I think the given sample answer includes a reference (“non-synchronous” return data) to last year’s Andrew Lo assignment, for which I am not aware of 2009 reference, but still relevant - David

Question:

E1.02. [source: sample 2009 FRM Full Exam I. Question 02] You are asked by your boss to estimate the exposure of a hedge fund to the S&P 500. Though the fund claims to mark to market weekly, it does not do so and marks to market once a month. The fund also does not tell investors that it simply holds an ETF which is indexed to the S&P500;. Because of the claims of the hedge fund, you decide to estimate the market exposure by regressing weekly returns of the fund on the weekly return of the S&P500;. Which of the following properties correctly describes a property of your regression estimates?

a. The beta of your regression will be one because the fund holds the S&P 500.
b. The beta of your regression will be zero because the fund returns are not synchronous with the S&P 500 returns.
c. The intercept of your regression will be positive, showing that the fund has a positive alpha when estimated using an OLS regression.
d. The beta will be misestimated because hedge fund exposures are non-linear.

My Adds:

E1.02e. If the S&P 500 were a proxy for the market (which it isn’t because it is large cap; the S&P 1500 is nearer to a proxy), what does beta represent in the regression?
E1.02f. As faithful disciples of Andrew Lo, among the 6-7 assumptions of the classical linear regression model (CLRM), which violation are we expecting here?
E1.02g. Can we call the intercept hedge fund alpha? (source: Grinold)
E1.02h. Is the alpha skill or luck (source: Grinold)?
E1.02i. If the alpha is skill, is it the only skill; i.e., can the manager add value aside from alpha? (source: Grinold)

Answers:

E1.02 [as given in sample exam]
CORRECT:  C
The alpha is spurious and results from the fact that returns are non-synchronous.  d.  is incorrect because the true exposure is linear.  The beta is greater than zero and less than one because of non- synchroneity. Reference:  Amenc and Le Sourd,  Portfolio Theory and Performance Analysis.  Chapter 4

I am not sure how this answer references the 2009 FRM assignments, but there is a growing literature thread on the challenges of performance attribution against (“to”) illiquid securities like hedge funds. I recommend the following paper as an accessible introduction (Clifford Asness, Robert Krail, & John Liew):

http://ssrn.com/abstract=252810

From their paper (emphasis mine):
“Many hedge funds hold, to various degrees and combinations, illiquid exchange-traded securities or difficult-to-price over-the-counter securities, which can lead to non-synchronous price reactions. Illiquid exchange-traded securities often do not trade at, or even near, the end of every month (even small and medium capitalization stocks may fall into this category).  Moreover, publicly available traded prices often do not exist for hard-to-price over-the-counter securities. The absence of these prices may leave hedge funds with “flexibility” in how they mark their positions for month-end reporting.  In some cases, hedge funds use the last available traded price and in others (often with hard-to-price over-the-counter securities) they guess-timate the price, perhaps based on a model, along with broker-dealer input, in order to value their portfolio for month end performance reporting ... The presence of stale prices due to either illiquidity or managed pricing can artificially lower estimates of volatility and correlation to traditional indices ... In some cases the securities may be so illiquid, or the “managing” of pricing so extreme, that they do not get accurately marked for several months.  Thus, there may be significant lagged relations between market returns and reported hedge fund returns rendering simple monthly regression betas understated, perhaps severely.”

Also excellent is the recent, free survey from the CFA Institute (“Investing in Hedge Funds: A Survey”):
http://www.cfapubs.org/doi/pdfplus/10.2470/rflr.v4.n2.1

This paper explicity shows how illiquidity can masquerade as alpha (page 8 , emphasis mine): “In these illiquid asset classes, many holdings are valued using a mark-to-model methodology. Because these assets do not have a liquid market, marking to market is not feasible. These assets also trade infrequently, so valuations change relatively slowly when compared with prices in more liquid markets. This tendency to change valuations slowly is termed stale pricing. When funds exhibit stale pricing, the risk of the fund’s holdings will be understated because volatility and the correlation with freely traded assets are likely to be understated. Kat (2004) estimates that this artificial smoothing of net asset values can underestimate risk by as much as 40 percent .  Al though it seems logical to include illiquidity in a factor model, Kat (2004) states that no study has adequately modeled this common risk of hedge fund investing. The Sharpe ratio of funds with smoothed returns is dramatically overstated, as the standard deviation of reported returns is far below the true economic standard deviation. [The implication is that illiquidity is a risk factor, the compensation for which, if not explicity built into the model, by definition, will manifest as alpha - David]”

E1.02e. If the S&P 500 were a proxy for the market (which it isn’t because it is large cap; the S&P 1500 is nearer to a proxy), what does beta represent in the regression?

Beta is similar to beta in CAPM, and from a functional regression standpoint, is the same: it is the sensitivity (factor exposure) of the portfolio to the index. Here, the beta is meant to quantify “factor exposure” to the index.

E1.02f. As faithful disciples of Andrew Lo, among the 6-7 assumptions of the classical linear regression model (CLRM), which violation are we expecting here?

Due to illiquidity, we expect autocorrelation: a violation of the assumption that the error terms are independent. Autocorrelation is Lo’s famous test of illiquidity.

E1.02g. Can we call the intercept hedge fund alpha? (source: Grinold)
Yes, alpha is the intercept in the regression.

E1.02h. Is the alpha skill or luck (source: Grinold)?
We don’t know, it is primia facia hard to parse skill from luck. Positive alpha does not imply skill! We can, however, test for significance; i.e., require several years of alpha.

From Grinold page 481 (emphasis mine):
“Fortunately or unfortunately, we observe only the combination of skill and luck. Both the blessed and the insufferable will show up with positive return histories. The challenge is to separate the two groups. The simple existence of positive returns does not prove skill. Almost half of all roulette players achieve positive returns each spin of the wheel, but over time they all lose. The existence of very large positive returns also does not prove skill. How much risk was taken on in generating that return? Performance analysis will involve comparing ex post returns to ex ante risk in a statistically”

E1.02i. If the alpha is skill, is it the only skill; i.e., can the manager add value aside from alpha? (source: Grinold)

No, per Chapter 17, the manager adds value also by deciding which and how much beta exposure to seek; this can be either “active beta” or “active benchmark timing.” Some term this “alternative beta.”