The Norwegian State Equity Ownership B A Ødegaard 15 November 2018 Contents 1 Introduction 1 2 Doing a performance analysis 1 2.1 Using R.................................................................... 7 3 Changing risk levels? 10 4 Event Study 13 1 Introduction As an example application we will look at the Norwegian Government Direct Ownership at the Oslo Stock Exchange. The issue is that the Norwegian Policy is that the Government is committed to a hands off policy regarding companies on the Oslo Stock Exchange, even those where the State holds a majority (> 50%) or blocking minority (> 33%). The state policy is that listed companies should act so that they maximize the stock value, ie. act in the shareholders interest. The state is not supposed to pursue political objectives that makes companies where they are majority owners deviate from value maximization. There are several ways we can empirically investigate whether this is the case. An obvious prediction we can look at is whether the companies on the exhange with state majority ownership earns less returns than they should. This is a question we can ask as a portfolio performance question. We evaluate the state portfolio using standard methods of portfolio performance. 2 Doing a performance analysis On the course homepage you will find a dataset which is taken from Ødegaard (2009), with the monthly returns from the government s portfolio (or part of it, Statoil is actually not here since that is owned by a different department). The returns are from 1992 to 2008. First doing the obvious descriptive analysis, using octave >> sp = dlmread("../data_set/state_portfolio_returns.txt",";"); >> sprets=sp(:,2); >> mean (sprets) ans = 0.010683 >> annret=(1+mean(sprets))^12-1 annret = 0.13600 We find that the annualized return on this portfolio is 13.6% per year. Another nice way to vizualize such data is to plot the evolution of the implied wealth from investing in this portfolio. We show one way to generate this, by adding the monthly return month by month. >> wealth=[1]; >> w=1; 1
>> for i=1:rows(sprets) > w=w*(1+sprets(i)); > wealth=[wealth;w]; > endfor > plot(wealth) 14 12 10 8 6 4 2 0 0 50 100 150 200 250 Now, whether this is a good or bad return is not something we can say without more information. In particular we need to compare this return to something else. An obvious first try is to look at an alternative investment, such as a market portfolio. You also have available various other comparable returns, such as the returns on two market portfolios ew and vw, in the period from 1980 onwards. I pull the matching market portfolio from the file with monthly market portfolios: > rm=dlmread("../../asset_pricing_ose/data_set/market_portfolios_monthly.txt",";",1,0); > ew=rm(133:348,2); > vw=rm(133:348,3); Note that I have used the dates to pick the relevant rows, investigate alternative ways of generating a matching set of returns. Generating similar wealth series for the market, we can then plot comparisons 2
30 25 20 15 10 5 0 0 50 100 150 200 250 60 50 40 30 20 10 0 0 50 100 150 200 250 (EW on the left, VW on the right) And then we compare the state portfolio with the market portfolios. Observe that the state s portfolio evolution is lower than either of the market portfolios. 60 state ew market vw market 50 40 30 20 10 0 0 50 100 150 200 250 3
But just comparing things to the market is not what we should be doing. Instead, this is of course when we need a model saying: What should the portfolio return have been? In particular, we need to formulate this as a finance question: What is the expected return on a portfolio with the same risk as the state portfolio? The classical performance measure is the calculation of an alpha relative to the CAPM. Let r p be the return on the state portfolio, r f be the risk free rate, r m the return on a market portfolio. Consider the CAPM relationship r pt = r ft + b p (r mt r ft ) Rewriting in excess return terms er pt = r pt r ft We see that the CAPM relationship is er mt = r mt r ft or To get a testable model we consider the regression r pt r ft = β p (r mt r ft ) er pt = β p (er mt ) er pt = a p + b p er mt + e pt If the CAPM holds a p = 0. This a p is the object of interest, and is typically called Jensens