Part VI: Active Portfolio Management

Transcription

1 1 Potolio anagement Pime Pime I: Top-Down Potolio anagement Capital vs. sset allocation aowitz secuity selection model Pime II: sset Picing odels CP (Theoy & Pactice Index & ulti-facto odels Pime III: ctive Potolio anagement Peomance easuement: Benchmas & Rewads Pat VI: ctive Potolio anagement

2 ctive Potolio anagement Two examples so a stocs -- aowtiz secuity selection model (need inputs! bonds -- ixed-income potolio management Relevant questions why? what? how? maet timing secuity analysis» index model» multi-acto model ey woy = contol o is ctive Potolio anagement -- Why? P -- a contadiction in tems? Nope! maet eiciency equies many investos to manage actively intuition mis -piced secuities > deviations om passive stategies pay o > pice pessues eliminate mis-picing > active management does not pay o > secuities become mis -piced again > Theoy» Gossman and Stiglitz

3 3 ctive Potolio anagement -- Why? Evidence othe manages may beat the maet» small but statistically signiicant» noise in secuity etuns > had to disclaim some potolio manages ae eally good» had to ague anomalies» Januay eect,» disappeaance? What is ctive Potolio anagement? Isn t evey stategy active? 1. Secuity selection -- clealy identiy mis -piced secuities. sset allocation -- yep dieent asset categoies» equie dieent oecasts example» long-tem bond etun deteminants» equity etun deteminants intenational assets» things get wose

4 4 What is ctive Potolio anagement? Isn t evey stategy active? 3. capital allocation -- even that! popotion invested in maet potolio E[ ] * m w = x0.005x xσ E[ m ] equies to oecast and σ might also lead to maet timing» maet conditions change ove time What is ctive Potolio anagement? 3 ppoach deinition puely passive stategy example» invest only in index unds» one und pe asset categoy (equity, bonds, bills» popotions unchanged egadless o maet conditions» 60% equity + 30% bonds + 10% bills» ixed o 5 yeas = entie investment hoizon active management» equies contol o is

5 5 What is ctive Potolio anagement? 4 Objectives concentate on potolio constuction CP > we can sepaate constuction o eicient potolio and allocation o unds» between isy asset and bills two components secuity analysis» maximize Shape atio (CP maet timing» shit assets in and out o isy potolio aet Timing Idea maet times shit money» om money maet ( to isy potolio based on thei oecasts o maet etun potential poits huge example ($1,000 einvested om 197 till 1978» 30-day T-bills: $3,600 ( =.49%» NYSE: $ 67,500 ( = 8.44%» peect maet timing: $5,360,000,000 ( = 34.71% (Tables on p. 985, 6 th edition

6 6 aet Timing Reasons o dieences compounding is» o all assets» impotance o pension unds mainly o equities (Fig. p th edition» T-bills ae mostly is-ee ielevant o maet timing» exception: T-bill ate vaies a little inomation» o maet timing aet Timing 3 aet timing as an option much less isy than equities standad deviation is misleading peect maet timing yields dominant payos in each state o the wold (Fig. 7.1» gives minimum etun guaantee» + a non-negative andom numbe maet timing ees maet times will chage o sevice» ees detemined by option picing

7 7 aet Timing 4 In pactice clients want manages to pic eicient potolios» maximize Shape atio still need to pic the optimal popotion» to invest in the is-ee asset manages need to update customes continuously» elative attactiveness o isy potolio changes costly solution let manages shit money in and out o unds» = solution used by most unds aet Timing 5 Evaluating maet times Basic idea Ris-etun tade-o (Q1c, ssignment und peomance should impove with the maet Intuition as maet impoves, a good maet time shits moe money to maet» caveat: tue i shot sales ae uled out Fomally Non-linea egessions (Fig. 4.5, BK6» Regess potolio excess etuns (ER on maet ER and ER^

