Asset pricing at the Oslo Stock Exchange. A Source Book. Bernt Arne Ødegaard 14 February 2006
Abstract This paper uses data from the Oslo Stock Exchange in the period 1980 to 2004 to calculate descriptive statistics relevant for asset pricing. We show average return calculations for various market indices and portfolios, including portfolios sorted on size, book/market, momentum and beta. Averages are shown for the whole period and for subperiods. We also illustrate how mean variance portfolios would be constructed using the average returns for the various portfolios.
Chapter 1 Introduction This paper is a source book for people doing empirical asset pricing at the Oslo Stock Exchange (OSE). The prime purpose of the paper is pedagogical. Using data starting in 1980, we describe properties of returns on the Oslo Stock Exchange during the period, for the whole market and for portfolios sorted according to various criteria. The data ends at the end of 2004. The data comes from two sources. All equity returns are from OBI, Oslo BørsInformasjon, the data provider of the Oslo Stock Exchange. Interest date is from Norges Bank. 1
Chapter 2 Data and sample selection The basis for the empirical investigations in this paper is daily observations of all equities traded at the Oslo Stock exchange. The data contains end of day bid and oer prices, as well as observations of the last trade price of the day, if there was any trading. Not all stocks traded at the Oslo Stock Exchange should necessarily be used for empirical asset pricing investigations. In particular stocks which are seldom traded are problematic. In the following calculations we therefore require the stocks to have a minimum number of trading days before they enter the sample. Low valued stocks (penny stocks) are also problematic since they will have very exaggerated returns. We therefore limit a stocks to have a price above NOK 10 before considering it in the sample. A similar requirement considers total value outstanding, which has a lower limit of NOK 1 million. 1 Table 2.1 provides some descriptive statistics for this ltering of the sample. 1 It should be noted that ltering such as this is very common for asset pricing investigations of this sort. See for example Fama and French (1992). 2
Table 2.1 Describing securities sample year number of average with securites number of more than 20 trading days listed trading and price above 10 days and value above 1 mill 1980 96 48 33 33 33 1981 98 60 48 48 48 1982 113 61 60 59 59 1983 124 108 91 90 90 1984 143 131 121 121 121 1985 163 149 150 148 148 1986 173 141 156 144 144 1987 171 138 147 131 131 1988 158 120 128 113 113 1989 175 132 151 136 136 1990 187 128 164 152 152 1991 173 132 153 121 121 1992 171 112 132 96 96 1993 186 140 149 111 111 1994 197 138 166 144 144 1995 196 148 168 148 148 1996 208 160 191 170 170 1997 252 157 229 199 199 1998 269 146 248 183 183 1999 263 152 241 181 181 2000 259 157 239 179 179 2001 247 150 224 139 139 2002 226 147 210 116 116 2003 214 152 195 108 108 2004 179 191 176 121 121 average 186 132 159 128 128 The table provides some descriptive statistics for the sample of equities traded on the Oslo Stock Exchange in the period 1980 to 2004. The rst column lists the year. The second column lists the number of stocks listed during the year. The third column the average number of trading days for all listed stocks. The fourth column lists the number of stocks which traded for more than 20 days. The fth column adds the requirement that the stock did not have a price below NOK 10. The nal column additionally requires an equity market value above 1 mill NOK. 3
Chapter 3 Market Portfolio The rst issue we consider is the evolution of the whole market. One typically wants to know what one would earn if one invested in the Oslo Stock Exchange. However, there are dierent ways to answer that question. If one picks a random stock, one wants to nd the expected return for the typical stock, in which case an equally weighted average is the relevant measure. Alternatively, one can invest in the whole market, in which case a value weighted average is most relevant. Table 3.1 shows monthly average returns, both raw returns and returns in excess of a risk free rate, 1 for the whole period 1980 till 2004 and for various subperiods. An alternative view of the dierence between equally weighted and value weighted indices is shown in gure 3.1, which illustrates the growth of the two indices in the period from 1980. Figure 3.1 The evolution of market indicies 250 200 150 100 50 0 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 vw ew The gures illustrates the growth of two OSE stock indices, one equally weighted and one value weighted, using data starting in 1980. Growth is shown by nding how much one NOK invested in January 1980 would have grown to. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 1 See section 8 for some details about the risk free rates. 4
Table 3.1 Describing market indices at the Oslo Stock Exchange from 1980 Panel A: Monthly returns Period index Dividend Yield Capital Gains mean (std) min med max mean med mean med 19802004 VW 2.01 (6.41) -23.96 2.58 19.58 0.22 0.02 1.37 2.22 EW 1.85 (5.94) -18.67 1.97 19.05 0.19 0.02 1.68 1.78 19801985 VW 2.32 (6.94) -18.62 2.84 19.58 0.24 0.00 1.61 2.44 EW 3.03 (6.23) -13.69 2.13 19.05 0.14 0.00 3.02 1.85 19851989 VW 2.58 (6.83) -23.96 3.32 19.36 0.15 0.00 1.89 3.19 EW 1.62 (5.78) -18.67 2.14 17.03 0.06 0.00 1.57 1.84 19901994 VW 1.38 (6.65) -14.49 2.58 13.35 0.16 0.00 0.65 1.19 EW 1.09 (6.82) -17.29 0.58 15.08 0.13 0.00 0.95 0.48 19951999 VW 2.21 (5.47) -20.10 2.23 16.55 0.23 0.03 1.54 1.79 EW 1.94 (4.94) -17.82 2.31 12.13 0.28 0.05 1.65 1.71 20002004 VW 1.72 (5.76) -13.06 1.63 14.07 0.31 0.08 1.31 1.21 EW 1.47 (5.32) -14.16 1.99 11.69 0.32 0.10 1.14 1.74 Panel B: Monthly excess returns Period index mean (std) min med max 19802004 VW 1.40 (6.32) -25.11 1.83 18.45 EW 1.00 (5.92) -19.81 1.19 17.86 19801985 VW 2.36 (6.56) -13.67 2.32 18.45 EW 2.20 (6.31) -14.79 1.42 17.86 19851989 VW 1.49 (6.85) -25.11 2.21 18.33 EW 0.54 (5.80) -19.81 0.90 16.00 19901994 VW 0.54 (6.64) -15.36 1.75 12.79 EW 0.26 (6.80) -18.15 0.13 14.31 19951999 VW 1.77 (5.47) -20.55 1.82 16.06 EW 1.49 (4.95) -18.27 1.84 11.80 20002004 VW 1.22 (5.80) -13.65 1.15 13.73 EW 0.97 (5.36) -14.76 1.65 11.34 The table describes two indices constructed from Norwegian equity market data, one equally weighted and one value weighted, using data starting in 1980. The rst panel is the percentage monthly returns, the second the percentage monthly excess returns, returns in excess of the risk free rate. are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 5
