## Stocks with Outperform Ratings Beat the Market

Categories Finance

## Introduction

I recently began investing and was wondering how good analysts are at predicting the future of a company. So here is a short data analysis of my curiosity!

In short, we will be answering these hypotheses:

1. Price targets can accurately reflect the future price of a company.
2. Some analysts can predict better than others.
3. A “buy” or “outperform” rating will on average predict a stock moving up.
4. Some analyst ratings are better than others.
5. If we were to invest only in stocks with “buy”/”outperform” ratings, we can beat the market.

A price target is the price a financial analyst believes that a stock will reach in a year.

A performance rating is the rating a financial analyst assigns a stock that comes from their combined research and analysis of the company.

## Methodology

Since my investments are mostly in Canada, I will be focusing on Canadian equities. To reduce the amount of noise, I looked at companies with the following conditions:

• Listed on the TSX
• Market cap over $1 billion • Stock price over$5

The source data for companies can be found here: http://www.theupside.ca/list-tsx-stocks-market-capitalization/.

All source code can be found here: http://github.com/ayoungprogrammer/price-targets

Next, to get the price targets and performance ratings, I used Marketbeat and for stock price information, I used the “unofficial” Yahoo Finance api. One restriction is that Marketbeat only had ratings for the last 2 years but it should be enough data to look back at enough ratings.

For each analyst rating assignment, I looked at the 10 day average centered around when it was assigned and the 10 days average centered around a year in time.

After some webscraping and html/json parsing we have the dataframe with sample rows:

ticker analyst target rating aver_close_at_analysis analysis_date aver_close_at_12m 12m_date
0 RY TD Securities 78.00 Hold 70.282856 2016-03-02 97.832857 2017-03-02
1 RY Scotiabank 77.00 Outperform 70.282856 2016-03-02 97.832857 2017-03-02
2 RY TD Securities 80.00 Buy 69.029999 2016-02-25 97.656251 2017-02-25

Each row corresponds to a rating issued by an analyst with the following attributes:

• ticker: Ticker symbol
• analyst: Analyst who rated
• target: Target price issued by analyst
• rating: Rating issued by analyst
• aver_close_at_analysis: 10 days average stock price centered on analysis date
• analysis_date: When the analysis was issued
• aver_close_at_12m: 10 days average stock price centered 12 months from analysis date
• 12m_date: 1 year from the analysis date

## Results

We can calculate the error between the target price and actual price as follows:

Let

$$t =$$ target price,

$$p_0 =$$ price at analysis,

$$p_1 =$$ price at 12 years after analysis

$$error = 100 \times \frac{t – p_0}{p_0} – \frac{p_1 – p_0}{p_0}$$

Intuitively, this is difference in percentage change from the prediction and the actual. For example, error = 5 means the target price was 5% higher than then actual percentage change.

In code:

df['target_perc'] = (df['target'] - df['aver_close_at_analysis'])/df['aver_close_at_analysis'] * 100
df['real_perc'] = (df['aver_close_at_12m'] - df['aver_close_at_analysis'])/df['aver_close_at_analysis'] * 100
df['error'] = (df['target_perc']-df['real_perc'])
df['abs_error'] = abs(df['error'])
ticker analyst target aver_close_at_12m target_perc real_perc error
0 RY TD Securities 78.00 97.832857 10.980122 39.198750 -28.218627
1 RY Scotiabank 77.00 97.832857 9.557300 39.198750 -29.641449
2 RY TD Securities 80.00 97.656251 15.891643 41.469292 -25.577649

A quick glance at the data shows that some of the ratings have very high variance. Therefore, we should try to reduce the noise of our error measurement by getting rid of some outliers. We will do so by removing outliers in the 10th and 90th percentiles. We also remove analysts with less than 100 ratings, so we can compare the most important analysts.