8 8 Secuity Selection ap. idea B. potolio constuction C. numeical example D. multi- acto models E. use in pactice» industy use» advantages vs. danges Secuity Selection. Idea (Teyno-Blac 1. conside the entie set o secuities» assume the entie set is thee» index model (passive potolio = maet poolio. ocus on a small subset» as many as analysts can easonably handle 3. analyze use index (single - o multi- acto model» to estimate alpha, beta(s and esidual is» o secuities in subset identiy secuities with positive expected alpha» assume secuities outside the subset ae coectly piced

9 9 Secuity Selection 3. (continued 4. mix non-zeo alpha secuities» with passive potolio (= maet poolio why?» want to maximize etun» but need to contol o is» small subset > too much is i invest only in subset how?» use the beta, alpha and esidual is estimated 5. optimal isy potolio» = mix o active and passive potolio Secuity Selection 4 B. Potolio constuction (NOT Exam at l 1. assumptions (index model maet potolio = eicient potolio E[ m ] and σ have been estimated» use them o passive potolio» no need o maet timing beta elationship = α + β ( + e i i i cov( e, e cov( e, = 0 i j = i i

10 10 Secuity Selection 5 B. (continued. eseach o estimate = + β ( + e + α 3. active potolio =0» α > done (i.e., eep secuity in passive pot.» α >0 > go long» α <0 > go shot α» optimal weights: w = n α j= 1 / σ j / σ ( e ( e j n w = 1 = 1 B. (continued active potolio Secuity Selection 6» compises all the assets with non-zeo alpha α = n w = 1 α σ = β σ + σ n ( e β = n w = 1 = β + σ w ( e σ cov( e i, e j = 0 = 1 β

11 11 Secuity Selection 7 B. (continued 4. mixing active ( & passive ( potolios potolio may lie above CL» intepetation (given analysis, is not eicient ate all» no need to now the oiginal eicient ontie new ontie (BK6 Fig. 7.» combine and» and not peectly coelated optimal isy potolio» tangency point, given is-ee asset B. (continued Secuity Selection 8 5. omal constuction intuition» optimal combo o isy assets & T-bills (Lectue 11 E[ P] ax w σ P s.t. w (1 w + w E[ R = 1 w (1 w, ax ] + w E[ R ] σ + w σ + (1 w wρ σ σ

12 1 Secuity Selection 9 B. (continued 6. Optimal isy allocation σ σ ] [ ( ] [ ( E E Den + = Den Num w =, cov( ] [ ( ] [ ( E E Num = σ, cov( ] [ ] [ ( E E + Secuity Selection 10 Optimal isy allocation intuition o w o» w o = atio o ewad-to-is atios o and» we mix o is divesiication easons» the highe the ewad o the exta is taen» the moe we invest in the (vey isy potolio σ σ α / ] [ ( ( / o E e w = o o w w w (1 1 * β + =

13 13 Secuity Selection 11 Optimal isy allocation w * w = o 1+ (1 β w o w =1 * w intuition o w *» w * = adjustment o beta» the weight o depends on divesi. oppotunities β <1» i then moe can be gained by divesiying w * < w o Secuity Selection 1 7. Optimal secuity weights: intuition = n w α α j= 1 / σ j / σ ( e ( e j» to max the composite potolio s Shape atio S P = S α E[ ] ( ( + = + α σ e σ σ e» given the Shape atio o the maet ( is ixed» we must maximize the appaisal atio o : α σ( e

14 14 Secuity Selection 13 Optimal secuity weights» given» and» we must have: = = n j j j e e w 1 ( / ( / σ α σ α = = n w 1 α α = + = n e w 1 ( σ σ β σ Secuity Selection 14 B. (continued 8. Individual secuity contibutions» the appaisal atio o each secuity» measue its contibution» to the peomance o the active potolio = = n e e 1 ( σ ( σ α α

15 15 Secuity Selection 15 C. Numeical example S S P P data (BK6 pp and intepetation E[ ] = 15%; = 7%; σ = 0% Shape atio 1/ [ ] ( 1 ( n α E = + α e σ = σ e 1/ 8 = S + σ = 8% 0% = 0.> =. 16= S 0 Secuity Selection 16 α optimal weights (see table potolio chaacteistics = n w = 1 α» lage alpha, but lage idiosyncatic is = x0.07+( 1.61 x( x0.03= 0.56% n = 1 β = w β = σ ( = 8.6% σ ( e e =

