Question:
In regard to Andrew Lo’s “Can Hedge-Fund Returns Be Replicated?”
(i) Why does he introduce (what is the point of) the fictional CDP & CMP strategies?
(ii) Under the linear multi-factor model employed, what are the sources of RETURN and the sources of RISK?
(iii) Among the several hedge funds strategies, which are BEST replicated with clones? Which LEAST afford themselves to clone replication?
(iv) How does Lo measure illiquidity?
Answers:
(i) Why introduce CDP and CMP?
The point is to illustrate two extremes:
Capital decimation partners (CDP) is a strategy which can be easily replicated with a clone; i.e., because the strategy writes insurance against sudden S&P500 declines, it has a high correlation with the S&P500 as a common factor.
But Capital Multiplication Partners (CMP) cannot be (easily) replicated (despite the high coefficient of determination) because “the actual performance of the linear clone falls far short of the strategy because a linear model will never be able to capture the option-like payoff structure of the perfect market-timer.”
CMP also gives a cautionary note about the danger of over-reliance on the coefficient of determination (R^2): CMP has a high R^2 but is still not a good candidate for linear clone. The authors say, “Despite the high R^2 achieved by the linear regression of CMP’s returns on the market index, the actual performance of the linear clone falls far short of the strategy because a linear model will never be able to capture the option-like payoff structure of the perfect market-timer.”
(ii) What are the sources of return and risk?
The sources following directly from the model employed: a linear regression model where return is a function of common factor exposures plus the residual alpha.
Sources of return:
1. beta exposures multiplied by the risk premia associated with those exposures, and
2. manager-specific alpha
The sources of risk are the source of variance:
1. The variances of the risk factors multiplied by the squared beta coefficients,
2. The variance of the residual (which may be related to the specific economic sources of alpha), and
3. The weighted covariances among the factors.
(iii) Which strategies are candidates for clones?
Strategies that are candidates for clone replication are those with more exposure to common factor and with less performance due to alpha. These include: Convertible arbitrage, managed futures, and perhaps global macro. In regard to the authors actual test, while not statistically significant, the average mean return of five of the fixed-weight clones was higher than the funds: Dedicated Short Bias (6.70% clone vs. 5.98% fund), Equity Market Neutral (10.00% vs. 8.09%), Global Macro (15.54% vs. 11.38%), and Managed Futures (27.97% vs. 13.64%), and Fund of Funds (9.29% vs. 8.25%).
In regard to the least clone-able strategies, we could argue:
1. Convertible arbitrage: while factor exposures are high (dollar, bond, commodity), the clones did not perform well
2. Emerging markets: only equity exposure was material, and clones showed lower performance
3. Equity market neutral: high alpha, low factor exposure. But fixed weigth clone performed well.
4. Event driven: low factor exposure and clones did not perform well versus funds. This is an expected finding: event driven strategies should not be correlated to common factors.
5. Arguably, fixed income arbitrage: debatable, but signficant credit (Bond) factor exposure clones underperformed funds.
(iv) How do they measure liquidity?
This is a signature methodology of Andrew Lo: the proxy for liquidity/illiquidity is the average first-order autocorrelation coefficients of clones and funds. The first-order autocorrelation is the correlation between a fund’s current return and the previous month’s return.