With pandas, we can easily group the data by analyst and aggregate attributes with different functions:

def filter_tail(data, p1=10, p2=90):
q1 = np.percentile(data, p1)
q3 = np.percentile(data, p2)
return data[(data > q1) & (data < q3)]

analysts = df.groupby(['analyst'], as_index=False)['error'].agg({
'mean_abs_err': lambda xs:np.mean(np.abs(filter_tail(xs))),
'count': 'count',
'10p': lambda xs: np.percentile(xs, q=10),
'90p': lambda xs: np.percentile(xs, q=90),
'mean': lambda xs: np.mean(filter_tail(xs)),
'std': lambda xs: np.std(filter_tail(xs)),
})
analysts = analysts[analysts['count'] > 100].sort_values(by='mean_no_outliers')
analyst std mean mean_abs_err 10p 90p count
48 National Bank Financial 16.365463 -2.532164 13.425469 -40.092491 30.074729 251
3 BMO Capital Markets 18.982738 -2.282366 14.435614 -55.866637 35.678834 248
7 Barclays PLC 16.120963 -0.586090 13.128664 -35.657920 37.853971 212
20 Desjardins 18.972093 -0.542214 15.355082 -49.563907 33.312509 115
12 Canaccord Genuity 18.101054 4.703447 14.967193 -35.795798 47.363220 302
10 CIBC 19.098723 4.960119 15.799013 -31.113204 48.409297 446
58 Royal Bank of Canada 18.198846 5.544864 15.402881 -34.362247 50.268754 584
66 TD Securities 20.179027 5.868849 17.002451 -44.254427 47.655748 551
54 Raymond James Financial, Inc. 21.500147 7.580748 18.711069 -42.025280 51.284896 269
62 Scotiabank 18.735960 7.741048 15.962621 -32.351408 53.038985 706

We can also plot the means and standard deviations as error plots:

From the aggregate table, we see that Barclays PLC has the least mean absolute error, i.e., its error is closest to 0 and is the most accurate. Barclays PLC also has the “tightest” standard deviation, so it is also the most precise. However, we see that the standard deviations for each analyst is very large; so the precision of each analyst is very low. Barclays PLC has a standard deviation of 16% which we can interpret as 95% of price targets will be +/- 32% off. For example, if TD Bank current stock price is $100 and Barclays PLC gives a price target for$100, all we can reasonably expect is the stock price to range from ~$70 to ~$130.

Thus we can answer our first two hypotheses:

1. Analysts are on average, accurate in their predictions with their mean error close to 0. However, price targets cannot precisely predict the future of a company in 12 months.
2. According to the data, Barclays PLC has the most accurate and precise price targets, but only by a small margin.

A more intuitive image of precision vs accuracy:

Next, we will look at analyst ratings and explore their relation to stock performance.

Using pandas again, we can easily filter out price targets with no rating and only take the ratings from analysts that care about (in the previous table). We can also easily group by each analyst and rating and aggregate with different functions on different attribute.

ratings = df[(df['rating'] != 'NaN') & (df['analyst'].isin(analysts['analyst']))]
ratings_agg = ratings.groupby(['analyst', 'rating'], as_index=False).agg({
'error': {
'mae': lambda xs: np.mean(np.abs(filter_tail(xs))),
},
'real_perc': {
'mean': 'mean',
'median': 'median',
'10p': lambda xs: np.percentile(xs, 10),
'90p': lambda xs: np.percentile(xs, 90),
'count': 'count',
},
'target_perc': {
'median': 'median',
'10p': lambda xs: np.percentile(xs, 10),
'90p': lambda xs: np.percentile(xs, 90),
}
})

ratings_agg.columns = list(map('_'.join, ratings_agg.columns.values))
ratings_agg[ratings_agg['real_perc_count'] > 10]



Attributes:

• target_perc_10p: 10th percentile for price target change percentage
• target_perc_90p: 90th percentile for price target change percentage
• tarc_perc_median: median for perice target change percentage
• error_mae: mean absolute error
• real_perc_10p: 10th percentile for real price change percentage
• real_perc_90p: 90th percentile for real price change percentage
• real_perc_median: median for real price change percentage
• real_perc_count: number of ratings
• real_perc_mean: mean of real price change percentage

Sample rows:

analyst_ rating_ target_perc_10p target_perc_90p target_perc_median error_mae real_perc_10p real_perc_count real_perc_mean real_perc_90p real_perc_median
0 BMO Capital Markets Market Perform -0.249542 23.049416 7.826429 17.048387 -13.624028 82 29.306269 86.571109 11.962594
2 BMO Capital Markets Outperform 9.333289 34.091310 18.863216 13.267287 -13.430220 116 22.215401 64.711223 15.109094
5 Barclays PLC Equal Weight -5.964636 10.834989 4.672844 11.317883 -23.540832 72 11.511754 37.461244 9.239600

