observtion tht investors must be coxed to move their money from riskless ssets like U.S. Tresury bonds into risky ssets. Consider n everydy exmple wherein investors cn obtin bout 7% return on Tresury security. Investors will not invest in brod mrket portfolio of risky securities unless they cn expect significnt return premium for ccepting the risk in excess of the riskless security. In terms of the bove exmple, investors would wnt n expected return tht is greter thn 7% if mteril risk is present. The usefulness of the CPM is in mesuring how much of n expected return premium is pproprite for investments in light of their riskiness reltive to the risk of benchmrk brod mrket index. The economic interprettion of the CPM eqution is s the bse risk-free rte of return (Rf) plus the mrket-wide risk premium of (Rm - Rf) tht is required to cox investors wy from exclusive investment in risk-free securities. The bet coefficient mesures the riskiness of given security or portfolio reltive to the overll mrket benchmrk. Bet expresses how much the given investment returns tend to vry s the returns on the benchmrk mrket index vry over the business cycle. Bet therefore my be viewed s the pproprite weight to pply to the mrket-wide risk premium (Rm - Rf ). The bet of the mrket portfolio must, by definition, be equl to 1. Consider n exmple of how the CPM estimtes the pproprite risk-djusted expected return on n investment. ssume tht the risk-free rte of return on U.S. Tresury bond is 7%, the expected return on the mrket is 15%, nd tht n investor wnts to determine the pproprite expected rte of return on stock with bet of 1.5. The mrket-wide risk premium is (15% - 7%) or 8%. This implies tht investors will not llocte money to investments with mrket-like riskiness unless they cn expect to get t lest n 8% premium over the risk-free rte of 7%. However, 8% premium will be insufficient if n investment is more vrible (i.e., riskier) thn the overll mrket. The returns on stock with bet of 1.5 tend to vry 1.5 times more thn the return on the overll mrket. The mrket-wide risk premium of 8% must therefore be incresed 1.5 times to 12% in order to ttrct investors. Thus, stock with bet of 1.5 should generte n expected return of 19% in order to dequtely compenste investors for the bove-mrket risk of the investment. The CPM is good for evlution of investment projects but it is not enough for the investor to rely on this model only. The mjor shortcoming of the model is tht it ssumes tht sset returns re normlly distributed rndom vribles. It is however frequently observed tht returns in equity nd other mrkets re not normlly distributed. s result, lrge swings (3 to 6 stndrd devitions from the men) occur in the mrket more frequently thn the norml distribution ssumption would expect. Besides the model ssumes tht the vrince of returns is n dequte mesurement of risk while it cn be justified under the ssumption of normlly distributed returns, but for generl return distributions other risk mesures (like coherent risk mesures) will likely reflect the investors' preferences more dequtely. The model does not pper to dequtely explin the vrition in stock returns. Empiricl studies show tht low bet stocks my offer higher returns thn the model would predict. Some dt to this effect ws presented s erly s 1969 conference in Bufflo, New York in pper by Fischer Blck, Michel Jensen, nd Myron Scholes. Either tht fct is itself rtionl (which sves the efficient mrkets hypothesis but mkes CPM wrong), or it is irrtionl (which sves CPM, but mkes EMH wrong - indeed, this possibility mkes voltility rbitrge strtegy for relibly beting the mrket). The model ssumes tht given certin expected return investors will prefer lower risk (lower vrince) to higher risk nd conversely given certin level of risk will prefer higher returns to lower ones. It does