# Empirical or theoretical quant insights that have shaped your thinking?

What are some quant theoretical or empirical insights that have shaped your thinking or provided a deeper conceptual basis for explaining returns and risk?

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@ Quant Guy: Converted to community wiki. –  olaker Sep 23 '11 at 20:13

Big Picture

• Time-series variance is driven mostly by discount rates, whereas expected cash flows dominate the cross-sectional variance. These results are important because they highlight the value of focusing on both dimensions of stock prices and returns: time-series and cross-section. On the other hand, however, they also show that a single mechanism is not capable of explaining both types of variation.

• The cash flows of growth stocks are particularly sensitive to temporary movements in aggregate stock prices, driven by shocks to market discount rates, while the cash flows of value stocks are particularly sensitive to permanent movements, driven by shocks to aggregate cash flows. Thus, the high betas of growth (value) stocks with the market's discount-rate (cash-flow) shocks are determined by the cash-flow fundamentals of growth and value companies. Growth stocks are not merely “glamour stocks” whose systematic risks are purely driven by investor sentiment. More generally, the systematic risks of individual stocks with similar accounting characteristics are primarily driven by the systematic risks of their fundamentals. - John Campbell

• “There is beta you understand and there is beta you do not understand.” – John Cochrane

• General equilibrium arguments. For example, systematic risk must be borne in aggregate, therefore alpha is a zero-sum game. Or, one cannot count the “distress” of the individual firm as a risk factor. Such distress is idiosyncratic and can be diversified away. Only aggregate events that average investors care about can result in a risk premium.

• Conventional linear asset pricing models imply a positive and monotonic risk-return relation (e.g., Merton, 1973). In contrast, changes between discrete regimes with different consumption growth rates can lead to increasing, decreasing, flat or non-monotonic risk return relations as shown by, e.g., Backus and Gregory (1993), Whitelaw (2000), and Ang and Liu (2007). The possibility of switching across regimes, even if it occurs relatively rarely, induces an important additional source of uncertainty that investors want to hedge against

• Better to think of risk as the co-variance of an asset's returns with an investor's cashflows rather than the merely the variance of the asset returns independent of the investor's circumstances

• Most returns and price variation come from variation in risk premia, not variation in expected cash flows or interest rates

• Bayesian decision-making

• Unconditional risk premia do not exist

Technical know-how

• Returns are typically leptokurtotic and left-skewed and non-stationary and exhibit autocorrelation of absolute returns . Good models will reflect the stylized empirical facts of the markets

• Regression coefficients in a time-series regression can be interpreted as portfolio weights or hedge ratios

• The square-root rule (to scaling variance) only applies under the assumption that the compounded returns are invariants, i.e. they behave identically and independently across time. Sharpe ratios scale with square root of horizon

• Optimizers are error-maximizers

• Robust regressions tends to outperform OLS or LAD when estimating Betas out-of-sample

• Neural networks can mimic any functional form of the DGP but imply the estimation of a large number of parameters with the consequent risk of overfitting and loss of forecasting ability

• Requiring that the residuals are mutually uncorrelated and uncorrelated in a factor model is different from requiring that the residuals are i.i.d. variables. The former is an assumption on the model, the latter is an assumption on how different samples are distributed

• In-sample significance testing is not that helpful...out-of-time testing is critical

• If you torture the data enough they will confess to anything

• Sometimes it is worth accepting bias to lower variance and improve ability to generalize

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+1. “There is beta you understand and there is beta you do not understand.”. Reminds me of a quote from one of his papers: "Exotic betas are my alpha". –  Ryogi Oct 29 '11 at 20:44
Brilliant. Can I ask (i) How can the distress of one firm be diversified away? To me that seems similar to saying that the small size of a firm can be diversified away because its size is firm specific (even though size is one of the most well established priced risks/anomalies). (ii) I think returns are stationary. Whenever I do adf or pp testing over a large number of return series what I find is consistent with a 5% false rejection rate by chance. –  Jase Dec 13 '12 at 6:20
Great answer, but is it possible to provide links or full references for the papers mentioned in the answer? For those of us that are not on a name-year familiarity with the literature. –  Artem Kaznatcheev Feb 27 '13 at 8:17
• Alpha is easier to measure and easier to obtain in the cross-section than in the time-series.
• Low information coefficient combined with high breadth still make for a decent information ratio.
• The breadth of your strategies is always lower than you think.
• When markets collapse, correlation goes to one.
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On your last point, have you read Forbes & Rigobon [Journal of Finance, 2002]? Based on my reading of the contagion literature there is not consensus that correlations increase. The authors find no evidence for increases in correlations (however there is accumulating recent evidence that this does occur). This is the case because the heterscedasticity can bias the Pearson estimates upwards. Also, I looked at 50 indices and their associated exchange rates and the DCC(1,1) correlations between them were only 0.1 on average over the 2001 dot-com crash. –  Jase Dec 13 '12 at 6:24
Granted, there was a large increase to 0.3 average DCC correlation during the GFC and Eurozone crisis. –  Jase Dec 13 '12 at 6:26
@jase it depends how you model correlation which distribution you choose matters greatly –  pyCthon Jan 29 '13 at 6:30
@Jase Lognin and Solnik (JoF 2002) test the relationship between volatility and correlation directly. Yes, volatility does bias correlation, however, even when this is adjusted for correlation increases with volatility. The effect is asymmetric, that is the effect is only present conditional on volatility from large negative returns, and not volatility from large positive returns. Effectively, correlations do not increase in bull markets they only increase in bear markets. –  papdog Feb 1 '13 at 6:18
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