Asset Pricing and Monetary Policy in Japan
Msc. thesis Finance (EBM866B20)
University of Groningen
Abstract
The objective of this paper is to investigate the relationship between monetary policy and the cross-section of stock returns in Japan. I find that investors require a positive risk premium for being exposed to co-movement with monetary policy for the period between 1989 an 2013. For carrying exposure to the target interest rate of the central bank investors require an 1.2% annualized return and for exposure to the monetary base investors require a 0.5% annualized return. The main conclusion of the paper is that monetary policy is a priced risk factor that has additional value in pricing assets.
Keywords Monetary Policy, Asset Pricing, Risk Premia
JEL Code E44, E52, G12
Author Joram Leander Kok
Student number S1609513
Supervisor Dr. L. Dam
Date 10-01-2014
Address Anna Paulownastraat 39
2518 BB Den Haag The Netherlands
E-mail Joramleanderkok@gmail.com
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1. Introduction
Central banks use several monetary policy tools to influence the economy in their mission to achieve objectives such as price stability, low unemployment, steady economic growth and/or lending at last resort. In doing so, the central bank influences the monetary environment in which firms operate. Firms selling durable goods might be impacted by stronger demand when the central bank influences the yield curve downward by lowering short-term interest rates. Other firms might be impacted by a tightening of monetary policy through their dependence on banks for loans, whom have less reserves available for loans in restrictive monetary environments (Mishkin, 1996). Changes in monetary environment, therefore, require investors to reassess the prospects of their stock holdings. Hence, changes in monetary policy can be viewed as a factor of risk to investor for which they expect higher returns. The main objective of this paper is to investigate the relationship between monetary policy and the cross-section of stock returns in Japan. This topic is investigated first by evaluating whether stock prices react to changes in monetary policy and, in turn, to see if investors require compensation for being exposed to the risk associated with changes in monetary policy.
To test the main research objective this paper applies two of the most commonly used asset pricing models; the three factor model of Fama and French (1993) and the Carhart (1997) four factor model. These models are in turn supplemented by several proxies for monetary policy. Since, monetary policy is an umbrella term that comprehends all the actions, either by word or deed, a central bank engages in to achieve their objectives, there is no variable that directly captures monetary policy as a whole. This leads to the use of two proxies for monetary policy; the central bank target rate and the monetary base. The first hypothesis is that monetary policy and stock returns do not exhibit significant co-movement. The second hypothesis states that investors require no compensation for the exposure to changes in the stance of monetary policy. This first hypothesis is tested by evaluating the time series estimation of the mentioned models including the monetary policy proxies. The second hypothesis is tested using the two stage regression technique of Fama and Macbeth (1973). This technique generates risk premia for each factor in the model. The risk premia represent the extent to which investors want to be compensated for being exposed to innovations of the respective factors. Besides the mentioned tests, the models also provide insight into the added value of monetary policy in pricing assets.
2 the central bank target rate investors require an annualized risk premium of -1.2%. This risk premium means that for being inversely unit-correlated with the central bank target rate, investors expect a 1.2% annualized return. In economic terms this translates to investors expecting higher returns from portfolios that move in line with the monetary environment. Moreover, this paper finds some evidence of co-movement between changes in monetary policy stance and stock returns. However, no clear pattern emerges in the cross-section of stock returns. The results are robust for the use of several monetary policy proxies, samples and portfolio weightings.
This study provides theoretical and practical insights for, policy makers and market participants, into the effectiveness and the impact on the returns of stock portfolios of monetary policy. The results can be interpreted as to what extend ‘the market’ believes monetary policy conducted by the central bank to be effective in influencing the economy. If monetary policy is perceived to be ineffective by investors changes in monetary policy should yield no response in stock returns and hence no risk premium should be required by investors. Moreover, this paper provides investors with information regarding the extent to which stock returns are affected by monetary policy. The paper shows what return has been expected for carrying exposure to monetary policy, this information can be used by investors when assessing the impact of monetary policy on their portfolios.
The following section presents first the theoretical literature on the relationship between monetary policy and stock returns, after which the results from the empirical research are reviewed. Next, the methodology used is presented. This is followed by the data and descriptive section. The penultimate section of this paper discusses the results. Lastly, the conclusions are discussed.