Chapter 4 Size base portfolios Sorting securities based on the equity value of companies outstanding is a popular investigation, starting with Banz (1981). Internationally, the typical result is that the portfolios of small stocks (ie stocks with a low total equity value) tend to have high returns relative to the portfolio of large stocks. We provide a number of dierent views of size sorted portfolios, starting with a number of tables of averages of raw returns, where we simply split the relevant equities into size based portfolios. We consider ve and ten portfolios. Note that there is no risk adjustment or anything here, we are just listing the raw returns. Also note that these are monthly percentage returns, they are not annualized. The sorting is done on an annual basis. At the beginning of each january, stocks are sorted based on their equity size at the end of last year, and placed in the relevant portfolio. Portfolios are rebalanced every year. Table 4.1 provide descriptive statistics for monthly returns for portfolios of 5 and 10 size sorted portfolios for the whole period. The sample is split into subperiods and shown for the case of ve portfolios in tables 4.2 and 4.3. All the tables show that the smallest portfolio is the one with the highest return, and return is roughly decreasing with size. Oslo Stock Exchange thus has the typical pattern. 6
Table 4.1 Size based portfolios, monthly returns, 19802004 Panel A: 5 EW portfolios Panel B: 5 VW portfolios Panel C: 10 EW portfolios Panel D: 10 VW portfolios 1 (smallest) 3.08 (6.7) -15.3 2.26 30.9 7 23 35 2 1.65 (6.7) -18.7 1.03 31.5 6 23 35 3 1.94 (6.3) -18.0 1.92 30.5 7 23 35 4 1.32 (6.5) -24.8 1.70 21.1 6 23 35 5 1.03 (6.9) -29.0 1.46 19.7 6 23 34 1 (smallest) 4.96 (9.0) -18.8 3.28 56.4 6 22 34 2 3.04 (7.3) -19.5 2.04 36.6 6 23 34 3 3.13 (7.2) -15.3 2.72 48.2 6 23 34 4 2.21 (6.6) -21.3 2.67 21.4 6 22 34 5 1.68 (6.8) -27.8 2.08 22.1 8 25 38 1 (smallest) 3.41 (7.9) -18.1 1.97 46.7 4 12 18 2 2.71 (7.6) -16.7 1.82 38.4 3 11 17 3 1.73 (7.3) -23.8 1.08 38.2 3 12 18 4 1.55 (7.4) -18.1 1.21 31.4 3 12 17 5 2.09 (7.3) -22.5 1.75 42.8 3 11 17 6 1.78 (6.6) -18.4 1.74 27.8 4 11 18 7 1.14 (7.0) -29.2 1.06 21.7 3 11 17 8 1.49 (6.9) -22.4 1.69 25.1 3 11 18 9 1.02 (7.5) -29.6 1.16 22.4 3 11 17 10 1.02 (7.0) -28.5 1.49 20.6 3 11 17 1 (smallest) 5.57 (11.9) -26.7 3.07 100.7 3 11 17 2 4.59 (9.4) -12.4 2.95 66.3 3 11 17 3 2.88 (7.9) -22.7 2.09 43.8 3 11 17 4 3.02 (8.1) -16.9 2.24 38.5 3 11 17 5 3.20 (7.6) -17.8 2.33 35.9 3 11 17 6 2.67 (8.3) -17.5 2.30 79.5 3 11 17 7 2.61 (7.7) -24.3 2.41 42.5 3 11 17 8 2.37 (7.3) -21.4 2.29 29.2 3 11 17 9 2.05 (7.8) -23.3 1.96 24.8 3 11 17 10 1.60 (6.8) -29.2 1.86 21.9 5 15 23 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 7
Table 4.2 5 equally weighted size portfolios split on subperiods Panel A. 1980-1985. Panel B. 1985-1989. Panel C. 1990-1994 Panel D. 1995-1999: Panel E. 2000-2004. 1 (smallest) 5.52 (8.5) -15.3 4.34 30.9 7 11 21 2 2.97 (8.7) -17.0 1.41 31.5 6 11 21 3 3.32 (7.5) -12.9 2.20 30.5 7 11 21 4 2.06 (6.2) -15.4 1.77 16.2 6 11 21 5 1.42 (6.3) -13.7 0.66 19.7 6 11 20 1 (smallest) 2.71 (6.2) -11.5 1.84 19.3 21 23 28 2 0.72 (5.6) -18.7 0.63 14.4 19 24 27 3 1.60 (5.2) -11.9 1.68 20.9 19 24 28 4 1.66 (6.5) -20.3 2.15 21.1 20 23 27 5 1.46 (7.6) -29.0 2.80 17.9 21 23 27 1 (smallest) 2.60 (8.2) -10.0 0.89 29.8 17 23 27 2 1.19 (7.4) -16.9 0.37 25.9 18 23 26 3 0.70 (7.2) -18.0 0.89 17.0 18 21 27 4 0.11 (8.2) -24.8 0.67 14.9 16 21 26 5 0.66 (7.1) -18.9 1.84 11.4 16 22 26 1 (smallest) 2.82 (4.6) -12.2 3.15 17.0 26 32 35 2 1.57 (5.4) -16.8 1.77 15.1 25 32 35 3 2.44 (5.1) -15.7 2.68 15.9 23 31 35 4 1.40 (5.5) -21.3 0.81 13.0 25 32 35 5 1.15 (5.7) -24.1 1.26 14.6 25 30 34 1 (smallest) 1.74 (4.0) -7.2 1.93 13.7 21 24 33 2 1.78 (5.7) -12.3 1.61 13.0 18 24 33 3 1.62 (5.9) -14.3 2.04 13.5 20 24 33 4 1.36 (6.0) -17.0 1.88 13.9 19 24 33 5 0.44 (7.6) -20.7 0.66 17.2 18 23 33 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 8
Table 4.3 5 value weighted size portfolios split on subperiods Panel A. 1980-1985. Panel B. 1985-1989. Panel C. 1990-1994 Panel D. 1995-1999: Panel E. 2000-2004. 1 (smallest) 8.27 (11.8) -13.9 6.08 56.4 6 11 20 2 4.59 (9.7) -19.5 1.78 36.6 6 11 20 3 4.69 (9.7) -13.8 2.89 48.2 6 11 20 4 2.88 (6.8) -13.6 2.43 21.1 6 11 20 5 1.48 (7.9) -22.1 1.25 22.1 8 11 24 1 (smallest) 4.71 (8.3) -18.8 3.34 40.3 20 22 27 2 2.39 (5.8) -16.2 2.43 19.5 19 23 27 3 2.79 (5.6) -11.1 2.44 26.5 19 24 27 4 2.87 (6.5) -19.9 3.21 21.4 20 23 27 5 2.37 (7.5) -27.8 3.15 18.7 22 25 29 1 (smallest) 4.16 (9.5) -9.4 1.49 32.2 17 22 26 2 2.67 (8.3) -14.1 1.36 26.1 18 22 26 3 1.70 (7.4) -14.0 2.26 18.8 18 21 26 4 1.09 (8.1) -21.3 1.28 18.0 16 21 26 5 1.24 (6.7) -14.9 2.44 13.9 16 26 28 1 (smallest) 4.47 (6.7) -11.5 4.21 31.1 25 31 34 2 2.56 (5.7) -15.9 2.31 18.6 24 31 34 3 3.69 (5.9) -15.3 3.38 20.5 23 30 34 4 1.96 (5.3) -18.4 1.83 13.5 23 31 34 5 1.82 (5.5) -22.7 1.70 14.9 29 33 38 1 (smallest) 3.16 (6.6) -8.0 2.34 33.9 20 24 33 2 2.98 (5.9) -11.2 2.63 20.5 18 24 33 3 2.79 (6.5) -13.4 2.54 21.0 20 24 33 4 2.23 (6.1) -13.1 2.89 15.2 18 24 33 5 1.49 (6.0) -13.1 0.92 14.6 20 24 33 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 9
