AIMs: Explain how survivorship bias poses a challenge for hedge fund return analysis. Describe how dynamic investment strategies complicate the risk measurement process for hedge funds. Describe how the phase-locking phenomenon and nonlinearities in hedge fund returns can be incorporated into risk models. Explain how autocorrelation of returns can be used as a measure of liquidity of the asset.
Questions:
8.1. A factor analysis of returns for hedge funds employing a equity market-neutral strategy produces strongly positive performance information for the strategy (for example, impressive Sharpe ratios). However, the analysis is guilty of neglecting the effects of survivorship bias. If the problem is survivorship bias, which of the following criticisms of the methodology is best?
a. The sample is too small
b. The historical window is too short
c. Risk metrics needs to be included along with return metrics
d. Past performance is no guarantee of future performance
8.2. Andrew Lo illustrates the impact of survivorship bias, as a type of selection bias, by assuming that X(j) is a random standard normal variable that characterizes the Sharpe ratio of a fund. Further, he assumes that "[no] funds possesses any superior performance or alpha, so E[X(j)] = 0". Note this is perfectly consistent with assuming X(j) is a random standard normal variable, as its mean is zero. He also defines the maximum REALIZED Sharpe ratio among a set of (n) hedge funds as X(*) = MAX[X(1),X(2) ... X(n)]. Which of the following is true?
a. As (n) increases, the standard deviation of (X*), SD[X*], increases
b. As (n) increases, the expected return of (X*), E[X*], increases
c. As (n) increases, the inter-percentile range between the 2.5% and 97.5% quantiles of the distribution of (X*) increases
d. Regardless of the sample size, X(*) must be positive, which is an illustration of survivorship bias
8.3. A hedge fund manager employs a strategy of shorting out-of-the-money S&P 500 (SPX) put options on each monthly expiration date for maturities less than or equal to three months, and with strikes approximately 7% out of the money (Andrew Lo's hypothetical example). Which of the following critiques related to this dynamic strategy is most valid?
a. It is inappropriate for an institutional investor to assume (be exposed to) this sort of "tail risk"
b. If hedge funds engage in this strategy, "position transparency" should be required: if the positions are transparent, the risks can be understood by institutional investors
c. The strategy is actually negatively correlated to the S&P 500 but short term linear correlations will not reveal this inverse correlation
d. Measures based on mean-variance framework, like the Sharpe ratio and standard deviation, will be artificially and deceptively favorable
8.4. Andrew Lo describes the phase-locking phenomenon; e.g., "In the physical and natural sciences, such phenomena are examples of 'phase-locking' behavior, situations in which otherwise uncorrelated actions suddenly become synchronized." This is the well-known fact that correlations tend to spike toward 1.0 in a crisis, such as when, during the summer of 1998, default in Russian government debt triggered a global flight to quality. Which of the following is a valid modeling issue created by phase-locking?
a. We cannot model the phase-locking phenomenon "with current technology, in any meaningfully practical sense"
b. We can model the phase-locking phenomenon, but it requires a totally separate model for the phase-locking period and there is no practical way to summarize returns that spans both regular and phase-locking periods
c. Unconditional correlations can easily remain very small despite the presence of phase-locking episodes in the sample
d. While unconditional correlations remain useful, conditional correlations become unusable as they require a conditional variance, which is impractical
8.5. Andrew Lo argues that autocorrelation (aka., serial correlation) of returns can be used as a measure of liquidity. EACH of the following is a valid argument for the use of return autocorrelations as a proxy for illiquidity EXCEPT for:
a. Managers have discretion in marking the portfolio’s value at the end of each month to arrive at the fund’s net asset value (NAV), and they are tempted to smooth their returns
b. Highly efficient markets should be frictionless with prices that exhibit random walks, but illiquidity is a key friction
c. Contributors to serial correlation include: transactions costs, borrowing constraints, information gathering/processing costs, and institutional restrictions on short sales
d. In an informationally efficient market, price changes must be unforecastable if they are properly anticipated
Answers:
Questions:
8.1. A factor analysis of returns for hedge funds employing a equity market-neutral strategy produces strongly positive performance information for the strategy (for example, impressive Sharpe ratios). However, the analysis is guilty of neglecting the effects of survivorship bias. If the problem is survivorship bias, which of the following criticisms of the methodology is best?
a. The sample is too small
b. The historical window is too short
c. Risk metrics needs to be included along with return metrics
d. Past performance is no guarantee of future performance
8.2. Andrew Lo illustrates the impact of survivorship bias, as a type of selection bias, by assuming that X(j) is a random standard normal variable that characterizes the Sharpe ratio of a fund. Further, he assumes that "[no] funds possesses any superior performance or alpha, so E[X(j)] = 0". Note this is perfectly consistent with assuming X(j) is a random standard normal variable, as its mean is zero. He also defines the maximum REALIZED Sharpe ratio among a set of (n) hedge funds as X(*) = MAX[X(1),X(2) ... X(n)]. Which of the following is true?
a. As (n) increases, the standard deviation of (X*), SD[X*], increases
b. As (n) increases, the expected return of (X*), E[X*], increases
c. As (n) increases, the inter-percentile range between the 2.5% and 97.5% quantiles of the distribution of (X*) increases
d. Regardless of the sample size, X(*) must be positive, which is an illustration of survivorship bias
8.3. A hedge fund manager employs a strategy of shorting out-of-the-money S&P 500 (SPX) put options on each monthly expiration date for maturities less than or equal to three months, and with strikes approximately 7% out of the money (Andrew Lo's hypothetical example). Which of the following critiques related to this dynamic strategy is most valid?
a. It is inappropriate for an institutional investor to assume (be exposed to) this sort of "tail risk"
b. If hedge funds engage in this strategy, "position transparency" should be required: if the positions are transparent, the risks can be understood by institutional investors
c. The strategy is actually negatively correlated to the S&P 500 but short term linear correlations will not reveal this inverse correlation
d. Measures based on mean-variance framework, like the Sharpe ratio and standard deviation, will be artificially and deceptively favorable
8.4. Andrew Lo describes the phase-locking phenomenon; e.g., "In the physical and natural sciences, such phenomena are examples of 'phase-locking' behavior, situations in which otherwise uncorrelated actions suddenly become synchronized." This is the well-known fact that correlations tend to spike toward 1.0 in a crisis, such as when, during the summer of 1998, default in Russian government debt triggered a global flight to quality. Which of the following is a valid modeling issue created by phase-locking?
a. We cannot model the phase-locking phenomenon "with current technology, in any meaningfully practical sense"
b. We can model the phase-locking phenomenon, but it requires a totally separate model for the phase-locking period and there is no practical way to summarize returns that spans both regular and phase-locking periods
c. Unconditional correlations can easily remain very small despite the presence of phase-locking episodes in the sample
d. While unconditional correlations remain useful, conditional correlations become unusable as they require a conditional variance, which is impractical
8.5. Andrew Lo argues that autocorrelation (aka., serial correlation) of returns can be used as a measure of liquidity. EACH of the following is a valid argument for the use of return autocorrelations as a proxy for illiquidity EXCEPT for:
a. Managers have discretion in marking the portfolio’s value at the end of each month to arrive at the fund’s net asset value (NAV), and they are tempted to smooth their returns
b. Highly efficient markets should be frictionless with prices that exhibit random walks, but illiquidity is a key friction
c. Contributors to serial correlation include: transactions costs, borrowing constraints, information gathering/processing costs, and institutional restrictions on short sales
d. In an informationally efficient market, price changes must be unforecastable if they are properly anticipated
Answers:
