TOPIC 9 - PERFORMANCE EVALUATION Flashcards
The simplest performance measure compares average return
to that on a benchmark such as an appropriate market index or even the median return of funds in a comparison universe.
alternative performance measures of the average return incl.
arithmetic and geometric average and time-weighted vs dollar weighted returns
appropriate performance measure depends on the
role of the portfolio to be evaluated.
Use Sharpe ratio as a performance measure where:
portfolio represents entire investment fund
Use Information ratio as a performance measure where:
when portfolio represents the active portfolio to be optimally mixed with the passive portfolio
Use Treynor as a performance measure where:
when the portfolio represents one subportfolio of many
Use Jensen (alpha) as a performance measure where:
all of these measures require a positive alpha for the portfolio to be considered attractive
Many observations and long sample periods are required to eliminate the effect of the “luck of the draw” from the evaluation process because:
because portfolio returns are commonly very “noisy”
Style analysis uses a multiple regression model where the factors are
category (style) portfolios such as bills, bonds and stocks.
The coefficients on the style portfolios indicate
a passive strategy that would match the risk exposures of the managed portfolio.
Shifting mean and risk of actively managed portfolios make it difficult
eg
to assess performance. An important eg of this problem arises when portfolio managers attempt to time the market, resulting in ever changing portfolio betas.
One way to measure timing and selection success simultaneously is to
estimate an expanded SCL for which the slope (beta coefficient) is allowed to increase as the market return increases
Another way to evaluate timers is based on the
implicit call option embedded in their performance.
Common attribution procedures decompose portfolio performance to
asset allocation, sector selection and security selection decisions.
With common attribution procedures, how is performance assessed?
by calculating departures of portfolio composition from a benchmark or neutral portfolio.
the greater the volatility, the lower or higher the geometric average comparative to the arithmetic average
the lower the geometric average comparative to the arithmetic average
Geometric average is a
time-weighted average –> each period’s return has equal weight
dollar weighted returns are the same as the
internal rate of return
Internal rate of return can be found from
the DCF approach
PV = C1/(1+r)^1 + C2/(1+r)^2 ….+Cn/(1+r)^n
if you know PV and CFs you can calculate r (which is the IRR)
Simplest and most popular way to adjust for risk is to
compare rates of return with those of other investment funds with similar risk characteristics
if the only risky asset held by the investor is shares what risk adjusted performance measure do you use
Sharpe ratio (divides average portfolio excess return over the sample period by the SD of the returns over that period) –> measures reward to total volatility trade off
If the stock is one of many stocks that the investor is analysing to form an actively managed stock portfolio what risk adjusted performance measure do you use?
Treynor’s measure: ratio of average portfolio excess return over sample period to SYSTEMATIC RISK over that period (uses systematic risk instead of total risk)
If the stock is mixed with the market index fund then the contribution to the overall Sharpe measure is determined by
the information ratio
divides alpha of portfolio by portfolio’s non-systematic risk
what does the information ratio measure
abnormal return per unit of risk that in principle could be diversified away by holding a market index portfolio
Alpha is often referred to as “excess return” or “abnormal rate of return,” which refers to the idea
that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole.
Alpha is often used in conjunction with beta which measures
the broad market’s overall volatility or risk, known as systematic market risk.
Jensen’s alpha takes into consideration
the CAPM and includes a risk-adjusted component in its calculation.
What’s the M^2 measure?
focuses on the total volatility as a measure of risk but its risk adjustment leads to an easy to interpret differential return relative to the benchmark index
survivorship bias
occurs when only the winners are considered while the losers that have disappeared are not considered.
This can occur when evaluating mutual fund performance (where merged or defunct funds are not included) or market index performance (where stocks that have been dropped from the index for whatever reason are discarded).
Survivorship bias skews the average results
upward for the index or surviving funds, causing them to appear to perform better since underperformers have been overlooked.
Style analysis a tool to do what?
systematically measure the exposures of managed portfolios introduced by Sharpe
what is the idea behind style analysis?
to regress fund returns on indexes representing a range of asset classes
–> Regression coefficient on each index would then measure the fund’s implicit application to that ‘style’
–> R2 of regression would measure % of return variability attributable to style choice rather than security selection
Performance attribution studies attempt to decompose overall performance into
discrete components that may be identified with a particular level of the portfolio selection process
simply put return on a stock over a year =
(capital gains + dividend)/price
= (P1-P0+ dividend)/P0
alpha is what intercept
the regression intercept (aka set beta =0)
does the sharpe ratio use systematic risk or total risk?
total risk (treynor’s measure pretty similar to sharpe only dif is that treynor’s just measures systematic risk, aka beta)
how to determine the contribution of security selection relative to performance
take the difference in returns (aka manager’s returns for the asset class - index’s returns) x manager’s portfolio weight for that asset class
differential return within market (manager returns - index) x manager’s portfolio weight of each asset class =
contribution of security selection to performance
contribution of asset allocation relative to performance
excess weight x index return
aka
(manager’s weight - benchmark weight) x index return
calculation of secrutiy selection contribution relative to performance + asset allocation contribution relative to performance =
excess performance
what does within sector selection effect?
The within sector selection calculates the return according to security selection. This is done by summing the weight of the security in the portfolio multiplied by the return of the security in the portfolio minus the return of the security in the benchmark
if a passive managed fund mimics the benchmark index, then will the R^2 of the regression be high or lower than that of an actively managed fund when looking at return-based style analysis
Because the passively managed fund is mimicking the benchmark, the R2 of the regression should be very high (and thus probably higher than the actively managed fund).
M^2 measure:
[(SD_m/SD_p)x r_p] + [(1-SD_m/SD_p)x rf ] - r_m