In table 4.4 we subtract the risk free rate from the returns and calculate excess returns. Table 4.4 Excess return for size based portfolios, 19802004 Panel A: 5 portfolios, equally weighted returns Excess 1 (smallest) 2.05 (6.4) -12.7 1.31 29.7 7 23 35 2 0.86 (6.7) -19.8 0.21 30.5 6 23 35 3 1.00 (6.0) -18.9 1.34 19.8 7 23 35 4 0.52 (6.6) -25.7 0.90 20.1 6 23 35 5 0.38 (7.1) -30.1 0.84 18.7 6 23 34 Panel B: 5 portfolios, value weighted returns Excess 1 (smallest) 3.84 (8.4) -20.1 2.22 39.2 6 22 34 2 2.30 (7.3) -20.6 1.27 35.6 6 23 34 3 2.14 (6.5) -15.8 2.10 25.4 6 23 34 4 1.38 (6.6) -22.2 1.73 20.3 6 22 34 5 1.16 (6.6) -29.0 1.50 21.0 8 25 38 Panel C: 10 portfolios, equally weighted returns Excess 1 (smallest) 2.22 (7.3) -15.5 0.99 45.5 4 12 18 2 1.87 (7.5) -17.6 1.00 37.3 3 11 17 3 0.95 (7.2) -24.9 0.21 37.3 3 12 18 4 0.76 (7.3) -18.6 0.64 30.4 3 12 17 5 1.23 (6.8) -23.4 1.19 23.7 3 11 17 6 0.77 (6.3) -18.8 0.95 22.2 4 11 18 7 0.35 (7.0) -30.0 0.43 17.9 3 11 17 8 0.70 (7.0) -22.8 1.03 24.1 3 11 18 9 0.30 (7.7) -30.8 0.73 21.3 3 11 17 10 0.46 (7.0) -29.6 0.98 19.6 3 11 17 Panel D: 10 portfolios, value weighted returns Excess 1 (smallest) 4.10 (9.8) -27.9 2.25 62.7 3 11 17 2 3.72 (9.3) -13.2 1.97 65.2 3 11 17 3 2.22 (7.9) -23.8 1.36 42.9 3 11 17 4 2.20 (7.9) -18.0 1.55 37.4 3 11 17 5 2.49 (7.5) -18.7 1.83 35.2 3 11 17 6 1.68 (6.9) -18.4 1.76 21.2 3 11 17 7 1.56 (7.0) -25.2 1.43 22.7 3 11 17 8 1.46 (7.0) -21.9 1.54 20.7 3 11 17 9 1.37 (7.9) -24.4 1.35 23.7 3 11 17 10 1.08 (6.6) -30.4 1.38 20.8 5 15 23 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 10
A useful way of getting some understanding of the properties of the dierent size portfolios is by investigating how they are mixed in mean-variance optimal portfolios. We use empirical data on monthly returns from a given subperiod to nd means and covariances, and describe the structure of the resulting mean-variance optimized portfolios. We consider the three subperiods 1980-89, 1990-99 and 2000-2004 and show the results in the following three tables. 11
Table 4.5 Mean variance optimal portfolios. 10 portfolios. Using data from 1990 to 1999 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.028 0.072 2 0.026 0.077 3 0.014 0.068 4 0.014 0.073 5 0.021 0.070 6 0.011 0.065 7 0.008 0.075 8 0.007 0.072 9 0.008 0.067 10 0.010 0.066 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.615 0.455 0.549 0.486 0.484 0.585 0.475 0.475 0.435 2 0.615 1 0.642 0.641 0.702 0.747 0.698 0.651 0.593 0.539 3 0.455 0.642 1 0.683 0.696 0.702 0.69 0.609 0.61 0.505 4 0.549 0.641 0.683 1 0.788 0.749 0.715 0.725 0.657 0.668 5 0.486 0.702 0.696 0.788 1 0.781 0.721 0.772 0.687 0.643 6 0.484 0.747 0.702 0.749 0.781 1 0.818 0.832 0.763 0.739 7 0.585 0.698 0.69 0.715 0.721 0.818 1 0.8 0.831 0.793 8 0.475 0.651 0.609 0.725 0.772 0.832 0.8 1 0.867 0.809 9 0.475 0.593 0.61 0.657 0.687 0.763 0.831 0.867 1 0.873 10 0.435 0.539 0.505 0.668 0.643 0.739 0.793 0.809 0.873 1 Panel C: Optimal unconstrained portfolios Asset Expected Return 0.00563 0.00916 0.0127 0.0162 0.0198 0.0233 0.0268 0.0303 0.0339 1 (small) 0.126 0.185 0.245 0.305 0.364 0.424 0.484 0.544 0.603 2-0.349-0.278-0.207-0.136-0.0654 0.00542 0.0762 0.147 0.218 3 0.438 0.415 0.393 0.371 0.349 0.327 0.305 0.283 0.261 4 0.0204-0.0187-0.0577-0.0968-0.136-0.175-0.214-0.253-0.292 5-0.3-0.191-0.0811 0.0284 0.138 0.247 0.357 0.466 0.576 6 0.54 0.499 0.459 0.418 0.378 0.337 0.296 0.256 0.215 7-0.17-0.247-0.324-0.401-0.478-0.555-0.631-0.708-0.785 8 0.13 0.0462-0.0371-0.12-0.204-0.287-0.371-0.454-0.537 9 0.234 0.213 0.192 0.172 0.151 0.13 0.109 0.0887 0.0679 10 0.332 0.375 0.417 0.46 0.503 0.545 0.588 0.631 0.674 Panel D: Optimal short sale restricted portfolios Asset Expected Return 0.00704 0.00969 0.0123 0.015 0.0176 0.0203 0.0229 0.0256 0.0282 1 (small) - - 0.0669 0.201 0.317 0.402 0.475 0.554 1 2 - - - - - 0.0202 0.0789 0.143-3 - 0.166 0.284 0.286 0.251 0.192 0.105 - - 4 - - - - - - - - - 5 - - - - 0.0727 0.175 0.245 0.304-6 - 0.118 0.175 0.144 0.0633 - - - - 7 - - - - - - - - - 8 1 0.149 - - - - - - - 9-0.357 0.121 - - - - - - 10-0.211 0.353 0.369 0.295 0.21 0.0961 - - Panel E: Illustrating portfolio frontiers 0.035 10 portfolios 0.03 0.025 exp return 0.02 0.015 0.01 0.005 0.05 0.055 0.06 0.065 0.07 0.075 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 12 st dev constr
Table 4.6 Mean variance optimal portfolios. 10 portfolios. Using data from 1980 to 1989 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.050 0.097 2 0.032 0.082 3 0.020 0.083 4 0.017 0.080 5 0.023 0.077 6 0.026 0.069 7 0.015 0.067 8 0.022 0.069 9 0.017 0.076 10 0.011 0.073 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.423 0.633 0.562 0.58 0.529 0.461 0.531 0.506 0.405 2 0.423 1 0.546 0.465 0.458 0.445 0.481 0.534 0.475 0.496 3 0.633 0.546 1 0.666 0.665 0.7 0.693 0.675 0.734 0.641 4 0.562 0.465 0.666 1 0.596 0.628 0.632 0.663 0.686 0.543 5 0.58 0.458 0.665 0.596 1 0.607 0.573 0.643 0.593 0.493 6 0.529 0.445 0.7 0.628 0.607 1 0.65 0.678 0.642 0.609 7 0.461 0.481 0.693 0.632 0.573 0.65 1 0.755 0.797 0.694 8 0.531 0.534 0.675 0.663 0.643 0.678 0.755 1 0.807 0.744 9 0.506 0.475 0.734 0.686 0.593 0.642 0.797 0.807 1 0.771 10 0.405 0.496 0.641 0.543 0.493 0.609 0.694 0.744 0.771 1 Panel C: Optimal unconstrained portfolios Asset Expected Return 0.00908 0.0155 0.0219 0.0283 0.0347 0.0411 0.0475 0.0539 0.0604 1 (small) -0.215-0.0892 0.0363 0.162 0.287 0.413 0.538 0.664 0.789 2 0.0563 0.115 0.175 0.234 0.293 0.352 0.411 0.47 0.53 3-0.0921-0.156-0.219-0.283-0.346-0.41-0.473-0.537-0.6 4 0.228 0.148 0.0676-0.0127-0.093-0.173-0.254-0.334-0.414 5 0.246 0.21 0.174 0.137 0.101 0.0644 0.0281-0.00831-0.0447 6 0.122 0.199 0.275 0.352 0.429 0.505 0.582 0.658 0.735 7 0.491 0.423 0.356 0.288 0.221 0.154 0.0861 0.0186-0.0489 8-0.0463 0.00396 0.0542 0.104 0.155 0.205 0.255 0.306 0.356 9-0.221-0.176-0.131-0.0856-0.0405 0.00454 0.0496 0.0947 0.14 10 0.43 0.321 0.212 0.103-0.00578-0.115-0.224-0.332-0.441 Panel D: Optimal short sale restricted portfolios Asset Expected Return 0.0114 0.0162 0.0211 0.026 0.0308 0.0357 0.0406 0.0454 0.0503 1 (small) - - - 0.0903 0.202 0.341 0.534 0.741 1 2-0.0331 0.161 0.207 0.248 0.285 0.283 0.259-3 - - - - - - - - - 4-0.0898 0.0166 - - - - - - 5-0.124 0.134 0.0876 0.0324 - - - - 6-0.0681 0.238 0.286 0.32 0.325 0.183 - - 7-0.372 0.273 0.199 0.0866 - - - - 8 - - 0.0383 0.0917 0.11 0.0498 - - - 9 - - - - - - - - - 10 1 0.313 0.14 0.0384 - - - - - Panel E: Illustrating portfolio frontiers 0.07 10 portfolios 0.06 0.05 exp return 0.04 0.03 0.02 0.01 0 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 13 st dev constr
