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The Sources of Return

For nearly two decades, Cardiff Park Advisors has worked with investors to create portfolios designed for optimal long-term performance. Our investment approach is built on the great ideas of finance, tested and proven over time. Our thinking is grounded in economic theory, backed by leading academic research, and supported by a century’s worth of empirical evidence. Much of our website is devoted to explaining our investment philosophy for those who wish to learn more.

History has shown that capital markets reward long-term investors. But staying invested during tough times requires discipline and reliance on a proven investment framework. Our framework at Cardiff Park centers on our belief in the market and market prices, which represent the collective viewpoints of hundreds of millions of individual and institutional investors. Up-to-the-minute market prices offer the most complete information available to investors in real time, and therefore the best prediction of the future.

Some investors seek to capitalize on “mistakes” in pricing, despite the potentially significant costs and challenges of this approach. A large number of academic studies have long documented that there's no compelling evidence that trying to find mistakes in markets has yielded better investment outcomes. This supports our belief that market prices are the best model we have for understanding expected returns.

Is it possible, then, to outperform the market without guesswork or attempting to predict the future? Cardiff Park answers this question with a research-based, systematic approach to portfolio design, using the market as a starting point and building from there.

A key takeaway from our investment framework is that not all securities offer the same expected returns. Research suggests that differences in returns can be found in price variables, such as market capitalization and relative price. Return differences can also be found in cash-flow variables, such as profitability.

From pricing and profitability data we can understand what an investor must be willing to pay (market prices) and what he or she can expect in return (book equity and future profits). For instance, a small company trading at a relatively low price with high profitability has a higher expected return than a large company trading at a higher price with low profitability.

Rather than trying to outguess the market, portfolio managers can use information contained in market pricing along with fundamental data from the balance sheet and the income statement to build portfolios that target higher expected return by overweighting smaller stocks, value stocks, and stocks with higher profitability.

A great deal of research is available for those who wish to dive deeper into what accounts for higher expected returns, and how those variables can be incorporated into portfolio design. The following is a condensed version of a research brief by Wei Dai, courtesy of Dimensional Fund Advisors, that surveys some of the classic studies related to differences in expected returns.


The potential for empirical work in the stock market greatly increased in the 1960s due to the collection of CRSP and CompStat1 data and the development of the Capital Asset Pricing Model (CAPM) as a theory of how expected returns should be determined.

Prior to the CAPM, there was not a theoretically sound benchmark for returns. While market beta is the only risk that should be compensated according to the CAPM, studies in the 1980s uncovered patterns in the cross-section of stock returns that contradicted this central prediction. For example, firms that have high earnings-to-price ratios (Basu, 1977, 1983), low market capitalizations (Banz, 1981), or high book-to-market equity2 (Rosenberg, Reid, and Lanstein, 1985) were shown to be associated with high average returns, even after controlling for betas.

Size & Relative Price

In an influential paper, Fama and French (1992) examined a number of different variables in regression tests and found that firm size and relative price (price scaled by the balance sheet) had the most explanatory power of the candidate variables for the cross section of average stock returns. Fama and French (1993) used this explanatory power to motivate the well-known three-factor model, which includes factors for the broad equity market, the size effect, and the value effect.

Expanding the time period available for study, Davis, Fama, and French (2000) examined size and value premiums using data back to 1926, more than three decades earlier than the original Fama/French (1993) sample. Their results further validated the size and value effects and confirmed the common variation among stocks with similar size and book-to-market characteristics.

Rizova (2006) summarized academic research on the size effect outside of the US. The average return differences between small and large cap stocks were reliably positive in most developed markets and major emerging markets, suggesting that the size effect has been a global phenomenon.

Extending the Fama and French (1998) international evidence on the value effect, Fama and French (2012) found positive value premiums in all four regions examined: North America, Europe, Japan, and Asia Pacific. They also showed that the poor, abnormal performance of small cap growth stocks (compared to a three-factor benchmark), first documented in Fama and French (1993), has persisted in the US and is present in developed markets outside the US.

Rizova (2012) confirmed this finding and studied its investment implication. The results indicate that the extreme small cap growth stocks account for the bulk of abnormal underperformance of small cap growth shares. By excluding these stocks from a small cap strategy, Rizova (2012) showed that it is possible to better deliver the size premium while maintaining broad diversification within the small cap universe.


Jegadeesh and Titman (1993) documented the momentum effect in US stock returns: When stocks are ranked on the basis of their past three to twelve month returns, those with the highest returns, on average, continue to outperform those with the lowest returns over the next few months, suggesting that the relative performance of stocks tends to persist. In addition, the abnormal return generated by the strategy of buying past winners and selling past losers appeared to be distinct from the size and value premiums.

Momentum has also been observed in international returns. Griffin, Ji, and Martin (2003) showed that momentum profits have been economically large under both good and bad economic conditions in 40 countries. Among four developed regions (North America, Europe, Japan, and Asia Pacific), Fama and French (2012) found Japan to be the only one without return momentum.

