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BU473 Lecture Notes - Csts, Capital Asset Pricing Model, Capitalization Rate

Course Code
Ning Tang

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CAPM assumptions: Ind’l inv are price-tkrs, single-perd inv horizn, inv ltd to trd, prcd, and
perf. divsble fn’l asst, no taxes, no transctn csts, no rstrctn on shrt sell, unltd lend/borrw at Rf
rate, inv are ratin’l, info is cstless, avlbl to all inv, homo exp, no infl’n
In eqil’m, all inv hold same port. of risky assets is the mkt por mkt port is on efficient
frontier and is the tangency port…in eqil’m excss dmd for any asst is 0
CML risk, SML B… only risk inv will pay to avd is covariance risk
Market Model to find Beta:
^^gives you Secrts Char Line…Betas more stable for large ports (avg’ing effect)
4 tests of CAPM: relat’p b/w retrn & B is linear is relat’p positve B is only measre of risk
tht’s pricd – intrcpt trm apprxmats Rf Test results: intrcpt trm generlly hghr than Rf mkt rsk
prmium (slpe) generlly less steep thn thry Joint Hypothesis Problem: can only tst CAPM if
we assme assts are pricd correctly in the mkt Rolls Critique: CAPM shws ex ante relat’p
impossle to fnd mkt port CAPM is untestble
Single Factor Model: Ri =
iii eF
whre F is unanticipated mvmnt in some macro
factor…Single Index Model: see mkt model to fnd B…Multifactor Models: same as Sgle Fctr,
but add in other fctrs w/ their Betas…
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
Ri = alpha + Bm(Rm-Rf) + BsizeSMB + BBMHML + ei
APT (Arbtge Prcng Thry): Law of 1 price, doesn’t assme: single-perd inv horizn, no taxes,
unltd lend/borrw at Rf rate, inv are ratin’l…E(Rit)=a0 + bi1(risk prm for fctr 1) + bi2(rk 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
mkt as a whole exp valu of ech fctr is 0 APT and CAPM best for well-diversified ports
APT: sgle fctr: RoR var
Arbitrage Qs: always need to short smth, long smth, to get higher rtrn for same beta (apt=B)
5 systmtc fctrs priced in mkt: Chgs in exp infl’n, Una chgs in infl’n, Una chgs in ind prod’n, Una
cgs in def-rsk prm, Una cgs in trm strc of disct rats 1st 3 affct CF, all but 3rd affct disct rate
Alloct’l Effcnt Mkt: mkt whr resrce alloct’n is soclly optm’l Alloct’l Effcny: effctvnss tht mkt
chnnls cap twds mst prd’v uses Info Effcnt Mkt: sec prcs adjst rapidly to new info
Cond’ns for Effcnt Mkt: Lg nmbr of rat’l, proft maxing invt’rs, info is cstlss, widely avlbl, genrtd
rdnmly, inv react qckly & fully reward for anlyss Low, new info indpd’t of past
Weak frm: mkt lvl data, fctr in histrc’l prices, techn’l anlyss is useless, past prices unrltd to futr
chgs contrdt’ns: momntm/prsistce in stk rtrns (6-12mths), Contrr’n strats (3-5yr, behv’l fnce)
Semi-strg: all publc info, fundmn’l anlyss useless, acting on new publc info does nth, test: spd
of adjstm’t – evnt stds: CAR=summing the average of AR:
supprt’g evidnce: annc’g divs, stk splts, acctng chgs, IPOs, avg fnd mgr suckage VS. smll frm
efft, Jan/sesnalty efft, size efft, nglctd frm efft
Strg frm: publc & prvt info, shud jus do pssve invmt strgy, test: perf of ppl w/ accss to nonpublc
info insdr trdng is strg evidnc against strg frm b/c they prft…evdnc favors weak frm in LR
Implc’ns for $$ mngrs: less tme on ind secrits (go passv), if mkt info effcnt then mntn diverfs,
mntn port rsk, mng tax brden, mng trans csts… shud avoid data mining…Grssmn argus AR
exist b/c thr’s csts for gathr’g & procs’g info, and rtrns compnste for expnses
Ind vs. Insti Inv: Ind”rsk” is lsng $, hve prsnalts, gols are key, hve freedm, taxs r imprtnt
Info needd to form inv polcy: Objtvs (rtrn req & rsk tolrnce), Cnstrnts + Prefs (liqdty, tme horz,