Table 4.7 Mean variance optimal portfolios. 10 portfolios. Using data from 2000 to 2004 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.014 0.031 2 0.021 0.060 3 0.019 0.062 4 0.017 0.065 5 0.018 0.070 6 0.014 0.058 7 0.012 0.063 8 0.016 0.062 9 0.001 0.086 10 0.008 0.074 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.528 0.45 0.479 0.516 0.552 0.468 0.504 0.41 0.411 2 0.528 1 0.644 0.533 0.605 0.63 0.501 0.588 0.599 0.527 3 0.45 0.644 1 0.618 0.638 0.685 0.601 0.705 0.703 0.745 4 0.479 0.533 0.618 1 0.601 0.736 0.598 0.748 0.78 0.693 5 0.516 0.605 0.638 0.601 1 0.696 0.816 0.716 0.786 0.737 6 0.552 0.63 0.685 0.736 0.696 1 0.784 0.759 0.781 0.771 7 0.468 0.501 0.601 0.598 0.816 0.784 1 0.801 0.772 0.769 8 0.504 0.588 0.705 0.748 0.716 0.759 0.801 1 0.81 0.781 9 0.41 0.599 0.703 0.78 0.786 0.781 0.772 0.81 1 0.794 10 0.411 0.527 0.745 0.693 0.737 0.771 0.769 0.781 0.794 1 Panel C: Optimal unconstrained portfolios Asset Expected Return - 0.00358 0.00672 0.00986 0.013 0.0161 0.0193 0.0224 0.0256 1 (small) 1.43 1.32 1.22 1.11 1.01 0.903 0.798 0.694 0.589 2-0.101-0.075-0.0489-0.0227 0.00344 0.0296 0.0558 0.0819 0.108 3-0.0883-0.0459-0.00353 0.0389 0.0812 0.124 0.166 0.208 0.251 4-0.207-0.146-0.0854-0.0244 0.0366 0.0976 0.159 0.22 0.281 5-0.49-0.405-0.321-0.237-0.153-0.0686 0.0156 0.0998 0.184 6-0.239-0.203-0.167-0.131-0.0946-0.0584-0.0223 0.0139 0.05 7 0.253 0.233 0.213 0.194 0.174 0.154 0.134 0.114 0.0942 8-0.293-0.237-0.18-0.124-0.0673-0.0108 0.0457 0.102 0.159 9 0.513 0.38 0.248 0.116-0.0165-0.149-0.281-0.413-0.546 10 0.227 0.178 0.128 0.0783 0.0287-0.0209-0.0706-0.12-0.17 Panel D: Optimal short sale restricted portfolios Asset Expected Return - 0.00314 0.00574 0.00833 0.0109 0.0135 0.0161 0.0187 0.0213 1 (small) - 0.199 0.398 0.597 0.797 0.985 0.643 0.293-2 - - - - - - 0.266 0.573 1 3 - - - - - - 0.0908 0.134-4 - - - - - - - - - 5 - - - - - - - - - 6 - - - - - - - - - 7 - - - - - 0.00761 - - - 8 - - - - - - - - - 9 1 0.801 0.602 0.403 0.203 - - - - 10 - - - - - 0.00772 - - - Panel E: Illustrating portfolio frontiers 0.03 10 portfolios 0.025 0.02 exp return 0.015 0.01 0.005 0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 14 st dev constr
Table 4.8 shows estimated Sharpe Ratios for the size based portfolios. Table 4.8 Sharpe Ratios, 10 EW Size portfolios Panel A: 5 EW portfolios Panel B: 5 VW portfolios Panel C: 10 EW portfolios 1 (small) 2 3 4 5 (large) 19801984 0.49 0.29 0.30 0.20 0.23 19851989 0.26-0.06 0.10 0.09 0.05 19901994 0.21 0.05-0.02-0.09-0.02 19951999 0.51 0.21 0.39 0.18 0.12 20002004 0.31 0.22 0.19 0.14-0.01 19801989 0.35 0.10 0.18 0.13 0.11 19901999 0.31 0.11 0.15 0.02 0.04 19802004 0.32 0.13 0.16 0.08 0.05 1 (small) 2 3 4 5 (large) 19801984 0.64 0.45 0.45 0.27 0.31 19851989 0.44 0.23 0.31 0.28 0.17 19901994 0.35 0.22 0.12 0.03 0.06 19951999 0.60 0.37 0.55 0.29 0.25 20002004 0.40 0.42 0.35 0.28 0.17 19801989 0.51 0.32 0.36 0.28 0.22 19901999 0.45 0.28 0.30 0.13 0.14 19802004 0.46 0.32 0.33 0.21 0.18 1 (small) 2 3 4 5 6 7 8 9 10 (large) 19801984 0.49 0.34 0.33 0.20 0.33 0.20 0.19 0.18 0.31 0.10 19851989 0.26 0.18-0.06-0.07 0.03 0.13-0.01 0.18 0.01 0.09 19901994 0.18 0.21 0.07 0.02-0.01-0.03-0.04-0.14-0.01-0.04 19951999 0.57 0.33 0.18 0.22 0.49 0.23 0.12 0.21 0.07 0.17 20002004 0.28 0.27 0.22 0.18 0.18 0.16 0.10 0.18-0.05 0.05 19801989 0.35 0.24 0.11 0.07 0.15 0.16 0.06 0.18 0.12 0.09 19901999 0.30 0.25 0.11 0.10 0.20 0.08 0.02 0.01 0.02 0.05 19802004 0.30 0.25 0.13 0.10 0.18 0.12 0.05 0.10 0.04 0.07 Panel C: 10 VW portfolios 1 (small) 2 3 4 5 6 7 8 9 10 (large) 19801984 0.58 0.51 0.50 0.33 0.48 0.35 0.26 0.38 0.34 0.23 19851989 0.47 0.34 0.14 0.26 0.28 0.16 0.28 0.30 0.16 0.16 19901994 0.33 0.32 0.16 0.22 0.16 0.05 0.10-0.01 0.05 0.07 19951999 0.58 0.51 0.38 0.33 0.55 0.43 0.31 0.28 0.24 0.24 20002004 0.41 0.42 0.36 0.35 0.29 0.35 0.25 0.27 0.16 0.16 19801989 0.50 0.40 0.29 0.27 0.35 0.23 0.27 0.33 0.23 0.19 19901999 0.41 0.40 0.24 0.26 0.35 0.21 0.17 0.10 0.13 0.15 19802004 0.42 0.40 0.28 0.28 0.33 0.25 0.22 0.21 0.17 0.16 The table shows estimated Sharpe ratios for dierent portfolios and sample periods, using monthly data to do estimation. In each table, the rst column lists the sample period used. Each of the following columns lists the Sharpe Ratio for a given portfolio. The Sharpe Ratio is calculated as average( r p r f )/σ( r p r f ), where r p is the realized portfolio return, and r f the risk free rate. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 15
Chapter 5 Book to market based portfolios Another way of sorting securities that has received a lot of attention is a sorting based on the book value vs market value of equity, or the B/M ratio. We show the same analyses as was done for size based portfolios in section 4. The sorting procedure is again performed annually. We sort stocks based on the B/M ratio calculated using the book value and market of the company's equity at the last yearend. Stocks are then placed in the relevant portfolio. Table 5.1 provide descriptive statistics for monthly returns for portfolios of sizes 5 and 10 for the whole period, which is split in subperiod for ve portfolios in tables 5.2 and 5.3. Excess returns are shown in table 5.4 and Sharpe Ratios in 5.8. 16
