rT3O CHAPTER 26 EVALUATToN oF PoRrFoLro PERFoRMANCE

CORRELATIONS AMONG ALTERNATIVE PORTFOLIO PERFORMANCE MEASURES

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(panicularly the Net Selectivity measure). This suggests that, although th€ measures provide agenerally consistent assessment of ponfolio p€rformance when taken as a whole. they remaindistinct at an individual level. This rcinforces our earlier point that it is best 10 consid€r thesecomDosiies collectiv€lv and that the user must understand what €ach means.

As noted earlier ponfolio managers can add value to their invertors in either of two ways: selecl-ing superior securities or demonstrating superior market liming skills by allocating funds to dif-ler€nt asset class€s or market segmenB. Attribution anallsis attempts to distinguish which ofth€se la€rors is the source ofth€ ponfolio s ovemll performance. Specifi€ally. this method com-pares the toial r€tum to the manager's actual investment holdings lo fte retum for a predetermined benchmffk ponfolio and decomposes the diffetence in ro an allocation etlect andaseLe.-rion e.r?cr The mo( slraightforward way to measure thes€ two effects is as follows:

>26.9Allocntion Efrecr =:,[(r;, r;,) x (&, Rr)]Selection Effed =:,1(,-) x (&, - RfJl

u.,, u, = tte invstm€nt proportions given lo the ilh l'|,rl"l r.aner, (e.&, a$.1 cl.s, iDdusa.ygrcup) in the nanagerrs rctual porlfolio and the benchmsrk po.tfolio. rcspecliiely

&i id = the investment rtium to the ith market s€8ment in the mm8e.!s octud Portfolio lndtte beDchm.rk porifollo, r€spe.lively

&2 = the tot l Ftu.n to the benchnark portfolio

Wirh Equation 26.9, the allocalion effect m€asures the manager's decision to over' or under-weight r pan;cular markel segm€nl (i.e.. thr, - ipl) in terms of that segmenfs retum perfoFmance relative to the overall retum to the benchmark (i.e., t4,, - &,1). Cood timing skill is there-lbre a matter of investirg more money in those market segments that end up producing greaterthan average retums. The selection effEJt measures the manager's ability to form specificmarkel segmenr ponlblios that g€nerate superior retums rclative to the way in which the com-parable markel segmenl is defined in the benchmark portfolio (i.e.. t&, - &,1). w€ighted by the

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manager's actual market segment investment proportions. When constructed in this manner tbemanager\ total value-added p€rformance is the sum ofth€ allocalion and selection effects.1t

Asset Class As an €xample of this process, consid€r an investor whose top-down portfolio stralegy €onsistsAttribution oftwo dimensions. Fint. he decides on a broad allocation ofhis investmenl dolnrs across tnree

Analysis: asset classes: U.S. slocks, U.S. long-term bonds, and cash equivalents, such as U.S. TreasuryAn ExamPle bills or certificates of deposit. Once this judgment is made, the investor's second general deci

sion is choosing which specific stocks, bonds, and cash instrumenN to buy. As a benchmark. heselects a hypothetical ponfolio with a 60 percent allocation to the Standard and Poor's 500 index,a 30 percent investment in th€ Lehman Corporate Long Bond index, and a l0 percent allocationto ttuee-month Treasury bills.

Suppose that at the start of the investmenl p€riod, the investor believes equity values aiesomewhat inflated and is not optimistic about the near-term p€rformance of the stock market.Compared io the benchmark, he therefore decides 10 underweight sto€ks and overweighr bondsand cash in his actual portfolio. The investment proponions he chooses are 50 perceot in equity,38 percent in bonds, and 12 percent in cash. Futher, instead of selecting a broad ponfolio ofequities, he decides to concentrate on the intercst rate sensitive sec|ors. such as utilities andfinancial companies, while de€mphasizing the technology and consumer durables sectors.Finally, he resolves b buy shoner duration bondr of a higher credit quality than are contained inthe benchmark bond index and to buy comnercial paper rather than Treasury bills.

In this example, the manager has made active investment decisions involving both the ailoca,tion of assets and the selection of individual securilies. To determine if either (or both) of thesed€€isions proved to be wise ones. at the end oflhe investment period he can calculak his over,all and s€gment-specific performance. Exhibil26.12 summarizes these hypothetical retums forthe investor's actual and benchmark asset class portfolios as well as the investment weightingsfor each, The ovemllactual and benchmark retums can be computed as follows:

Overall Aclual Relum = (0.50 x 0.097) + (0.38 x 0.091) + (0-12 x 0.056)= 4.98q.

Overall Benchmark Retum = (0.60 x 0.086) + (0.10 x 0.092) + (0.10 x 0.054)= 8.46%

Thus, the manager beat rhe ben€hmark by 52 basis points (= 0.0898 - 0.0846) overrhis panicu-lar inveslment horizon.

L'wainscon hd trgued rhar a bener way to mersure rhe selection effed is ro nuxiply $e ndket segnent etud difreFenral by rhe b.hchndk for$at sgm.nt, oi tt.r) x (n,, Rr)]. A drawbek of this appro&h. however. is lhat lhe allo-carion and el.dion eltet no longer sum ro fie roral value-added rctum. To babnce the equation, he calculats an tn,.r,adi.h .fed ^s t,l$aj - rt) t (&, - Rr)l ro me.sure rhe iesidual Frf(mmce. S* Cra'g B. wain*ott. AttributionAoalysn ltr Eqnniesl in P?ddd.. Eraluati t, Ben.hno*s, anl Autibutbn Anetrstr, ed. !. Sqlnes lcharloltesviue.Va.: Assiarion lbr lNe(me.r Mahag€ment and Rerarch. | 995 ).

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