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  • Writer's pictureKai Wu

Brand in the Influencer Era

October 2021

Executive Summary

Social media is democratizing consumer influence, empowering ordinary individuals to shape brand perception. We identify brands with strong positioning using social media discourse and network structure. We find strong brands have outperformed the stock market. We also explore the trends of sustainable and Millennial brands.

Democratizing Influence

Mad Men’s Demise

“Change is neither good nor bad. It simply is.”
📺 Don Draper

The modern history of branding began in the early 1900s with the rise of mass media -- print, radio and television. The advertising industry rose to prominence with iconic brands such as Coca-Cola, Campbell’s Soup, and Quaker Oats. In particular, the unprecedented reach and creative flexibility of TV advertising helped turn brands into household names.

In the past few decades, technology has once again ushered in a wave of change. The internet is empowering consumers. Access to the world’s knowledge on sites like Google, Yelp and Amazon is breaking down informational asymmetries. Meanwhile, e-commerce is giving consumers a much larger and more diverse selection of products.

Yet the most empowering trend is the democratization of consumer influence. Purchase decisions are based on the wisdom of the crowd rather than that of Don Draper. The customer is truly king when he can persuade thousands of others by posting his buying experience online.

Exhibit 1

Influencers: Then and Now

Source: AMC, Instagram, Sparkline.

However, not all customers are created equal. In the creator economy, some wield undue influence. Influential bloggers, YouTube stars, Instagram influencers, and popular podcast hosts can reach audiences of millions. Moreover, they are often perceived as more authentic, credible, and relatable than the brands themselves.

In the social media age, brand perception arises emergently from the conversations of millions of individual consumers. Brands can no longer count on their customers sitting at home staring at the TV absorbing corporate messaging. Instead, they must proactively spark engagement through viral marketing or by entering the fray themselves.

Exhibit 2

#Burn 🔥

Source: Twitter.

While brand perception is no longer tightly controlled by the suits on Madison Ave, brands are not powerless. Savvy firms have merely shifted their resources to digital, social, and influencer marketing. While the internet may have killed the Mad Men, the industry as a whole is thriving.

Customer is King(maker) 👑

“Your brand is what other people say about you when you’re not in the room.”
📚 Jeff Bezos, Amazon Founder

With the democratization of consumer influence, the image brand managers hope to project is irrelevant. We want to know what actual customers are saying when brands are not in the room. We need to be in the room where it happens.🚪

The internet is a big place -- where should we focus our attention? Below is a rough estimate of the distribution of brand-related chatter across major websites. The bulk takes place on Facebook, Twitter, and Reddit, although this varies widely by product (e.g., Lululemon is much more active on Instagram, JetBlue on Twitter and Kraft on Facebook).

Exhibit 3

The (Chat)room Where It Happens

Source: Google, Facebook, Twitter, Reddit, Amazon, Sparkline.

This paper will focus on Twitter for three reasons. First, it is one of the top three forums for brand-related discussion. Second, we can enrich our analysis using the social graph of Twitter. Third, the Twitter API is far less restrictive than that of Facebook and Instagram.

While social media do have some well-known biases, these are diminishing with broader internet adoption. Moreover, the costs of using digital datasets are far outweighed by the benefits, especially relative to traditional studies, such as those that rely on small-sample surveys of college students.

Brand Personality

Brand Personality

Marketers have long recognized that people prefer brands that reflect their identities. Brands give us the ability to manifest our desired values and personality traits. In fact, many researchers even believe that brands themselves have personalities.

Firms craft their brand personalities to appeal to their target customers. A perfect example is Apple’s prolific “Get a Mac” advertising campaign, in which two actors literally portrayed a Mac and a PC. Apple imbued its Mac with a young, casual, and trendy personality, while it presented the PC as stuffy, unattractive and nerdy.

Exhibit 4

Hello, I’m a Mac

Source: Apple, Sparkline.

The research on brand personality begins with Aaker (1997), who defines five dimensions of brand personality. These dimensions emerge from factor analysis of a survey in which participants were asked to rank 40 popular brands on 114 personality traits. Aaker found that the top five principal components explained over 90% of the variance in brand personality. These components are: sincerity, excitement, competence, sophistication and ruggedness.

Exhibit 5

Dimensions of Brand Personality

Source: Aaker (1997), Sparkline.