Table 5.1 of B/M based portfolios 19802004 Panel A: 5 EW portfolios Panel B: 5 VW portfolios Panel C: 10 EW portfolios Panel D: 10 VW portfolios 1 (smallest) 1.98 (8.2) -24.6 1.70 44.3 5 21 34 2 1.25 (6.4) -22.7 1.59 24.0 5 20 34 3 1.90 (6.6) -21.1 1.73 34.3 5 20 33 4 1.98 (7.1) -24.0 2.03 28.0 5 20 34 5 2.58 (7.2) -22.5 1.88 33.1 5 20 33 1 (smallest) 2.15 (8.1) -29.4 1.96 55.0 4 20 33 2 1.57 (7.5) -28.8 1.63 25.4 5 20 33 3 2.26 (7.6) -25.0 2.07 26.3 5 20 33 4 2.42 (8.4) -24.6 2.09 31.1 5 20 33 5 3.00 (8.2) -26.0 2.65 29.1 6 22 36 1 (smallest) 2.27 (9.9) -24.2 1.54 64.3 2 11 17 2 1.77 (8.5) -26.3 1.73 45.1 3 10 17 3 1.52 (7.2) -24.1 1.41 24.8 2 10 17 4 0.94 (7.0) -24.0 1.37 27.6 2 10 17 5 1.84 (6.9) -24.1 1.59 23.7 2 10 16 6 1.99 (8.0) -18.4 1.64 66.2 3 10 17 7 1.99 (7.9) -22.4 1.99 46.7 3 10 17 8 1.98 (8.1) -44.1 2.47 33.3 2 10 17 9 2.47 (7.5) -20.4 1.85 29.7 3 11 17 10 2.67 (8.5) -24.7 1.74 38.2 2 10 16 1 (smallest) 2.65 (9.0) -25.9 2.48 66.3 1 10 16 2 2.72 (10.6) -33.1 2.14 67.8 2 9 16 3 1.40 (8.6) -33.8 1.46 32.1 2 10 16 4 1.60 (7.9) -27.5 1.41 23.2 2 10 16 5 1.85 (8.1) -25.2 1.74 30.2 2 10 16 6 2.16 (9.2) -32.2 1.58 47.0 2 10 16 7 2.63 (8.6) -21.2 2.87 31.2 2 9 16 8 2.43 (9.1) -32.2 2.65 32.9 2 10 16 9 2.43 (9.9) -27.7 1.67 46.1 2 10 16 10 3.78 (9.4) -28.1 2.61 39.0 6 14 24 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 17
Table 5.2 5 equally weighted B/M portfolios, subperiods Panel A. 1980-1985. Panel B. 1985-1989. Panel C. 1990-1994 Panel D. 1995-1999: Panel E. 2000-2004. 1 (smallest) 4.11 (11.0) -19.6 2.36 44.3 5 9 19 2 2.63 (7.6) -14.0 1.59 24.0 5 8 18 3 2.79 (6.4) -14.1 1.99 18.1 5 9 18 4 3.24 (8.2) -13.9 2.23 28.0 5 8 18 5 4.51 (7.8) -19.8 3.69 24.1 5 8 18 1 (smallest) 1.72 (6.4) -18.9 1.75 17.9 16 20 22 2 1.09 (6.4) -22.7 1.75 15.6 16 19 21 3 2.15 (7.9) -21.1 2.39 34.3 15 20 22 4 2.13 (6.7) -18.0 2.37 19.8 16 20 21 5 2.03 (7.1) -20.4 2.16 25.6 15 19 21 1 (smallest) 0.64 (5.5) -10.9-0.35 16.9 13 19 22 2 0.20 (6.5) -16.9 1.21 14.7 15 19 22 3 0.99 (7.1) -20.0 0.63 18.7 14 19 21 4 0.90 (9.0) -24.0 0.41 25.3 12 19 22 5 2.91 (10.1) -22.5 1.06 33.1 14 19 21 1 (smallest) 2.62 (7.4) -24.6 1.95 20.5 23 26 34 2 1.24 (5.9) -20.7 2.08 15.7 20 26 34 3 2.02 (5.0) -15.9 1.80 12.0 22 26 33 4 1.41 (5.1) -19.3 2.07 10.1 21 26 34 5 1.88 (4.8) -14.9 1.96 11.8 20 26 33 1 (smallest) 0.82 (9.2) -21.2 0.61 38.3 21 24 31 2 1.07 (5.2) -12.8 0.11 10.0 18 22 31 3 1.57 (5.9) -15.6 1.66 18.3 19 23 31 4 2.22 (5.7) -13.9 2.33 16.0 18 22 31 5 1.59 (3.9) -8.5 1.49 11.8 19 23 31 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 18
Table 5.3 5 value weighted B/M portfolios, subperiods Panel A. 1980-1985. Panel B. 1985-1989. Panel C. 1990-1994 Panel D. 1995-1999: Panel E. 2000-2004. 1 (smallest) 2.76 (11.3) -28.2 1.88 55.0 4 8 18 2 1.54 (8.6) -14.3 0.61 25.4 5 8 18 3 2.92 (7.9) -14.7 1.83 26.3 5 8 18 4 3.07 (8.6) -13.1 2.39 31.1 5 8 18 5 4.14 (7.9) -15.4 2.85 29.1 6 10 19 1 (smallest) 1.94 (7.5) -29.4 2.25 20.1 15 18 21 2 2.03 (8.0) -28.8 2.86 20.7 16 17 21 3 2.89 (8.7) -25.0 3.30 25.9 15 19 21 4 3.21 (8.7) -18.3 2.44 25.2 14 19 21 5 3.50 (8.9) -21.9 3.73 27.3 16 22 24 1 (smallest) 1.29 (6.1) -13.0 1.26 16.1 12 19 21 2 1.46 (7.4) -20.1 2.15 18.6 14 18 21 3 1.80 (8.3) -23.0 2.03 19.6 14 19 21 4 1.43 (10.0) -24.6 0.86 26.5 11 19 21 5 2.66 (10.3) -26.0 2.46 25.4 17 20 25 1 (smallest) 2.80 (6.8) -21.7 3.01 22.4 22 26 33 2 1.64 (6.9) -25.7 1.94 13.2 20 26 33 3 2.31 (6.2) -19.6 2.81 18.4 21 26 33 4 2.00 (6.2) -18.8 2.59 17.5 21 26 33 5 2.07 (5.8) -15.0 1.72 16.2 20 26 36 1 (smallest) 1.98 (7.7) -15.3 1.90 38.0 20 23 31 2 1.20 (6.4) -12.4 0.97 15.9 18 22 31 3 1.36 (6.7) -19.3 1.61 14.3 19 23 31 4 2.41 (8.1) -16.5 1.39 18.8 17 22 31 5 2.65 (7.1) -11.3 2.53 18.7 21 24 31 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 19
Table 5.4 Excess returns for B/M based portfolios, 19802004 Panel A: 5 portfolios, equally weighted returns Excess 1 (smallest) 0.88 (7.4) -25.1 0.62 37.8 5 21 34 2 0.49 (6.4) -23.8 0.77 22.8 5 20 34 3 1.07 (6.5) -22.3 1.07 33.2 5 20 33 4 1.20 (7.0) -24.8 1.27 26.8 5 20 34 5 1.75 (7.2) -23.4 1.31 32.3 5 20 33 Panel B: 5 portfolios, value weighted returns Excess 1 (smallest) 1.46 (7.7) -30.5 1.33 53.9 4 20 33 2 1.11 (7.5) -30.0 1.49 24.3 5 20 33 3 1.37 (7.6) -26.2 1.45 25.1 5 20 33 4 1.78 (8.5) -25.4 1.50 29.9 5 20 33 5 2.25 (8.3) -26.9 1.92 28.1 6 22 36 Panel C: 10 portfolios, equally weighted returns Excess 1 (smallest) 0.89 (8.1) -24.8 0.76 32.8 2 11 17 2 0.90 (8.2) -26.8 0.73 44.6 3 10 17 3 0.70 (7.2) -24.6 0.59 23.8 2 10 17 4 0.30 (6.9) -25.2 0.55 26.4 2 10 17 5 0.95 (6.8) -25.3 0.69 22.0 2 10 16 6 1.19 (8.0) -19.3 0.95 65.1 3 10 17 7 1.16 (7.3) -23.2 1.18 28.8 3 10 17 8 1.23 (8.2) -45.0 1.50 32.1 2 10 17 9 1.63 (7.6) -21.2 1.06 28.9 3 11 17 10 1.86 (8.4) -25.6 0.86 36.2 2 10 16 Panel D: 10 portfolios, value weighted returns Excess 1 (smallest) 2.07 (8.9) -27.1 1.59 65.3 1 10 16 2 0.90 (8.2) -34.3 1.18 36.3 2 9 16 3 0.96 (8.3) -34.9 0.88 31.0 2 10 16 4 0.99 (7.9) -28.6 1.14 21.9 2 10 16 5 1.19 (7.6) -26.1 1.28 26.2 2 10 16 6 1.28 (9.3) -32.8 0.89 46.0 2 10 16 7 1.82 (8.7) -22.2 1.93 30.4 2 9 16 8 1.76 (9.2) -33.0 1.94 31.7 2 10 16 9 1.82 (9.7) -26.3 1.07 45.0 2 10 16 10 3.08 (9.6) -29.0 1.76 38.2 6 14 24 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 20
