market timing factor premiums - newfound research of loss from the risk being realized equal the...

© Newfound Research LLC, 2016. All rights reserved. 1

Market Timing Factor Premiums Exploiting Behavioral Biases for Fun and Profit

Corey Hoffstein, co-Founder & Chief Investment Officer, Newfound Research Justin Sibears, Managing Director & Portfolio Manager, Newfound Research

February 2016 Abstract When outperformance fixation leads to large inflow temptation: premiums erode, investors unload, enabling factor rotation!


Introduction

In recent years, factor investing has come into vogue as a better

mousetrap than traditional stock picking. Proponents of factor investing

argue that instead of focusing on picking individual securities, investing in

an index weighted towards a certain characteristic can more consistently

harvest alpha.

Numerous studies on empirical asset pricing have shown that

portfolios formed on selected stock characteristics can deliver superior

risk-adjusted returns. These characteristics include value, size,

momentum, quality, low-volatility and high yield. In their five-factor model,

Eugene Fama and Kenneth French identify four non-market factors: value,

size, investment, and profitability.

In the purest academic sense, factor returns are measured via a

long/short portfolio. For example, the returns of the value factor would

capture buying cheap securities and shorting expensive ones. Long-only

practitioners can seek to take advantage of these same factors by tilting

their portfolio away from a passive, market-cap weighted index and

towards the long leg of the factor trade. So a long-only value tilt will seek

to buy or overweight cheap securities.


While these factor tilts have historically exhibited significant

outperformance, the realized premium considerable short-term variability.

Value, for example, has historically delivered an average 2-year return

premium of 547 basis points (“bps”). But this average disguises the wide

distribution 2-year return premiums, which range from -4046bp and

+5753bp.

Before exploring why premiums vary, it is worth asking why they exist in

the first place. Traditionally, the answer falls in one of two camps: risk or

behavioral.

The risk camp believes that the premium earned by an investor is

compensation for bearing a specific risk. For example, the premium

-6000

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Time Varying Premium: Value


earned by buying cheap stocks (the value factor) may be compensation for

higher default probabilities. Similarly, the premium earned by buying

smaller-capitalization companies (the size factor) may be payment for

bearing their relative illiquidity.

In this line of thinking, holders of these securities act like insurance

companies: they earn a premium in exchange for bearing the risk of loss

should certain bad events materialize. The open question is whether the

premium earned is fair compensation for the risks (i.e. does the expected

value of loss from the risk being realized equal the premium earned) or

whether the market has mispriced the risks, overpaying for protection

because it overestimated the probability or the magnitude of the risks.

The behavioral camp argues that the premiums exist because

investors exhibit behavioral biases that cause them to act irrationally.

These irrational actions can therefore be exploited by rational agents to

generate return premiums. For example, loss aversion may account for

the value premium, while over- and under-reaction may account for the

momentum premium.

In either case, there are solid arguments for the existence of the

factor premiums. Why, then, do they vary so significantly over time?


Alpha is a zero-sum game1. The positive excess return generated by

one investor is to the detriment of another. The simple answer for why the

premiums must be time-varying is that if they were not they would be

viewed as free, which would cause an influx of investors, driving up prices

and driving down forward return expectations to the point where there

would be no premium. As an example, consider the group that believes

premiums are paid as compensation for bearing risk. If the premium (i.e.

excess return) were constant and positive, the investor would not actually

be bearing any risk and so should not be rewarded in the first place.

Otherwise, it would be like an insurance company collecting premiums for

fire insurance on 100% fire proof homes, it would make no logical sense.

Volatility in the premium itself causes weak hands to fold, passing

the premium to the strong hands that remain.

Annualized Premium v. Market

(7/1963 – 12/2015) Average Standard Deviation

Value Cheap 2.93% 7.50%

Size Small 2.14% 11.62%

Investment Low 2.18% 4.94%

Profitability High 1.12% 3.31%

1Moreaccurately,alphaisazero-sumgameinsingleperiodmodelswhereinvestorshaveuniformtimehorizons.


While this may be a philosophical argument for why they must vary, it

provides little insight into what market events cause the magnitude and

sign of the premium to change over time.