laws/reg’n, taxs, pref + circmsncs)
Prudnt Man Rule: mngr for othr’s assts mst act as how prdnt ppl govrn own affrsreq assts
be divsf and stndrds be appld to mgmt of port Cap Mkt Exptat’ns: Macro: exp’ns abt cap
mkts, devlpng contrys Micro:exp’ns inflc’g slct’n of part’r asst for part’r port RoR: hist’l from
varity of sorces, base Equity Rsk Prem = rtrn of index rtrn on Rf…base on arthmtic mean
Constrct’g Port: Defn secrtis elgble for incls’n (Asst Allct’n) use optmz’n procdr to slct
secrtis and dtrmne prpr port wgt Asst Allct’n cnsdr’ns: rtrn req, rsk tolrnce, tme hrzn, invstr age
4 phases of wlth: Accml’n: sml nw, tme hrzn long, can take lg rsk Consld’n: mid-late carer
stg of life, balnce b/w trde-off of rsk & rtrn Spnd’g: livng expnse frm accmlt’d assts, focs on
safety Giftng: same as spnd’g Strtgc Asst Allct’n: LR asst mix, siml’n detrmnes likely
rng of outcms w/ each asst mix, “buy & hld Tctc’l Asst Allct’n: chg in asst mix drvn by chg
in exp rtrns…mkt tim’g apprch Rebalnc’g Csts: brkr commish, possble impct of trde on mkt
prc, tme invlvd in dcd’g to trde…cst of Not rebalnc’g is hld’g unfavorble pst’ns
Perf Measrs: key for who emply mngr, OR invst persn’l at mngr’s rstrct’ns whn
eval’g Consdr’ns: rsk lvls, tme prds, relatv perf compr’ns (bnchmrk), port mngr vs port, how
divsf’d? Glbl Invtmt Perf Stds (GIPS) obj: get wrld-wde accptnc of std for invmt perf, ensre
accrt&conssnt data for rprt’g (full disclsre), prmte fair glbl comp, fostr indsty slf-reg
Rp = (VE - VB)/VB assms no fnds added/wthdrwn
Dllr-wght rtrns: PV(start’g wlth + contrb’ns) = PV(Cash distrb’ns + Wthdrwls + Ending wlth)
slve for r, then Reff =(1+r)2 -1 eq’v to IRR, can’t compre ths to bnchmrks
Tme-wgt rtrns:r1=(V1-V0)/V0 r2=[(V2+wthdrwl)(V1+contrb’n)] / (V1+contrb’n) r=(1+r1)*(1+r2)1
Dllr-wgt’d bttr for port ownrs, tme-wgt’d bttr for port mngrs…GIPS uses tme-wgt
Sharpe: = avg excss rtrn / total rsk bnchmrk = expost CML
Treynor: =avg excss rtrn/mkt rsk bnchmrk = expost
SML…implies a divrsf’d port b/c its rsk prm per unt of MKT rsk (systmtc) Jenson’s Alpha:
alpha in mkt model shud be 0, it msrs contrb’n of port mngr Apprs’l Ratio: αp / σ(ep)
Jnsn’s Alph / nonsystmc rsk. If port divsf, Jnsn&Appr’l&Capm will agree
M2Measre:find wgt to make mngd port hav same rsk as mkt port w/ Rf, find rtrn, compare mkt
vs mngd ports 2 mjr probs for msr’g: need lots of obs, actv mgmt causes shfts in paramtrs
Perf diff frm bnchmrk comes from: Mkt Tme’g OR secrty slct’n
Bond Pricing: PVAr,n = (1 (1/(1+r)^n) ) / r Cupon rte > crrnt yield > YTM prm, Cupon rte
= crrnt yield = YTM par, Cupon rte < crrnt yield < YTM discnt
bond prc & int rte inverse… YTM for zero-coupon bond: P=F/(1+r)n
use YTM as dscnt rte BEY = annlzd r (aka YTM) Effctv Annl Yield = (1+r)2 -1 Crrnt
Yield = annl int/mkt prc…is a 1-prd RoR Fisher Eq’n: Rf = RR + EI (exp inf)
Invoice Price/Dirty Price
Clean Price is sans acrued int
Cash Price=quotd prc+acrd int
Acrd Int = Coupon*(1-w) = 980 +(1000*cuponrate*(15/365))
Cllble Bnds:incntv to call whn bnd prc > call prc prc of cllble bnd cappd at cll prc
in rl lf, cupons not reinvt at ytm, crt’g reinvt rsk lngr mat, hghr cupn rte, hghr reinvt rsk
Rlzd Yild: (ttl ftre $/prch prc of bnd)^(1/n) - 1
Taxs: prc apprc/deprc taxd as ordny incm; prc chg frm yild chg taxd as cap ganscalc P0,
then P1 at sme YTM (intrst), thn P1 at new YTM(cp gan)
b/c bnd prcg is convx, an incr in YTM rslts in smllr prc dcln than prc incrs frm decrs in YTM;
prc senstvy invrsly rltd to cupn rte & ytm
Modf’d Duration=Durt’n / (1+y) cupn invrsly rltd to dur’n; ytm invrsly rltd to dur’n
Convexity lg’st for low-coupon bonds, long-mat bonds, and low YTM
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