2. Literature Review
Three mechanisms are often cited as the main transmission channels between monetary policy and the cross-section of stock returns. These are the interest rate channel, portfolio rebalancing channel and the credit channel.
3 The second channel, The portfolio rebalancing theory, is based on the interference of central banks in asset markets. By buying assets in the open market the central bank changes the composition of the asset portfolio of institutions from whom they bought the assets. These institutions now hold cash instead of the sold security. If cash and the sold security are not perfect substitutes, the financial institutions will use the cash to buy other assets in order to rebalance their portfolios of assets to the desired composition of cash and other assets. By rebalancing, some other institution will hold excess cash and will also rebalance until the desired portfolio composition is obtained. This process repeats itself, driving up asset prices, until the balance between assets held and cash held, is at the desired level for all institutions1 (Rozeff, 1974).
The third mechanism through which asset prices and the economy are influenced by monetary policy is the credit channel (Bernanke and Gertler, 1995). The credit channel explanation is based on the idea of central banks trying to influence the external finance premium of companies. The external finance premium is the difference between the cost of attracting external financing and the opportunity cost of internally generated funds. This wedge is especially strong when information asymmetries exist between lenders and borrowers. By decreasing this difference, financing becomes cheaper for companies, making them more willing and able to invest. This is especially true for firms over which less information is publicly available (Ehrmann and Fratzscher, 2004), and hence have a larger wedge. As such, these firms are among the first to notice a reduction in the supply of loans. The credit channel works through two mechanisms that influence the external finance premium, the bank lending channel and the balance sheet channel. The former is related to the monetary policy stance of the central bank; if a central bank has a restrictive monetary policy stance, it reduces the supply of central bank reserves and raises interest rates. This monetary tightening leads to banks getting a shock on the funding side (i.e. liability side) of their balance sheet, since banks might become less willing to lend to one another. To undo this shock they can either raise other liabilities by issuing stock or acquiring more deposits. Alternatively, it can reduce the outstanding assets, for instance loans. Banks will still be willing to loan to firms and consumers, but as their supply of funds (central bank reserves) has become more expensive and harder to obtain, their loans to businesses and consumers will also become more expensive (i.e. a higher external financing premium). The other mechanism of the credit channel is the balance sheet channel which is related to the financial position of companies. According to this theory variation in the borrower’s balance sheet quality influences the financial position of the companies. By changing the
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4 short-term interest rate the central bank does not only influence market interest rates but also the financial position (net worth) of firms directly. This is achieved by changing rollover costs of short-term debt and by changing the valuations of collateral held by firms. Especially firms that exhibit high information asymmetries depend on collateral to obtain loans. To conclude, firms that are bank dependent for financing or financially constraint, (i.e. those with larger information asymmetries and higher external financing premia) will be more strongly impacted by monetary policy.
The described channels show the influence of monetary policy on companies’ operations and hence on their stock prices assuming that investors are processing all public information into the stock price directly (Fama, 1970). The portfolio rebalance theory shows a more general relation between asset prices and monetary policy. Whereas, the credit channel shows the heterogeneous impact of monetary policy on stock returns through the external finance premium (Bernanke and Gertler, 1995). Therefore, value stocks which are characterized as being financially constrained (Fama and French, 1995; as explained in Maio, 2013) should be more exposed to changes in monetary policy compared to growth stocks.2 Moreover, smaller firms are generally more bank dependent and/or have less access to capital markets. They therefore might be impacted more by monetary policy changes (Gertler and Gilchrist, 1994). Hence, differentiated reactions of firms to monetary policy might be expected for value versus growth stocks and large versus small stocks. Moreover, differentiated responses to asset prices in the cross-section of stocks can occur since producers of more interest sensitive goods or more cyclical goods would be more exposed to this interest rate channel of monetary policy (Ehrmann and Fratzscher, 2004).