16 16 Secuity Selection 17 optimal isy potolio despite high alpha, small popotion in active potolio» lage is needs to be balanced out small adjustment o beta» beta is close to 1 α / σ ( e wo = = ( E[ ] / σ * w = o w = = 14.95% 1+ (1 β w o w 1 * = w =85.05% Secuity Selection 18 peomance gain Shape atio S 8% 0% P = 0.19= > = 0. 4= measue = 1.4% (lage numbe, given only 3 secuities» match is (i.e., std-dev o potolio» by mixing optimal isy potolio and T-bills» in popotions σ P and σ P 1 espectively σ σ S

17 17 Secuity Selection 19 D. ulti-acto models (NOT Exam at l so a: index model E now: -acto illustation o multi-acto extension extension om index model is staightowad» the entie analysis is based on esidual analysis» computations equied, then poceed as beoe [ ] = β 1( E[ 1 ] + β ( E[ ] + e + α cov(, σ = β 1 1 ( 1σ + β e σ + β 1β + σ cov(, i j = β i1 β j1σ 1 + β iβ j σ + ( β i1β j + β i β j1cov( 1, Data: Secuity Selection 0 potolio management house appoximates the etun-geneating pocess by a twoacto model and uses two-acto potolios to constuct its passive potolio. The input table that is consideed by the house analysts loos as ollows: ico Foecasts sset Expected Retun (% Beta on Beta on H Residual SD (% Stoc Stoc B Stoc C Stoc D aco Foecasts sset Expected Retun (% Standad Deviation (% T-bills 8 0 Facto potolio 16 3 Facto H potolio The coelation coeicient between the two-acto potolio is 0.6.

18 18 Secuity Selection 1 Questions: (a What is the optimal passive potolio? (b By how much is the optimal passive potolio supeio to the single-acto passive potolio,, in tems o Shape s measue? (c What is the Shape measue o the optimal isy potolio and what is the contibution o the active potolio to that measue? Secuity Selection optimal combo o isy assets & T-bills (Lectue 9 E[ P] ax w σ P s.t. w H (1 w + w E[ R = 1 ] + w E[ R H w (1 w, ax σ H + wσ + (1 w w ρ H σ σ H ] Num w = Den Num= ( E[ ] σ H ( E[ H ] cov( Den= ( E[ ] σ H+ ( E[ H ] σ ( E[ H ] + E[ ] cov(, H, H

19 19 Secuity Selection 3 Num w = Den Num= ( E[ ] σ ( E[ ] cov( Den= ( E[ ] σ H+ ( E[ H ] σ H ( E[ H ] + E[ ] cov(, H H, H Secuity Selection 4 nswes: (a The optimal passive potolio is obtained om equation (7.8 in Chapte 7 on Optimal Risy Potolios see Lectue 9. w = [E(R σ H E(R HCov( H, /{E(R σ H + E(R σ [E(R H+E(R ]Cov( H, } whee R = 8%, RH = % and Cov( H, = ρσ σ H = 0.6 x 3 x 18 = Thus, w = 8 x 18 ( x 48.4/[8 x 18 + ( x 3 ( ] = 1.797, and wh = Because the weight on H is negative, i shot sales ae not allowed, potolio H would have to be let out o the passive potolio.

20 0 Secuity Selection 5 nswes: (bwith shot sales allowed, E(Rpassive = x 8 + ( x = 1.78% σ passive = (1.797 x 3 + [( x 18] + x x ( x 48.4 = σpassive = 34.68%. Shape s measue in this case is given by: Spassive = 1.78/34.68 = , and compaed with the (simple maet s Shape measue o S = 8/3 = We now must Secuity Selection 6 eseach o estimate = + β ( + e + α ind the active potolio =0» α > done (i.e., eep secuity in passive pot.» α >0 > go long» α <0 > go shot α» optimal weights: w = n α j= 1 / σ j / σ ( e ( e j n w = 1 = 1

