Facebook (NASDAQ:FB) was recently upgraded from a 'Hold' to a 'Buy' by Evercore Analyst, Ken Sena. Ken placed a price target of $75.00 on Facebook. How accurate is this price target in the historical context? Does this mean that the price of Facebook will go up to $75.00 within the next week, month, or 3-months? We put together a regression model to determine how this usually plays out, and how it has played out during the last two years since the 2012 IPO of Facebook.

**Current Analyst Opinions in Summary:**

First, here is a chart from Tip Ranks showing the level of support on the part of analysts during the last year and the current number who are indicating that it is a 'Buy.'

However, if we take a look at each individual price target of these different analysts, it would appear that they have historically been overly optimistic with respect to the subsequent stock performance.

**Prior Research:**

Regression analysis has been done in the past by researchers to determine how analyst price targets impact the subsequent price of stocks. In these studies, a portfolio approach is generally utilized, and analyst recommendations are considered in a collective manner as opposed to looking at a single stock. Brav & Lehavy have shown through their analysis the following:

Price target revisions are accompanied by a mean five-day abnormal stock return of -3.9% around downward revision announcements and +3.2% for upward revisions.

Asquith, Mikhail, and Au have also found similar results, but have mostly focused on the creation of models that can show a connection between various metrics used for analysis and the subsequent market reaction to the type of price target set. They also noted that their R^2 was fairly high compared to other types of research. R^2 is a measure of accuracy with respect to a given regression model, and generally a high one is a good thing, as it increases the percentage of accuracy. However a high R^2 is also sometimes the sign of a problem with respect to the interdependency of data sets.

We will assume that, for the purposes of our analysis, that the analysts base their price targets off of estimates that they generate internally as opposed to looking simply at the current price and stating that it should be higher. This assumption is how analysts are supposed to create price targets (even if they sometimes do not follow this rule) and therefore, this is not an unfounded assumption.

Analyst estimates of future EPS with respect to Facebook have generally been correct (at least the consensus has been) over the last two years:

Since analyst price targets are essentially based off of a run-through of the earnings/revenue figures with some analysis of the balance sheet, we can assume that in general analysts have been correct with respect to Facebook. However have the price targets been accurate as well with subsequent historical performance of the price? This is what we look at in our analysis and regression model.

**Analysis & Methodology of Regression Model:**

Using the Analyst Ratings Network as our source for the Price Targets that have been put out by analysts over the last two years, we managed to gather 303 price targets that we could use from the last two years for our analysis. This will be used as our Independent Variable within the regression model as a means to explain the behavior of the stock price. We gathered the historical pricing data for the last two years using Google Finance. We then put together the average price for the subsequent week, two weeks, four weeks, eight weeks, and twelve weeks, after each analyst price target announcement.

We then ran a regression analysis utilizing the analyst price target as a means to explain the change in average price. We ran this analysis for each time period subsequent to the announced price target. Here, in summary, is what we found:

Regression Statistics | |||||

Time Frame |
12-Weeks |
8-Weeks |
4-Weeks |
2-Weeks |
1-Week |

R Square | 0.796 | 0.832 | 0.855 | 0.868 | 0.873 |

Adjusted R Square | 0.795 | 0.831 | 0.855 | 0.868 | 0.873 |

Standard Error | 6.697 | 6.270 | 5.841 | 5.488 | 5.375 |

Observations | 264 | 274 | 296 | 298 | 300 |

Coefficients: | |||||

Intercept | 1.521 | 1.011 | 2.494 | 2.825 | 2.847 |

Price Target | 0.852 | 0.846 | 0.793 | 0.778 | 0.774 |

As you can see, our R^2 is really quite high. R^2 is a measure of our model's fitness or accuracy in utilizing the independent variable or analyst price target to explain the dependent variable or subsequent stock price. Here is a little graph which shows a visual demonstration of 'back-testing' so to speak of our model. As you can see, it would not always be accurate.

However for the 12-week or 3-month model, the model above would have a roughly 79.6% level of accuracy in plotting the Price Target of Analysts as a predicting variable with respect to explaining the subsequent 3-month average stock price.

However, this does not mean necessarily that analysts are actually correct 79.6% of the time with respect to their price targets. This is where the Coefficients come into play. What our model shows instead, is that we can create a model utilizing analyst price targets as a way of explaining the subsequent stock price 79.6% of the time.

The adjustment to the analyst price target that is required is given by the well-remembered formula y = mx + b. So, stated another way, 79.6% of the time, we can take the analyst price target, multiply it by the co-efficient (or slope which in this case is 0.852) and add the y-intercept of 1.52. In the case of Evercore's most recent analysis by Ken Sena, the $75.00 price target is not so much an indicator that the price will go to $75, but given how generally prices correspond with the targeted price, we can state the following based on each regression model per timeframe:

This most likely indicates, therefore that over the next 90 days, we can assume a roughly $4.00-$5.00 increase in the stock price, assuming that the analyst price targets hold up to a reasonable level within the context of their prior performance.

**Discussion of Assumptions & Limitations:**

There are a number of assumptions underlying this model and to the extent that any of them do not hold true, then the model is reduced in accuracy (as previously indicated by R^2).

As discussed briefly earlier, we have assumed here that the analyst price target is created independent of the current price of the stock. This is something that should be the case, as analysts generally create price targets based on their analysis of the company's intrinsic properties/performance. So to the extent that the analyst price target is actually the dependent variable and can be explained by the current price of the stock, this analysis would be rendered partially inaccurate.

As it is generally impossible to 'weed-out' the portion of data from our independent variable that is interdependent on the dependent variable, we must simply live with this issue. It does not render the entire model inaccurate. Far from this, it would simply reduce the current level of expected accuracy as represented by R^2.

**Conclusion:**

So how does one utilize all of this information in order to invest better? As any reader of this analysis should already know, this type of analysis should not be the only analysis done by a potential investor or trader. Clearly, one should do a good analysis of the fundamentals and qualitative factors behind the company.

However, the reason why I believe this analysis is a good method to measure one's own analysis against is because it gives us a good method of considering the analyst price targets. For example, we might have simply assumed that we ought to 'buy' Facebook and hold until the price hit $75.00 (yes, I understand that I am oversimplifying this). But, if we properly understand the probability involved and how often the analysts are not correct and by what margin they are incorrect, then we can better proceed when the price hits our own established benchmarks as based on the prior two years of analyst price recommendations. Facebook is a 'Buy' at current price levels based on this analysis, but the upside potential is most likely not as high as the analysts seem to indicate through their price targets.

Here is our Regression Model in Excel so you can download all of the data for yourself. This should give you a solid framework for analysis in the future - Enjoy!

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.