Empirical research into the relationship between monetary policy and stock market returns has found the relationship to be significant3. Research has shown that investors perceive monetary policy as a priced risk factor, that is, they expect higher returns for bearing exposure to it. Bernanke and Kuttner (2005) find that the announcement of an unexpected 25 basis point rate cut in the federal funds target rate leads to a 1% increase in stock returns. They find this result using event study methodology for U.S. stocks over the period between 1989 and 2002. Bernanke and Kuttner (2005) also investigate whether the impact of unexpected monetary policy shifts on stock returns works through real interest rates, expected future dividends or expected future stock returns. They conclude that the impact of monetary policy surprises on stock returns comes through either expectations on future dividends, or expectations
2 Value stocks are characterized as high book-to-market stocks whereas growth stocks are low book-to-market stocks 3
5 on future excess stock returns. They interpreted the result to suggest that “tight money (for example) lowers stock prices by raising the expected equity premium”. Thorbecke and Alami (1992) find that innovations in the federal funds rate4 is a common factor when added to the factor model as used in Chen, Roll and Ross (1986). They reach this results by estimating a nonlinear seemingly unrelated regression, for 45 U.S. stock portfolios constructed over the period 1974 till 1986. Of the 45 portfolios based on industry specification, 43 have a negative relation with the federal funds rate, hence expansionary monetary policy for these 43 portfolios yields higher stock returns. Furthermore, they find a positive risk premium for the monetary policy proxy indicating that stronger co-movement (i.e. positive beta coefficient) with the federal funds rate results in higher expected returns by investors. This leads them to conclude that if a firm has higher returns when the central bank has accommodative monetary policy investors require a lower risk premium due to the desirability of stocks with this characteristic. Thorbecke (1997) finds that U.S. monetary policy has large effects on ex-ante and ex-post U.S. stock returns. This research shows that monetary policy is a priced factor in an asset pricing framework hence investors want to be compensated for being exposed to the systematic risk of monetary policy. He finds that investors require a 7.5% annualized return to have inverse co-movement with monetary policy, as measured by the change in the federal funds rate. The results are robust for several econometric techniques and several proxies for monetary policy, for the period between January 1969 and December 1990.
The previously mentioned empirical research provides evidence of the general relationship between monetary policy and stock returns. Other research has shown, more specifically, that firms with differences in size, financial constraints and industry have heterogeneous responses to monetary policy. Ehrmann and Fratzscher (2004) show that, in the U.S., capital intensive and cyclical firms have stronger responses to monetary policy then non-cyclical firms. Furthermore, they provide evidence that firms that are financially constrained as measured by their small size, low cash flows, poor credit ratings, low debt to capital ratios, high price-earnings ratios or high Tobin’s Q react more strongly to changes in monetary policy then firms with opposite characteristics. Besides their general result mentioned above, Bernanke and Kuttner (2005) also find that the response in stock returns is heterogeneous over industries. Kontonikas and Kostakis (2013) find that small, value and past loser stocks have greater exposures to monetary policy shocks than big, growth and past winner stocks. This result is obtained by using a vector autoregressive framework for a sample that covers U.S. stocks between 1967 and 2007. In
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6 one of the robustness checks they find that the effect is mainly driven and only significant due to the pre-1983 period. Guo (2004) provides evidence of the credit channel of monetary policy. He finds that financially constraint, small and value stocks, respond more strongly to central bank rate changes then the overall market. He does so by looking at changes in stock returns on days of target rate announcements of the central bank. Furthermore, his results indicate that the reaction of stocks to changes in monetary policy are state dependent and that in times of bad business conditions smaller firms react stronger to monetary changes then big firms, this effect disappears in the 1990’s. The results of Guo (2004) are in line with the results from Jensen and Mercer (2002) who find that in restrictive monetary environments a factor which proxies for size is insignificant whereas in the expansionary environment it is significant. Jensen and Mercer (2002) investigate the difference of a regression model across monetary environments. The model includes the overall market, market capitalization of firms and book-to-market value as explanatory variables, for U.S. stocks between 1965 and 1997. They conclude that the monetary policy environment has a significant impact on the relationship between risk factors and stock returns. Lastly Chen (2007) adds to the literature, using a markov switching model, that the monetary policy has a stronger impact on stocks during bear markets then during bull markets. The results of Chen (2007) are obtained using the S&P 500 between 1965 and 2004.
7 In summary, this section shows that stock returns react positively to expansionary monetary policy changes and tend to be higher for periods of expansionary monetary policy versus restrictive monetary policy periods. Also, research mainly driven by Thorbecke (Thorbecke, 1997; Thorbecke and Alami, 1992) found that monetary policy is a priced risk factor for which investors expect to be compensated.