We posit that the mechanics for why they vary is behavioral. It has

been well established that investors tend to chase performance. Superior

past performance is rewarded with capital inflows while inferior

performance is punished by capital outflows.

We believe that performance chasing behavior could at least partially

drive realized premiums:

1. Short-term outperformance of a factor attracts inflows.

2. These inflows cause a short-term, self-fulfilling cycle of further

outperformance.

3. Excess inflows cause return premiums to turn negative.

4. Negative returns lead to outflows.

5. Outflows cause a short-term self-fulfilling cycle of further outflows.

6. Excess outflows cause return premiums to return to positive territory.

If this is indeed the case, then there is an argument that the factor

premiums themselves could be timed to generate further excess returns


by building a momentum portfolio to ride the wave of short-term

performance chasing and a value portfolio to capture the eventual long-

term valuation reversion.

The Data

Data for this study was procured from the Fama and French Data Library2.

This study uses the four non-market factors identified by the Fama French

five-factor model: value, size, profitability and investment. Specifically, for

each factor we look at the long-only tilt expected to outperform the broad

market: cheap, small, highly profitable, and low re-investment respectively.

Equity curves for each factor are generated using monthly total

returns. The returns represent a market-cap weighted portfolio of either

the top or bottom 30% of securities ranked on the corresponding factor.

For example, the value equity curve represents a portfolio holding the top

30% of securities ranked on their book-to-market with individual positions

weighted by market-cap.

Returns are from the period of 7/1/1963 to 11/1/2015.

2http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html


The Momentum Cycle

In our model describing the mechanics of time-varying risk premiums,

inflows chasing strong short-term performance lead to a self-fulfilling

prophecy of further strong performance. On the other hand, outflows

arising from weak performance lead to a similarly self-fulfilling prophecy of

more weak performance.

If true, this behavior could be exploited by employing a momentum-

based investment methodology, investing in recent winning factors and

avoiding recent loser factors.

In effort to exploit this behavior, we implement the conventional 12-

minus-1-month model, which examines the prior 12-month total return of

each factor less the most recent month’s total return (the performance of

which is commonly driven by short-term reversal). Each month, factors

are ranked on this calculation and sorted into four portfolios, from ranging

from “losers” to “winners.”

If our thesis is correct, we would expect “winners” to outperform

“losers” in a consistent manner over time. We find that this to be the case,

with the “winners” portfolio outperforming the “losers” portfolio by 468bp

per year.


For long-only, leverage-averse investors, the “winners” portfolio must clear

two bars to be a viability strategy. First, it must outperform the market

over the long-term. However, this is not enough. Why? To begin with,

our investment universe consists of factors with positive risk premiums. It

is quite possible that the “winners” portfolio may outperform by default

0.1

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100

1000

MomentumQuartiles(LogarithmicScale)

Short-termWinners 2ndQuartile 3rdQuartile Short-TermLosers

0

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12

Short-TermWinners/Short-TermLosers


due to its favorable investment universe and that it may add no value – or

even destroy value – relative to a naively diversified portfolio of the factors.

To test this, we compare performance to a second bar: an equal-weight

factor portfolio.

The “winners” portfolio clears both hurdles on both on a total return

and a risk-adjusted basis.

An important takeaway is that while annualized return increased

monotonically across quartiles from losers to winners, the largest increase

in Sharpe ratio was from the short-term losers to the 3rd quartile, indicating

that the majority of excess performance may come from avoiding the

short-term losing factor rather than picking the winning factor.

4.95

% 9.78

%

12.2

7%

9.26

%

11.9

6%

12.9

7%

13.9

4%

0.91

%

15.8

7%

16.5

8%

18.1

0%

16.9

1%

16.6

2%

18.8

1%

0.00

00

0.30

43

0.44

15

0.23

81

0.41

45 0.48

26

0.47

79

0%

10%

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30%

40%

50%

60%

Risk-Free Market EW Factors Short-Term Losers

3rd Quartile 2nd Quartile Short-term Winners

Annualized Returns, Volatility, and Sharpe Ratio

Ann. Return Ann. Volatility Sharpe


A critical test is to determine whether our approach has added value

through timing or whether it simply data-mined a strong average allocation

profile. To perform this test, we find the average allocations of the short-

term winner portfolio and construct an index from holding these average

weights over time.