Now we take only analyst ratings with at least 20 and then sort by stock performance (change in stock price over a year). We can take the top 10 and perform more analysis on those.

top_ratings = ratings_agg[ratings_agg['real_perc_count'] > 20]
top_ratings = top_ratings.sort_values('real_perc_mean', ascending=False)
top_ratings['analyst_rating'] = top_ratings['analyst_'] + ' ' + top_ratings['rating_']
top_analyst_ratings

Sorted by real price change percentage:

analyst_ rating_ target_perc_10p target_perc_90p target_perc_median error_mae real_perc_10p real_perc_count real_perc_mean real_perc_90p real_perc_median analyst_rating
32 National Bank Financial Sector Perform 0.277827 45.337101 8.695651 14.170428 -5.738096 81 29.887596 61.182293 17.410111 National Bank Financial Sector Perform
0 BMO Capital Markets Market Perform -0.249542 23.049416 7.826429 17.048387 -13.624028 82 29.306269 86.571109 11.962594 BMO Capital Markets Market Perform
54 TD Securities Action List Buy 18.333724 77.701954 38.001830 19.629657 -0.893705 36 28.334038 71.459495 15.928740 TD Securities Action List Buy
21 Canaccord Genuity Buy 8.340735 61.226203 24.085974 18.796959 -16.561733 177 27.086690 86.234464 18.039215 Canaccord Genuity Buy
31 National Bank Financial Outperform 7.705539 53.579343 18.929633 12.407454 -1.526925 115 24.524428 59.093628 22.213398 National Bank Financial Outperform
2 BMO Capital Markets Outperform 9.333289 34.091310 18.863216 13.267287 -13.430220 116 22.215401 64.711223 15.109094 BMO Capital Markets Outperform
14 CIBC Sector Outperformer 9.714648 59.846481 33.652243 21.688542 -14.518562 44 22.205022 60.020932 22.218981 CIBC Sector Outperformer
43 Royal Bank of Canada Sector Perform -0.678788 36.516168 11.101983 13.099112 -11.590060 220 21.330160 51.282201 10.498096 Royal Bank of Canada Sector Perform
36 Raymond James Financial, Inc. Outperform 9.437804 54.483693 21.236522 15.914385 -18.695776 106 20.773835 59.159844 13.004491 Raymond James Financial, Inc. Outperform
49 Scotiabank Outperform 7.239955 50.402485 19.082141 15.926344 -21.632875 246 18.407885 51.023159 14.897374 Scotiabank Outperform

We can make an error plot for the mean and standard deviation of the real percentage change for each analyst rating:

We can see that stocks with the top analyst ratings go up on average 25% in a year which is very good. Based on the error plot, TD Security Action List Buy seems to perform the best in terms of high mean and lower variance. Although there is high variance, the mean is more meaningful in this case. If we were to invest $1000 in each of the stocks when were given the rating, we would make about$1250 on average after a year, which is what we really care about. The TSX index went up 11% and TSX index annualized return is 9.1%. So we’re actually beating the market by ~16% with this strategy!

However, keep in mind that this data is for the last 2 years and is not indicative of future performance. On the other hand, I believe this strategy could make sense since analysts put significant effort and research into their rating and also because of the influence of the rating. People probably trust the analysts and would likely invest knowing that the stock has a good rating thus self fulfilling the rating.

With this analysis, we can conclude our last 3 hypotheses:

1. A buy or outperform rating will on average go up on average by 15-20%.

2. TD Security Action List Buy appears to be the strongest indicator for a stock to perform well.

3. If we buy stocks with the top 10 ratings when they get issued and sell in exactly one year, we will beat the market by ~16%.

## Conclusion

• Price targets aren’t a good indicator of where the price of a stock will go.
• The top performance ratings are a good indicator for a stock performing well.
• You could possibly beat the market by only buying stocks with sector outperforms or buy ratings.

Please keep in mind that I am by no means a financial expert and am not certified to give financial advice.

