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Ning Tang

  slope E(Rm)R f  i i im,m ,  E E(ri) i rf fEir )i m m f  f  m  m m CAPM assumptions: Ind’l inv are price-tkrs, single-perd inv horizn, inv ltd to trd, prcd, and Prudnt Man Rule: mngr for othr’s assts mst act as how prdnt ppl govrn own affrsreq assts perf. divsble fn’l asst, no taxes, no transctn csts, no rstrctn on shrt sell, unltd lend/borrw at Rf be divsf and stndrds be appld to mgmt of port Cap Mkt Exptat’ns: Macro: exp’ns abt cap rate, inv are ratin’l, info is cstless, avlbl to all inv, homo exp, no infl’n mkts, devlpng contrys Micro:exp’ns inflc’g slct’n of part’r asst for part’r port RoR: hist’l from In eqil’m, all inv hold same port. of risky assets  is the mkt por mkt port is on efficient varity of sorces, base Equity Rsk Prem = rtrn of index – rtrn on Rf…base on arthmtic mean frontier and is the tangency port…in eqil’m excss dmd for any asst is 0 Constrct’g Port: Defn secrtis elgble for incls’n (Asst Allct’n)  use optmz’n procdr to slct CML  risk, SML  B… only risk inv will pay to avd is covariance risk secrtis and dtrmne prpr port wgt Asst Allct’n cnsdr’ns: rtrn req, rsk tolrnce, tme hrzn, invstr age Market Model to find Beta: R itRF  αtβ (RMi RFit e t t it 4 phases of wlth: Accml’n: sml nw, tme hrzn long, can take lg rsk  Consld’n: mid-late carer ^^gives you Secrts Char Line…Betas more stable for large ports (avg’ing effect) stg of life, balnce b/w trde-off of rsk & rtrn  Spnd’g: livng expnse frm accmlt’d assts, focs on 4 tests of CAPM: relat’p b/w retrn & B is linear – is relat’p positve – B is only measre of risk safety  Giftng: same as spnd’g Strtgc Asst Allct’n: LR asst mix, siml’n detrmnes likely tht’s pricd – intrcpt trm apprxmats Rf – Test results: intrcpt trm generlly hghr than Rf – mkt rsk rng of outcms w/ each asst mix, “buy & hld” Tctc’l Asst Allct’n: chg in asst mix drvn by chg prmium (slpe) generlly less steep thn thry – Joint Hypothesis Problem: can only tst CAPM if in exp rtrns…mkt tim’g apprch Rebalnc’g Csts: brkr commish, possble impct of trde on mkt we assme assts are pricd correctly in the mkt – Rolls Critique: CAPM shws ex ante relat’p – prc, tme invlvd in dcd’g to trde…cst of Not rebalnc’g is hld’g unfavorble pst’ns impossle to fnd mkt port – CAPM is untestble Perf Measrs: key for who emply mngr, OR invst persn’l at mngr’s rstrct’ns whn Single Factor Model: R = i    F  e whre F is unanticipated mvmnt in some macro eval’g  Consdr’ns: rsk lvls, tme prds, relatv perf compr’ns (bnchmrk), port mngr vs port, how i i i factor…Single Index Model: see mkt model to fnd B…Multifactor Models: same as Sgle Fctr, divsf’d? Glbl Invtmt Perf Stds (GIPS) obj: get wrld-wde accptnc of std for invmt perf, ensre but add in other fctrs w/ their Betas… accrt&conssnt data for rprt’g (full disclsre), prmte fair glbl comp, fostr indsty slf-reg R p (V -EV )BV Bssms no fnds added/wthdrwn Fama and FRA 3 fctr mdl: E(r) of sml mkt cap stks less the rtrn of lg mkt cap stk SMB, E(r) of high Bk-to-Mkt stks less the rtrn of low B-t-M stk HML, E(r) on mkt index Dllr-wght rtrns: PV(start’g wlth + contrb’ns) = PV(Cash distrb’ns + Wthdrwls + Ending wlth) slve for r, then R eff+r) -1 eq’v to IRR, can’t compre ths to bnchmrks Ri = alpha + B (Rm-Rm + f sizeB + B HMBM+ e i APT (Arbtge Prcng Thry): Law of 1 price, doesn’t assme: single-perd inv horizn, no taxes, Tme-wgt rtrns:r =1V -V1)/0 r 0[(2 +wt2drwl)–(V +cont1b’n)] / (V +con1rb’n) r=(1+r )*(1+r1)–1 2 Dllr-wgt’d bttr for port ownrs, tme-wgt’d bttr for port mngrs…GIPS uses tme-wgt unltd lend/borrw at Rf rate, inv are ratin’l…E(Rit=a 0 b i1isk prm for fctr 1) + bi2rk prm fctr 2)... firm spec evnts aren’t APT rsk fctrs – rsk fctr must infl’ce E(r) – rsk fctrs must be unpred’le for Sharpe: RVAR  TR RF /SDp  p = avg excss rtrn / total rsk bnchmrk = expost CML mkt as a whole – exp valu of ech fctr is 0 – APT and CAPM best for well-diversified ports Treynor: RVOL  TR RF / p  =avg excss rtrn/mkt rsk  bnchmrk = expost 2 2 2 2 SML…implies a divrsf’d port b/c its rsk prm per unt of MKT rsk (systmtc) Jenson’s Alpha: APT: sgle fctr: RoR  i  E(r i F ie i var  p   p (F ) p Arbitrage Qs: always need to short smth, long smth, to get higher rtrn for same beta (apt=B) alpha in mkt model shud be 0, it msrs contrb’n
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