not llow for investors who will ccept lower returns for higher risk. Csino gmblers clerly py for risk, nd it is possible tht some stock trders will py for risk s well. The model ssumes tht ll investors hve ccess to the sme informtion nd gree bout the risk nd expected return of ll ssets. The model ssumes tht there re no txes or trnsction costs, lthough this ssumption my be relxed with more complicted versions of the model. The mrket portfolio consists of ll ssets in ll mrkets, where ech sset is weighted by its mrket cpitliztion. This ssumes no preference between mrkets nd ssets for individul investors, nd tht investors choose ssets solely s function of their risk-return profile. It lso ssumes tht ll ssets re infinitely divisible s to the mount which my be held or trnscted. The mrket portfolio should in theory include ll types of ssets tht re held by nyone s n investment. In prctice, such mrket portfolio is unobservble nd people usully substitute stock index s proxy for the true mrket portfolio. Unfortuntely, it hs been shown tht this substitution is not innocuous nd cn led to flse inferences s to the vlidity of the CPM, nd it hs been sid tht due to the inobservbility of the true mrket portfolio, the CPM might not be empiriclly testble. This ws presented in greter depth in pper by Richrd Roll in 1977, nd is generlly referred to s Roll's Critique. Theories such s the rbitrge Pricing Theory (PT) hve since been formulted to circumvent this problem. Becuse CPM prices stock in terms of ll stocks nd bonds, it is relly n rbitrge pricing model which throws no light on how firm's bet gets determined. It is possible tht the CPM holds, the true mrket portfolio is efficient, nd empiricl contrdictions of the CPM re due to bd proxies for the mrket portfolio. The model clls for the mrket portfolio of invested welth, but the mrket proxies used in empiricl work re lmost lwys restricted to common stocks. In response to this problem, one cn len on Stmbugh's (1982) evidence tht tests of the CPM re not sensitive to expnding the mrket proxy to include other ssets, bsiclly becuse the voltility of expnded mrket returns is dominted by stock returns. nd it is unlikely tht the CPM problems exposed by price rtios like B/M re due to bd mrket proxy. Portfolios formed by sorting stocks on price rtios produce little vrition in bets clculted with respect to mrket portfolio of stocks (Lkonishok, Shleifer, nd Vishny (1994)). It seems unlikely tht dding other ssets to the mrket proxy will produce the spreds in bets needed to explin the vlue effect. But there is no clen solution to the mrket proxy problem. nd if stndrd mrket proxies cuse tests of the CPM to fil, they lso cuse problems in pplictions. Specificlly, pplictions of the CPM tht use stndrd mrket proxy to estimte expected returns will mke systemtic nd predictble errors. For exmple, finnce textbooks often recommend using the Shrpe-Lintner CPM risk-return reltion to estimte the cost of equity cpitl. The prescription is to estimte stock's mrket bet nd combine it with the riskfree rte nd the verge mrket premium to produce n estimte of the cost of equity. The lrge stndrd errors of estimtes of the mrket premium nd of bets for individul stocks probbly suffice to mke such estimtes of the cost of equity meningless, even if the CPM holds nd the estimtes use the true mrket portfolio (Fm nd French (1997), Pstor nd Stmbugh (1999)). But if one of the common mrket proxies is used, the problems re compounded. Empiricl work, old nd new, tells us tht the reltion between bet nd verge return is fltter thn predicted by the Shrpe-Lintner CPM. s result, CPM cost of cpitl estimtes for high-bet stocks re too high (reltive to 17 historicl returns) nd estimtes for low-bet stocks re too low (Friend nd Blume (1970)). Similrly, CPM cost of equity estimtes for high B/M (vlue) stocks