大浩浩的笔记课堂——FRM考试学习笔记135

Topic 64 Portfolio Construction

1.Introduction:

⑴implementation(safe guards against poor research):

①construction:

including current portfolio,alphas,covariance estimates,transactions cost estimate,active risk aversion

②trading

⑵objective(the standard objective):

maximizing (active returns-an active risk penalty),or to maximize risk-adjusted actual active return

2.Portfolio construction process:

⑴current portfolio:

It is the most measurable input.

⑵refining alphas:

①definition:

It is an alternative to including constraints in the portfolio optimization process.

②objective:

By refining the alphas and then optimizing,it is possible to include constraints of both the investor and the manager.

③motivation:

A.It can achieve the same goal as a constrained optimization approach.

B.It has the advantage of focusing on the alpha inputs and the effects of individual constraints on portfolio returns.

④methods:

A.scaling technique:

a/ formula:

b/ distribution:

The α should have mean 0 and standard deviation(scale) of volatility*IC.

B.trimming technique:

Deleting alphas due to questionable data:

a/ Closely examine all stocks with alphas are greater in magnitude than,3 times the scale of the alphas.

b/ For them into a normal distribution with benchmark alpha is equal to 0 and the required scale factor.

C.neutralization:

a/ definition:

It means that removing biases or undesirable portfolio risk from out alphas.

b/ approaches:

△benchmark neutralization:

·消除benchmark portfolio alpha

·the new modified alpha=original alpha-beta coefficient×benchmark alpha

△cash-neutral alphas:

消除cash alpha

△risk-factor-neutral alphas:

·It matches specific factor risk in the active portfolio to those of the benchmark.

·消除基金经理运气导致的alpha

D.proper alpha coverage addressing the case:

a/ The manager has forecasts of stocks that are not in the benchmark:

The weight of benchmark is 0.

b/ The manager does not have forecasts for assets in the benchmark:

Alphas can be inferred and there should be a function of the alphas of the other assets.

⑶transactions cost estimate:

①general rule:

The annualized transactions cost is the around-trip cost divided by the holding period in years.

②influence dimension:

A.trade: 

The transaction costs must be amortized over the horizon of the benefit from the trade because the benefit occurs over time while the transaction costs generally occur at a specific time when the portfolio is adjusted.

B.rebalancing:

Rebalancing decisions dependent on the estimated holding period of portfolio assets:

a/ They may make it optimal not to rebalance ever with the arrival of new information.

b/ Transaction costs increase the importance of robust alpha estimates.

③portfolio revisions:

A.As long as the alpha stays within that band,the portfolio will remain optimal,we should not react to new information:

-sales cost(SC)≤marginal contribution to value added(MCVA)≤purchase cost(PC)

B.MCVA and alpha of asset:

a/ MCVA=(alpha of asset)-[2×(risk aversion)×(active risk)×marginal contribution to active risk of asset(MCAR)]

b/ [2×(risk aversion)×(active risk)×MCAR]-(cost of selling)<alpha of asset<[2×(risk aversion)×(active risk)×MCAR]+(cost of purchase)

·特别注意！

·When the new information arrives,there is no-trade range for alpha.

C.the after-cost information ratio declines as a function of both the cost and the half-life of the signals:

a/ When we trade,we pay the costs.

b/ The transaction cost makes us less eager,we lose by intimidation.

①formula:

A.risk aversion:

B.utility:

utility=active return-risk aversion×variance

②example:

③characteristics:

A.concerning aversion to specific as opposed to common factor risk

B.We will cover here concern alpha coverage.

④reasons:

A.帮助基金经理意识到huge losses

B.appropriate aversion risk factors

·特别注意！

·These inputs are all subject to estimation error and possible bias.

·In the process of portfolio revisions and rebalancing,there are trade offs between alpha,risk,transaction costs and investment horizon.

·The shorter the horizon,the more uncertain the alpha.

3.Techniques for portfolio construction:

⑴screens:

①definition:

Simply choosing assets by ranking alpha.

②recipe:

Recipe for building a portfolio from scratch:

A.rank the stocks by alpha

B.choose the top performers such as first 50 stocks

C.equal-weight the stocks:

Form either an equally-weighted portfolio or a capitalization-weighted portfolio of stocks.