Table 5.5 Mean variance optimal portfolios. 10 portfolios. Using data from 1980 to 1989 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.037 0.120 2 0.023 0.090 3 0.024 0.081 4 0.012 0.079 5 0.027 0.075 6 0.023 0.093 7 0.026 0.091 8 0.028 0.079 9 0.032 0.075 10 0.033 0.094 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.511 0.444 0.388 0.423 0.347 0.565 0.411 0.415 0.355 2 0.511 1 0.681 0.697 0.606 0.534 0.607 0.726 0.598 0.558 3 0.444 0.681 1 0.555 0.616 0.613 0.622 0.726 0.675 0.648 4 0.388 0.697 0.555 1 0.517 0.557 0.564 0.66 0.551 0.545 5 0.423 0.606 0.616 0.517 1 0.477 0.455 0.593 0.55 0.49 6 0.347 0.534 0.613 0.557 0.477 1 0.539 0.618 0.5 0.48 7 0.565 0.607 0.622 0.564 0.455 0.539 1 0.595 0.556 0.544 8 0.411 0.726 0.726 0.66 0.593 0.618 0.595 1 0.696 0.692 9 0.415 0.598 0.675 0.551 0.55 0.5 0.556 0.696 1 0.618 10 0.355 0.558 0.648 0.545 0.49 0.48 0.544 0.692 0.618 1 Panel C: Optimal unconstrained portfolios Asset Expected Return 0.00944 0.0139 0.0183 0.0227 0.0271 0.0315 0.036 0.0404 0.0448 1 (small) -0.141-0.0951-0.0491-0.00311 0.0429 0.0889 0.135 0.181 0.227 2-0.147-0.147-0.147-0.147-0.147-0.147-0.147-0.147-0.146 3 0.342 0.258 0.174 0.0899 0.00597-0.0779-0.162-0.246-0.33 4 0.928 0.738 0.549 0.359 0.169-0.0206-0.21-0.4-0.59 5 0.268 0.29 0.312 0.334 0.357 0.379 0.401 0.423 0.445 6 0.0308 0.0359 0.0409 0.046 0.0511 0.0561 0.0612 0.0662 0.0713 7 0.0998 0.0934 0.0869 0.0805 0.0741 0.0677 0.0613 0.0548 0.0484 8-0.13-0.0733-0.0166 0.0401 0.0968 0.153 0.21 0.267 0.324 9-0.0161 0.0714 0.159 0.246 0.334 0.422 0.509 0.597 0.684 10-0.233-0.171-0.109-0.0462 0.0162 0.0786 0.141 0.203 0.266 Panel D: Optimal short sale restricted portfolios Asset Expected Return 0.0118 0.015 0.0182 0.0214 0.0246 0.0278 0.031 0.0341 0.0373 1 (small) - - - - - 0.0327 0.104 0.376 1 2 - - - - - - - - - 3-0.0966 0.116 0.0707 0.0204 - - - - 4 1 0.774 0.565 0.4 0.235 0.0867 - - - 5-0.128 0.242 0.286 0.328 0.338 0.307 - - 6-0.00122 0.0347 0.0441 0.0534 0.0509 0.00234 - - 7 - - 0.00569 0.0361 0.0676 0.0597 - - - 8 - - - - 0.011 0.0547 0.0448 - - 9 - - 0.0369 0.163 0.285 0.351 0.445 0.438-10 - - - - - 0.0261 0.0975 0.186 - Panel E: Illustrating portfolio frontiers 0.045 10 portfolios 0.04 0.035 0.03 exp return 0.025 0.02 0.015 0.01 0.005 0.06 0.07 0.08 0.09 0.1 0.11 0.12 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 21 st dev constr
Table 5.6 Mean variance optimal portfolios. 10 portfolios. Using data from 1990 to 1999 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.017 0.074 2 0.016 0.072 3 0.008 0.067 4 0.007 0.066 5 0.013 0.063 6 0.017 0.071 7 0.014 0.069 8 0.009 0.092 9 0.022 0.084 10 0.026 0.091 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.66 0.647 0.538 0.562 0.635 0.515 0.451 0.412 0.285 2 0.66 1 0.76 0.649 0.708 0.632 0.685 0.686 0.635 0.426 3 0.647 0.76 1 0.743 0.692 0.725 0.713 0.636 0.634 0.516 4 0.538 0.649 0.743 1 0.686 0.729 0.64 0.676 0.71 0.437 5 0.562 0.708 0.692 0.686 1 0.705 0.617 0.661 0.651 0.469 6 0.635 0.632 0.725 0.729 0.705 1 0.66 0.708 0.656 0.424 7 0.515 0.685 0.713 0.64 0.617 0.66 1 0.68 0.743 0.466 8 0.451 0.686 0.636 0.676 0.661 0.708 0.68 1 0.677 0.543 9 0.412 0.635 0.634 0.71 0.651 0.656 0.743 0.677 1 0.631 10 0.285 0.426 0.516 0.437 0.469 0.424 0.466 0.543 0.631 1 Panel C: Optimal unconstrained portfolios Asset Expected Return 0.00541 0.00857 0.0117 0.0149 0.018 0.0212 0.0244 0.0275 0.0307 1 (small) 0.0529 0.0782 0.103 0.129 0.154 0.179 0.204 0.23 0.255 2-0.0888-0.0228 0.0432 0.109 0.175 0.241 0.307 0.373 0.439 3 0.178 0.0659-0.0457-0.157-0.269-0.38-0.492-0.604-0.715 4 0.607 0.52 0.433 0.346 0.259 0.172 0.0854-0.00157-0.0885 5 0.444 0.417 0.389 0.362 0.334 0.307 0.279 0.252 0.224 6-0.149-0.0578 0.0333 0.124 0.215 0.307 0.398 0.489 0.58 7 0.393 0.386 0.379 0.372 0.365 0.357 0.35 0.343 0.336 8-0.0939-0.151-0.209-0.267-0.324-0.382-0.439-0.497-0.554 9-0.436-0.374-0.312-0.251-0.189-0.127-0.0647-0.00273 0.0592 10 0.0927 0.139 0.186 0.232 0.279 0.325 0.372 0.418 0.465 Panel D: Optimal short sale restricted portfolios Asset Expected Return 0.00677 0.00912 0.0115 0.0138 0.0162 0.0185 0.0209 0.0232 0.0256 1 (small) - 0.0147 0.125 0.197 0.247 0.292 0.348 0.191-2 - - - - - 0.00707 0.00262 - - 3-0.263 0.106 - - - - - - 4 1 0.414 0.295 0.21 0.0531 - - - - 5-0.263 0.315 0.321 0.302 0.16 - - - 6 - - - - 0.0437 0.127 0.154 - - 7-0.0454 0.141 0.178 0.183 0.119 - - - 8 - - - - - - - - - 9 - - - - - 0.0173 0.145 0.235-10 - - 0.0196 0.0944 0.172 0.278 0.35 0.573 1 Panel E: Illustrating portfolio frontiers 0.035 10 portfolios 0.03 0.025 exp return 0.02 0.015 0.01 0.005 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 22 st dev constr
Table 5.7 Mean variance optimal portfolios. 10 portfolios. Using data from 2000 to 2004 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.005 0.093 2 0.012 0.098 3 0.012 0.059 4 0.010 0.056 5 0.012 0.067 6 0.019 0.064 7 0.020 0.069 8 0.024 0.055 9 0.015 0.048 10 0.017 0.042 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.863 0.641 0.44 0.683 0.436 0.577 0.471 0.498 0.421 2 0.863 1 0.65 0.455 0.664 0.445 0.514 0.441 0.519 0.449 3 0.641 0.65 1 0.654 0.767 0.542 0.666 0.6 0.519 0.612 4 0.44 0.455 0.654 1 0.683 0.619 0.67 0.675 0.55 0.611 5 0.683 0.664 0.767 0.683 1 0.604 0.727 0.612 0.541 0.503 6 0.436 0.445 0.542 0.619 0.604 1 0.608 0.677 0.628 0.584 7 0.577 0.514 0.666 0.67 0.727 0.608 1 0.719 0.582 0.548 8 0.471 0.441 0.6 0.675 0.612 0.677 0.719 1 0.68 0.663 9 0.498 0.519 0.519 0.55 0.541 0.628 0.582 0.68 1 0.491 10 0.421 0.449 0.612 0.611 0.503 0.584 0.548 0.663 0.491 1 Panel C: Optimal unconstrained portfolios Asset Expected Return 0.00371 0.00692 0.0101 0.0133 0.0165 0.0197 0.023 0.0262 0.0294 1 (small) 0.313 0.225 0.138 0.0498-0.0379-0.126-0.214-0.301-0.389 2-0.349-0.284-0.22-0.155-0.0911-0.0267 0.0377 0.102 0.166 3 0.16 0.129 0.0989 0.0685 0.0381 0.00772-0.0227-0.0531-0.0835 4 0.414 0.299 0.183 0.0674-0.0483-0.164-0.28-0.395-0.511 5 0.109 0.107 0.105 0.102 0.1 0.098 0.0958 0.0935 0.0913 6-0.151-0.133-0.115-0.0969-0.0789-0.061-0.043-0.0251-0.00711 7-0.235-0.19-0.144-0.0987-0.0532-0.00774 0.0377 0.0832 0.129 8-0.599-0.443-0.287-0.131 0.0243 0.18 0.336 0.491 0.647 9 0.684 0.625 0.566 0.507 0.448 0.39 0.331 0.272 0.213 10 0.653 0.664 0.676 0.687 0.698 0.71 0.721 0.732 0.744 Panel D: Optimal short sale restricted portfolios Asset Expected Return 0.00464 0.00712 0.0096 0.0121 0.0146 0.017 0.0195 0.022 0.0245 1 (small) 1 0.53 0.215 0.107 0.0108 - - - - 2 - - - - - - - - - 3 - - 0.0224 0.0448 0.0479 - - - - 4-0.47 0.604 0.398 0.195 - - - - 5 - - - - - - - - - 6 - - - - - - - - - 7 - - - - - - - - - 8 - - - - - 0.0801 0.36 0.663 1 9 - - 0.158 0.261 0.333 0.293 0.11 - - 10 - - - 0.189 0.413 0.627 0.53 0.337 - Panel E: Illustrating portfolio frontiers 0.03 10 portfolios 0.025 0.02 exp return 0.015 0.01 0.005 0 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 23 st dev constr
