This document presents an analysis of factors to use in filtering stocks for long and short positions in a portfolio. For long positions, the factors of alpha, dividend yield, price-to-book ratio, and changes in stock outstanding are analyzed. For short positions, the factors of market value, price-to-book ratio, capital investment, and liquidity are considered. Principal component analysis is used to analyze the factors and scores are calculated to select 50 stocks for long and short positions that are backtested for returns. The results show the filtered portfolio outperformed the total market.

1. FIN 608 CAPITAL MARKETS AND INVESTMENT STRATEGY GROUP YLC
FIN 608 PROJECT 1
Yue Ma, Ran Zhang, Qiao Chen
M.A. students in Applied Economics, heymy@umich.edu, zhran@umich.edu, chenqiao@umich.edu
Xiaoyu Dong
M.S. student in Industrial and Operations Engineering, xydong@umich.edu
In this project, our goal is to pick up 50 stocks for short and long respectively from 248 stocks for both
sections, which are sorted by annual growth theory. In this paper, we pick up four long filter candidates:
alpha, dividend yield, price to book vale and changes in amount of stock out standing, four short filter
candidates: market value, price to book ratio, capital investment and liquidity. We conduct factor analysis
and backup test for both part and come to components which can help investors to decide stocks building a
portfolio, in order to increase expected return. Our conclusion is consistent with previous research and also
the historical data test.
1. FILTER OF LONG CANDIDATES
The purpose of picking custom filters is to somehow enhance the market signal, which will lead
to a better stock return. In the long-position list, we would like to pick some factors which would
lead to an increasing stock return.
1.1. Alpha
Alpha is used to determine by how much the realized return of the portfolio varies from the required
return, as determined by CAPM. the formula for alpha is presented as follows:
↵ = Rp (Rf + (Rm Rf ))
We measure alpha by ”Alpha Relative to Local Index” in ”FactSet Global - FG MKT VALUE”
in FactSet database.
In Christopherson, Ferson, and Turner (1999), they figured that companies with higher alpha
outperform those with lower alpha. A bigger alpha might lead to bigger future stock return. There-
fore, we factor alpha in our following analysis.
1

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Proposition 1. Alpha is positively related to the future stock return.
1.2. Dividend Yeild
Dividend Yield is a financial ratio that indicates how much a company pays out in dividends each
year relative to its share price. Dividend yield is represented as a percentage and can be calculated
by the following formula.
We measure dividend by ”Dividend Yeild - Current” in ”Price - 1984 - Global - Daily -
P ALPHA PR” in FactSet database.
In Ang and Bekaert (2007), they examine the predictive power of the dividend yields for fore-
casting excess returns. And they found that dividend yields predict excess returns only at short
horizons together with the short rate and do not have any long-horizon predictive power. At short
horizons, the short rate strongly negatively predicts returns. Since our investment period is only
one year, therefore, we could factor dividend yields in.
Proposition 2. Dividend Yield is positively related to the future stock return.
1.3. Price To Book Ratio
Price To Book Ratio compares a stock’s per-share price (market value) to its book value (share-
holders’ equity).
We measure price to book ratio by ”Price to Book Value” in ”FactSet Fundamentals Consolidated
- Global - FF PBK” in FactSet database.
PB ratio is an appropriate index for measurement of book to market ratio.
So we decide to include PB Ratio on our filters. Then we expect to have a higher return on the
group of Small PB Ratio compared to High PB Ratio. Lower PB ratio reflects the firms undertake
a plunge from price. So the price is underestimated compared to High PB Ratio. Then we could
expect a return from recession. Below are brief industry cases why low PB could be more attractive.
Formula for PB PB = PE ⇤ ROE
Low PB: High ROE and Low PE happens on bank industry often. When experiencing a bear
market, public are not only afraid of increasing number of bad debt and also the rigid regulation