21 1 Secuity Selection 7 nswes: (c The ist step is to ind the beta o the stocs elative to the optimized passive potolio. Fo any stoc i, the covaiance with a potolio is the sum o the covaiances with the potolio components, accounting o the weights o the components. Thus, Theeoe, β i = Cov(i, passive/σ passive = (β iwσ + β ih w Hσ H /σ passive. β = [1. x x x ( x 18 ]/10.54 = β B = [1.4 x x x ( x 18 ]/10.54 = β C = [0.5 x x x ( x 18 ]/10.54 = β D= [1.0 x x x ( x 18 ]/10.54 = Secuity Selection 8 Now the alphas elative to the optimized potolio can be computed: α i = E( i - βi, passive x E(passive so that α = 0 8 (0.561 x 1.78 = 4.8% α B = 18 8 ( x 1.78 = -1.1% α C = 17 8 ( x 1.78 = 8.07% α D = 1 8 ( x 1.78 = -5.55%

22 Secuity Selection 9 nd the esidual vaiances ae now obtained om: σe (i:passive = σ i (β i:passive x σ passive, whee σi = β σ + σe (i. σe ( = (1.3 x (0.561 x = σe (B = (1.8 x ( x = σe (C = (0.7 x ( x = σe (D = (1.0 x ( x = Secuity Selection 30 Fom this point, the pocedue is identical to that o the index model: Stoc α/σe (α/σe /(Σα/σe B C D Total The active potolio paametes ae: α = x ( ( (1.717 x ( ( 5.55 = 7.7% β = x ( ( x ( ( = σe = x ( x x ( x =,714.03

23 3 Secuity Selection 31 Optimal isy allocation (index model w * w = o 1+ (1 β w o α wo = ( E[ / σ ] ( e / σ intuition o w o» w o = atio o ewad-to-is atios o and P» we mix o is divesiication easons» the highe the ewad o the exta is taen» the moe we invest in the (vey isy potolio Secuity Selection 31 The popotions in the oveall isy potolio can now be detemined: w0 = (α/σe /[E(Rpassive/σ passive] = (7.71/,714.03/(1.78/10.54 = w* = /[1 + ( x ] = Shape s measue o the optimal isy potolio is: S = S passive + (α/σe = [7.71 /,714.03] = S = , compaed to Spassive =

24 4 Secuity Selection 3 E. Potential beneits (Teyno-Blac in pactice not yet used oten widely» had to estimate alphas (bias coection needed» coection equies constant monitoing & appaisal» shows alphas impecise, second-guesses analysts» do you thin analysts lie that? yet, signiicant beneits» easy to implement» allows o decentalized decisions» can add signiicant etun» amenable to multi-acto analysis Pat VI.B: ctive Potolio anagement Evaluation

25 5 Potolio Peomance Evaluation Retuns etun measuement ove seveal peiods Peomance measues maet timing secuity analysis» Teyno, Shape, Jensen, appaisal atio,» pactical cases Peomance attibution bogey; asset allocation; secto and secuity decisions Potolio Retun easuement One peiod vs. multiple peiods easy vs. unclea» depends on numbe o peiods» aected by intemediate investments/withdawals Time-weighted vs. dolla-weighted aveage etun vs. IRR examples (Table 4.1 why use a time aveage?» peomance measuement assigns esponsibilities» cash ins and outs?

26 6 Potolio Retun easuement Geometic vs. aithmetic aveages aithmetic unbiased oecast o expected utue peomance» oiented towads the utue geometic constant ate» compounded, would yield same total etun ove peiod» downwad bias elative to aithmetic» oiented towads the past G σ Question: Potolio Retun easuement 3 XYZ stoc pice and dividend histoies ae as ollows: Yea Beginning o Yea Pice Dividend Paid at Yea-End $100 $4 199 $110 $ $ 90 $ $ 95 $ n investo buys thee shaes o XYZ at the beginning o 1991, buys anothe two shaes at the beginning o 199, sells one shae at the beginning o 1993, and sells all ou emaining shaes at the beginning o (a What ae the aithmetic and geometic aveage time-weighted ates o etun o the investo? (b What is the dolla-weighted ate o etun? (Hint: Caeully pepae a chat o cash lows o the ou dates coesponding to the tuns o the yea o Januay 1, 1991 to Januay 1, Calculate the intenal ate o etun.

