5. Data
5.5 Factor Data
In this section we proceed to explain how the Small minus Big (SMB) and the High minus Low (HML) in the Fama-French (1993) 3-factor model factors were constructed, and which data we will apply to replicate the momentum factor (MOM) for the Carhart 4-factor (1998) model.
In studies were multifactor models are applied; academics sometimes experience problems with the construction of the factor proxies. The problem often lies in the magnitude of data needed to construct the proxies correctly, which can be very time-consuming without access to the most sophisticated financial software available. Kenneth R. French, one of the creators of the Fama-French model, has constructed a data library providing daily, weekly and monthly updates for the SMB and HML proxies for the American market. Additionally, he provides monthly updates on the American MOM proxy used in the Carhart 4-factor model.
Thus, the Kenneth R. French data library is a very useful database for academics doing
61 research on the American market only. However, in this paper we also perform a study on the European and the Scandinavian market, and if we were to apply the SMB, HML and MOM from the American market on these two markets, our results could be misleading.
To cope with this problem, a popular solution among academics is to construct the proxies from indices. This has been done in several previous studies on ethical investing and fund performance. For instance in Rennebog’s (2008B) study of Ethical Fund performance in the US, Europe and Asia. In order to create the SMB and HML factor for the countries outside the US, Renneboog used the WorldScope indices for the given countries to construct the most accurate factors as explanatory variables. This was also done in Bauer et al. (2005) investigation of ethical fund performances in Germany, UK and America compared to conventional funds. However, instead of using the WorldScope indices, this study used the MSCI indices for the given countries.
For this paper, we have therefore decided to construct the HML and SMB factors ourselves for the European and the Scandinavian markets. In this process we are once again using DataStream to extract the returns of the different indices, below we will explain which indices we used to construct the SMB and the HML factors and how we did it. Unfortunately we were not able to construct the MOM factor ourselves. We will explain why later in this section.
5.5.1 The Small minus Big factor (SMB)
As described earlier in this paper, the Fama-French (1993) 3-factor model used the SMB factor, or firm size, as an extension to the CAPM to improve its predictions. To create this factor they used all the listed American stocks, and sorted them in two different groups. One group consisted of the 20% of the stocks characterized as small cap, i.e. companies with a low market value. The other group consisted of the 80% of the stocks characterized as mid or large cap, i.e. companies with medium and big market value. Then they subtracted the portfolio containing big stocks from the portfolio containing small stocks, which resulted in the SMB proxy (Bodie, Kane, Markus 2009).
This factor was constructed on the background that small companies are generally riskier than big companies, because small companies have fewer financial resources and more uncertainty in regards to future cash flow than large companies. This is especially visible during periods of recession, where small companies are more likely to default than large companies. Then
62 again the small companies have outperformed the big companies by over 3% per year during the last 50 years. Thus, since small companies generally offer a higher return, they are more risky to invest in than large companies5
5.5.1.1 The SMB proxy on the American market .
As mentioned earlier, the American SMB proxy is available on the Kenneth R. French Data Library. Therefore, we have extracted the factor data from the data library instead of constructing it ourselves.
5.5.1.2 SMB proxy for the European market
To construct the SMB proxy for the European market we have selected the MSCI European Small Cap Index, for companies with a low market value. This index consists of European companies with a market value from $200 million up to $1.500 million and it covers around 14% of the total free floated market capitalization6
The returns from the European Large Cap index are then subtracted from the European Small Cap index, to construct the European SMB factor.
. For companies with a high market value, we have selected the MSCI European Large Cap Index.
5.5.1.3 SMB proxy for the Scandinavian market
To construct the SMB factor for the Scandinavian market we use the MSCI Nordic Small Cap index, to replicate the low market value companies. This index consists of companies with small market capitalization within the Nordic region. However, the MSCI Nordic Large Cap index that we wanted to apply has only existed since the middle of 2007, which resulted in a problem since we are doing our analysis from January 2006.
We therefore had to find another index to substitute the MSCI Nordic Large Cap. The most appropriate choice was the OMX Nordic 40, which consists of the 40 most valued companies in Denmark, Sweden and Finland. The Norwegian companies are unfortunately not included in this index since Oslo Børs is not a part of the OMX Nordic. Nevertheless, since we were
5 http://www.ifa.com/12steps/step8/step8page4.asp
6 http://www.msci.com/products/indices/size/small_cap/
63 unable to find any other index that would be better suited for our investigation we have decided to use this. To construct the proxy we subtracted the OMX Nordic 40 from the MSCI Nordic Small Cap.
