Is Low Net Actually Low Risk? A Book Value Example

26 Aug Is Low Net Actually Low Risk? A Book Value Example

The first post on this subject used an earnings-based example to show portfolios with non-zero net exposures that have lower volatilities relative to their dollar-neutral counterparts. A natural question is whether this observation is specific to the earnings-based example. This post applies the same empirical review to a different example using book value; the correlation between the earnings and the book value portfolios is not significant (< 0.5).  The conclusion is the same: the lowest risk portfolio has a net exposure greater than zero. In addition, the sensitivity to the market increases. The Book Value Example

I created an equity long/short portfolio based on “Book-to-Market” gross monthly return data from the Kenneth French library. The long portfolio is the top 30% of securities ranked by book value relative to market capitalization (“BV/MC”) and the short portfolio contains securities with a negative BV/MC – another “buy cheap, short expensive” example. The securities are equal-weighted in the long and short portfolios.

The dot plot below shows that the portfolio with net exposure (“nee”) equal to 55% has the lowest volatility of all scenarios when varying nee from -100% to 100%. The volatility declines between nee = -100% and nee = 55% then increases as nee approaches 100%.

The volatility at nee = 55% is half the volatility at nee = 0% and roughly equal to the volatility at nee = 100%. In fact, the volatility at nee = 55% is lower than the volatility of a broad market index (See Note) and the S&P 500.  The graph below shows the cumulative variances.

A performance plot of the portfolio (less cash) with nee = 0% and nee = 55% also makes clear that the higher nee time series is less volatile and has less severe drawdown events.

The lower volatility and improved performance result in higher risk-adjusted returns. As volatility decreases, average performance increases to 5.01% from -4.33%. Consider the following table containing a couple of risk-adjusted return measures:

This result begs the question:  What is the appropriate tradeoff between market beta and lower risk?  The market beta increases to 0.41 from -0.32. Is this too high despite the lower risk profile?  Presumably, part of the concern is that investors are paying high fees for market return.  So, how much of the performance is attributable to the increased market beta?  I estimate that 49.89% of the performance improvement is due to increased market beta; the value is 0.37% assuming that the S&P 500 is the market benchmark. (See earnings-based example for methodology).  As in the earnings-based example, the index used to gauge market sensitivity is an important consideration.

Earlier in this post, I referenced differences in the severity of the drawdown events.  A Calmar ratio (or Drawdown ratio) comparison shows that the lower volatility portfolio (nee = 55%) consistently dominates – outperforming in 84% of the months with an average spread of 1.37. In the figure below, the lower volatility portfolio’s ratio is greater than the nee = 0% portfolio’s ratio when the line is above the horizontal axis.

To summarize, I have shown that you can increase net exposure while increasing risk-adjusted return with lower volatility and higher return. In addition, I show that a half of the performance increase is due to increased market exposure.

Common Factor Risk

To understand what common factors beyond the market might account for the performance change, I regressed the returns over the following Fama/French benchmark factors: Market, Value/Growth, Size, and Momentum.  The market return is the broad market index return in excess of cash.

The t-statistics significant at the 1% level are as follows:

Note: Number of observations = 762

The adjusted R² for the nee = 0% and the nee = 55% are 0.16 and 0.41, respectively.

The model fit is better for the portfolio at nee = 55%. All factor sensitivities increase except for momentum. Also, unexplained return becomes negative.  As in the earnings example, the size effect is significant.

The same analysis applied to a value-weighted version of the portfolios produces similar results. The lowest volatility portfolio is at nee = 65%.  Volatility and returns improve resulting in better, consistent risk-adjusted performance.

Regarding the common factor analysis, exposure to the market and size factors increases along with higher adjusted R², 0.45 compared with 0.21. As an aside, the exposure to the value/growth spread is high relative to the equal-weight version and the earnings example portfolios.

The t-statistics significant at the 1% level are as follows:

Note: Number of observations = 762

Conclusion

A diversified long/short portfolio constructed by comparing market price to book value has a lower risk profile at nee > 0%.  This comports with the conclusion in the earnings-based example.  To recap the key observations:

1. A portfolio with net equity exposure different from zero has a lower volatility profile than the same portfolio at nee = 0%

2. Changes in other common factor exposures may be just as relevant as the changes in market exposure

In my next couple of posts, I will consider the net exposure question using a momentum portfolio.

Note:  The market return is the value-weighted US return available at the Kenneth French data library.