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requirement. However, when the market turns out to recover from recession, high ROE would lead
to a rebound.
Low ROE and Low PE happens on the firms on steel, public service, highway industry where
the e ciency of capital is low and marginal profit is compressed by competition and regulation.
Whereas, the firm would be relatively stable due to sustaining cash flow to defend market recession.
Low ROE and High PE happens when market looks good on firms future and expect it would
reverse probably upon current price.
Proposition 3. Price to book ratio is negatively related to future stock return.
1.4. Changes in Amount of Stock Outstanding
We measure Changes in Amount of Stock Outstanding by ”P COM SHS OUT(11/13/2015) -
P COM SHS OUT(11/13/2014)” in FactSet database.
Change in amount of stock outstanding relates to two major actions that a firm conduct, the
equity issuance and repurchase. Equity issuance is a way to finance a company or its new project
by sales of ownership interest. Equity repurchase, otherwise, is a way to reduce the outstanding
stocks, which usually is viewed as another kind of dividend. Both of them can have an e↵ect on
the earnings per share.
New equity issuance usually comes with a fall on stock price because investors all focus on the
net earnings and more stock outstanding means that earnings of the company would spread among
a greater number of stocks. However, stock repurchase is viewed by analyst as that the managers
think the companys stock is undervalued among the market, and thus investors in the market
might think highly of the stock they own now which lead to a price increase on the current stock
market.
Proposition 4. Amount of stock outstanding has negative relationship with future stock return.
2. PRINCIPLE ANALYSIS OF LONG FILTER, CHOSEN STOCKS,
AND BACK TEST
We run the principle analysis for the long filter. We take minus value to the indicators ”Price To
Book Ratio” and ”Changes in Amount of Stock Outstanding” because thay have negative relation

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Figure 1 Total Variance Explained in Principle Component Analysis for Long Filter
Note. Extraction Method: Principal Component Analysis. a. When components are correlated, sums of squared
loadings cannot be added to obtain a total variance.
with stock return. The results show that the four indicators can be integrated into two principle
components. The total variance explained by the two components are shown in Figure 2
In order to sort the short candidtes and select 50 from them, we calculate the scores of the first
principle component which explains 27.943% of the total variance, and sort all the long candidates
according the score. Since we take minus value to the indicators ”Price To Book Ratio” and
”Changes in Amount of Stock Outstanding”, the four indicators have positive relation with the
stock return. Therefore, the first principle component should also have positive relation with the
stock returns. Therefore, we choose the 50 candiates with the highest scores as our long porfolio.
The chosen short stocks are presented in the sheet ”Chosen Long Stocks”. The back test suggest
that the return of those stocks in the recent quarter (8/11/2015 to 11/11/2015) is 3.8% (see the
sheet ”Long Chosen Stock Back Test”), whereas the the average return of all long candidates is
5.9%. The first component scores for all the short candidates are presented in the sheet ”Long
Filter Scores for All”.
3. FILTER OF SHORT CANDIDATES
3.1. Market Value
Market value is the price an asset would fetch in the marketplace.

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We measure market value by ”Market Value (Current Only)” in ”FactSet Global -
FG MKT VALUE” in FactSet database.
A companys market value is a good indication of investors perceptions of its business prospects.
Market value can fluctuate a great deal over periods of time, and is substantially influenced by
the business cycle. Market value is also dependent on numerous other factors, such as the sector
in which the company operates, its profitability, debt load and the broad market environment.
Market value for a firm may diverge significantly from book value or shareholders equity.
So we decide to include Market Value on our filters. Then we expect to have a higher return on
the group of Small Market Value compared to Big Market Value.
There is kind of risk premium between two groups. The Big Market Value firms are less vulnerable
under turmoil of financial market and are easier to get support from government in terms of loan
and recapitalization. On the other side, Small Market Value firms have more risk open to the
markets, the volatility term as from CAPM model is higher, so we expect higher return.
Proposition 5. Market value is negatively related to future stock return.
3.2. Price To Book Ratio
Price To Book Ratio compares a stock’s per-share price (market value) to its book value (share-
holders’ equity).
We measure price to book ratio by ”Price to Book Value” in ”FactSet Fundamentals Consolidated
- Global - FF PBK” in FactSet database.
As we stated before in the long filter, we make the following prediction.
Proposition 6. Price to book ratio is negatively related to future stock return.
3.3. Capital Investment
Capital investment generally refers to the money invested by the firm to further business objectives.
We measure capital investment by ”Invested Capital - Total” in ”FactSet Fundamentals Consol-
idated - Global - FF INVEST CAP” in FactSet database.