This paper adds to the literature by investigating the relationship between monetary policy and stock returns in Japan which despite being the World’s third largest economy is relatively under researched. Japan has a rich history in conducting monetary policy with often innovative and large-scale monetary experiments such as the “Quantitative Easing Program” between 2001 and 2006. By investigating Japan new insights can be gained or common theories can be confirmed outside an U.S. monetary policy setting. Also, this paper takes the perspective of an investor by identifying the response of investors to monetary policy changes and whether they view monetary policy as a factor of systematic risk. The combination of monetary policy and asset pricing has been limited thus far in the literature5 and could add to the understanding of the dynamics of monetary policy in relation to stock markets. Finally, this paper uses the most commonly applied asset pricing models, the three factor model by Fama and French (1993) and the four factor model (Carhart , 1997). These models are to a lesser extent driven by theory. Therefore, by adding monetary policy to these models insights can be obtained into the relationship between the factors in these models and monetary policy.
3. Methodology
First the relationship between monetary policy and stock market returns is investigated. This is done by dividing the sample in two monetary environments; a restrictive environment and an accommodative environment. By dividing the sample in different monetary environments the (real) returns and volatility between these periods can be compared and tested. The sample is divided by using the central bank target rate as in Jensen, Mercer and Johnson (1996) and Jensen, Johnson and Mercer (2000). A central bank lowers or raises its target interest rate to influence demand for loans by banks and (possibly) in turn by consumers and businesses. This rate can therefore be used to identify monetary periods as expansionary or restrictive.6 Therefore, an expansionary monetary environment is defined as a series of downward interest rate changes by the central bank and a restrictive monetary policy is defined as series of upward interest rate changes by the central bank. An interest rate change in the opposite direction as the previous rate change is identified as the first rate change in a new series that moves in
5 with the exceptions of Thorbecke (1997) and Thorbecke and Alami (1992) 6
8 the opposite direction as the previous series. The period in which the first rate change of a new series falls is excluded from the data since the period can be identified as either expansionary or restrictive due to the rate change that occurs somewhere within the period.7 After having identified the monetary policy environments the nominal and real (inflation adjusted) returns and associated standard deviations of the Japanese stock market index are calculated. It then becomes possible to perform a T-test with the null hypothesis of equality of (real) returns of the restrictive and expansionary monetary periods. Also a Wilcoxon signed rank test is performed, with a similar null hypothesis, to ensure that the results are robust and not driven by a few outliers which bias the overall results.
Secondly, the relation between monetary policy and the cross-section of stock returns is investigated by using asset pricing models to assess whether monetary policy is a priced factor. In these models portfolios of stocks based on firm characteristics are used as dependent variables to give insights into the heterogeneity of monetary policy exposures in the cross-section of stocks. In this paper I assume that markets are efficient of the semi-strong form, hence investors respond immediately to new news that enters the public realm (Fama, 1970). Therefore, changes in monetary policy proxies should be reflected by changes in stock prices, if investors are of the opinion that it influences stock valuations. The three factor model (Fama and French, 1993) and the four factor model (Carhart, 1997) are used as workhorse models upon which further investigation is performed by adding several proxies for monetary policy. The three factor model is specified as follows;
(1)
In which, represents the return of portfolio i on time t in excess of the risk free rate, refers to
the excess return of the market over the risk free rate, represents the return of a long short portfolio which proxies for size. represents the return of a long short portfolios which proxies for value stocks. refers to the exposure of the ith dependent variable to the kth variable (e.g.
refers to the exposure of portfolio i to the market factor). The four factor model (Carhart, 1997) is an extended version of the three factor model which adds momentum as a factor;
(2)
in which represents the return of a long short momentum portfolio where last periods highest return stocks are bought and the lowest return stocks are sold.
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9 The two workhorse models described above are expanded upon to asses the relation between monetary policy and stock returns by adding a monetary variable to the equation. This leads to the following extensions of (1) and (2);
(3)
(4)
in which, is a proxy for monetary policy and measures the exposure of to
.
By using time series regression8 in (1) through (4) the significance of the exposures of the k independent variables to the i dependent variables, , can be tested using a T-test. These i time series regressions
(per model (1) trough (4)) can be stacked in a system which allows for testing whether the exposure to a variable differs in the cross-section of stock returns. The difference in, , over the i dependent
variables is tested using a Wald test with the null hypothesis that, , is equal over the i dependent
variables.