alpha. Our next step is to estimate this. To return to the question of the state s portfolio performance, this is answered by asking whether the alpha is significantly negative. If it is, it is consistent with the state ownership influencing these companies in a negative fashion. Now, step 1 is to input data > sp = dlmread("../data_set/state_portfolio_returns.txt",";",1,0); > sprets=sp(:,2); > rm=dlmread("../../asset_pricing_ose/data_set/market_portfolios_monthly.txt",";",1,0); > ew=rm(133:348,2); > vw=rm(133:348,3); To calculate excess returns we need an estimate of a risk free rate. NIBOR. We use montly observations of > RFmonthly=dlmread("../../asset_pricing_ose/data_set/NIBOR_monthly.txt",";",1,0); > RFmonthly(133,1) ans = 19910131 > RFmonthly(132,1) ans = 19901231 > rf=rfmonthly(131:131+rows(sprets)-1,2); Note a particular issue here. The interest rate is the interest rate observed on that date for one month borrowing going forward. We therefore have to lag this one period. We are now ready to do estimation. Here are the simple OLS estimates ols(er_s,[ones(216,1) er_m_ew]) ans = -0.0026668 0.8673143 >> ols(er_s,[ones(216,1) er_m_vw]) ans = -0.0068980 0.9257646 4
Note the beta estimates. In both cases the beta is less than one. So the return on this portfolio should be less than the return on the market portfolio (according to t The economically interesting numbers here are the alpha estimates, 0.0026668 when we use the ew index, and 0.0068980 when we use the value weighted index. In both cases the estimates are negative. So on first glance there is some evidence that the returns on this portfolio is less than it should. But this ignores the uncertainty in the parameter estimate. Before we can conclude anything we need to estimate the uncertainty about the parameter estimate. The typical first step to inference is to calculate the variance covariance matrix of the parameter estimates. In OLS settings the following are the relations we need to crank through Under normality: b ols n y = Xb + e = (X X) 1 X y S 2 = 1 n (e e) b ols n N ( b, S 2 (X X) 1) We need to calculate the covariance matrix of the estimates Let us do this for the ew index. er_s=sprets-rf; er_m_ew=ew-rf; i=ones(rows(sprets),1); X_ew = [i er_m_ew]; b_ew=ols(er_s,x_ew) e_ew=er_s-[i er_m_ew]*b_ew; S2_ew=e_ew *e_ew/t Sigma_ew = S2_ew*inv(X_ew *X_ew) t_ew=b_ew(1)/sqrt(sigma_ew(1,1)) Σ = S 2 (X X) 1 This set of commands produces the following useful results The covariance matrix of the estimates. Sigma_ew = 1.1584e-05-3.3953e-05-3.3953e-05 3.4518e-03 What we want to base inference on alpha on is the t statistic > t=b_ew(1)/sqrt(sigma_ew(1,1)) t = -0.78352 Although negative estimate of alpha, the t stat is nowhere near significant. This result relies on the CAPM as the true model of returns. Now, an alternative model of returns than CAPM is very popular among acadmics is the Fama French 3 factor model. Essentially, this model uses two additional factors SM B and HM L to explain asset returns r pt = r ft + b p (r mt r ft ) + b HML HML + b SMB SMB Let us estimate the alpha in this setting. The additional work needed is reading in the FF factors 5
> FFmonthly=dlmread("../../asset_pricing_ose/data_set/pricing_factors_monthly.txt",";",13,0); > FFmonthly(108,1) ans = 19901231 >> FFmonthly(109,1) ans = 19910131 > SMB=FFmonthly(109:109+T-1,2); > mean(smb) ans = 0.0070112 > HMB=FFmonthly(109:109+T-1,3); > mean(hmb) ans = 0.0042439 Doing the regression is then a matter of the following commands i=ones(rows(sprets),1); X_ew = [i er_m_ew SMB HML]; b_ew=ols(er_s,x_ew) e_ew=er_s-x_ew*b_ew; mean(e_ew) S2_ew=e_ew *e_ew/t Sigma_ew = S2_ew*inv(X_ew *X_ew) t_alpha_ew =b_ew(1)/sqrt(sigma_ew(1,1)) Which produces the following interesting estimates b_ew = 0.0026404 0.7795461-0.6296832-0.0068324 S2_ew = 0.0016597 Sigma_ew = 8.2668e-06-2.7099e-05-3.6017e-05-1.5081e-05-2.7099e-05 2.4416e-03 5.2452e-04-1.4008e-04-3.6017e-05 5.2452e-04 4.0520e-03 5.7697e-04-1.5081e-05-1.4008e-04 5.7697e-04 2.9250e-03 t_alpha_ew = 0.91832 and b_vw = -0.0047058 0.8513460-0.2286168 0.1028720 S2_vw = 0.0012064 Sigma_vw = 6.3944e-06-3.2154e-05-4.3421e-05-1.4546e-05-3.2154e-05 1.7111e-03 1.1427e-03 1.3060e-04-4.3421e-05 1.1427e-03 3.6264e-03 5.2847e-04-1.4546e-05 1.3060e-04 5.2847e-04 2.1302e-03 t_alpha_vw = -1.8609 Again, the interesting numbers are the alpha estimates and their t-stats ew: 0.0026 (0.918) vw: -0.0047 (-1.86) 6
