I need help in understanding some results that I have obtained.

I am doing some out-of-sample performance analysis for different targets of volatility in mean-variance optimization where I solely change the way the covariance matrix has been estimated. HC in the figure refers to the sample covariance matrix, whereas GS refers to the Gerber-Statistic based covariance matrix (see here) which is supposedly more robust to outliers and noise in the data.

Now, if we observe the below figures, one can see that the risk-adjusted-return (adjusted according to HC) for GS is generally lower in expansionary times while its much higher in recessionary times. Now, a plausible explanation for this is that GS works better under more volatile times influenced by noise and outliers. However, I can't find any theories that support the fact that returns are more volatile in recessionary times, compared to expansionary times. Do you have any ideas regarding this matter?

Expansionary out-of-sample performance (evaluated during expansionary periods)

Recessionary out-of-sample performance (evaluated during recessionary periods)

  • $\begingroup$ The 2015 Markowitz paper linked above, describing the Gerber Statistic based covariance matrix has been withdrawn from SSRN (2627803). A description of the method can be found in a Royal Inst. of Tech. thesis by Zakaria Marakbi diva-portal.org/smash/get/diva2:1060405/FULLTEXT01.pdf $\endgroup$
    – Alex C
    Mar 18, 2018 at 12:37

1 Answer 1


See http://www.princeton.edu/~yacine/leverage.pdf

The leverage effect refers to the observed tendency of an asset’s volatility to be negatively correlated with the asset’s returns. Typically, rising asset prices are accompanied by declining volatility, and vice versa. The term “leverage” refers to one possible economic interpretation of this phenomenon, developed in Black (1976) and Christie (1982): as asset prices decline, companies become mechanically more leveraged since the relative value of their debt rises relative to that of their equity. As a result, it is natural to expect that their stock becomes riskier, hence more volatile.

  • $\begingroup$ It's implied by the skew too. $\endgroup$
    – will
    May 23, 2016 at 10:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.