Table 5.8 Sharpe Ratios, 10 B/M portfolios, monthly returns 1 (small) 2 3 4 5 6 7 8 9 10 (large) 19801984 0.28 0.14 0.29 0.31 0.28 0.25 0.38 0.30 0.35 0.56 19851989 0.09 0.11 0.09-0.09 0.17 0.08 0.08 0.21 0.21 0.04 19901994-0.10 0.03-0.05-0.12 0.00 0.03 0.04-0.01 0.15 0.22 19951999 0.31 0.23 0.09 0.17 0.25 0.32 0.24 0.12 0.28 0.24 20002004-0.00 0.07 0.11 0.09 0.11 0.22 0.21 0.35 0.21 0.29 19801989 0.16 0.12 0.17 0.07 0.20 0.12 0.18 0.24 0.27 0.23 19901999 0.14 0.13 0.02 0.01 0.10 0.15 0.11 0.03 0.19 0.21 19802004 0.11 0.11 0.10 0.04 0.14 0.15 0.16 0.15 0.22 0.22 The table shows estimated Sharpe ratios for dierent portfolios and sample periods, using monthly data to do estimation. In each table, the rst column lists the sample period used. Each of the following columns lists the Sharpe Ratio for a given portfolio. The Sharpe Ratio is calculated as average( r p r f )/σ( r p r f ), where r p is the realized portfolio return, and r f the risk free rate. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 24
Chapter 6 Momentum based portfolios A third popular sorting criterion is momentum. Stocks are at the beginning of each year sorted based on the stock return over the last 12 month period. We show the same results as was shown for the other two cases below. 25
Table 6.1 Momemtum portfolios 19802004 Panel A: 5 EW portfolios Panel B: 5 VW portfolios Panel C: 10 EW portfolios Panel D: 10 VW portfolios 1 (smallest) 1.93 (8.0) -26.8 1.24 33.7 7 21 32 2 1.74 (6.1) -19.8 1.49 18.7 6 21 32 3 1.53 (6.0) -21.5 1.42 30.0 7 20 32 4 1.62 (5.9) -20.9 1.88 20.8 6 21 32 5 2.27 (8.1) -19.7 1.55 51.2 6 21 32 1 (smallest) 2.20 (9.1) -31.0 1.71 32.9 6 21 32 2 2.21 (7.0) -25.0 2.05 23.2 6 21 32 3 1.71 (6.9) -27.5 1.32 24.0 6 20 32 4 1.79 (7.8) -26.6 2.12 46.4 6 20 32 5 2.59 (8.2) -21.7 2.30 49.0 8 23 32 1 (smallest) 2.31 (9.9) -24.5 1.51 45.9 4 11 16 2 1.52 (7.6) -29.4 0.78 33.0 3 10 16 3 1.75 (6.8) -23.5 1.55 25.6 3 11 16 4 1.76 (6.7) -19.9 1.59 20.2 3 11 16 5 1.65 (6.8) -21.5 1.02 50.2 3 10 16 6 1.40 (6.3) -23.6 1.20 28.0 4 10 16 7 1.60 (6.3) -19.3 1.50 25.6 3 11 16 8 1.64 (6.4) -22.5 1.92 26.0 3 10 16 9 2.23 (8.5) -25.9 1.39 49.4 3 11 16 10 2.31 (9.2) -21.7 1.41 53.9 3 10 16 1 (smallest) 2.95 (11.8) -39.9 1.82 49.8 3 10 16 2 1.83 (8.3) -22.8 1.11 28.2 3 10 16 3 2.30 (7.8) -24.6 1.98 27.9 3 10 16 4 1.99 (7.7) -25.5 2.10 26.5 3 10 16 5 1.84 (7.2) -23.6 1.56 35.4 3 10 16 6 1.62 (8.0) -30.5 1.25 45.8 3 10 16 7 1.52 (7.6) -27.0 1.52 37.8 3 10 16 8 1.89 (8.5) -27.4 1.75 66.8 3 10 16 9 2.01 (7.3) -24.9 2.34 29.0 3 10 16 10 2.94 (9.6) -23.3 2.43 58.1 5 14 20 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 26
Table 6.2 5 equally weighted momentum portfolios, subperiods Panel A. 1980-1985. Panel B. 1985-1989. Panel C. 1990-1994 Panel D. 1995-1999: Panel E. 2000-2004. 1 (smallest) 2.53 (7.9) -11.9 1.15 25.0 7 11 19 2 2.87 (6.0) -14.1 1.32 18.6 6 10 19 3 2.82 (5.8) -9.4 2.05 24.4 7 11 19 4 2.54 (7.3) -16.1 3.37 18.2 6 10 19 5 5.65 (11.5) -19.7 2.54 51.2 6 10 18 1 (smallest) 1.14 (6.9) -18.8 0.48 20.9 17 21 25 2 1.41 (5.9) -19.8 2.46 18.7 20 22 25 3 1.39 (7.0) -20.8 1.77 30.0 19 21 24 4 2.64 (5.5) -13.6 2.89 20.8 18 20 25 5 1.79 (6.4) -19.7 1.76 19.0 19 22 24 1 (smallest) 2.42 (10.5) -26.8 1.56 33.7 14 18 23 2 1.19 (7.5) -17.4 0.06 15.9 17 20 22 3 0.80 (7.2) -21.5 0.05 17.8 16 19 23 4 0.36 (6.6) -13.1 0.33 16.2 17 20 22 5 0.65 (6.6) -12.4 0.77 17.1 15 19 22 1 (smallest) 2.07 (5.6) -16.2 2.36 14.7 20 27 31 2 1.72 (4.9) -17.8 1.54 15.9 23 25 31 3 1.51 (4.6) -14.5 1.59 12.1 22 27 31 4 1.57 (4.7) -20.9 1.88 10.2 23 26 31 5 2.14 (6.2) -19.0 1.95 24.0 23 26 31 1 (smallest) 1.38 (7.9) -16.9 1.45 18.8 20 24 32 2 1.49 (5.6) -16.5 1.52 13.1 18 22 32 3 1.01 (4.0) -7.8 1.21 11.8 17 22 32 4 0.83 (3.9) -11.0 0.99 8.6 20 22 32 5 0.83 (7.7) -17.0 0.37 22.0 19 21 32 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 27
Table 6.3 5 value weighted momentum portfolios, subperiods Panel A. 1980-1985. Panel B. 1985-1989. Panel C. 1990-1994 Panel D. 1995-1999: Panel E. 2000-2004. 1 (smallest) 1.53 (8.6) -13.8 1.30 25.7 6 10 18 2 2.59 (5.6) -12.8 1.96 22.5 6 10 18 3 2.20 (5.3) -7.5 1.11 24.0 6 10 18 4 2.69 (10.6) -25.7 0.52 46.4 6 10 18 5 5.60 (10.8) -19.7 3.51 49.0 8 12 22 1 (smallest) 2.34 (8.2) -19.0 1.68 30.1 17 21 24 2 2.60 (7.4) -25.0 2.85 23.2 18 21 24 3 2.28 (8.0) -27.5 2.94 23.9 19 21 24 4 3.27 (7.6) -22.5 3.69 17.3 16 20 24 5 2.17 (7.1) -21.7 2.66 18.9 19 23 27 1 (smallest) 3.03 (11.0) -21.3 1.80 32.2 14 17 22 2 2.11 (8.5) -16.4 1.69 16.7 15 18 22 3 1.74 (7.4) -19.6 1.01 18.9 15 18 22 4-0.16 (7.5) -16.9 1.64 12.7 16 19 22 5 1.21 (7.0) -12.9 1.41 20.9 19 22 23 1 (smallest) 2.46 (5.9) -10.5 2.18 18.2 20 26 31 2 1.75 (6.0) -18.1 1.81 16.0 22 25 31 3 1.28 (6.5) -21.5 1.25 21.4 22 26 31 4 2.08 (6.2) -26.6 2.02 17.3 23 26 31 5 2.28 (6.4) -21.6 3.19 20.7 23 28 31 1 (smallest) 1.52 (11.3) -31.0 2.44 32.9 20 22 32 2 1.97 (7.1) -15.6 1.70 17.9 18 22 32 3 0.91 (6.9) -13.0 0.49 20.9 17 22 32 4 0.89 (5.2) -13.6 1.31 10.9 19 22 32 5 1.49 (8.0) -13.3 1.24 29.2 19 24 32 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 28