re too low nd estimtes for low B/M (growth) stocks re too high. The CPM is lso often used to mesure the performnce of ctively mnged portfolios. The pproch, dting to Jensen (1968), is to estimte the time-series regression for portfolio (mutul funds re commonly studied), nd use the intercept (Jensen's lph) to mesure bnorml performnce. The problem is tht, becuse of the CPM's empiricl filings, even pssively mnged (indexed) portfolios tht ssume rtionl pricing will produce bnorml returns if their investment strtegies involve tilts towrd CPM nomlies (Elton, Gruber, Ds, nd Hlvk (1993)). For exmple, funds tht concentrte on low bet stocks or vlue stocks will tend to produce positive bnorml returns reltive to the predictions of the Shrpe-Lintner CPM. The version of the CPM due to Shrpe (1964) hs never been n empiricl success. From the first, empiricl work on the model consistently finds tht the reltion between verge return nd mrket bet is fltter (the risk premium per unit of mrket bet is lower) thn predicted by the model. nd this problem is serious enough to invlidte most pplictions of the model. The CPM, like Mrkowitz' (1959) portfolio model on which it is built, is evertheless theoreticl tour de force. nd its fundmentl insights bout risk nd return crry over in generlized form to models like Merton's (1973) ICPM. We continue to tech the CPM, s n introduction to the fundmentl concepts of portfolio theory nd sset pricing, to be built on by more dvnced models, nd with wrnings tht despite its seductive simplicity, the CPM's empiricl problems probbly invlidte its use in pplictions. Bibliogrphy: 1. Bonds." Journl of Finncil Economics. 33:1, pp. 3-56. 2. Elton, Edwin J., Mrtin J. Gruber, Snjiv Ds nd Mtt Hlvk. 1993. "Efficiency with Costly 3. Fm, Eugene F. nd Kenneth R. French. 1993. "Common Risk Fctors in the Returns on Stocks nd 4. Finnce. 23:2, pp. 389-416. 5. French, Crig W. (2002). Jck Treynor's 'Towrd Theory of Mrket Vlue of Risky ssets' (December). vilble t http://ssrn.com/bstrct=628187 6. French, Crig W. (2003). The Treynor Cpitl sset Pricing Model, Journl of Investment Mngement, Vol. 1, No. 2, pp. 60-72. vilble t http://www.joim.com/ 7. Friend, Irwin nd Mrshll Blume. 1970. "Mesurement of Portfolio Performnce under Uncertinty." mericn Economic Review. 60:4, pp. 607-636. 8. Informtion: Reinterprettion of Evidence from Mnged Portfolios." Review of Finncil 9. Jensen, Michel C. 1968. "The Performnce of Mutul Funds in the Period 1945-1964." Journl of 10. Lkonishok, Josef, ndrei Shleifer nd Robert W. Vishny. 1994. "Contrrin Investment, Extrpoltion, nd Risk." Journl of Finnce. 49:5, pp. 1541-1578. 11. Mrkowitz, Hrry. 1959. Portfolio Selection: Efficient Diversifiction of Investments. Cowles Foundtion Monogrph No. 16. New York: John Wiley & Sons, Inc. 12. Mehrling, Perry (2005). Fischer Blck nd the Revolutionry Ide of Finnce. Hoboken: John Wiley & Sons, Inc. 13. Merton, Robert C. 1973. "n Intertemporl Cpitl sset Pricing Model." Econometric. 41:5, pp. 867-887. 14. Mullins, Dvid W. (1982). Does the cpitl sset pricing model work, Hrvrd Business Review, Jnury-Februry 1982, 105-113. 15. Pstor, Lubos, nd Robert F. Stmbugh, 1999, "Costs of Equity Cpitl nd Model Mispricing." Journl of Finnce. 54:1, pp. 67-121. 16. Qurterly Review 140, Mrch, reprinted in J. Steindl, Economic Ppers 1941-88, London: Mcmilln, 1990. 17. Ross, Stephen . (1977). The Cpitl sset Pricing Model (CPM), Short-sle Restrictions nd Relted Issues, Journl of Finnce, 32 (177) 18. Shrpe, Willim F. 1964. "Cpitl sset Prices: Theory of Mrket Equilibrium under Conditions of Risk". Journl of Finnce. 19:3, pp. 425-442. 19. Stmbugh, Robert F. 1982. "On The Exclusion of ssets from Tests of the Two-Prmeter Model: Sensitivity nlysis." Journl of Finncil Economics. 10:3, pp. 237-268. 20. 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