7. Benchmarking and Performance Attribution

Question 1

1. What is the common name for a comparison group of funds with similar risk and return objectives and characteristics?

Answer 1

• Peer group (or comparison group)

Question 2

2. Describe a theoretical, normative, time-series model of equity returns that might be used by a hedge
   fund to guide a high frequency trading strategy.

Answer 2

• Theoretical models tend to explain behavior accurately in more simplified situations where the relationships among variables can be somewhat clearly understood through logic.
• Normative economic models tend to be most useful in helping explain underlying forces that might drive rational financial decisions under idealized circumstances and, to a lesser extent, under more realistic conditions.
• Time-series models analyze behavior of a single subject or a set of subjects through time.
➢ For example, a model that hypothesized the impact of large orders in an equity market with risk- averse traders of limited capital in a world of informational asymmetries in which the large orders were driven by exogenous shocks to the institutions placing the orders would qualify.

Question 3

3. Consider two hedge funds each of which attempt to benefit from identifying pairs of securities in which temporary mispricing is expected to correct as the prices converge. What would differentiate a normative model from a positive model?

Answer 3

• A normative model attempts to describe how people and prices ought to behave. A positive model attempts to describe how people and prices actually behave.

Question 4

4. Compare the role of the intercept in the ex post versions of the CAPM and the single factor market model.

Answer 4

• In the ex post version of the CAPM the risk-free rate can serve as the intercept, or can be subtracted from the asset’s return to form its excess return. In a single-factor market model the intercept is allowed to differ in theory from the riskless rate in order to indicate abnormally high or low returns due to mispricing. Thus the difference between a CAPM model and the single- factor risk model is that whether consistently abnormal returns are allowed to be captured in the intercept term or disallowed through a presumption of informational market efficiency.

Question 5

5. What is the traditional difference indicated by the use of “a” to denote an intercept rather than α?

Answer 5

• “a” is used to represent variables estimated in and outputted from a statistical procedure, in this case the y-intercept. α is used to represent the true and unobservable variables, in this case α = Rp – [Rf + (Rm – Rf) β].

Question 6

6. An analyst is using a multi-factor return model to estimate the overperformance or underperformance of a fund. What would be the anticipated effect of omitting systematic risk factors to which the fund was negatively exposed in an “up” market?

Answer 6

• In an “up market” (i.e., a market in which major indices outperformed the riskless rate), the omission of systematic risk factors will cause an analysis to overestimate the risk-adjusted performance of assets positively exposed to the omitted factors and underestimate the performance of assets negatively exposed to the omitted risk factors.

Question 7

7. Explain the relationship between the effect of omitted systematic risk factors and the overall direction of the market in a performance attribution.

Answer 7

• In an “up market” (i.e., a market in which major indices outperformed the riskless rate), the omission of systematic risk factors will cause an analysis to overestimate the risk-adjusted performance of assets positively exposed to the omitted factors and underestimate the performance of assets negatively exposed to the omitted risk factors. In a down market the anticipated effect would be the opposite. Most long-term studies are more likely to be up markets since risky assets on average outperform the riskless asset.

Question 8

8. Summarize the primary conclusion of the differences in Fund A’s estimated intercepts in Exhibits 7.1, 7.2 and 7.3.

Answer 8

• Exhibits 7.1 and 7.2 indicate that Fund A is generating superior returns. However, Exhibit 7.3 indicated that Fund A’s return included exposures to size, value, and momentum factors in addition to its exposure to the market index. Note that the annual idiosyncratic performance (the intercept) is now estimated as being 2.91% lower than would be obtained in a perfectly efficient market. What was previously estimated as a 1.3% positive alpha using a single-factor model is now estimated as a -2.9% alpha using multiple factors. Apparently, the intercept of Fund A using a single-factor model was erroneously identified as an indication of superior return rather than as compensation for the omitted risk exposures that the fund was incurring by investing in small- capitalization value stocks with a high degree of momentum. This indication that performance was inferior is in marked contrast to the estimated superior performance shown in Exhibits 7.1 and 7.2 using a simple benchmark and single-factor approach, respectively.

Question 9

9. List three reasons why the CAPM is an especially poor model with which to benchmark alternative investments.

Answer 9

• Multiperiod issues, nonnormality, illiquidity of returns and other barriers to diversification

Question 10

10. Why might nonnormality of returns be a more important concern for managing a portfolio of alternative investments rather than a portfolio of traditional investments?

Answer 10

• Alternative investment returns often tend to skew to one side or the other and/or have excess kurtosis, with fatter tails on both sides. Nonnormality of returns tends to be greater for larger time intervals, and alternative investments by their nature often tend to be illiquid and are less likely to be managed with short-term portfolio adjustments. Another reason for the nonnormality of many alternative investment returns is the structuring of their cash flows into relatively risky and asymmetric patterns.

Question 11

abstract models

Answer 11

also called basic models, tend to have
applicability only in solving real-world challenges of the
future.

Question 12

applied models

Answer 12

are designed to address immediate real world

challenges and opportunities.

Question 13

benchmarking

Answer 13

often referred to as performance
benchmarking, is the process of selecting an investment index,
an investment portfolio, or any other source of return as a
standard (or benchmark) for comparison during performance
analysis.

Question 14

cross-sectional models

Answer 14

analyze behavior at a single point in

time across various subjects, such as investors or investments.

Question 15

panel data sets

Answer 15

combine the two approaches by tracking
multiple subjects through time and can also be referred to as
longitudinal data sets and cross-sectional time-series data sets.

Question 16

peer group

Answer 16

is typically a group of funds with similar

objectives, strategies, or portfolio holdings.

Question 17

performance attribution

Answer 17

also known as return attribution,
is the process of identifying the components of an asset’s
return or performance.

Question 18

Find the systematic and idiosyncratic returns for
the following: Assume that the risk-free rate is 2%, the realized return of asset i in
year t was 16%, the realized return of the market portfolio was 14% (which was
12% more than the riskless rate), and the beta of asset i is 1.25.

Answer 18

R(it) - R(f) = Beta (R(mt) - R(f)) + E(it)

systematic portion of its realized return:
Beta (R(mt) - R(f))
1.24(0.14 - 0.02)
= 0.15

0. 14 - 0.15 = - 1 = E(it)
1. 16 - 0.02 = 1.25 (0.14 - 0.02) - 0.01

Step One: Press 0.14 → - → 0.02
Step Two: Press x → 1.25
Step Three: Press = “.15” (systematic return)
Step Four: Press 0.16 → - → 0.02
Step Five: Press = “14”
Step Six: Press 0.14 → - → 0.15
Step Six: =
Answer: -0.01 (idiosyncratic return)