③strengths:

A.simplicity,easy to understand,clear link between cause and effect

B.easy to computerize

C.robust,wild estimates alphas do not alter the result

D.concentrating in the high-alpha stocks

E.limiting the transactions costs by controlling turnover

④shortcomings:

A.It ignores all information in the alphas from the rankings.

B.It does not protect against biases in the alphas.

C.It ignores certain industry with low alpha.

D.It fails in addressing risk control purposes.

⑵stratification:

①definition:

A.Choosing stocks based on screens,including assets from all asset classes(glorified screening).

B.It applies screening separately to categories of stocks and weights the active portfolio across these categories with their weights in the benchmark portfolio.

②process:

A.The key is splitting the list of followed stocks into mutually exclusive categories.

B.Stratification ensures that the portfolio matches the benchmark.

③strengths:

A.It has the same benefits as screening.

B.It can solve the problem of the possible exclusion of some categories of assets.

④shortcomings:

A.It ignores some information.

B.The risk control is rudimentary.

C.It still suffers from possible errors in measuring alphas.

⑶linear programming:

①definition:

Attempting to construct a portfolio that closely resembles the benchmark portfolio with respect to such risk factors in all of the dimensions used for risk control(space age stratification).

②characteristic:

It is an improvement on stratification.

③objective:

To maximize the portfolio´s alpha less transaction costs,while remaining close to the benchmark portfolio in the risk control dimensions.

④process:

It uses a type of stratification based on characteristics such as industry,size,volatility,beta and so on without making the categories mutually exclusive,and it can also include transactions costs.

⑤strengths:

A.It takes all the information.

B.It controls risk by keeping the characteristics of the portfolio close 

to the characteristics of the benchmark.

⑥shortcomings:

It can be different from the benchmark with respect to the number of assets and risk characteristic:

A.It has difficulty producing portfolios with a prespecified number of stocks.

B.The risk characteristics should not work at cross-purposes with the alphas.

⑷quadratic programming(QP):

①elements:

It Explicitly consider 3 elements(alpha,risk,transaction costs)

②characteristic:

A.It improves on the linear programming method.

B.It is an ultimate approach,theoretically the best optimization method.

③process:

The value added in the active portfolio which is quite sensitive to the level of estimation error in the covariance inputs.

④lessons:

A.Errors in the estimates of covariance lead to inefficient implementation.

B.It is vital to have good estimates of covariance.

4.Dispersion:

⑴definition:

It is the difference between the maximum return and minimum return for these separate account portfolios.

⑵characteristic:

It is a measure of how an individual client´s portfolio may differ from the manager´s reported composite returns.It is a client support problem for investment managers.

⑶reasons(sources):

the different histories and cash flows of each of the clients:

①client-driven:

Clients impose different constraints,beyond the manager´s control.

②lack attention:

It arises through a lack of attention to separate accounts.

⑷treatment:

Managers should reduce it only until further reduction would substantially lower returns on average due to incurred transaction costs.

⑸methods:

There are 2 methods the manager could reduce dispersion to 0:

①sacrificing returns:

Investing the new portfolio in the rebalanced existing portfolio.

②paying excess transaction costs:

Investing the composite in the new optimum.

⑹controlling:

①If transactions cots were zero,dispersion would disappear,at no cost to investors.

②With transactions costs,managers should consider transactions costs.

③It can try to increase the proportion of assets that are common to all portfolios.

⑺managing:

①If alphas and risk stay absolutely constant over time,then dispersion will never disappear.

②If alphas and risk vary over time as the usual case,then convergence will occur.

③In real-life situations,client-initialed constraints and client-specific cash flows will act to keep separate accounts from converging.

④Unless you are willing to give up return in order to lower dispersion,do not implement the dual-benchmark optimization approach to managing dispersion.

5.Other knowledge points:

⑴The standard reaction is to do in the portfolio construction process:

placing limits on active stock positions,limiting turnover,constraining holdings in certain categories of stocks to match the benchmark holding

⑵The higher the expected payoff of an asset in bad times,the lower the asset´s expected return.

⑶High-yield bond returns appear indifferent to change in economic growth.

⑷adding multiple factors to the regression analysis:

①potentially improvement:

A.the adjusted R²measurement

B.the tests of statistical significance

②a search:

a search for a benchmark that is more representative of a portfolio´s investment style

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