More recently, Novy-Marx (2015) presented evidence that price momentum, rather than being an independent effect, is largely explained by earnings momentum—the tendency of stocks that recently announced strong earnings to outperform stocks that recently announced poor earnings. When recent earnings surprises are added as explanatory variables, past stock returns have no additional power to explain the variation in cross-sectional returns. In addition, momentum strategies do not retain a positive excess return once controlling for market, size, value, and earnings momentum factors.

Despite the consensus on the existence of momentum, debates still exist over the cost-effectiveness of momentum strategies. There are many challenges in trying to estimate the cost of implementing any strategy, and this is particularly true with high turnover strategies. Since market micro structures have changed over time, trading cost estimates need to be date matched with the returns for each security at its transaction time. The estimation of trading costs, especially the implicit components such as bid-ask spread and market impact, can yield very different results depending on the model used and the assumptions made.

Profitability and Investments

One particularly fruitful development has been to explore how firms’ accounting fundamentals are related to their stock returns. The main message is that expected cash flows to investors are informative of average returns.

The valuation equation connects the relative price and cash flow dimensions of expected stock returns. The core of the valuation equation expresses the share price as the firm’s discounted expected future cash flows to investors. That is, where the discount rate is roughly the long-term expected return on the stock.

Building on the insights from the valuation equation, Fama and French (2006) investigated its implications for stock returns. If two stocks are expected to have the same cash flows scaled by book, the valuation equation implies that the one with lower relative price should have higher expected return (discount rate)—the value effect. Now suppose that two stocks are traded at the same relative price but one has higher expected cash flows, then it must also have higher expected return for the equation to hold. More specifically, since profits increase cash flow, we should see a positive relation between profitability and expected returns in the cross-section after controlling for relative price; likewise, as investments tend to decrease cash flow to shareholders, when accounting for relative price, there should be a negative investment effect across stocks.

Controlling for relative price, investment and profitability have additional explanatory power for average expected returns. Average returns are positively correlated with profitability and inversely related to investment. That is, firms with higher profitability tended to have higher returns than those with low profitability. This is referred to as a profitability premium.

Evidence on cash flow dimensions, backed by the valuation equation, suggests that there is potential for improving existing asset pricing models. Fama and French (2014, 2015a) showed that the five-factor model that includes profitability and investment factors provides a more complete description of the cross-section of expected stock returns than the original three-factor model. Compared with existing models, it better captures the extremely low average returns of small growth stocks. The additional factors also help to improve the explanatory power for some other return patterns discussed below, including those related to volatility and net share issues.

Net Share Issues

A number of studies examined the link between public share issuance activities and long-run average stock returns: Ikenberry, Lakonishok, and Vermaelen (1995) documented that firms tend to have positive abnormal returns during the four years after an open market share repurchase announcement. Loughran and Ritter (1995) found that companies that issued stock, either through IPO or seasoned equity offering, have generated poor returns in the five years following the issue compared to non-issuers. Through a reexamination of long-term return anomalies, Fama (1998) showed that the abnormal returns associated with share issuance have largely disappeared after controlling for size and book-to-market effects.

Motivated by the observations in these long-term event studies, researchers investigated whether share issuance conveys information about cross-sectional differences in returns. Fama and French (2014) studied portfolios formed by sorting stocks into net share issues groups. While average returns were flat across the lowest three quintiles of positive net share issues, they did appear to be much lower in the highest quintile.

Fama and French (2008b) suggested that the explanatory power of net share issues can be attributed to the information therein about expected cash flows. Since firms that issue stock tend to have high investment relative to earnings, and the opposite holds for firms that repurchase stock (Fama and French, 2005), net share issues provide information about expected cash flows to help better estimate expected returns across stocks. Consistent with this intuition, Fama and French (2014) showed that the returns of portfolios formed on net share issues can be well explained by the five-factor model that includes profitability and investment factors. In other words, the net share issues anomaly is subsumed by known drivers of expected returns.

Beta and Volatility

Recently, there has been a surge in academic interest in the performance of low market beta and low volatility stocks.3 By rebalancing the volatility deciles monthly and equally weighting the stocks in each decile, Blitz and van Vliet (2007) found a positive CAPM alpha spread between the bottom and top volatility deciles, which cannot be fully explained by size, value, and momentum effects.

This phenomenon was observed in both the global and regional (US, Europe, and Japan) stock markets. Baker, Bradley, and Wurgler (2011) confirmed the volatility effect in the US: The highest-beta (volatility) quintile portfolios, where stocks are market cap-weighted and rebalanced monthly, have underperformed their low beta counterparts in terms of both raw returns and CAPM alphas.

Fama and French (2014) and Novy-Marx (2014) showed that, except for the extremely low returns to the highest-beta (volatility) stocks, market cap-weighted beta (volatility) portfolios have yielded similar returns over the past decades. More importantly, they found that the return patterns can be well explained by known drivers of expected returns such as relative price, profitability, and investment, some of which were not accounted for in previous studies. In particular, the returns of low beta (volatility) stocks behaved like stocks of profitable firms with low levels of investment trading at low relative prices.

It is unclear, however, whether low beta (volatility) strategies will maintain their emphasis on these premiums going forward. Crill (2014) provided evidence that the emphasis on the relative price premium has been inconsistent and mostly isolated to the past few decades—low volatility portfolios had no such tendency prior to the sample periods studied in Fama and French (2014) and Novy-Marx (2014).