We find that this average portfolio returns 12.27% annualized, while the

short-term winners portfolio returns 13.94%. However, the short-term

winners portfolio also comes with an extra 170bp of volatility.

Nevertheless, the momentum timing increases annualized Sharpe by 0.05,

indicating that the individual timing decisions did indeed add value beyond

the average allocation identified.

Annualized Premium v. Market (monthly dollar-neutral long/short;

5/1974 – 12/2015) Average Standard

Deviation Momentum Rotation 3.91% 8.68%

Equal-Weight Factor Portfolio 2.30% 4.16%


It is worth noting that the high level of standard deviation for the

momentum rotation premium may be largely due to vintage luck. Vintage

luck occurs when we expect a premium to mature over a certain time-

frame, but are unable to use overlapping portfolios within that timeframe.

In this case, we expect momentum to mature over a 1-month period. Only

holding one portfolio at a time makes us susceptible to significant luck in

the momentum cycle. To smooth this out, we could use four overlapping

portfolios, each held monthly but rebalancing on a different week of the

month. In other experiments, we have seen the use of overlapping

portfolios reduce premium volatility by half. Unfortunately, the data used

in this study is only available on a monthly basis, so rebalancing portfolios

more frequently is not possible.

The Value Cycle

A security’s fair value tends to be like gravity: it can be overcome with

great effort, but it usually wins in the end. In our flow-based model, while

short-term performance chasing creates momentum, driving price away

from fair value in the short run, the gravity of fair value creates a longer-

term reversionary pull that eventually wins out.


Similarly, as investor flows flee negative returns, they drive price

below fair value, creating a positive gravitational pull.

Based on this model, we hypothesize that a value-based methodology

could be employed to successfully time factor premiums. The objective is

to avoid those factors that are “rich,” which indicates a low or negative

forward premium, and favor those factors that are currently “cheap” and

likely offer higher rewards.

Without the availability of traditional value measures, we must use an

easily available proxy. In this analysis, we use dividend yield. We defend

this choice for multiple reasons:

1. The most common measure of value is book-to-market (B/M), which

assumes that the fair valuation – or at least on average a reasonable

valuation - of a company is its book value. Another such model of

valuation is the dividend discount model. If we assume a constant

growth rate of dividends (g) and constant cost of capital for the

company (r), then book value should be proportional to total

dividends (D), or, equivalently, book-to-market proportional to

dividend yield.


𝐵𝑀 =

𝐷𝑟 − 𝑔𝑀 =

1𝑟 − 𝑔

𝐷𝑀 ⇒ 𝐵 ∝ 𝐷

2. Similarly, if you assume a constant long-term payout ratio (p),

dividends per share (D) are proportional to earnings per share (E),

which makes yield inversely proportional to price-to-earnings, a

popular valuation ratio.

𝐷𝑃 =

𝑝×𝐸𝑃 ⇒ 𝐸 ∝ 𝐷

Under these assumptions, yield is proportional to commonly quoted

valuation metrics: book-to-market and earnings yield. We argue,

therefore, that by normalizing yield relative to historical levels, we can

approximate relative valuation changes over time.

Monthly dividends, in percentage terms, are calculation by

subtracting the monthly price return from the monthly total return.

Multiplying this monthly yield by the value of the price return index

provides an estimated monthly dividend. Summing prior 12-month


dividends and dividing by the current level of the price return index

provides the forward yield estimate.

To construct a valuation measure, forward yield estimates are

normalized against trailing estimates from the prior 5-year period to

calculate a z-score. This z-score allows us to make a normalized

comparison between factors to determine how over- or under-valued they

currently are relative to historical norms. This normalization is important

because there are good reasons why certain factors may have lower or

higher long-term valuations. As an example, we would expect the a value

factor to have low valuations since that is precisely how we are screening

stocks in the first place.

Below we plot the monthly z-score for the size factor going back to

6/1969. We can see that there are periods where our model identifies the

size factor as exceedingly cheap (highly positive z-score) and periods

where our model identifies size as prohibitively expensive (highly negative

z-score).


