大浩浩的笔记课堂——FRM考试学习笔记139

Topic 68Portfolio Performance Evaluation

1.The introduction of alpha(α) and beta(β):

⑴alpha(α):

①definition:

It is a measure of the excess return of a manager over the peer group or benchmark that relates to skill apposed to pure luck.

②excess return:

A.The excess returns of an investment can be regressed against the excess returns of its benchmark.An output from this regression is alpha(α).

B.The excess returns of a manager can be regressed against the excess returns of the manager´s peer group.It is different from the linear regression with a benchmark portfolio,due to survivorship bias.

⑵beta(β):

It is a measure of the amount of leverage used compared to the peer group or a measure of the underweighting or overweighting of the market compared to the benchmark.

2.The conventional theory of performance evaluation:

⑴average rates of return:

①arithmetic average return

②geometric average return→time-weighted average return

⑵time-weighted returns vs. dollar-weighted returns:

①time-weighted returns:

A.definition:

It measures compound growth,and it is the rate at which $1 compounds over a specified time horizon.

B.formula:

C.characteristics:

a/ It measures compound growth.

b/ It is the process of averaging a set of values over time.

c/ It is not affected by cash inflows or outflows.

②dollar-weighted returns:

A.definition:

It is the internal rate of return(IRR) on a portfolio taking into account all cash inflows and outflows,such as DCF approach.

B.formula:

PV_inflows=PV_outflows,求IRR

⑶risk-adjusted returns:

①Sharpe ratio:

A.definition:

It calculates the amount of excess return (over the risk-free rate) earned per unit of total risk.

B.characteristic:

It is the reward to total volatility trade-off.

C.formula:

②Treynor ratio:

A.definition:

It uses beta(systematic risk) as the measure of risk.

B.characteristic:

It shows excess return earned per unit of systematic risk.

C.formula:

③Jensen´s alpha:

A.definition:

It is the difference between actual return and return required to compensate for systematic risk.

B.characteristic:

It is the average return on the portfolio over and above that predicted by the CAPM.

C.formula:

④information ratio:

A.definition:

It is the ratio surplus return to its standard deviation.

B.characteristic:

It indicates the amount of risk undertaken to achieve a certain level of return above the benchmark.

C.formula:

·特别注意！

·Hedge funds or other active positions meant to be mixed with a passive indexed portfolio should be evaluated based on their information ratio.

⑤M²:

A.definition:

It compares return earned on the managed portfolio against the market return,after adjusting for differences in standard deviations between two portfolios.

B.characteristic:

It can be illustrated by comparing the CML for the market index and the CAL for the managed portfolio,the difference in return between the two portfolios equals the M²square.

C.formula:

⑷Sharpe´s ratio is the criteria for overall portfolios:

the particular utility function:

⑸Appropriate performance measures in two scenarios:

①the portfolio represents the entire risky investment fund→Sharpe ratio,M²

②the portfolio is one of many portfolios combined into a large investment 

fund→Treynor ratio

⑹actual performance measurement:

The example is the right way to evaluate a portfolio depends in large part on how the portfolio fits into the investor´s overall wealth.

⑺performance manipulation:

Manipulation-proof performance measure(MPPM) must fulfil:

①The measure should produce a sing-value score to rank a portfolio.

②The score should not depend on the dollar value of the portfolio.

③An uninformed investor should not expect to improve the expected score by deviating from the benchmark portfolio.

④The measure should be consistent with standard financial market equilibrium conditions.

⑻the Morningstar risk-adjusted rating(MRAR):

It is introduced in 2002,and it is particularly relevant to hedge funds.

3.Other methods of performance evaluation:

⑴market timing:

①definition:

To estimate an expanded security characteristic line,with a quadratic term added to the usual index model.

②model:

Extending basic return regression models offer a tool to assess superior market timing skills of a portfolio manager:

A.A market timer will include high(low) beta stocks in her portfolio if she expects an up(down) market.

B.If her forecasts are accurate,her portfolio will outperform the benchmark portfolio.

③ability:

The correct measure of timing ability:

P₁+P₂-1

A.P₁:the proportion of the correct forecasts of bull markets

B.P₂:the proportion of bear market

④importance:

The importance of long-run asset allocation has been established empathically:

Historical results suggest that the returns to market timing and security selection are minimal at best and at worst insufficient to cover the associated operating expenses and trading costs.

⑵call option model:

valuing market timing as a call option:

①basing:

It is based on the implicit call option embedded in their performance.

②definition:

The key to valuing market timing ability is to recognize that perfect foresight is equivalent to holding a call option on the equity portfolio.

4.Style analysis:

⑴definition:

It was a multiple regression model where the actors are category(style) portfolios such as bills,bonds,and stocks.A regression of fund returns on the style portfolio returns generates residuals that represent the value added of stock selection in each period.There residuals can be used to gauge fund performance relative to similar-style funds.

⑵goal:

①general:

Its goal is to determine the investment behavior of a fund manager by finding the best asset class exposures in his portfolio.

②example:

Sharpe´s style analysis,used to evaluate an active portfolio manager´s performance,measures performance relative to a passive benchmark of the same style.

⑶model:

Fama-French model explains asset returns based on:

①traditional capital asset pricing model(CAPM) market risk factor

②factor that captures size effect:

small cap minus big cap(SMB)

③factor that captures value/growth effect:

high book-to-market value minus low book-to-market value(HML)

⑷effect:

long winners and short losers,or winners minus losers(WML):

This strategy has outperformed both size and value growth effect,however,it is subject to crashes.

5.Performance attribution procedures:

⑴decomposition:

①components:

Common attribution system decomposes performance into 3 components:

A.broad asset market allocation choices across equity,fixed-income,and money markets

B.industry or sector choice within each market

C.security choice within each other

②formula:

⑵asset allocation contribution:

It equals the difference in returns attributable to active asset allocation decisions of the portfolio manager.

⑶sector/security selection contribution:

It equals the difference in returns attributable to superior individual security selection(correct selection of mispriced securities) and sector allocation(correct over- and underweighting of sectors within asset classes)

⑷summing up component contribution:

6.Performance measurement for hedge funds:

the difficulties in evaluating:

⑴The risk profile of hedge funds may change rapidly:

So the risk is not constant over time.

⑵Hedge funds tend to invest in illiquid assets:

The illiquid assets are difficult to price and need data smoothing.

⑶Pursuing strategies that may provide apparent profits over long periods of time.

⑷There are ample latitude to change their risk profiles.

⑸When they are evaluated as a group,survivorship bias can be a major considerations.

⑹Sensitivity with traditional markets increases in times of a market crisis and decreases in times of market strength.

大浩浩的笔记课堂之FRM考试学习笔记合集