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We predict that capital investment is negatively related to future stock return for the following
several reasons.
Firstly, capital investment and future stock return have contrary convariation with interest rate
(Lamont 2000). On one hand according to basic economic theory, when the interest rate decreases,
the capital cost will decrease, and therefore the investment will increase because more projects will
pass the net present value threshold. On the other hand, when the interest decreases, the discount
rate falls, the discounted sum of future cash flows rises, and therefore, the stock price will rise.
Secondly, stock price deviations from fundamental value may have a direct e↵ect on the invest-
ment policy of a firm. According to Polk and Sapienza (2009), the investment decision K by
the manager satisfies the equation V 0
(K) = c
where c is a constant and is positively related to
measures the extent to which the firm is misprice, and the optimal investment decision satisfies
V 0
(K⇤
) = c. On one hand, when the firm is overpriced, the manager will invest more than the
optimal investment value. If managers expect the current overvaluation to last, then managers
will take advantage of the mispricing and increase investment. On the other hand, if the firm is
underpriced, then the manager will invest less than the optimal investment value.
Proposition 7. Capital investment is negatively related to future stock return.
3.4. Liquidity
Liquidity is the extent to which the stock is easy to transact.
We measure liquidity by ”Look at average volume, and taks the maximum. use to help analyze
liquidity” in ”LIQUIDITY” in FactSet database.
We predict that liquidity is negatively related to future stock return for the following several
reasons.
Firstly, liquidity is related to risk (Baele, Bekaert, and Inghelbrecht 2010). If a stock is not very
liquid, then when an investor buys that stock, he will not be very easy to sell that stock. When the
investor finally finds an opportunity to sell that stock, the stock price may already fell. Therefore,
in order to conpensate for the the risk, the future expected return should be high for stocks with

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Figure 2 Total Variance Explained in Principle Component Analysis for Short Filter
Note. Extraction Method: Principal Component Analysis. a. When components are correlated, sums of squared
loadings cannot be added to obtain a total variance.
low liquidity. In CAPM world, liquidity should be neagatively related to beta. Therefore, on one
hand, stocks with low liquidity should have high beta and therefore should have high expected
future return. On the other hand, stocks with high liquidity should have low beta and therefore
should have low expected future return.
Secondly, liquidity is related to transaction cost citepam. When an investor holds a stock with
low liquidity will incur higher transaction cost than an investor holding a stock with high liquidity
to sell the stock, and therfore this invest should require higher return than an investor holding a
stock with high liquidity.
Proposition 8. Liquidity is negatively related to future stock return.
4. PRINCIPLE ANALYSIS OF SHORT FILTER, CHOSEN
STOCKS, AND BACK TEST
We run the principle analysis for the short filter. The results show that the four indicators can be
integrated into two principle components. The total variance explained by the two components are
shown in Figure 2
In order to sort the short candidtes and select 50 from them, we calculate the scores of the first
principle component which explains 62.810% of the total variance, and sort all the short candidates

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8 GROUP YLC
according the score. Since our analysis suggest that the four indicators have negative relation with
the stock return, the first principle component should also have negative relation with the stock
returns. Therefore, we choose the 50 candiates with the highest scores as our short porfolio.
The chosen short stocks are presented in the sheet ”Chosen Short Stocks”. The back test suggest
that the return of those stocks in the recent quarter (8/11/2015 to 11/11/2015) is 17.3%, suggest-
ing that if we short this portfolio, our return should be 17.3% (see the sheet ”Short Chosen Stock
Back Test”), where as the everage return of all short candiates through this period is 13.1%. The
first component scores for all the short candidates are presented in the sheet ”Short Filter Scores
for All”.
5. BACK TEST FOR WHOLE PORTFOLIO
The return rate of our 130/30 portfolio with initial endowment of $500K should be
1.3 ⇤ ( 3.8%) 0.3 ⇤ ( 17.3%) = 0.0025
The money return of our 130/30 portfolio with initial endowment of $500K should be
0.0025 ⇤ 500000 = 1250
The return rate of the 130/30 portfolio without filtering with initial endowment of $500K should
be
1.3 ⇤ ( 5.9%) 0.3 ⇤ ( 13.1%) = 0.0374 < 0.0025
Therefore, our filtering strategy is more successful than the total asset growth anomaly in the
recent quarter.
References
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Review of Financial Studies, 23(6) 2374–2428.
Polk C, Sapienza P (2009) The stock market and corporate investment: A test of catering theory. Review of
Financial Studies 22(1) 187–217.

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