Investment Management Active Portfolio Management

Transcription

1 Investment Management Actve Portfolo Management Road Map The Effcent Markets Hypothess (EMH) and beatng the market Actve portfolo management Market tmng Securty selecton Securty selecton: Treynor&Black model 1

2 The problem Is t possble to beat the performance of a passve portfolo? If markets are fully effcent, the answer s NO But what f markets are only nearly effcent Actve portfolo management seeks to explot perceved market neffcences Two forms of actve portfolo management market tmng securty selecton Market neffcency Actvely-managed portfolos are not fully dversfed may nclude msprced securtes Competton amongst actve managers ensures that securtes trade close to ther far values on a rsk-adjusted bass, most portfolo managers wll not beat passve strateges managers wth exceptonal sklls and/or prvleged nformaton can beat passve strateges Some actve managers must earn abnormal profts otherwse there would be no actve portfolo managers securty prces would stray from far values, nducng portfolo managers to adopt actve strateges

3 Beatng the market portfolo Market tmng Two technques for mprovng performance: adjust the bond/stock mx of the portfolo n antcpaton of market changes modfy portfolo n favour of equtes (bonds) f nvestor s bullsh ( bearsh ) about the stock market adjust the equty beta of the portfolo nvest n hgh-beta (low-beta) stocks f nvestor s bullsh ( bearsh ) about the stock market Both technques mpact the average beta of the overall portfolo therefore we can use beta to measure how successful market tmng has been 3

4 Market tmng: Adjustng bond-stock mx Lttle evdence of market tmng ablty Drect comparson wth market return Evaluate market tmng by comparng the return on the portfolo wth the return on the market No market tmng average beta of portfolo (farly) constant portfolo return s a constant fracton of return on market (assumng no specfc rsk) Market tmng hgh β n rsng market, low β n fallng market portfolo return > market return 4

5 Evdence of market tmng (returns comparson) Market tmng Example: Merton s exercse holdng perod 1 January December 1978 nvestment strateges: 1. nvest $1000 n 30-day T-blls, rolled over every 30 days. nvest $1000 n NYSE ndex, and re-nvest dvdends 3. nvest $1000 n ether 30-day T-blls or NYSE ndex, swtchng from one to the other every 30 days on the bass of perfect foresght (certanty) How do the three strateges compare (December 1978)? Strategy 1. All-safe asset Strategy. All-equty Stretegy 3. Perfect foresght $3,600 $67,500 $5,360,000,000 5

6 Market tmng Why does perfect market tmng result n such huge gans? compoundng over a large number of years prvleged nformaton Monthly returns on NYSE ndex and swtchng portfolo (σ TBll =.10%, σ equtes =.14%) : Securty selecton Ams at dentfyng msprced securtes whch offer opportunty to acheve returns hgher than pre-specfed benchmarks (or the market portfolo) Problems: adjustng composton of portfolo n favor of msprced securtes moves away from beng full dversfed ncur costs of carryng specfc (or dversfable) rsk Trade-off between achevng abnormal returns reducng rsk va dversfcaton 6

7 Treynor-Black model: preamble The Treynor-Black model s a model embeddng the use of securty analyss Analysts look at the market and nvestgate n depth only few securtes (the others are assumed to be farly prced). They form actve portfolos as follows: Estmate for each securty betas and resdual rsk Gven a certan equlbrum model (say the CAPM) the dentfy the magntude of msprcng (alpha) They also estmate the mpact of holdng a less than fully dversfed portfolo lookng at the varance of stock resduals (=resdual rsk) Gven the estmates of betas, alphas and resdual rsks they compute the optmal weghts of each securty n the actve portfolo Treynor-Black model: assumptons Assume: there s a sngle common source of rsk the market s nearly effcent (.e. the CAPM/sngle ndex model nearly holds) Asset returns: rk = rf + βk( rm rf) + ek + αk where α k s the abnormal return (=Jensen s alpha) of the msprced assets k. Expected return on actve portfolo (comprsng msprced securtes): E( ra) = α + rf + β A E( rm) r f Wth varance: σ ( r ) = β σ + σ ( e ) A A M A 7

8 Treynor-Black model: ntuton Treynor-Black model: soluton The optmal actve portfolo s a combnaton of the passve market portfolo and the actve portfolo of msprced securtes How do we judge the success of the strategy? The mathematcs of the effcent fronter reveals that N α A α S = S + = S + σ( ea) = 1 σ( e) P M M Sharpe rato of the Market portfolo (squared) Informaton rato of the actve portfolo (squared) Only for the optmal actve portfolo (P), the Sharpe rato (squared) s gven by the sum of the sharpe rato of the (passve) market portfolo (squared) the standardsed degree of msprcng, apprasal rato or nformaton rato, (squared) 8