Over the past two decades, several other researchers have found Aaker’s taxonomy to be quite stable both across time and product categories (e.g., toothpastes, soups, TVs).

Brand Embeddings

In Measuring Culture (Aug 2021), we laid out a methodology for creating “company culture profiles.” We used Glassdoor reviews to assign firms scores on each of seven dimensions of company culture (e.g., innovation, integrity, teamwork).

We can repurpose this method to build “brand personality profiles.” We only need to make two modifications. First, we measure the dimensions of brand personality rather than company culture. Second, we train our model on Twitter instead of Glassdoor.

Following the procedure laid out in our last paper, we start by training word embeddings. Word embeddings encode words in a dense matrix, where the distance between pairs of words corresponds to their similarity. For example, the words “customer” and “client” have similar meanings and thus are near each other in embedding space.

Social media text presents a couple of unique challenges. First, since its vernacular can vary widely by topic, we train our model only on brand-related chatter to help reduce this noise. Second, since social media slang rapidly changes, we retrain our models on rolling two-year periods and include combinations of words (n-grams) to capture emerging idioms, such as “weekend warrior,” “side hustle,” and “boy shorts.”

Once we have trained the embeddings, we seed five word clusters using the keywords from Aaker’s taxonomy. The visualization below plots words that fall within a specified distance from each seed group. The five factors form distinct clusters, implying they are indeed reasonably independent.

Exhibit 6

Brand Embeddings

Source: Twitter, Sparkline. As of 10/15/2021.

The next exhibit zooms in on some top phrases. We find many intuitive but non-obvious word combinations, such as “not all heroes wear capes” for sincerity and “made in the USA” for ruggedness. The embeddings seem to accurately capture the essence of brand personality.

Exhibit 7

Brand Personality Keywords

Source: Twitter, Sparkline. As of 10/15/2021.

Once we are satisfied with our model, we use it to measure the personality of each brand. The next exhibit shows chatter about Tiffany & Co. While some words are merely descriptive (e.g., “necklace”), many others relate to brand personality. The prevalence of words like “luxury,” “bling,” “exquisite,” and “timeless” indicate high sophistication. In addition, phrases such as “true love” and “excited” suggest secondary traits of sincerity and excitement.

Exhibit 8

Tiffany & Co

Source: Twitter, Sparkline. As of 10/15/2021.

The radar chart below compares Tiffany & Co to a few other brands. First Republic Bank is seen as competent, Christian Mingle as sincere, and WD-40 as rugged.

Exhibit 9

Brand Personality

Source: Twitter, Sparkline. As of 10/15/2021.

Follower Overlap

“Birds of a feather flock together.” 🐦

While embeddings provide an effective way to measure brand personality, the social graph of Twitter enables a very different approach. This technique leverages the homophily principle, which is the tendency for individuals to associate with similar others. We can learn a lot about a person by the company she keeps.

More precisely, we can compute the similarity of any two accounts based on the overlap of their followers. For example, there is high overlap between the followers of the World Wildlife Fund and Patagonia. This is because people who care about the environment are likely to follow both WWF and Patagonia. In contrast, there is less overlap between the followers of WWF and ExxonMobil.

Exhibit 10

Follower Overlap

Source: Twitter, Sparkline. As of 10/15/2021.

In order to use this technique, we first need to define representative accounts for each of the brand personality dimensions. This is similar to our use of embedding seed words. We implement a modified version of the method from Culotta and Cutler (2016), which mines Twitter lists to find accounts associated with a given topic. For each dimension, this produces 30 to 80 seed accounts owned by celebrities, media outlets, influencers, agencies, non-profits, and brands.

Exhibit 11

Seed Accounts

Source: Twitter, Sparkline. As of 10/15/2021.

These seed accounts embody each of the five dimensions. Sincerity is represented by the American heartland (e.g., country music and farming). Competence is symbolized by scientific and academic expertise. Ruggedness is reflected by the great outdoors.

Next, we compute follower overlap between seed accounts and brands. For example, we first compute the overlap of @YETICoolers with each of the ruggedness seed accounts. We take the average to arrive at a composite ruggedness score. We then repeat for the other four dimensions.

Exhibit 12

Follower Overlap Example

Source: Twitter, Sparkline. As of 10/15/2021.