On a monthly basis, each factor’s z-score is calculated and the factors are

ranked from cheapest (highest z-score) to most expensive (lowest z-

score).

To allow the value premium time to mature, we hold these positions

in their respective value quartiles for 60 months (5 years). Each quartile

portfolio is therefore comprised of 60 overlapping sub-portfolios, where

each sub-portfolio invests only in a single factor at a time. For example, if

last month’s cheapest factor is value and this month’s cheapest factor is

size, then these two sub-portfolios would each represent 1/60th of the total

portfolio. Each month, the oldest sub-portfolio (the factor identified as

cheapest 61 months ago) is removed and a new sub-portfolio (the factor

identified as cheapest today) is added.

-4

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Size Factor Valuation Z-Score


We find that the cheap portfolio outperforms the expensive portfolio by

187bp per year.

0%10%20%30%40%50%60%70%80%90%

100%

Cheap Portfolio Allocations over Time

Small Value High Profitable Low Investment

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100

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Value Quartiles (Logarithmic Scale)

Cheap 2nd Quartile 3rd Quartile Expensive


Unlike momentum, we see a more consistent drop in both annualized

returns and risk-adjusted returns across the value quartiles, indicating that

buying what is cheap is just as important as avoiding what is expensive.

Similar to our momentum process, we need to test whether this

methodology simply data-mined a strong average allocation profile or

0

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1.5

2

2.5

Cheap/Expensive

4.90

% 11.1

8%

13.6

1%

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9%

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9%

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0%

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%

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8%

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2%

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4%

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2%

0.00

0.39

0.53

0.60

0.54

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0%

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Risk-Free Market EW Factors Cheap 2nd Quartile 3rd Quartile Expensive

Annualized Returns, Volatility, and Sharpe Ratio

Ann. Return Ann. Volatility Sharpe


whether timing actually added value. To perform this test, we find the

average allocations of the cheap portfolio over time and construct an

index representing these average weights.

We find that this average portfolio returns 13.38% annualized, while

the cheap portfolio returns 14.87%. Furthermore, the cheap portfolio

exhibits a Sharpe ratio of 0.60, while the average weight portfolio has a

Sharpe ratio of 0.51, indicating that the timing decisions were additive on

both a total return and a risk-adjusted basis.

Annualized Premium v. Market (monthly dollar-neutral long/short; 7/1964 –

12/2015) Average Standard Deviation

Value Factor Rotation 3.26% 5.59%

Equal-Weight Factor Portfolio 2.16% 4.08%

Exploring Anti-Factors

For each factor, there is an opposite leg of the trade that is expected to

underperform. While we expect cheap stocks to outperform the market

over the long run, we conversely expect expensive stocks to

underperform.


We have outlined the factor, and its anti-factor, in the table below

along with their long-term associated premiums versus the market (from a

monthly rebalanced, dollar neutral long/short portfolio versus the broad

market).

Annualized Premium v. Market (7/1963 – 12/2015)

Average Standard Deviation

Value Cheap 2.93% 7.50%

Expensive -0.46% 3.65%

Size Small 2.14% 11.62%

Large -0.29% 1.99%

Investment Low 2.18% 4.94%

High -0.87% 4.77%

Profitability High 1.12% 3.31%

Low -1.36% 5.34%

If the anti-factors have negative long-term premiums, why bother even

exploring them? Reflecting the opposite side of the factor trade, their

premiums exhibit significant negative correlations. Therefore, while

allocating to these factors long-term may be to our detriment, there may

be times when the anti-factor is a more favorable investment.


On Their Own

Our first test is to determine if the same value and momentum approaches

applied above work when applied to the anti-factors instead of the factors.

Unfortunately, we find the results wanting. While the momentum

winners did out-perform losers over the long run, it did so with little

consistency. The value approach, on the other hand, out-right failed.

It is worth noting that both the momentum portfolio and the value

portfolio failed to outperform the broad market.

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Time Varying Value Premiums

Cheap Expensive


Treated as Independent Factors

Another approach is to treat the anti-factors as completely independent

and unique factors – giving us eight total factors – that can be selected

based upon their own momentum strength or relative valuation.

