**What Behavioral Economics Can Tell Us About Investing: Anchoring Bias**

July 21, 2014

Question 1: 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = ?

Question 2: 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = ?

When viewed together, it is clear that the two questions above are identical. The correct answer for both is 40,320. But if a group of people are shown Question 1 and asked to estimate the value of the equation within 5 seconds, the median estimate will approach 500. Show another group Question 2 instead, and their answer quadruples to more than 2,000. Why does the presentation impact the estimate? Why are the estimates for both groups so low? The answers to these questions have important implications for Redwood’s investment process.

Anchoring

In 1974, Amos Tversky and Daniel Kahneman introduced the concept of “Anchoring”, which explains a structural deficit in human estimation (Tversky & Kahneman, 1974). Their research highlighted two important effects. First, when people are asked to estimate a value that requires adjustment from a prior value, the adjustment is often insufficient. Second, the value of the initial “anchor” – either an existing estimate or even an unrelated number – will impact their final estimate. In the example above, people generally take a few seconds to calculate the first few multiplications, and then adjust their estimate up to account for the rest of the formula. In this case, both groups made estimates that were too low. The estimates from the group that saw Question 1 were likely lower because the quick calculation they performed started with “1x2x3” (6) whereas their counterparts who saw Question 2 started by calculating “8x7x6” (336). Both groups were adjusting from their initial value, but the initial value for those who saw question 2 was much higher, which led to higher estimates.

Impact on EPS Estimate Revisions

Anchoring impacts a wide and diverse range of estimations, but for our purposes, none more directly than forecasting future corporate earnings. Earnings estimate revisions, which is a key factor in Redwood’s investment process, measures Wall Street analysts’ most recent adjustments to earnings estimates for a company. As new information becomes available, analysts revise their initial estimates to incorporate the news. If anchoring is as persistent as Kahneman and Tversky demonstrated, there should be an anchoring bias in earnings estimate revisions. Specifically, for those companies with recent positive estimate revisions (rising earnings estimates), those estimates should be too low. We should therefore expect to see positive revisions in the future, as analysts incrementally “catch up” to the most likely corporate earnings. That is, estimate revisions should be serially correlated.

In fact, this is exactly what happens. To illustrate this point, a historical graph of 2013 earnings per share (EPS) estimate revisions for Apple (AAPL) follows. AAPL is among the largest and most closely followed companies in the world. If any company was going to have enough public data to generate accurate estimates, AAPL would be a likely candidate. Instead, we see exactly what Kahneman and Tversky’s research suggests – serial correlation of earnings estimates.

When AAPL’s 2013 EPS estimates started moving higher in early 2011, they continued to rise all the way through mid-2012. Conversely, once analysts began revising EPS estimates lower in late 2012, the trend lasted for 6 months until mid-2013. There are countless examples of the serial correlation of earnings estimates, and empirical studies have demonstrated the significance of the effect (Chen, Narayanamoorthy, Sougiannis, & Zhou). This phenomenon means that investors looking for stocks that will have rising earnings estimates going forward should start by looking at those stocks that have rising estimates today.

Estimate Revisions Work

In a Redwood Investments proprietary research study that includes two decades of historical data, large cap stocks with high earnings estimate revisions generated a compounded annual return of 13.3% and outperformed the investment universe return of 10.0% by 330bps. Companies experiencing negative earnings estimate revisions underperform the universe by 330bps and produced only a 6.3% return. The 2o-year timeframe from 1/1/1992 - 12/31/2013 captures both bull and bear markets, recessions and periods of accelerated growth.

Said differently, successfully identifying stocks that will have positive earnings estimate revisions is likely to lead to outperformance over long market cycles. Overlaying the AAPL EPS estimate chart with the stock price illustrates the correlation between EPS estimate revisions and stock price.

Many factors eventually lose their predictiveness as investors flock to the winning strategy and eliminate the inefficiency in the market. Over a relatively long period, EPS Estimate Revisions have sustained their predictive power. Unlike some of the more objective metrics like Dividend Yield or Market Capitalization, EPS Estimate Revisions rely on human estimation, which is subject to cognitive bias. Redwood believes that anchoring explains this persistence, and suggests that it should continue into the future.

How Does Redwood Capitalize on Anchoring?

Anchoring yields two key insights to Redwood’s investment process: 1) companies with rising (or falling) estimates tend to see estimates continue to rise (or fall), and 2) stock prices are correlated with EPS estimate changes. That is, companies with rising estimates in the future are likely to outperform. By narrowing the investment candidates to those with rising estimates today, among other attractive factors, Redwood selects its best ideas from an already advantaged list. The investment team then focuses its fundamental research effort on these stocks to understand the business drivers leading to earnings estimate revisions for each company and determining the sustainability of those revisions.

The Redwood portfolio team strives to avoid errors from anchoring in its own forecasts by being aware of the inherent bias in human nature. Redwood analysts are cognizant of the need to make estimates that are outside of consensus. Further, the team routinely challenges each member’s estimates to minimize the impact of anchoring and ensure that estimates are objective and logical.