Using the ew portfolio as the market, we have a positive (albeit not significant) alpha. Using the vw portfolio we have a negative alpha. Whether it is significant depends on the significance level. Calculating the probability levels Using the normal distrubution > normcdf(t_alpha_ew) ans = 0.82077 > normcdf(t_alpha_vw) ans = 0.031377 Using the t distribution > tcdf(t_alpha_ew,t-4) ans = 0.82025 > tcdf(t_alpha_vw,t-4) ans = 0.032070 If we use a value weighted index we would reject that alpha is zero at the 5% level but not at the 2.5% level. 2.1 Using R Let us now illustrate using R in this setting. It is actually much less work. sp <- read.table ("../data_set/state_portfolio_returns.txt",header=true,sep=";"); sprets <-sp[,2]; T=dim(sp)[1] rm <- read.table("../../asset_pricing_ose/data_set/market_portfolios_monthly.txt",header=true,sep=";" ew<-rm[133:(133+t-1),2]; vw<-rm[133:(133+t-1),3]; RFmonthly<-read.table("../../asset_pricing_ose/data_set/NIBOR_monthly.txt",header=TRUE,sep=";"); rf<-rfmonthly[132:(132+t-1),2]; ers <- sprets-rf; ermew <- ew-rf; ermvw <- vw-rf; lm(formula="ers ~ ermew") lm(formula="ers ~ ermvw") Produces the output > lm(formula="ers ~ ermew") Coefficients: (Intercept) ermew -0.002667 0.867314 > lm("ers ~ ermvw") Coefficients: (Intercept) ermvw -0.006898 0.925765 Once we have done this, we can also ask for the complete results of the analysis 7
> summary(runs.ew) Call: lm(formula = "ers ~ ermew") Residuals: Min 1Q Median 3Q Max -0.136666-0.032503 0.000495 0.028317 0.143298 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) -0.002667 0.003419-0.78 0.436 ermew 0.867314 0.059026 14.69 <2e-16 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 0.04953 on 214 degrees of freedom Multiple R-squared: 0.5022,Adjusted R-squared: 0.4999 F-statistic: 215.9 on 1 and 214 DF, p-value: < 2.2e-16 > runs.vw=lm(formula="ers ~ ermvw") > summary(runs.vw) Call: lm(formula = "ers ~ ermvw") Residuals: Min 1Q Median 3Q Max -0.188068-0.019195 0.001841 0.021188 0.095807 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) -0.006898 0.002557-2.698 0.00753 ** ermvw 0.925765 0.038871 23.816 < 2e-16 *** --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 0.03674 on 214 degrees of freedom Multiple R-squared: 0.7261,Adjusted R-squared: 0.7248 F-statistic: 567.2 on 1 and 214 DF, p-value: < 2.2e-16 Adding the FF factors is then simply a matter of: > FFmonthly <- read.table("../../asset_pricing_ose/data_set/pricing_factors_monthly.txt",header=true,sep=";",ski > FFmonthly[108,1] [1] 19901231 SMB <- FFmonthly[109:(109+T-1),2]; HML <- FFmonthly[109:(109+T-1),3]; runs.ew=lm(formula="ers ~ ermew + SMB + HML ") Which produces the following results > runs.ew=lm(formula="ers ~ ermew + SMB + HML ") > summary(runs.ew) Call: lm(formula = "ers ~ ermew + SMB + HML ") 8
Residuals: Min 1Q Median 3Q Max -0.129983-0.027959-0.000457 0.022391 0.128678 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) 0.002640 0.002902 0.910 0.364 ermew 0.779546 0.049877 15.630 <2e-16 *** SMB -0.629683 0.064253-9.800 <2e-16 *** HML -0.006832 0.054591-0.125 0.901 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 0.04112 on 212 degrees of freedom Multiple R-squared: 0.66,Adjusted R-squared: 0.6552 F-statistic: 137.2 on 3 and 212 DF, p-value: < 2.2e-16 and > runs.vw=lm(formula="ers ~ ermvw + SMB + HML ") > summary(runs.vw) Call: lm(formula = "ers ~ ermvw + SMB + HML ") Residuals: Min 1Q Median 3Q Max -0.179301-0.017631 0.001181 0.019386 0.091664 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) -0.004706 0.002552-1.844 0.066635. ermvw 0.851346 0.041754 20.390 < 2e-16 *** SMB -0.228617 0.060785-3.761 0.000219 *** HML 0.102872 0.046587 2.208 0.028305 * --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05. 0.1 1 Residual standard error: 0.03506 on 212 degrees of freedom Multiple R-squared: 0.7529,Adjusted R-squared: 0.7494 F-statistic: 215.3 on 3 and 212 DF, p-value: < 2.2e-16 So, the gains to going to the statistical framework are substantial, since R actually knows about the relevant statistical methods it is merely a matter of getting the data aligned. Once the data is in R it is also simple to do additional statistical analysis. Let us for example calculate a confidence interval > confint(runs.ew) 2.5 % 97.5 % (Intercept) -0.003080516 0.008361234 ermew 0.681228726 0.877863567 SMB -0.756339599-0.503026841 HML -0.114443324 0.100778509 The default is a 95 % confidence interval. If we want to relax it specify the level > confint(runs.ew,level=0.9) 5 % 95 % 9