Therefore, although low volatility strategies have achieved appealing market-like returns with lower than market volatility over the past 40 to 50 years, caution is warranted in expecting that they will continue to do so.


Amihud (2002) presented evidence that expected returns are inversely proportional to liquidity, which suggests that investors demand a premium for holding less liquid stocks. In this study, illiquidity is proxied by the price impact of trade volume, as illiquid stocks tend to experience greater price changes in response to the temporary price pressure created by large order flows than liquid stocks.

Pástor and Stambaugh (2003) proposed an alternative proxy for liquidity risk by measuring liquidity beta—the sensitivity of stock returns to market-wide liquidity shocks. Controlling for size, value, and momentum factors, they found that, on average, stocks with high liquidity betas have outperformed stocks with low sensitivities.

Other studies employed turnover-based liquidity measures. For example, Haugen and Baker (1996) used the ratio of annual average trading volume to market capitalization and its trend to define low vs. high liquidity (turnover) stocks.

Crill, Davis, and Lee (2014) revisited the return-liquidity relation by analyzing various commonly used metrics of liquidity, including the aforementioned liquidity and liquidity risk proxies.

Their analysis suggested that return spreads have not been robust across different time periods, firm sizes, and different proxies for liquidity. While the lack of a reliable liquidity premium may be specific to the sample period under review, or due to the proxies not measuring illiquidity properly, there is also a possibility that liquidity and liquidity risk are not meaningful drivers of expected returns.

The authors pointed out that, regardless of the interpretation, it is still important to consider the impact of illiquidity on trading costs when managing portfolios. Using a flexible and patient trading approach is likely to result in more favorable transaction prices and lower costs, compared to liquidity seekers who demand immediacy when trading a security.

Mutual Fund Performance

Methods for analyzing mutual fund performance have evolved with advances in empirical asset pricing research. Since the Fama/French three-factor model largely replaced CAPM for return-adjustment in empirical studies, it has also become a standard benchmark to measure mutual fund excess returns, or alpha. More generally, one can utilize empirical factor models to evaluate a fund’s performance in excess of its exposure to the known drivers of expected returns—typically company size and relative price, but also momentum and profitability more recently. With this evaluation tool, researchers have attempted to answer interesting questions, such as whether portfolio managers possess sufficient skill to consistently generate positive alphas.

One interpretation of this research is that market prices are fair and difficult to outguess. These studies highlight the importance for portfolio managers to have a deep understanding of the systematic drivers of differences in expected returns among securities and to minimize unnecessary costs in the pursuit of long-term expected returns.

Summary and Conclusions

In this piece we discussed breakthrough economic research that has influenced our investment approach at Cardiff Park Advisors. At the core of our thinking is the belief, stemming from research in the 1960s, that market prices contain up-to-the-minute, relevant information about an asset’s expected return and risks. If market prices provide the best estimate of a security’s value, it stands to reason that market prices are also the best model we have for understanding expected returns. Attempting to outguess market prices and identify over and undervalued securities is likely to be costly and not a reliable way to improve returns.

We presented a wide body of empirical studies, courtesy of DFA, that describes the dimensions of expected returns. Many variables have been examined in recent decades, leading to the conclusion that not all securities offer the same expected returns. Differences in returns can be found in price variables and cash-flow variables. Using this information, portfolio managers can target higher expected returns by overweighting smaller stocks, value stocks, and stocks with higher profitability.

The research noted in this section has advanced the understanding of financial markets and enabled a variety of innovative portfolio-design solutions. Cardiff Park applies a systematic, research-based approach to build well-diversified portfolios suited to a range of investment objectives, timelines, and individual risk tolerance.

A Note About Performance Drivers

In any portfolio, there will be periods of time when a particular driver of returns outperforms or underperforms the market. Investors pursuing higher expected returns in the equity market must therefore determine an asset allocation appropriate to their personal goals and preferences. An important component of this decision is deciding on the level of “tilt” toward stocks with higher expected returns. Cardiff Park works with clients to illustrate a range of possible outcomes, enabling a better understanding of the effects and tradeoffs of different allocations. The goal is to balance long-term expectations with the potential for periods of underperformance, benefiting from the dimensions of higher expected returns when they occur and achieving market-like returns when they don’t.

We encourage reading Perspective on Returns (Volatility and Premiums) for a greater understanding of how volatility can affect size, value and profitability premiums over long periods of time. Charts illustrate the risks and rewards, as well as the tremendous importance of remaining diversified with a long-term perspective.


1. CRSP is the Center for Research in Security Prices at the University of Chicago. The Compstat database is produced by Standard & Poor’s Corporation.

2. While book-to-market equity is widely used in academia, finance professionals may prefer using its inverse, price-to-book ratio (i.e., relative price). Here they are used interchangeably in the sense that a higher book-to-market equity is equivalent to a lower price-to-book ratio.

3. Here beta and volatility are grouped together because they tend to be highly correlated. While some studies use past volatility to sort stocks and some use past market betas, both metrics tend to yield similar results


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