0.85

0.9

0.95

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1.05

1.1

1.15

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Anti-Factors Cheap / Expensive

0

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Anti-Factors Winners / Losers


We find that this approach has greater promise than the anti-factors

on their own. However, the value approach is less consistent than when it

is applied only to the factors.

Momentum winners, on the other hand, consistently and

impressively trounce momentum losers. However, on their own,

momentum winners using both factors and anti-factors underperforms

momentum winners using just factors on a total return basis.

0

0.2

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1.2

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All Factors Cheap / Expensive


The Problem with Anti-Factors

So what’s going on here? Given the opportunity that negative correlation

presents, why are we struggling to harvest any benefit?

We would argue there are two reasons.

First, the cost of carry is too high. If we return to our insurance

metaphor from the introduction, factor holders receive the premium for

bearing the risk while anti-factor holders pay it. In other words, by holding

an anti-factor, we are consistently paying a fee that drags down our

performance.

Put slightly differently, we know that the factors have historically

outperformed the broad market. As a result, any additional benefit derived

0

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All Factors Winners / Losers


from overlaying momentum or value on top of the factors themselves is

additive to performance. On the other hand, by adding the anti-factors to

the universe, we purposely create performance drag. For the rotation

process to beat out a strategically diversified factor portfolio, it must make

up for this performance drag and then some.

Second, the variation in the premium for anti-factors may be too

small to exploit. For example, while the annualized premium for small

stocks against the market is 214bp, it has a standard deviation of 1162bp.

Large stocks, on the other hand, have an annualized premium of -29bp

but only a standard deviation of 199bp. We see a similar disconnect in

premium variation with cheap and expensive stocks.

So part of the problem may simply be that there is not enough

premium variation, relative to drag, in the anti-factors to be exploited.

These reasons combined may help explain why the nimbler

momentum approach was more successful than the slower value

approach. With the value approach, even if an anti-factor is cheaper than

a factor, the consistent drag paid over a 60-month holding period and the

smaller potential for reversion (due to lower premium variation) may make

it a sub-optimal choice. With such a long holding period, it is preferable to


select a factor that may be relatively more expensive, but has positive

carry and higher premium variation to exploit.

Conclusion In the constant search for excess returns, factors may be a beacon of

hope for investors. Instead of performing individual security selection,

investors can simply tilt their portfolio towards characteristics that have

academically and empirically demonstrated the ability to outperform the

market on either a total return or a risk-adjusted return basis. That the

factors are often well-grounded in either economic or behavioral theory

and have demonstrated consistency going back over fifty years only

makes them more attractive.

Unfortunately, with their long-term outperformance comes short-

term variability and inevitably periods of underperformance. The easiest

example is value stocks during the dot-com boom, which were eschewed

by investors as being washed up and part of the “old economy.” From

12/31/1997 to 2/28/2000, value stocks underperformed the market by

3191bp. Yet over the next three years, value outperformed by 3374bp.

Turns out they were not dead after all.


We argue that for these premiums to have positive long-term

expected returns, they must vary over time. If they did not vary, the trade

would become crowded and the premium would converge towards zero.

However, the time varying nature of the factor premiums themselves force

us to ask whether the premiums can be timed.

We propose a simple model, based on performance chasing

behavior, that drives factor premiums. In the short-run, flows chase

performance creating momentum. The short-term momentum creates

over- and under-valuation, which reverts over the long-run.

We posit that the same behavioral framework, which creates

premium variation in the first place, can be exploited by simple

momentum- and value-based investment approaches. We find that

momentum-based factor rotation and value-based factor rotation

outperform a naïve equal-weight factor portfolio by 167bp and 126bp

annualized respective. Furthermore, we find that a winners-minus-losers

and cheap-minus-expensive long/short portfolios built from factors exhibit

considerable consistency over time.

Finally, we explore whether there is value in incorporating anti-

factors into our process, recognizing that the anti-factors have negatively


correlated premiums to the traditional factors. We find that incorporating

the anti-factors only dilutes, likely due to the considerable premium drag

and the lack of significant variation to be exploited in the anti-factor

premiums themselves.

We believe that with the proliferation of factor-based ETFs, these

methodologies can be employed by investors to harvest the long-term

benefits that factors can offer while reducing the often times painful short-

term variability.