(Intercept) -0.002154294 0.007435013 ermew 0.697146519 0.861945774 SMB -0.735833670-0.523532769 HML -0.097020895 0.083356080 3 Changing risk levels? When we run the regression er pt = a p + b p er mt + e pt we are assuming that the risk is constant. But the portfolio composition is changing over time. (See the data on the shares owned.) One way deal with that is to let the beta change over time: er pt = α p + β pt er mt If we have an estimate of beta we can simply plug in the estimated beta, calculate the ex post alpha, and take the average. On the homepage find portfolio beta estimates. β pt = i w i β it where β it is a rolling beta estimate for the beta of each stock. In figure 1 we plot the estimates of beta. Doing the calculations we find the ex post average abnormal returns Let us look at the distribution of these estimates Histogram: Ex post excess returns relative to ew portfolio 60 50 40 30 20 10 0-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2 10
Figure 1 Time series of estimated beta 1.4 1.2 1 0.8 0.6 0.4 0.2 0 50 100 150 200 250 11
Histogram: Ex post excess returns relative to vw portfolio 60 50 40 30 20 10 0-0.2-0.15-0.1-0.05 0 0.05 0.1 0.15 0.2 Calculating t-stats for testing whether the estimated excess returns are different from zero: >> t=mean(e_ew)/(std(e_ew)/sqrt(t)) t = -0.52374 >> t=mean(e_vw)/(std(e_vw)/sqrt(t)) t = -2.1540 12
4 Event Study Exercise 1. Consider state ownership of Norwegian Listed Companies. There are arguments that state ownership will depress the price of a company, as the management does not feel the market pressure to perform, the state owner is represented by bureaucrats that do not feel it in their pockets if suddenly the stock price falls. One way this has been investigated is to do a performance evaluation of the state s direct ownership portfolio. However, there are always alternative methods to get at an issue. Let us think about the times when the state changes its ownership stake. For example cases where they lower the stake. If there is something to the monitoring story, a higher fraction of shares on private hands will increase the need for management to perform. If the market realizes that, on the date when the news that the state lowers its stake hits, the stock price should react. If there is a price increase on dates with a significant decrease in state ownership, this can be used as an estimate of a negative state premium. Your mission is to carry out such an investigation. You have access to the dates with changes in the state s portfolio. Pick those dates with a significant change in state ownership. Is there evidence of a negative state premium? Hint: You will find daily returns for some of the component stocks in the state portfolio on the web page with the state portfolio examples. Solution to Exercise 1. There is no obvious way to choose the dates, one want to choose dates with significant selling. It is also not clear whether one should take all dates with large sells, or just the first. I choose to take the first (only) date with large sells, which gives the following six observations: 15668 Norsk Vekst 18 sep 1995-0.077945 6180 Norsk Hydro 14 jul 2006 0.027018 6224 Raufoss A/S 22 dec 1997-0.068986 6059 Den norske Bank 10 apr 2001-0.032780 47454 Telenor 4 jul 2003-0.027574 56559 Yara International 21 dec 2006 0.173180 lag CAR J 1 0-0.0192-1.500 1-0.0032-0.241 2-0.0116-0.867 3-0.0022-0.163 4-0.0012-0.085 5-0.0070-0.492 6-0.0146-1.006 7-0.0111-0.755 8-0.0136-0.903 9-0.0171-1.122 10-0.0177-1.143 11-0.0252-1.598 12-0.0159-0.995 13-0.0010-0.060 14 0.0041 0.248 15-0.0006-0.036 16-0.0028-0.165 17-0.0032-0.187 18 0.0010 0.058 19 0.0035 0.201 20-0.0012-0.066 13
0.005 Event study 0-0.005-0.01 CAR -0.015-0.02-0.025-0.03-0.035-20 -15-10 -5 0 5 10 15 20 lag References Bernt Arne Ødegaard. Statlig eierskap på Oslo børs. Praktisk Økonomi og Finans, 25(4), 2009. 14