This gives us a five-dimensional brand personality profile for every brand in our universe. The results are similar (but not identical) to those produced by the brand embeddings. This provides some reassurance that we are accurately extracting brand personality. However, since both approaches have their own strengths, we combine them to create an even more robust brand personality composite.

Exploring Brand Personality

We can now begin our exploration of brand personality. We will restrict our universe to consumer brands that are or have been owned by publicly-traded companies. This will allow us to conduct backtests of the stock market performance of brand-related factors.

We will start by surveying a few major consumer product categories. We find that some industries tend to emphasize certain personality traits. Apparel brands tend to exude sophistication, consumer finance firms project an image of competence, and restaurants emphasize sincerity.

Exhibit 13

Product Category Averages

Source: Twitter, Sparkline. As of 10/15/2021.

However, as with human personality, individual variation dominates group averages. The next exhibit shows brands that score highly on each of the five dimensions. There is a wide range of product categories represented. Sincerity is manifested in restaurants, cereals and even motorcycles. Excitement can be found in cars, cameras and websites.

Exhibit 14

Top Brand Personalities

Source: Twitter, Sparkline. As of 10/15/2021.

Our analysis also reveals that brand personality is malleable. Instead of using the entire sample, we continually re-train our model on rolling two-year periods. This allows us to track the evolution of brands, such as YETI.

Exhibit 15

The Ascent of YETI

Source: Twitter, Sparkline. As of 10/15/2021.

YETI sells expensive coolers (some upward of $500). Started by two Texan outdoorsman brothers, YETI has over the years established itself as an aspirational brand through clever marketing (e.g., YouTube testimonials). Its success creating a high-end reputation shows in its rising sophistication score.

Brand Positioning

Brand Mapping

“The way a company brands itself is everything. It will ultimately decide whether a business survives.”
🚀 Richard Branson, Virgin Group Founder

Brand mapping is a popular tool in the marketing industry. The idea is to map out the competitive landscape to see how one’s brand is positioned relative to competitors. Brand maps can be used to identify gaps in the market, potential strategic partners and crowded segments to avoid. Newer brands in particular should think twice before positioning themselves directly against more established competitors.

While brand is multidimensional, marketers usually select just two dimensions for visualization. The brand map below rates apparel brands on sophistication and ruggedness. We draw circle size based on Twitter follower count.

Exhibit 16

Apparel Brand Map

Source: Twitter, Sparkline. As of 10/15/2021.

We find a strong inverse relationship between ruggedness and sophistication. Luxury brands such as Versace and Jimmy Choo anchor one end of the spectrum and outdoor brands like Rocky Boots and Mountain Hardwear the other. Meanwhile, Canada Goose and to some extent Lululemon have tried to appeal on both dimensions.

In order to visualize all five dimensions of brand personality simultaneously, we use a technique called t-SNE to project our data onto a two-dimensional plane. Unlike the prior exhibit, the axes no longer have any meaning. We care only about where each brand lies in relation to others.

Exhibit 17

5D Brand Map

Source: Twitter, Sparkline. As of 10/15/2021.

We color code three clusters. As we saw earlier, apparel brands use ruggedness and sophistication as brand moats. We also find a less distinct but still noticeable cluster of sincere brands. While excitement and competence are not irrelevant in apparel, they are not salient enough to get their own clusters. The most differentiated brand in this analysis is Lululemon, which scores well on all five factors and has carved out its own territory in the brand map.

Strong Brands

As with human personality, there is no one dominant brand personality type. Extraverts are not inherently better than introverts, nor are rugged brands superior to sophisticated ones. The ideal brand depends both on the target customer and competitive landscape.

Firms imbue their products with a combination of attributes tailored to their target customers. The best mix can vary widely. Harley-Davidson and Peloton have very different brand personalities, but both enjoy immense loyalty from their respective fans.

While having a well-defined brand personality is necessary, it is not sufficient. Brands also need to differentiate from competitors in a crowded field. Business is game theoretic. Strong brands must be both well-defined and unique.

In order to identify strong brands, we create metrics for each of these subcomponents. We identify well-defined brands as those that score highly on one or more of the five brand personality factors. It is more important that a brand scores highly on a factor than which factor it scores highly on. We calculate uniqueness based on a brand’s distance from its industry competitors.

The next exhibit shows some outstanding brands in eight important product categories. These brands all have great recognition and strong positioning, despite representing a diverse range of industries and brand personalities.

