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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,Active Portfolio Management,-Passive is relative,Active is absolute,Reference:,Grinold,Active Portfolio Management，（BGI）,1,Overview,Investors care about active risk and active return(relative to a benchmark).,CAPM is on return,Factor model tells risk,Exceptional expected return includes benchmark timing and residuals.,The information ratio is the ratio of the expected annual residual return to the annual volatility of the residual return.,Portfolio Selection between residual return and risk,The fundamental law of active management,there are two sources of information ratio:,IR=IC*(BR)1/2,2,researching ideas (Secrets to beat the market),forecasting exceptional returns,constructing and implementing portfolios,observing and refining their performance,1 What does a process of active investment management include?,3,2 Consensus Expected Returns:The CAPM,The CAPM is about expected returns,not risk.,Forecasts of betas based on the fundamental attributes of the company,rather their returns over the past 60 or so months,turn out to be much better forecasts of future beta.,Beta allows us to separate the excess returns of any portfolio into two uncorrelated components,a market return and a residual return.,4,3 Risk,Defining risk,Variance will add across time if the returns in one interval are uncorrelated with the returns in other intervals of time.The autocorrelation is close to zero for most assets.Thus,variances will grow with the length of the forecast horizon and the risk will grow with the square root of the forecast horizon.,Active risk=Std(active return)=Std(r,P,r,B,),We can prove Residual risk,of portfolio P relative to portfolio B is:,6,3 Risk,Beta is the beta between portfolio and benchmark.,Active position,is the difference between the portfolio holdings and the benchmark holdings.,h,PA,=h,P,-h,B,Active variance:,PA,Is active Beta of portfolio P,given by,P,-1,7,Example:Core-Satellite approachs active return and risk(Level III,Los33),Investor has a core holding of a passive index and/or an enhanced index that is complemented by a satellite of active manager holdings.Active risk is mitigated by the core,while active return is added by the satellites.,Assume correlation of active return is 0.,8,3 Risk,Choosing the factors,All factors must be a priori factors.That is,even though the factor returns are uncertain,the factor exposures must be known a priori,i.e.,at the beginning of the period.,Three types of actors:,Responses to external influence:macro-factors.,Cross-sectional comparisons,Statistical factors,10,3 Risk,Choosing the factors(contd),Criteria:incisive,intuitive.,-Incisive factors distinguish returns.,-Intuitive factors relate to interpretable and recognizable dimensions of the market.-,Typical factors,:,-Industries,-Risk indices:measure the differing behavior of stocks across other,non-industry dimensions,such as,volatility,momentum,size,liquidity,growth,value,earnings volatility and financial leverage,.,11,4,Components of Expected return,Management of total risk and return,Active management starts when the managers forecasts differ from the consensus.,The forecast of expected excess return for portfolio p can be expressed as:,Where,f,p,is the forecast of expected excess return for the portfolio.These forecasts will differ from consensus forecasts to the extent that,f,B,differs from the consensus estimate,B,and alpha differs from zero.,Or,expressed with Active Beta,13,5 Utility function of Active Manager,Expected utility components,of active manager,For manager with total risk aversion coefficient,Optimal,p,where f,p,is the expected excess return and the second term is a penalty for risk.measures aversion to total risk.,Active beta,(,PA,),is the ratio of our forecast for benchmark exceptional return to the consensus expected excess return on the benchmark,15,Expected utility components,Expected utility objective,.The root cause is our evenhanded treatment of benchmark and active risk.However,managers are much more adverse to the risk of deviation from the benchmarkActive Beta than they are adverse to the risk of the benchmark.,risk and return are splited into three parts,:,Intrinsic,This component arises from the risk and return of the benchmark.It is not under the managers control.is aversion to total risk.,Timing,This is the contribution from timing the benchmark.It is governed by the managers,active beta,.Risk aversion,BT,to the risk caused by benchmark timing.,-,Residual,This is due to the managers residual position.Here we have an aversion to the residual risk.,5 Expected utility and Value Added,16,6 Ex-ant&Ex-post:Alpha and Information Ratio,There are two types of Alpha:,ex-ante and ex-post,Look-forward(ex-ante),alpha is a forecast of residual return.,Looking backward(ex-post),alpha is the average of the realized residual returns:,Where,rs are excess returns,.The estimates of alpha and beta obtained from the regression are the realized or historical
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