investments notesLecture 12.doc

此文档收集于网络，如有侵权，请联系网站删除Lecture 121. Performance Evaluation Measures1.1Sharpe RatioSharpe Ratio SP = We can use Sharpe Ratio to rank portfolio performance.Sharp ratio for the market portfolio SM = is often used as a benchmark to assess risk-adjusted performance (= slope of the capital market line CML) If Portfolio P beats the market; above the CML 0; underperform, M2 -Portfolio P beats the market; above the SML If 0; underperform, T2 0 the portfolio beats the market (lies above the SML) P aP2 0, can we conclude portfolio 1 outperforms portfolio 2? See Figure 24.3.Relation between Alpha and Treynor measureP = - - (-) - = P + (-)Treynor measure: TP = = P/+ (-) = P/+ TMRelation between alpha and Sharpe ratioSharpe ratio:SP = = + () = + () ()= + () = + SM(Note: bP = = =)2. Which Performance Measure to use?Two main considerations:(1) Size of the portfolio determine the nature of the risk faced by the manager(2) Investment constraints determine the risk the manager is accountable forSmall(favour Sharpe)Large (favour Treynor)No constraints(favour Sharpe) Many constraints(favour Treynor) Note: Your book focuses on the size factor only.3.Market Timing SkillsRegression 1(RP RF) = a + bP1 (RM RF)+ bP2 (RM RF)2 + ePNote: the intercept is the performance measure alpha.bP2 = 0 no market timing skill bP2 0 evidence of market timing skillbP2 RF D = 0 otherwise Beta of the portfolio during bear market = bP1Beta of the portfolio during bull market = bP1 + bP2bP2 = 0 no market timing skill bP2 0 evidence of market timing skillbP2 0 negative market timing skill4. Performance AttributionA portfolio manager typically makes three decisions:I. Investment policy or asset allocation decision What asset classes to include/exclude? Set the strategic asset allocation (SAA) the long-term, normal weights assigned to each asset class SAA should be governed by the funds investment objectives or risk tolerance of investorsII. Style rotation or market timing decision Tactical asset allocation (TAA): Strategic under- or overweighting of the asset classes relative to their SSA weights to achieve return above the policy returnIII. Security selection decision Selection of underpriced securities w/i each asset class to achieve return above the policy returnPerformance attribution provides a unified framework to trace the total performance of a fund to the above three skills.ExampleConsider an evaluated portfolio withSAA = 60% equities, 40% bondsTAA = 70% equities, 30% bondsStep 1: Compute the return of a benchmark portfolio BP (a.k.a “policy portfolio” or “normal portfolio”) Your book calls this a “bogey” portfolio.This is the universe of all assets the fund manager can consider according to the funds investment style.Let return of a passive equity funds return = 25% return of a passive bond funds return = 15%RBP = (0.6)(25%) + (0.4)(15%) = 21%RBP is the “policy return” of the evaluated portfolio since it is solely due to its SAA. Step 2: Compute the actual return of the evaluatedportfolio RPLet actual portfolio return of equity = 30% actual portfolio return of bond = 13.3% Given TAA is 70/30,RP = (0.7)(30%) + (0.3)(13.3%) = 25%RP RBP = 25% - 21% = 4%This 4% should capture: market timing skills, security selection skills, and luck. (1) Market timing abilityConstruct a portfolio called “Policy & Timing” such that: - it uses the TAA of the evaluated portfolio (70%/30%)- its asset classes only earn a return equal to passively managed asset class (25% return on equities, 15% return on bonds)Return of “Policy and Timing” RPT = (0.7)(25%) + (0.3)(15%) = 22%Market timing ability = Return of “Policy and Timing” Return of “policy portfolio”= RPT RBP= (0.7)(25%) + (0.3)(15%) (0.6)(25%) + (0.4)(15%) = 22% - 21% = 1%(2) Security selection abilityConstruct a portfolio called “Policy & Selectivity” such that: - it uses the SAA of the evaluated portfolio (60%/40%)- its asset classes earn a return equal to the actual returns in the evaluated portfolio (30% for equities, 13.3% for bonds)Return of “Policy & Selectivity” RPS = (0.6)(30%) + (0.4)(13.3%)= 23.3%Security selection ability=Return of “policy & selectivity” Return of “policy portfolio”=(0.6)(30%) + (0.4)(13.3%) (0.6)(25%) + (0.4)(15%) = 3.3% - 21% = 2.3%Total return 25% can be decomposed intoAsset allocation ability = 21.0% (passive)Market timing ability = 1.0% (active)Security selection ability = 2.3%