Exhibit 18

Strong Brands (By Industry)

Source: Twitter, Sparkline. As of 10/15/2021.

Finally, let’s test if strong brands have produced superior stock market performance. In order to run a backtest, we need to first map brands to public companies (e.g., Tide, Pampers and Gillette are all owned by P&G). We also need to create rolling point-in-time snapshots of Twitter data. While this is mostly doable, we cannot recover deleted (or protected) Tweets, accounts or follows. It is unclear what bias this introduces, but please be forewarned.

Our strong brand factor buys the stocks with the strongest brands and shorts those with the weakest. We neutralize industry exposure (i.e., zero net exposure to each industry), to ensure brands are compared only to their competitors.

Exhibit 19

Strong Brand Outperformance

Source: Twitter, S&P, Sparkline. Line shows the performance of the strong brand factor in a universe consisting of U.S. consumer stocks trading on NYSE and Nasdaq. The strategy is industry-neutral (zero net exposure to each industry). We exclude transaction and financing costs. From 1/1/2010 to 10/15/2021. See important backtest disclosure below.

Over the past decade, our strong brand strategy has produced consistent outperformance. Strong brands are a deep moat that affords firms greater pricing power, sales volume, and customer loyalty. Furthermore, the robust historical performance of the factor implies that the market does not fully recognize the value of this powerful but intangible asset.

Brand Social Networks

“Our experience of the world depends on the actual structure of the networks in which we're residing and on all the kinds of things that ripple and flow through the network.”
🎓 Nicholas Christakis, Yale Professor

Social scientists have found that phenomena as diverse as obesity, smoking, and voting patterns spread through social networks like viruses. Social ties serve as channels to propagate these phenomena.

Researchers have uncovered similar dynamics in the spread of shocks through networks of economically-linked firms. Cohen and Frazzini (2006) show that strong stock returns tend to predict future outperformance for a focal firm’s customers. Hoberg and Phillips (2014) find a similar effect for firms based on text-based industry linkages. Bekkerman et al (2021) find the same for stocks based on the textual similarity of their patent portfolios.

The motivating idea behind network momentum strategies is that shocks propagate with a lag through a network. Investors able to accurately model the structure of networks can react more quickly to these shocks, generating excess returns.

We can use Twitter to build a “brand social network.” If two brands have a lot of common followers, we draw a link between them. In addition, we use the Louvain community detection algorithm to color code each cluster and set node size proportional to network centrality.

Exhibit 20

Brand Social Network

Source: Twitter, Sparkline. As of 10/15/2021.

Most noticeably, cliques form around brands selling into the same product market (e.g., dating apps, luxury bags, casinos, and dollar stores). These cliques make sense inasmuch as sneakerheads follow many shoe brands and powder hounds follow multiple ski resorts. While not a revelation in itself, these product-level groupings have the advantage of being much more granular than traditional GICS industry classifications.

But our brand social network is not solely composed of isolated product-level cliques. It is not like high school. In contrast, strong social ties do form across industries. The next exhibit shows pairs of brands that are linked in the social graph despite operating in different industries.

Exhibit 21

Friends in Faraway Places

Source: Twitter, Sparkline. As of 10/15/2021.

Many brand pairs are intuitive complements. Hikers buy both PowerBars and CamelBaks; homeowners use Terminix and Scotts lawn care. Other pairs are less obviously related. New couples buy an engagement ring from Brilliant Earth before moving in together using; fans of disruptive tech are likely to follow both $TSLA and $COIN.

Now that we have built our brand social network, we can use it to backtest a network momentum strategy. We assign each brand a score based on the 12-month rolling return of the brands to which it is connected. When a brand’s friends do well, we buy. When they do poorly, we sell. Since research has shown that stock returns are higher after industry peers outperform (i.e., industry momentum), we run our strategy industry-neutral.

Exhibit 22

Brand Network Momentum

Source: Twitter, S&P, Sparkline. Line shows the performance of the brand network momentum factor in a universe consisting of U.S. consumer stocks trading on NYSE and Nasdaq. The strategy is industry-neutral (zero net exposure to each industry). We exclude transaction and financing costs. From 1/1/2011 to 10/15/2021. See important backtest disclosure below.