5.5.2 The High minus Low factor (HML)
The third factor Fama and French (1993) applied in their 3-factor model was the HML factor, which is measured by the book-to-market ratio. A listed company with a low book-to-market ratio is characterized as a “growth” company, and a company with high book-to-market value is characterized as a “value” company.
The factor was constructed by sorting the listed American growth and value companies into two separate groups. Next, they subtract the portfolio containing value stocks from the portfolio containing growth stocks, resulting in the HML proxy (Bodie, Kane, Markus 2009).
The HML factor is constructed on the background that accountants value the assets of companies with high book-to-market ratios higher than the stock market values the companies. High book-to-market ratios often indicate that the stock is risky, has poor earnings and that the company may be in financial distress. Therefore investors will demand a higher return for this type of stock as a reward for the extra risk exposure7
5.5.2.1 The HML proxy on the American market
. Fama and French (1998) did a study on the performance of growth stocks compared to value stocks in the period from 1975 to 1995. The study showed that value stocks outperformed growth stocks in twelve of the thirteen markets the study was conducted on.
The HML proxy for the American market is available on the Kenneth R. French Data Library.
Therefore, we have extracted the factor data from the data library instead of constructing it ourselves.
5.5.2.2 The HML proxy on the European market
To construct the HML proxy on the European market we have selected the MSCI Europe Growth Index for companies with a low book-to-market ratio. For companies with a high
7 http://www.ifa.com/12steps/step8/step8page4.asp
64 book-to-market value, we have selected the MSCI Europe Value Index. We thereafter subtracted the MSCI European Value index from the MSCI Europe Growth index to construct the proxy.
5.5.2.3 The HML proxy on the Scandinavian market
For the Scandinavian market we have chosen the MSCI Nordic value index to represent the stocks with high book-to-market ratio, and then subtracted the MSCI Nordic Growth Index to create the HML proxy for the Scandinavian market.
5.5.3 The Momentum factor (MOM)
The momentum effect was as previously mentioned, first investigated and proven by Jegadeesh and Titman (1993) and adopted as an extra factor to the Fama French 3-factor model by Carhart (1998). The momentum effect explains the behavior of stock returns over a 3 to 12 month period. Jegadeesh and Titman (1993) results indicate that good or bad performance of a particular stock tends to continue over time. Their findings suggest that while performance of single stocks are following a random walk and are highly unpredictable, a portfolio consisting of “winning” stocks with top performance in the past outperform
“loosing” stocks with enough predictability to create arbitrage opportunities (Bodie, Kane, Markus 2009).
When Carhart (1998) conducted his study he constructed the momentum factor by categorizing listed companies based on their financial performance for the past 11 months, lagged 1 month. The top 30% of the best performing companies were pooled into one value weighted portfolio of winning stocks while on the opposite, the bottom 30% of the worst performing companies where gathered into one value weighted portfolio of loosing stocks.
The portfolios were rebalanced every month in order to create a rolling momentum factor.
The construction of the momentum factor is very complicated to replicate. Since the factors have to be rebalanced monthly, enormous amounts of data have to be gathered. For instance, in order to create a momentum factor for the Scandinavian market we would have had to gather monthly data from over 60 companies at the Oslo Børs and 40 companies from the OMX top 40, and then sort out the winners and losers for each of the 60 months.
65 Fortunately, the Kenneth R. French Data Library provides data for the monthly momentum effect on the American market. However, it does not provide this data for the European and the Scandinavian markets. Nevertheless, we have decided to apply the American momentum factor data provided by the Kenneth R. French Data Library to the European and Scandinavian market as well as the American.
This is not the most desirable way to do the study, but given our limited resources we feel this is the most appropriate alternative. It is therefore important to stress that the momentum factor for both the Scandinavian and European market should be analyzed with care, since the results might be misleading given that the numbers we have applied are derived from the American market.
Table 5.2: The table below summarizes the fund data.
Market # Funds Benchmark
Index
Risk-free rate
SMB Factor
HML Factor
MOM Factor
US 46 MSCI US
Broad Market Index
US 3-month Treasury Bills
Kenneth French Library
Kenneth R. French Library
Kenneth R. French Library
European 38 MSCI
Europe Index
Eurozone 3-month Treasury Bill
MSCI European Small Cap - MSCI European Large Cap
MSCI European Growth - MSCI European Value
Kenneth R.
French Library
Scandinavian 35 MSCI
Nordic Index
Eurozone 3-month Treasury Bill
MSCI Nordic Small Cap
- OMX
Nordic 40
MSCI Nordic Growth - MSIC Nordic Value
Kenneth R. French Library