Table 2, page 51, displays the descriptive statistics for factor portfolios over the time period 1993-2010. The results indicate that the market portfolio has the highest monthly returns, in line with the expectations, since the market portfolio holds the highest standard deviation. When comparing the portfolios related to size, book-to-market ratio and momentum, the statistics indicates that an investment strategy tilted towards small stocks would offer a better risk-reward for the investor than begin tilted towards value- or momentum stocks. In fact, by investing in the factor portfolio related to size, SMB, the investor would have 0.50% higher monthly returns and at the same time less risk, compared to an investment in the HML portfolio. Comparing the size and the momentum portfolios shows that the investor would have earned 0.34% more monthly returns by investing in the SMB portfolio relative to the PR1YR portfolio. These portfolios have the same standard deviation, which indicates that the SMB portfolio offered the best risk-reward ratio.
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TABLE 3: DESCRIPTIVE STATISTICS ON FACTOR PORTFOLIOS 1993-1998
Factor portfolio n Mean Std.
RMRF 72 .0104 .061
SMB 72 .0103 .048
HML 72 .0064 .055
PR1YR 72 .0016 .042
Descriptive statistics on the factor portfolios in the time period 1993-1998
Table 3 contains the descriptive statistics over the sub period 1993-1999. The statistics displays some similarities to the total time period. The SMB portfolio had even higher return and lower standard deviation in this time period compared to the total time period, making it an even better strategy. The portfolio related to value stocks, HML, had higher return at almost the same risk level, when comparing to the total time period. However, the return on the HML portfolio increased more relative to both the SMB portfolio and the PR1YR portfolio, indicating that value stocks outperformed both small stocks and momentum stocks. The return on the momentum portfolio was relative low in this period, only showing a monthly mean return of 0.16% while maintain almost the same level of risk. One argument for the relative strong performance of the SMB portfolio and the relative weak performance of the HML portfolio may be related to the business cycle. In the time period 1993 to 1999, the market was moving upwards as a result of the technology bubble, and interest rates were high. As presented in section 4.2, Zhang (2005) argues that value stocks underperform when the market is moving upwards.
TABLE 4: DESCRIPTIVE STATISTICS ON FACTOR PORTFOLIOS 1999-2004
Factor portfolio n Mean Std.
RMRF 72 .0046 .068
SMB 72 .0070 .035
HML 72 .0084 .055
PR1YR 72 .0026 .057
Descriptive statistics on the factor portfolios in the time period 1999-2004
Table 4 displays the descriptive statistic over the time period from 1999 to 2004. This time period contains both a recession and an expansion period. It can be observed that the excess return on the market was only 0.46%, down from 0.104% in the prior time period. This is clearly a result of the high volatility in the market. On interesting result in this time period is the high return on the portfolio related to value stocks, HML. While remaining the same level
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of risk, the HML portfolio has passed the SMB portfolio as the best portfolio in terms of returns. However, when evaluating both risk and return, the SMB portfolio still offers the best risk to return ratio.
TABLE 5: DESCRIPTIVE STATISTICS ON FACTOR PORTFOLIOS 2005-2010
Factor portfolio n Mean Std.
RMRF 72 .0092 .089
SMB 72 .0019 .060
HML 72 -.0067 .061
PR1YR 72 .0088 .046
Descriptive statistics on the factor portfolios in the time period 2005-2010
Table 5 displays the descriptive statistic over the time period from 2005 to 2010. The time period was highly volatile, due the financial crisis in 2008-2009. The volatile market explains the high standard deviation the RMRF factor. The portfolio did deliver monthly excess return of 0.92%, but at the cost of a higher than normal risk profile. Another interesting remark is the negative return on the HML portfolio. This indicates that growth stocks outperformed value stocks in this time period. Following the argument that risk is the reason why these factor portfolios deliver positive returns, the HML factor is associated with risk related financial distress. One can argue that under the financial crisis stock with high book-to-market ratio fell more than stocks with low book-to-market ratio. This supports to the argument of Fama and French (1992) and further Zhang (2006) that value stock underperform relative to growth stocks in times when the price of risk is high. In contrast to prior time periods, the factor portfolio related to momentum offered the best risk-reward ratio in this period, by having the highest return and the lowest standard deviation.
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TABLE 6: DESCRIPTIVE STATISTICS ON SELECTED FUNDS
Fund n Mean Std. Min Max
Skagen Vekst 204 0.0105 0.0549 -‐0.2059 0.1551
ODIN Norge 216 0.0121 0.0700 -‐0.2464 0.2203
Pareto Aksje Norge 111 0.0142 0.0657 -‐0.2664 0.1595
Delphi Norge 198 0.0110 0.0793 -‐0.2553 0.2250 PLUSS Aksje 168 0.0072 0.0716 -‐0.2611 0.1724 Holberg Norge 120 0.0093 0.0712 -‐0.2445 0.1570 Storebrand Norge 216 0.0084 0.0688 -‐0.2938 0.1652 DnBNor Norge (1) 216 0.0073 0.0652 -‐0.2471 0.1563 PLUSS Index 207 0.0070 0.0676 -‐0.2543 0.1681
Carnegie Norge Index 216 0.0073 0.0671 -‐0.2559 0.1671
Equally weighted portfolio. Conventional Funds 216 0.0089 0.0649 -‐0.2570 0.1545
Equally weighted portfolio. Behavioral Funds 216 0.0137 0.0665 -‐0.2409 0.2203
Oslo Stock Exchange Mutual Fund Index 216 0.0081 0.0733 -‐0.2882 0.2016
The table displays the descriptive statistics for all funds. Mean is calculated on excess return level and denoted as monthly excess return. The return of OSEFX is the same as the factor RMRF.
Table 6 displays the descriptive statistics for the behavioral funds, the matching funds, the market benchmark index and the two equally weighted portfolios, on an excess return basis It can be observed that Pareto Aksje Norge has the highest mean excess return over the time period, followed by ODIN Norge and Delphi Norge. Skagen Vekst has lowest standard deviation, followed by Pareto Aksje Norge and ODIN Norge, while Delphi Norge is the fund with the highest standard deviation. The market index, OSEFX, has an average monthly excess return of 0.0081 or 9.72% annualized. The market outperformed only Pluss Aksje of the behavioral funds, but managed to outperform DnBNor Norge (1) and both index funds. The equally weighted portfolios of behavioral funds reports both highest excess return and highest standard deviation of the two equally weighted portfolios. Both portfolios are able to outperform the market, and also have less standard deviation that the market.
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