Over the past decade, our brand network momentum strategy delivered consistently positive returns. Moreover, it had a blowout year in 2020, when the fast-moving Covid pandemic disrupted both supply chains and financial market price discovery. In times of crisis, having a detailed graph of the links between firms can be invaluable.

The Future of Branding

Sustainable Brands

“If people believe they share values with a company, they will stay loyal to the brand.”
☕ Howard Schultz, Former Starbucks CEO

One of the hottest current marketing trends is sustainable branding. Surveys indicate that rising generations are more likely to buy from brands that reflect their values, and firms are rushing to capitalize on this growing demand.

Exhibit 23

Sustainable Brand Demand

Source: 5WPR, Sparkline.

In turn, investors want to know which brands are perceived by consumers as sustainable. Unfortunately, the scourge of corporate greenwashing has muddied the waters. Almost every large company now runs ads highlighting diversity and inclusion, even those with racist or sexist leaders. Meanwhile, an endless parade of consumer products are labeled sustainable, even those manufactured with toxic chemicals, fibers and other pollutants by exploited workers.

Thus, more than ever we need to look beyond corporate propaganda. Fortunately, social media can be used to directly measure the perceptions of actual consumers. While consumers are of course susceptible to manipulation, we would hope the public is savvy enough to filter out at least some of this deception.

We identify sustainable brands using the same techniques as earlier (i.e., brand embeddings and follower overlap). However, rather than measure the five facets of brand personality, we focus instead on two facets of sustainability: environmentalism and equality.

The exhibit below shows the seed accounts and keywords we will use to find sustainable brands. In addition to the World Wildlife Fund from earlier, our methodology identifies several other seed accounts, many of which are non-profits. The keywords are also quite intuitive (e.g., ♻️).

Exhibit 24

Sustainable Accounts and Keywords

Source: Twitter, Sparkline. As of 10/15/2021.

Next, we compute the similarity of each brand to these seed accounts and keywords. Below are some of the top brands that emerge from this analysis.

Exhibit 25

Sustainable Brands

Source: Twitter, Sparkline. As of 10/15/2021.

Our eco-friendly brands make plant-based meat, electric vehicle chargers, sustainable flooring, and lab-grown diamonds. Our equality-focused brands own properties in progressive media, mental health, online education, and female-led dating.

While we believe our approach identifies many interesting sustainable brands, the correlation with popular ESG scores is not very high. This may be because we focus solely on consumer perception, while ESG scores address a plethora of other stakeholders (e.g., labor, investors). It may also reflect the broadly unsettled nature of ESG ratings, which can vary widely even amongst established vendors.

Millennial Brands

“My biggest fear for this company, of which I have very few, is that we lose the connection with millennials.”
🍦 Paul Polman, Former Unilever CEO

While sustainable branding is an important marketing trend, it is being driven by an even bigger demographic trend -- the rise of the Millennial consumer. Millennial spending power recently surpassed that of Boomers, and this gap will only grow over time. Let the reign of the Millennial begin!

Exhibit 26

Coming of Age

Source: World Data Lab, Financial Times, Sparkline.

This demographic inevitability is worrying for established brands that cater to aging generations. As with any major market inflection, companies must take great care to avoid being disrupted by shifting consumer preferences.

On the other hand, brands able to win over Millennial (and Gen Z) buyers are likely to experience happy tailwinds as their relative incomes continue to rise. Investors should look into how to get exposure to this generational torch-passing.

In order to do this, we need to determine the exposure of each brand to each demographic cohort. While most Twitter users do not explicitly provide their age, extensive research (1, 2, 3, 4) has shown that this and many other demographic attributes can be estimated with frightening accuracy from online behavior (e.g., likes, follows, posts). 😱

The techniques used by social media and digital advertising firms to predict user behavior are extremely sophisticated. Since our ambition is more modest, we train a simple (and anonymized) model to estimate users’ generational cohort based only on who they choose to follow. Below are the accounts most revealing of their followers’ vintage.

Exhibit 27

Tell Me Your Age Without Telling Me Your Age

Source: Twitter, Sparkline. As of 10/15/2021.

Gen Z users are more likely to follow Dream (a Minecraft Twitch/YouTube streamer), Millennials tend to like Becky G (a 24-year-old singer), and Boomers still watch Ben Affleck (a 49-year-old actor). I guess telling people we like Blink-182 or, worse, Bon Jovi dates us! 🤷

Now that we have a model to identify Millennial accounts, we can determine which brands have the highest share of Millennial followers. We can do the same for Gen Z and Boomer brands. Our results are shown below.

