In Part I of this article, "The Equity Growth Value Paradigm Part I," we quashed the often cited "recession based" logic used to explain the oscillating growth / value performance disparity. This post focuses on creating a duration-based framework borrowed from fixed income to distinguish between equity growth and value and then graphically illustrates how extended periods of over performance between these styles can be explained using factors consistent with the duration-based framework.

The Fixed Income Framework

The distinguishing characteristics of equity style are:

**Growth Equity:**Higher PE multiples, low or no dividend payment (earnings are plowed back into the company), with higher expected earnings growth, and lower book to market values**Value Equity:**Lower book-to-market values, higher dividends, with lower expected earnings growth, and higher book to market values

To begin to understand the driving factors for style performance disparity, consider equity valuation in a bond framework of duration. Duration is defined as the percentage change in bond price given a unit change in interest rates. Another way to think about duration, which is useful for our discussion, is the average weighted maturity of cash flows. Take note of the present value and maturity schedule below for a 2% coupon bond a zero coupon bond both maturing in 10 years, priced using the following 10 year yield curve. *(Click to enlarge)*

Year | Yield | 2% Coupon | Payment PV | Years⋅PV | Zero Coupon | Payment PV | Years⋅PV |
---|---|---|---|---|---|---|---|

1 | 0.69% | $2.00 | $1.99 | 1.99 | $0.00 | $0.00 | 0.00 |

2 | 1.61% | $2.00 | $1.94 | 3.87 | $0.00 | $0.00 | 0.00 |

3 | 2.08% | $2.00 | $1.88 | 5.64 | $0.00 | $0.00 | 0.00 |

4 | 2.40% | $2.00 | $1.82 | 7.28 | $0.00 | $0.00 | 0.00 |

5 | 2.64% | $2.00 | $1.76 | 8.78 | $0.00 | $0.00 | 0.00 |

6 | 2.83% | $2.00 | $1.69 | 10.15 | $0.00 | $0.00 | 0.00 |

7 | 3.00% | $2.00 | $1.63 | 11.39 | $0.00 | $0.00 | 0.00 |

8 | 3.14% | $2.00 | $1.56 | 12.50 | $0.00 | $0.00 | 0.00 |

9 | 3.26% | $2.00 | $1.50 | 13.49 | $0.00 | $0.00 | 0.00 |

10 | 3.37% | $102.00 | $73.24 | 732.43 | $100.00 | $71.81 | 718.1 |

The total prices and durations of the bonds can be calculated using the Present Value column and the Year⋅PV column in the following formulas:

Using the values from the respective columns and the formulas provided, the price and duration are then:

Bond | Price | Duration |
---|---|---|

2% Coupon Bond | $89.00 | 9.07 Yrs. |

Zero Coupon Bond | $71.81 | 10 Yrs. |

Therefore given a coupon paying bond and a zero coupon bond of the same maturity, the duration of the zero coupon bond is greater. Because all of the cash flows for a zero coupon bond occur at the final payment this intuitively reflects our second definition, where duration is the time weighted average maturity of cash flows.

Fixed Income Framework and Research

Extending this analogy, one might guess that equities termed "growth equities" that pay out large fractions of their cash flows in the future (e.g. pay no dividends, plow back their earnings and have high earnings growth expectations) will also have higher duration -- average weighted maturity of cash flows -- than companies with large dividend payouts and lower earnings growth expectations (i.e. "value equities").

In fact, a brief survey of the literature shows considerable exploration of "Implied Equity Duration" since first proposed in 2004 by Dechow et al where equity duration and book to market ratios were found to be closely connected.[1] Schröder and Esterer 2008 specifically find that "ceteris paribus, companies with a high cash-flow growth rate exhibit long equity duration [where a] relatively large fraction of cash flows occurs in the far future, such that the share price is very sensitive to changes in the discount rate."[2]

The financial literature corroborates our intuition comparing different equity styles to bond duration, implying that growth companies should have higher duration than value equities, and therefore greater sensitivity to discount factors. Furthermore, because equities represent long term investments whose expected cash flows extend far into the future, one could further conclude that longer term interest rates would have greater capacity to describe style over performance, where:

- (Declining / increasing) long term interest rates would explain (growth / value) over performance
- (Declining / increasing) term spreads -- the difference between a long-dated rate and short-dated rate -- would explain (growth / value) over performance

Illustration of Out Performance

To illustrate style performance disparity relative to yield curve levels and term spread, the period from April 1953 - December 2012 is broken up into decades. The "Ratio of Value to Growth" is a custom made index, starting with a value of 1,000 at the beginning of each decade period (performance information value and growth can be found on Kenneth French's website). A declining Value Growth Index indicates that growth is outperforming where an increasing index can be interpreted as value equity out performing. For ease of observation, the ratio of the index (i.e. value to growth) is chosen (i.e. value over growth instead of growth over value) so a declining Value Growth Index mirrors an interest rate and term spread decline.

