Create Presentation
Download Presentation

Download Presentation
## Portfolio Evaluation

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Portfolio Evaluation**• Outline • Investment return measurement • conventional measurement theory • Evaluation with changing portfolio composition • Evaluation with market timing • Performance attribution procedures and evaluation**Measuring Returns**• Dollar-weighted returnis the internal rate of return. It is a return equal across a multiperiod. • Time-weighted return is the arithmetic average of each one- period return • Time-weighted return is important for money managers. Because they cannot control cash inflow and outflow for each period, return per period measure is more relevant.**Arithmetic Average is simply the average of returns over**several periods.Geometric return average is the return over several periods is computed as:(1+rG)=[(1+r1)(1+r2)...(1+rn)]1/n For past returns performance evaluation, the geometric return is a better measure than arithmetic average. For estimating the expected future return, using historic average, arithmetric average is a better as it is an unbiased estimator.**Conventional Approaches to Performance Evaluation**• Sharpe measure: (rp-rf)/sp is the excess return per unit risk of standard deviation • Treynor measure: (rp-rf)/bp is the excess return per unit systematic risk. • Jensen measure: abnormal returnap =rp - [rf+bp(rm-rf)] • Appraisal ratio: ap/s(ep), which is the alpha (abnormal return) divided by the nonsystematic risk.**Evaluations among Different Measures**Excess Return Treynor lines . Q . P SML Market 1.0 Beta**Treynor measure assumes (1) the portfolio is**well-diversified and (2) accurate estimates. Illustration: according to security characteristic line (SCL), a=0.2%, b=1.2,s(e)=2%. The standard error for the “a” is roughly equal to s(a)=s(e)/N1/2 which means for 5% significance, we have the following: t = 1.96 = (a-0)/s(a) = 0.2N0.5/2 N = 384 months (too long to be reliable!)**In practice, the portfolio management industry uses a**benchment for performance measurement. In academics, other measurements include stochastic dominance method. Frequency g(y) f(x) Return G(y) F(x) 1**Changing Portfolio Composition**% excess return 27 3 -1 Quarter -9 Mean return (first 4 quarters) =(-1+3-1+3)/4=1% sd =[ (4%+...+4%)/4]0.5=2%**Mean of the last 4 quarters:**= (-9+27-9+27)/4=9% Sd =[(18%x18%+...]/4]0.5=18% The two years have a Sharpe Measure of 0.5 but the distribution of the return is different. Combination of the two years would yield a mean excess return is 5% and its sd is: [(6%)2+...+(22%)2/8]0.5=13.42% The Sharpe index = 5%/13.42%=0.37(inferior to 0.4 which is the passive strategy and 0.5 individual year) Portfolio mean shift will bias the evaluation performance**Market Timing and slope shift of beta**• If the proportion between risky asset and riskfree asset is constant, the beta of the entire portfolio remains the same over time as shown below: rp-rf slope=0.6 rm-rf**If the portfolio manager shifts funds**from the riskfree assets to the risky asset in anticipation of the rise in market return, then we will observe: rp-rf rm-rf Slope of the beta rises**That is, there is a regime shift in the regression analysis.**To capture the regime shift, we can formulate the several regression models as: (1) rp-rf=a+b(rm-rf)+c(rm-rf)2+ep Hypothesis: c>0 (2) rp-rf=a+b(rm-rf)+c(rm-rf)D+ep where D is a (0,1) dummy - 1 when rm> rf 0 elsewhere. Empirical results show no market timing evidence, i.e., we cannot reject c=0 in both regressions**Performance Attribution**• Portfolio managers constantly make broad-brush asset market allocation and sector and security allocation within markets • Performance is measured in terms of managed portfolio performance and the benchmark portfolio**Benchmark Performance and Excess Return**• Component Benchmark Return WeightS&P500 0.6 5.81%Bond Index 0.3 1.45Money Mkt 0.1 0.48 • Benchmark return=0.6x5.81%+0.3x1.45%+0.1x0.48%=3.97% • Managed portfolio excess return=actual return - benchmark=5.34%-3.97%=1.37%**Asset Allocation Decisions**The performance of the managed fund is due to different proportion of funds allocated as shown: MKT Equity Fixed Inc. TB Actual wt 0.7 0.07 0.23 Benchmark 0.6 0.30 0.10 Excess wt. 0.1 -0.23 0.13 (a) Mkt excess return 1.84 -2.52 -3.49 (b) (5.81-3.97) (1.45-3.97) (0.48-3.97) Contribution 0.184 0.5796 -0.4537 (a x b=) Total contribution =0.1840+0.5796-0.4537=0.3099**Sector and Security Selection**This analysis captures the super results of the portfolio due to their greater performance: Mkt Equity Fixed Income Return 7.28% 1.89% Index 5.81 1.45 Excess ret 1.47 0.44 (a) Port. wt. 0.7 0.07 (b) Contribution 1.03 0.03 (a x b) Total contribution=1.03+0.03=1.06**Portfolio Attribution Summary:**Asset allocation 0.31% Sector/security selection 1.06 Total excess return 1.37