9 Example Equty analyst n HK selects the followng msprced stocks: BOC HK MTR Corp Esprt Holdgs Cathay Pac Ar β E(r ) 0% 17% 14% 8% σ(e ) 60% 50% 45% 40% Other nformaton: E(r M ) = 10%, σ RM = 5%, R F = 4% Example (cont d) Step 1: calculate expected abnormal returns and nformaton ratos BOC HK MTR Corp Esprt Holdgs α = E( r) rf β E( rm) r f Cathay Pac Ar α 1.40% 9.40% 7.00%.80% Ths mples a Sharpe rato of the actve portfolo of α / σ(e ) α SP = SM + = 1 σ ( e ) = = ( 0.4) + ( 0.1) + ( 0.19) + ( 0.16) + ( 0.07) =

10 Example (cont d) Step : construct the actve portfolo mpled by the securty analyst nput lst (algebra s not requred) BOC HK MTR Corp Esprt Holdgs Cathay Pac Ar total w = α / σ 4 = 1 α / σ ( e ) ( e ) 0.14/(0.60 ) = /(0.50 ) = /(0.45 ) = /(0.40 ) = α / σ ( e ) α / σ α / σ ( e) ( e ) 0.344/1.41 = /1.41 = /1.41 = /1.41 = Example (cont d) The formed actve portfolo exhbts the followng estmates α n = w α = A = = (8.6%) β n = w β = A = = n σ( e A) = wσ ( e) = ( 0.8) ( 0.60) + ( 0.30) ( 0.50) + = 1 ( 0.8) ( 0.45) + ( 0.14) ( 0.40) = 0.64 (6.4%) 1 10

11 Example (cont d) The expected return and standard devaton of the actve portfolo are equal to: E( ra) = αa + rf + β A E( rm) r f = [ ] = 0.16 ( 16% ) σa = βaσm + σ () e = ( 0.516) ( 0.5) + ( 0.64) = = 0.9 ( 9% ) cov ( ra, rm) = βσ A M = ( 0.5) = 0.03 cov ( ra, rm) 0.03 ρ ( ra, rm) = = = 0.44 σσ A M Example (cont d) Step 3: determne composton of the overall rsky portfolo (actve portfolo + market portfolo) A ( ea) w w = α / σ 0 0 w* R / σ = β w ( ) M M A where w* denotes the share of the actve portfolo wthn the overall rsky portfolo. The weght attached to the market portfolo wthn the overall rsky portfolo s gven by 1 w* In our example: 0.086/ ( 0.64) w0 = = 1.9 ( )/( 0.5) 1.9 w* = = ( )

12 Example (cont d) BOC HK MTR Corp Esprt Holdgs Cathay Pac Ar Actve portfolo Market portfolo w = = = = 0.11 w* S A = 0.41 S = 0.4 M Example (cont d) 0.4 CAL (SR= 0.41) 0.19 expected return E(r) 0.14 CML (SR=0.4) total rsk (sgma) 1

13 Treynor-Black model: summng up Optmzng model for portfolo managers who use securty analyss under the assumpton that markets are nearly effcent securty analyss can assess n depth only a small number of securtes (securtes not assessed are assumed to be farly prced) market ndex portfolo s the passve portfolo perceved msprcng gudes the composton of the actve portfolo Treynor-Black model: summng up analysts follow several steps to make up the portfolo and evaluate ts expected performance 1. Estmate beta and resdual rsk for each analysed securty; from these, determne the requred return. Gven the degree of msprcng, determne the expected return for each securty (abnormal return) 3. The nonsystematc rsk component of the msprced stock s the cost of not fully dversfyng by specalsng n underprced securtes 4. Determne the optmal weght of each securty n the actve portfolo 5. determne the optmal rsky portfolo, whch s a combnaton of passve and actve portfolos 6. Compare CAL w.r.t CML 13

14 BKM Readngs Secton 4.4, Chapter 7 Other readngs (optonal) Treynor, J.J. and Black F. (1973), How to use securty analyss to mprove portfolo selecton, Journal of Busness, 46, Black, F. and Ltterman, R. (199), Global portfolo optmzaton, Fnancal Analysts Journal, September- October