Disclosures

This document (including the hypothetical/backtested performance results) is provided for informational purposes only and is subject to revision. This document is not an offer to sell or a solicitation of an offer to purchase an interest or shares (“Interests”) in any pooled vehicle. Newfound does not assume any obligation or duty to update or otherwise revise information set forth herein. This document is not to be reproduced or transmitted, in whole or in part, to other third parties, without the prior consent of Newfound. Certain information contained in this presentation constitutes “forward-looking statements,” which can be identified by the use of forward-looking terminology such as “may,” “will,” “should,” “expect,” “anticipate,” “project,” “estimate,” “intend,” “continue,” or “believe,” or the negatives thereof or other variations or comparable terminology. Due to various risks and uncertainties, actual events or results or the actual performance of an investment managed using any of the investment strategies or styles described in this document may differ materially from those reflected in such forward-looking statements or in the hypothetical/backtested results included in this presentation. The information in this presentation is made available on an “as is,” without representation or warranty basis. There can be no assurance that any investment strategy or style will achieve any level of performance, and investment results may vary substantially from year to year or even from month to month. An investor could lose all or substantially all of his or her investment. Both the use of a single adviser and the focus on a single investment strategy could result in the lack of diversification and consequently, higher risk. The information herein is not intended to provide, and should not be relied upon for, accounting, legal or tax advice or investment recommendations. You should consult your investment adviser, tax, legal, accounting or other advisors about the matters discussed herein. These materials represent an assessment of the market environment at specific points in time and are intended neither to be a guarantee of future events nor as a primary basis for investment decisions. The hypothetical/backtested performance results and model performance results should not be construed as advice meeting the particular needs of any investor. Past performance (whether actual, hypothetical/backtested or model performance) is not indicative of future performance and investments in equity securities do present risk of loss. The ability to replicate the hypothetical or model performance results in actual trading could be affected by market or economic conditions, among other things. Investors should understand that while performance results may show a general rising trend at times, there is no assurance that any such trends will continue. If such trends are broken, then investors may experience real losses. No representation is being made that any account will achieve performance results similar to those shown in this presentation. In fact, there may be substantial differences between backtested performance results and the actual results subsequently achieved by any particular investment program. There are other factors related to the markets in general or to the implementation of any specific investment program which have not been fully accounted for in the preparation of the hypothetical/backtested performance results, all of which may adversely affect actual portfolio management results. The information included in this presentation reflects the different assumptions, views and analytical methods of Newfound as of the date of this presentation. Performance during the backtested period is not based on live results produced by an investor’s actual investing and trading, but was achieved by the retroactive application of a model designed with the benefit of hindsight, and is not based on live results produced by an investor’s investment and trading, and fees, expenses, transaction costs, commissions, penalties or taxes have not been netted from the gross performance results except as is otherwise described in this presentation. The performance results include reinvestment of dividends, capital gains and other earnings. As the information was backtested, it does not reflect contemporaneous advice or record keeping by an investment adviser. Actual, live client results may have materially differed from the presented performance results. The Hypothetical Information and model performance assume full investment, whereas actual accounts and funds managed by an adviser would most likely have a positive cash position. Had the Hypothetical Information or model performance included the cash position, the information would have been different and generally may have been lower. While Newfound believes the outside data sources cited to be credible, it has not independently verified the accuracy of any of their inputs or calculations and, therefore, does not warranty the accuracy of any third-party sources or information. This document contains the opinions of the managers and such opinions are subject to change without notice. This document has been distributed for informational purposes only and should not be considered as investment advice or a recommendation of any particular security, strategy or investment product. This document does not reflect the actual performance results of any Newfound investment strategy or index. This purpose of this document is to explain Newfound’s beliefs that: there is no holy grail investment style that will out-perform in all market environments; being systematic and disciplined in use of active strategies is the best way to capture out-performance because we don’t know when the out-performance will happen; and diversifying across several active approaches – all of which have independently proven to add value in different market environments – can help smooth out short-term underperformance of a single approach. The investment strategies and themes discussed herein may be unsuitable for investors depending on their specific investment objectives and financial situation. No part of this document may be reproduced in any form, or referred to in any other publication, without express written permission from Newfound Research.

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