27 7 Potolio Retun easuement 4 nswe: (a Time-weighted aveage etuns ae based on yea-by-yea ates o etun. Yea Retun [(capital gains + dividend/pice] [( ]/100 = 14% [( ]/110 = % [( ]/90 = 10% ithmetic mean = 3.15% Geometic mean =.33% Potolio Retun easuement 5 (b Time Cash Flow Explanation Puchase o 3 shaes at $100 each Puchase o shaes at $110 less dividend income on 3 shaes held 110 Dividends on 5 shaes plus sale o one shae at pice o $90 each Dividends on 4 shaes plus sale o 4 shaes at pice o $95 each $110 $396 Date 1/1/91 1/1/9 1/1/93 1/1/94 ($300 ($08 Dolla-weighted etun = Intenal ate o etun o cash-low seies = %.

28 8 aet Timing Evaluation Idea maet times shit money ( < > isy potolio» based on thei oecasts o maet etun etun om maet timing» depends on # o times the time is coect two scenaios: bull vs. bea must be coect in each scenaio» example 1: always pedict snow in Winte in onteal ight 95% o the time» example : owad hedges but always wong when no snow oveall quality vs. is adjustment aet Timing Evaluation Oveall quality measue 1 measue = P 1 + P - 1» P 1 = popotion o coect bull pedictions = 1 i 100% coect» P = popotion o coect bull pedictions = 1 i 100% coect example: etun maximization» coect 100% o bulls, 0% o beas > measue = 0» coect 50% o bulls, 50% o beas -> measue = 0

29 9 aet Timing Evaluation 3 Oveall quality measue unclea» how lage (P 1 + P - 1 must be» to ensue that we have seen good peomance solution» statistical signiicance» application: hedging decisions (as time allows aet Timing Evaluation 4 Ris adjustment poblems» neithe measue so a accounts o is» maet times constantly change potolio is poile solutions» time-vaying dummy D (=1 o bull, 0 o bea = a+ b( + c( D+ e P» Squaed tem P = a+ b( + c( D+ e P P

30 30 aet Timing 5 Bottom line -- evaluating maet times Basic idea Ris-etun tade-o (Q1c, ssignment und peomance should impove with the maet Intuition as maet impoves, a good maet time shits moe money to maet» caveat: tue i shot sales ae uled out Fomally Non-linea egessions (Fig. 4.5, BK6» egess potolio excess etuns (ER on maet ER and ER^ o on ER and ER*timing dummy Basic Evaluating Secuity Selection idea and poblems Taditional esponse to poblems» Shape, Teyno, Jensen, appaisal atio time-changing beta and maet timing In pactice peomance attibution

31 31 Evaluating Secuity Selection Basic idea compae etuns with those o simila potolios depict pecentiles (BK 4-5-6, Fig. 4.1 poblems» ex.: manage outpeoms 90 out o 100 und manages is in the 90 th pecentile» 5th, 95th pecentiles; median, 5th and 75th_ equities: allocations die within goups ixed income: duations vay Evaluating Secuity Selection 3 Taditional idea account o is taen by manage assume index model holds (and past peomance mattes» and compute is-adjusted excess etuns poblems does exta peomance cove ees» diiculty to beat S&P 500 estimation in pactice» statistical signiicance?