Exhibit 28

Generation Gap

Source: Twitter, Sparkline. As of 10/15/2021.

The generational divide is clearly visible. Boomers are most comfortable with the real world, being loyal consumers of boats, tools, appliances and ETFs (📈). On the other hand, Gen Z are true digital natives, embracing virtual products like Roblox, Sony and Netflix.

Fashion trends can be fickle, so we are not recommending investors rush out to buy the hottest Gen Z and Millennial brands. Case in point is the 100-year-old Champion brand, which is seeing a surprising resurgence in popularity among young consumers after being left for dead. It is especially hard to pick individual winners in fashion.

On the other hand, the broader underlying themes driving the popularity of these Millennial and Gen Z brands are likely to persist. Younger people do tend to have a greater focus on health and wellness, convenience and digital experience. These are less likely to be fads than secular trends. Investors may do well to consider a diversified portfolio of brands with exposure to these big trends.


“Products are made in the factory, but brands are created in the mind.”
📋 Walter Landor

Branding can be a powerful intangible asset. Strong brands evoke powerful positive emotions in customers, turning them into advocates and apostles. In the words of Seth Godin, “People do not buy goods and services. They buy relations, stories and magic.”

In Investing in the Intangible Economy (Oct 2020), we argued that, like other intangible assets, brand tends to be both under- and mis-valued due to its intangibility. Our strong brand backtest supports this view. Companies invest billions of dollars to build up their brand equity, but this intangible capital does not appear on balance sheets.

The accounting profession’s decision to not capitalize brand investment is not completely without merit. Efforts to build brand equity can produce a very wide range of potential outcomes. Marketing campaigns can go viral, flop or even backfire. Since historical outlays on marketing have only a weak link to brand equity, investors need to focus instead on measuring the actual value of the brand.

Fortunately, in the influencer era, the nexus of consumer power has migrated online. It has moved to the very domain that is the most fertile ground for NLP and other modern data analysis techniques. With the exponential growth in user-generated data, investors are better positioned than ever to quantify this important intangible asset. Let’s get to work!



This paper is solely for informational purposes and is not an offer or solicitation for the purchase or sale of any security, nor is it to be construed as legal or tax advice. References to securities and strategies are for illustrative purposes only and do not constitute buy or sell recommendations. The information in this report should not be used as the basis for any investment decisions.

We make no representation or warranty as to the accuracy or completeness of the information contained in this report, including third-party data sources. This paper may contain forward-looking statements or projections based on our current beliefs and information believed to be reasonable at the time. However, such statements necessarily involve risk and uncertainty and should not be used as the basis for investment decisions. The views expressed are as of the publication date and subject to change at any time.

Backtest Disclosure

The performance shown reflects the simulated model performance an investor may have obtained had it invested in the manner shown but does not represent performance that any investor actually attained. This performance is not representative of any actual investment strategy or product and is provided solely for informational purposes.

Hypothetical performance has many significant limitations and may not reflect the impact of material economic and market factors if funds were actually managed in the manner shown. Actual performance may differ substantially from simulated model performance. Simulated performance may be prepared with the benefit of hindsight and changes in methodology may have a material impact on the simulated returns presented.

The simulated model performance is adjusted to reflect the reinvestment of dividends and other income. Simulations that include estimated transaction costs assume the payment of the historical bid-ask spread and $0.01 in commissions. Simulated fees, expenses, and transaction costs do not represent actual costs paid.

Index returns are shown for informational purposes only and/or as a basis of comparison. Indexes are unmanaged and do not reflect management or trading fees. One cannot invest directly in an index. The S&P 500 is a popular gauge of large-cap U.S. equities that includes 500 leading companies. The Russell 1000 Index consists of the approximately top 1000 U.S. stocks by market cap. The Russell 1000 Value (Growth) Index includes those Russell 1000 companies with lower (higher) price-to-book ratios and expected and historical growth rates.

No representation or warranty is made as to the reasonableness of the methodology used or that all methodologies used in achieving the returns have been stated or fully considered. There can be no assurance that such hypothetical performance is achievable in the future. Past performance is no guarantee of future results.



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