Term spread is defined as the 10 year Treasury yield less the 3 year Treasury yield, and a dotted line is placed at the 0.0 for term spreads to clearly indicate inversions of the yield curve (i.e. term spreads fall below the dotted line). Long term interest rates are calculated using the 10 year Treasury yield, and the shaded grey region represents a recession as defined by the OECD. *(Click to enlarge)*

In the first decade, (from April of 1953 to March of 1963) over performance between growth and value appears to be explained quite well using term spreads and long term interest rates, however the influence appears to oscillate with first interest rates, then term spread, then again interest rates, and finally term spread explaining the performance disparity. Over this decade, a multivariate regression of the Value Growth Index with independent variables of 10 year Treasury yield and 10yr - 3yr term spread yields an adjusted R-Squared of 0.3854.

During the first half of the decade from April 1963 to March 1973, there is a relationship between interest rates and equity style over performance, whereas term spreads seem to describe the relationship only after . A multivariate regression of the Value Growth Index with independent variables of 10 year Treasury yields and 10yr - 3yr term spreads yields an adjusted R-Squared of 0.5303 during this decade.

The remainder of the illustrations are left to the reader to observe, however multivariate regression statistics are provided below each of the respective years.

April 1973 - March 1983 | P Value |
---|---|

10 Year Treasury Yield | 2.58e-20 |

10 Year - 3 Year Spread | 7.35e-08 |

**Regression Adjusted R-Squared:** 0.511

April 1983 - March 1993 | P Value |
---|---|

10 Year Treasury Yield | 0.04 |

10 Year - 3 Year Spread | 3.0e-06 |

**Regression Adjusted R-Squared:** 0.157

April 1993 - March 2003 | P Value |
---|---|

10 Year Treasury Yield | 4.91e-12 |

10 Year - 3 Year Spread | 2.17e-09 |

**Regression Adjusted R-Squared:** 0.365

April 2003 - December 2012 | P Value |
---|---|

10 Year Treasury Yield | 5.90e-20 |

10 Year - 3 Year Spread | 4.67e-22 |

**Regression Adjusted R-Squared:** 0.8363

Summary Table

Period | Adjusted R-Squared |
---|---|

04-01-1953 to 03-01-1963 | 0.385 |

04-01-1963 to 03-01-1973 | 0.530 |

04-01-1973 to 03-01-1983 | 0.511 |

04-01-1983 to 03-01-1993 | 0.157 |

04-01-1993 to 03-01-2003 | 0.365 |

04-01-2003 to 12-01-2012 | 0.836 |

Entire Sample (1953-2012) | 0.389 |

Conclusion

The reader should note the style behavior during yield curve inversions -- when investors demand higher rates for short term Treasuries than long term Treasuries. As term spreads decline and approach zero, long term investment decisions become secondary to preservation of capital. Because value equities have higher book to market values than growth stocks (book to market can be thought of as the hard asset value of the firm relative to its market value), zero or negative term spreads imply that investors have the greatest appetite for long term stores of value. Therefore, value equities frequently outperform growth during and prior to yield curve inversions.

The weakened (yet still significant) relationship between style over performance and rates during the decade of '73 - '83 is also worth mention. A closer look at the chart indicates that term spreads consistently fluctuated around 0 during that decade, with numerous inversions. One can imagine the volatile impact on long term investment decisions from a persistent disjoint between the traditional demand for maturity premiums and high levels of uncertainty regarding purchasing power displayed during this decade. However, as more traditional monetary policy began to take hold, the explanatory power of long term rates and term spreads has continued to increase after March of 1983, and we are therefore unlikely to see similar divergence of rates and style over performance in the near future.

Overall, the relationship between long term interest rates, term spread, and style over performance holds up pretty well over the past 60 years. There has been a 3 year trend-less period since 2009 consisting of little over performance between equity styles. However, interest rates will likely trend towards normal behavior in the coming years as the Fed begins to remove many of its tools used to "grease the rails" of our economy. During that time, we expect longer periods of style over performance as was seen over much of the past 60 years, during which time the model presented here should continue to do a decent job in describing over performance using long term rates and term spreads.

- Dechow, Patricia M., Sloan, Richard G. and Soliman, Mark T., Implied Equity Duration: A New Measure of Equity Security Risk (June 2001).↩
- Esterer, Florian and Schröder, David, The Implied Equity Duration - Empirical Evidence for Explaining the Value Premium (August 27, 2011). ↩

**Business Disclosure:** Newfound Research is a quantitative asset management firm. This article was written by Benjamin Gross, one of our Managing Directors in our Product Development & Quantitative Strategies Group. We did not receive compensation for this article (other than from Seeking Alpha), and we have no business relationship with any company whose stock is mentioned in this article.

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