32 3 Evaluating Secuity Selection 4 Taditional measues(continued Shape P σ P» appopiate o entie isy investment Teyno P β P» appopiate o one o many potolios (Fig. 4.3 Evaluating Secuity Selection 5 Taditional measues(continued Jensen appaisal atio α = β P α σ P ( e P P [ + ] P (» beneit-to-cost atio» appopiate o active potolio (active P

33 33 Evaluating Secuity Selection 6 Question Conside the two (excess etun index-model egession esults o Stocs and B. The is-ee ate ove the peiod was 6%, and the maet s aveage etun was 14%. i. - = 1% + 1.( - R-squae = 0.576; esidual std deviation, σ(e =10.3%; standad deviation o ( - = 6.1%. ii. B - = % + 0.8( - R-squae = 0.436; esidual std deviation, σ(eb =19.1%; standad deviation o (B - = 4.9%. (a Calculate the ollowing statistics o each stoc: i. lpha. ii. ppaisal atio. iii. Shape measue. iv. Teyno measue. Evaluating Secuity Selection 7 nswe: (a To compute the Shape measue, note that o each potolio, ( p can be computed om the ight-hand side o the egession equation using the assumed paametes = 14% and = 6%. The standad deviation o each stoc s etuns is given in the poblem. The beta to use o the Teyno measue is the slope coeicient o the egession equation pesented in the poblem. Potolio Potolio B (i α is the intecept o the egession 1% % (ii ppaisal atio = α/σ(e (iii Shape measue = (p / σ (iv Teyno measue = (p / β

34 34 Evaluating Secuity Selection 8 (b Which stoc is the best choice unde the ollowing cicumstances? i. This is the only isy asset to be held by the investo. ii. This stoc will be mixed with the est o the investo s potolio, cuently composed solely o holdings in the maet index und. iii. This is one o many stocs that the investo is analyzing to om an actively managed stoc potolio. Evaluating Secuity Selection 9 nswe: (a (i I this is the only isy asset, then Shape s measue is the one to use. s is highe, so it is peeed. (ii I the potolio is mixed with the index und, the contibution to the oveall Shape measue is detemined by the appaisal atio. Theeoe, B is peeed. (iii I it is one o many potolios, then Teyno s measue counts, and B is peeed.

35 35 Evaluating Secuity Selection 10 Poblems does exta peomance cove ees?» diiculty to beat S&P 500 estimation in pactice? bottom line» statistical signiicance?» time-vaying beta? (Fig. 4.4» solution: add a quadatic tem in egession (Fig. 4.5» still used» but not so much any moe Idea Split Peomance ttibution had to evaluate manages on is-adjusted basis impotant to allocate bonuses excess etuns between contibutions» boad asset allocation» industy choices within each maet» secuity choices within each secto

36 36 Peomance ttibution Bogey (BK6 Table 4.5 base-line passive potolio assumed ixed o investment hoizon Splits (BK6 Tables 4.6 to 4.8 boad asset industy secuity» compae to bogey» given weights, compae with maet weights Question 9 (0 points Peomance ttibution 3 Conside the ollowing inomation egading the peomance o a money manage in a ecent month. The table epesents the actual etun o each secto o the manage s potolio in Column 1, the action o the potolio allocated to each secto in Column, the benchma o neutal secto allocations in Column 3, and the etuns o secto indices in Column 4. ctual Retun ctual Weight Benchma Weight Index Retun Equity % % (S&P 500 Bonds 1% % (SB Index* Cash 0.5% % * S&B Index = Salomon Bothes Index. (a What was the manage s etun in the month? What was his o he ovepeomance o undepeomance? (b What was the contibution o secuity selection to elative peomance? (c What was the contibution o asset allocation to elative peomance? Conim that the sum o selection and allocation contibutions equals his o he total excess etun elative to the bogey.

37 37 Peomance ttibution 4 nswe: (a Bogey: 0.60 x.5% x 1.% x 0.5% = 1.91% ctual: 0.70 x.0% x 1.0% x 0.5% = 1.65% Undepeomance: 0.6% (a Secuity Selection: aet Dieential Retun anage s Potolio Contibution Within aet Weight to Peomance Equity -0.5% % Bonds -0.% % Cash % Contibution o secuity selection -0.39% Peomance ttibution 5 (a sset llocation: aet Excess Weight: Index Retun Contibution anage - Benchma minus Bogey to Peomance Equity % 0.059% Bonds % 0.071% Cash % 0% Contibution o asset allocation 0.13% Summay: Secuity selection = -0.39% sset allocation = 0.13% Excess peomance = -0.6%