All the code can be found here: https://www.github.com/ayoungprogrammer/price-targets

## Tutorial: Getting Started with Machine Learning with the SciPy stack

Categories Machine Learning, Uncategorized
There are many machine learning libraries out there, but I heard that SciPy was good so I decided to try it out. We will be doing a simple walkthrough a k means clustering example:

## SciPy Stack

The contents of the SciPy stack are:

Python: Powerful scripting language
Numpy: Python package for numerical computing
SciPy: Python package for scientific computing
Matplotlib: Python package for plotting
iPython: Interactive python shell
Pandas: Python package for data analysis
SymPy: Python package for computer algebra systems
Nose: Python package for unit tests

### Installation

I will go through my Mac installation but if you are using another OS, you can find the installation instructions for SciPy on: http://www.scipy.org/install.html.

You should have Python 2.7.

#### Mac Installation

I am using a Mac on OS X 10.8.5 and used MacPorts to setup the SciPy stack on my machine.

Install macports if you haven’t already: http://www.macports.org/

Otherwise open Terminal and run: ‘sudo macports selfupdate’

Next in your Terminal run: ‘sudo port install py27-numpy py27-scipy py27-matplotlib py27-ipython +notebook py27-pandas py27-sympy py27-nose’

Run the following in terminal to select package versions.

sudo port select –set python python27
sudo port select –set ipython ipython27

## Hello World

IPython allows you to create interactive python notebooks in your browser. We will get started by creating a simple hello world notebook.
Create a new directory where you want your notebooks to be placed in.
In your directory, run in terminal:
ipython notebook

This should open your browser to the IPython notebook web interface. If it does not open, point your browser to http://localhost:8888.

Click New -> Notebooks -> Python 2

This should open a new tab with a newly create notebook.

Click Untitled at the top, rename the notebook to Hello World and press OK.

In the first line, change the line format from Code to Markdown and type in:

# Hello World Code

And click run (the black triangle that looks like a play button)

On the next line, in code, type:

print ‘Hello World’

and press run.

## K Means Clustering Seed Example

Suppose we are doing a study on a wheat farm to determine how much of each kind of wheat is in the field. We collect a random sample of seeds from the field and measure different attributes such as area, perimeter, length, width, etc. Using this attributes we can use k-means clustering to classify seeds into different types and determine the percentage of each type.

Sample data can be found here: http://archive.ics.uci.edu/ml/datasets/seeds

The sample data contains data that comes from real measurements. The attributes are:

1. area A,
2. perimeter P,
3. compactness C = 4*pi*A/P^2,
4. length of kernel,
5. width of kernel,
6. asymmetry coefficient
7. length of kernel groove.

Example: 15.26, 14.84, 0.871, 5.763, 3.312, 2.221, 5.22, 1

#### Code

Create a new notebook and name it whatever you want. We can put all the code into one cell.

First, we need to parse the data so that we can run k-means on it. We open the file using a csv reader and convert each cell to a float. We will skip rows that contain missing data.

Sample row:

['15.26', '14.84', '0.871', '5.763', '3.312', '2.221', '5.22', '1']
# Read data
for row in bank_csv:
missing = False
float_arr = []
for cell in row:
if not cell:
missing = True
break
else:
# Convert each cell to float
float_arr.append(float(cell))
# Take row if row is not missing data
if not missing:
data.append(float_arr)
data = np.array(data)


Next, we normalize the features for the k means algorithm. Since Scipy implements the k means clustering algorithm for us, all the hard work is done.

# Normalize vectors
whitened = vq.whiten(data)

# Perform k means on all features to classify into 3 groups
centroids, _ = vq.kmeans(whitened, 3)


We then classify each data point by distance to centroid:

# Classify data by distance to centroids
cls, _ = vq.vq(whitened, centroids)


Finally, we can graph the classifications of the data points by the first two features. There are seven features total, but it would be hard to visualize. You can graph by other features for similar visualizations.

# Plot first two features (area vs perimter in this case)
plt.plot(data[cls==0,0], data[cls==0,6],'ob',
data[cls==1,0], data[cls==1,6],'or',
data[cls==2,0], data[cls==2,6],'og')
plt.show()


Note: to show the plot inline in the cell, we put ‘%matplotlib inline’ at the beginning of the cell.