Table 6.4 Excess return of momentum based portfolios, 19802004 Panel A: 5 portfolios, equally weighted returns Excess 1 (smallest) 1.19 (8.0) -27.7 0.62 33.0 7 21 32 2 0.99 (6.2) -21.0 0.92 17.7 6 21 32 3 0.72 (6.1) -22.4 0.81 28.9 7 20 32 4 0.82 (5.8) -21.3 1.21 19.8 6 21 32 5 0.92 (7.1) -20.8 0.58 27.9 6 21 32 Panel B: 5 portfolios, value weighted returns Excess 1 (smallest) 1.80 (9.2) -31.5 1.46 32.3 6 21 32 2 1.48 (7.2) -26.2 1.37 22.1 6 21 32 3 0.95 (7.2) -28.6 0.72 22.8 6 20 32 4 1.04 (7.5) -27.0 1.63 45.3 6 20 32 5 1.32 (7.3) -22.8 1.51 28.7 8 23 32 Panel C: 10 portfolios, equally weighted returns Excess 1 (smallest) 1.65 (10.0) -25.4 1.07 45.1 4 11 16 2 0.69 (7.6) -30.3 0.32 32.1 3 10 16 3 1.06 (6.8) -24.6 0.75 24.7 3 11 16 4 0.93 (6.8) -20.3 0.76 19.5 3 11 16 5 0.85 (6.9) -22.4 0.45 49.1 3 10 16 6 0.58 (6.3) -24.7 0.41 26.8 4 10 16 7 0.82 (6.2) -19.7 0.73 24.6 3 11 16 8 0.82 (6.3) -22.9 1.53 25.0 3 10 16 9 0.92 (7.3) -27.0 0.68 39.7 3 11 16 10 0.91 (8.4) -22.3 0.45 34.7 3 10 16 Panel D: 10 portfolios, value weighted returns Excess 1 (smallest) 2.28 (11.9) -40.5 1.24 49.0 3 10 16 2 1.26 (8.3) -23.6 0.75 27.4 3 10 16 3 1.60 (8.0) -25.8 1.56 27.5 3 10 16 4 1.22 (7.9) -26.7 1.41 25.9 3 10 16 5 0.97 (7.4) -24.5 0.85 34.3 3 10 16 6 0.94 (8.3) -31.7 0.92 44.7 3 10 16 7 0.74 (6.9) -24.7 0.82 17.4 3 10 16 8 1.19 (8.7) -27.9 1.16 65.7 3 10 16 9 1.13 (7.2) -26.0 1.77 28.4 3 10 16 10 1.57 (8.7) -23.7 1.41 48.3 5 14 20 are percentage monthly returns. The returns are not annualized. Data for stocks listed at the Oslo Stock Exchange during the period 1980-2004. Calculations use the stocks satisfying the lter criteria discussed in section 2. 29
Table 6.5 Mean variance optimal portfolios. 10 portfolios. Using data from 1980 to 1989 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.020 0.091 2 0.017 0.073 3 0.019 0.070 4 0.025 0.067 5 0.024 0.076 6 0.018 0.070 7 0.026 0.071 8 0.026 0.071 9 0.037 0.109 10 0.037 0.098 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.627 0.617 0.573 0.511 0.566 0.529 0.526 0.481 0.488 2 0.627 1 0.634 0.621 0.536 0.598 0.602 0.633 0.555 0.498 3 0.617 0.634 1 0.545 0.596 0.575 0.58 0.589 0.563 0.478 4 0.573 0.621 0.545 1 0.531 0.61 0.565 0.569 0.561 0.429 5 0.511 0.536 0.596 0.531 1 0.53 0.552 0.567 0.456 0.409 6 0.566 0.598 0.575 0.61 0.53 1 0.617 0.674 0.56 0.545 7 0.529 0.602 0.58 0.565 0.552 0.617 1 0.664 0.589 0.546 8 0.526 0.633 0.589 0.569 0.567 0.674 0.664 1 0.564 0.549 9 0.481 0.555 0.563 0.561 0.456 0.56 0.589 0.564 1 0.689 10 0.488 0.498 0.478 0.429 0.409 0.545 0.546 0.549 0.689 1 Panel C: Optimal unconstrained portfolios Asset Expected Return 0.0135 0.0174 0.0214 0.0253 0.0292 0.0331 0.0371 0.041 0.0449 1 (small) -0.0805-0.0933-0.106-0.119-0.132-0.145-0.157-0.17-0.183 2 0.298 0.187 0.0764-0.0343-0.145-0.256-0.366-0.477-0.588 3 0.399 0.327 0.256 0.184 0.112 0.0406-0.031-0.103-0.174 4 0.219 0.283 0.348 0.412 0.477 0.541 0.606 0.67 0.735 5 0.0381 0.0689 0.0997 0.13 0.161 0.192 0.223 0.254 0.284 6 0.391 0.266 0.141 0.0158-0.109-0.234-0.359-0.484-0.609 7 0.112 0.147 0.181 0.216 0.25 0.285 0.319 0.353 0.388 8-0.023 0.0357 0.0944 0.153 0.212 0.271 0.329 0.388 0.447 9-0.292-0.239-0.186-0.132-0.0791-0.0259 0.0274 0.0806 0.134 10-0.0613 0.0172 0.0957 0.174 0.253 0.331 0.41 0.488 0.567 Panel D: Optimal short sale restricted portfolios Asset Expected Return 0.0169 0.0195 0.022 0.0246 0.0272 0.0297 0.0323 0.0349 0.0374 1 (small) - - - - - - - - - 2 1 0.203 0.0674 - - - - - - 3-0.289 0.213 0.142 0.00168 - - - - 4-0.16 0.267 0.329 0.35 0.295 0.228 0.15-5 - 0.0502 0.0937 0.118 0.138 0.0888 0.0471 - - 6-0.287 0.158 0.0412 - - - - - 7-0.0107 0.13 0.179 0.197 0.158 0.112 0.051-8 - - 0.07 0.133 0.144 0.0816 0.0239 - - 9 - - - - - 0.0265 0.12 0.214-10 - - - 0.0572 0.168 0.35 0.469 0.585 1 Panel E: Illustrating portfolio frontiers 0.045 10 portfolios 0.04 0.035 exp return 0.03 0.025 0.02 0.015 0.01 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 30 st dev constr
Table 6.6 Mean variance optimal portfolios. 10 portfolios. Using data from 1990 to 1999 Panel A: Expected Panel B: Correlations matrix Asset mean std 1 (small) 0.029 0.103 2 0.015 0.082 3 0.018 0.069 4 0.011 0.067 5 0.012 0.067 6 0.010 0.062 7 0.009 0.062 8 0.010 0.061 9 0.012 0.062 10 0.016 0.078 ρ(i, j) 1 (small) 2 3 4 5 6 7 8 9 10 1 (small) 1 0.631 0.654 0.645 0.597 0.624 0.561 0.57 0.598 0.519 2 0.631 1 0.617 0.63 0.607 0.658 0.573 0.591 0.571 0.38 3 0.654 0.617 1 0.717 0.656 0.701 0.668 0.648 0.655 0.56 4 0.645 0.63 0.717 1 0.683 0.777 0.688 0.677 0.711 0.563 5 0.597 0.607 0.656 0.683 1 0.767 0.714 0.723 0.709 0.55 6 0.624 0.658 0.701 0.777 0.767 1 0.787 0.763 0.797 0.689 7 0.561 0.573 0.668 0.688 0.714 0.787 1 0.758 0.718 0.61 8 0.57 0.591 0.648 0.677 0.723 0.763 0.758 1 0.746 0.63 9 0.598 0.571 0.655 0.711 0.709 0.797 0.718 0.746 1 0.698 10 0.519 0.38 0.56 0.563 0.55 0.689 0.61 0.63 0.698 1 Panel C: Optimal unconstrained portfolios Asset Expected Return 0.007 0.0105 0.0139 0.0174 0.0209 0.0244 0.0278 0.0313 0.0348 1 (small) -0.243-0.122-0.12 0.241 0.361 0.482 0.603 0.724 2 0.0517 0.0612 0.0706 0.0801 0.0895 0.099 0.108 0.118 0.127 3 0.0918 0.194 0.296 0.398 0.5 0.602 0.705 0.807 0.909 4 0.163 0.0902 0.0176-0.0551-0.128-0.2-0.273-0.346-0.418 5 0.0548 0.0698 0.0847 0.0997 0.115 0.13 0.145 0.16 0.174 6 0.121 0.0268-0.0676-0.162-0.256-0.351-0.445-0.54-0.634 7 0.267 0.161 0.0549-0.051-0.157-0.263-0.369-0.475-0.581 8 0.284 0.247 0.211 0.174 0.138 0.101 0.0644 0.0278-0.00875 9 0.216 0.217 0.218 0.219 0.22 0.22 0.221 0.222 0.223 10-0.00642 0.0549 0.116 0.177 0.239 0.3 0.361 0.423 0.484 Panel D: Optimal short sale restricted portfolios Asset Expected Return 0.00875 0.0113 0.0138 0.0163 0.0189 0.0214 0.0239 0.0265 0.029 1 (small) - - - 0.107 0.226 0.366 0.573 0.779 1 2 - - 0.0602 0.0485 0.0319 - - - - 3-0.0994 0.295 0.359 0.415 0.442 0.331 0.218-4 - 0.073 0.00522 - - - - - - 5-0.0373 0.0738 0.0499 0.014 - - - - 6-0.0825 - - - - - - - 7 1 0.22 0.0434 - - - - - - 8-0.278 0.209 0.132 0.0348 - - - - 9-0.21 0.21 0.162 0.102 - - - - 10 - - 0.103 0.141 0.176 0.191 0.0969 0.0032 - Panel E: Illustrating portfolio frontiers 0.035 10 portfolios 0.03 0.025 exp return 0.02 0.015 0.01 0.005 0.05 0.06 0.07 0.08 0.09 0.1 0.11 uncons The table describes the construction of mean-variance optimal portfolios using historical data from the Oslo Stock Exchange. 31 st dev constr