The following step is to investigate the risk premia investors expect for being exposed to the independent variables in (1) trough (4). The three factor model in (1) and the four factor model in (2) are estimated by using the returns of replicating portfolios as factors on the right hand side of the equation that proxy for some form of risk. One advantage of using replicating portfolios is that the variables on both sides of the equation are returns. Therefore, the replicating portfolios on the right hand side of the equation can be shorted and the dependent variable on the left hand side of the equation can be bought. If the factors on the right hand side of the portfolio capture all risk factors, then the outcome of the right hand side of the equation should equal the left hand side. In line with this reasoning if both sides of the equation are not equal the alpha coefficient (the intercept) ensures equality on average. Therefore, alpha can be interpreted as the pricing error of the asset pricing model when using returns on both sides of the equation. Testing whether or not the asset pricing model captures all the factors of risk can be done by a T-test, with the null hypothesis that is equal to 0. Moreover, the null hypothesis that is jointly equal to zero over the i dependent variables is tested. This provides insights into the cross-sectional robustness of the asset pricing model.
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10 This latter hypothesis can be tested using the GRS Test (Gibbons, Ross and Shanken, 1989) which is composed as follows:
(5) In which, T refers to the number of observations in the time series, N equals the number of regressions/dependent variables used for each model and L represents the number of ’s in the
model. is a Lx1 vector of the expected values of the factors. represents the inverse of the LxL covariance matrix of the factors. is a Nx1 vector of the alpha’s and is the inverse of the NxN covariance matrix of the residuals from the N regressions. The GRS statistic follows a F-distribution with N, T-N-L degrees of freedom.9
The GRS Statistic is useful for models (1) and (2) since these models only have returns on the right hand side of the equation which yields alpha as the average pricing error. For models (3) and (4) running a time series regression and applying (5) to asses whether the pricing errors significantly deviate from zero becomes no longer applicable since the independent variables are no longer solely returns. This is due to the addition of the monetary policy proxy as a factor. Therefore, the intercept can no longer be interpreted as the pricing error of the model since there is no return associated with the monetary policy proxy.
In order to research an asset pricing model that includes macro economic variables, in this case a monetary variable, a two stage regression technique is applied to once again end up with risk premia for all factors. In the first stage, time series regression beta coefficients are estimated. In the second stage, a cross-sectional regression is estimated with the average returns of the dependent variables i as dependent variables and with the Beta coefficients from the time series regression of the first stage as independent variables. This technique does not take in to account the variability of the risk premia since one cross-sectional regression is estimated over the average returns of the i dependent variables, therefore information related to the variability of the risk premia is lost (Cochrane, 2005).
To overcome this problem the Fama-Macbeth regression technique is used (Fama and Macbeth, 1973). This techniques is on the one hand applicable for non- return variables since it is a two stage regression technique. On the other hand it improves upon the econometric limitations of the basic two stage regression technique.
9 For further information on the construction of the GRS Statistic I refer to Cochrane (2005) and the university of Chicago,
11 The Fama-Macbeth regression can be applied as follows; first a time series regression is performed of (3) and (4). Next, the (static) betas estimated from these time series regressions over the full sample are used in cross-sectional regressions at each moment in time, t;
(6)
(7)
Where refers to the risk premia of the kth factor for the time period t (e.g. refers to time t and
the market factor). The second stage of the Fama-Macbeth regression yields KxT risk premia.
The time series of risk premia can be averaged to obtain the risk premia for the exposure to each factor;
(8)
The standard deviation of these risk premia can be calculated as follows;
(9)
And the T-statistic can be calculated as;
(10)
Another benefit of using Fama-Macbeth regressions is that the second step of the technique yields a time series of risk premia which ”represents the return series to a minimum variance portfolio with an unit exposure to that factor” (Asness, Moskowitz and Pedersen, 2013). In other words the risk premia associated to a factor can now be interpreted as the return of a replicating portfolio (Fama and Macbeth, 1973; as applied in Asness, Moskowitz and Pedersen, 2013). Using the time series of the risk premia in a time series regression with the original portfolios as dependent variables ensures that both sides of the equation are returns. This enables the use of the GRS Statistic to formally test and compare the asset pricing models including monetary variables with other asset pricing models constructed in a similar fashion.
4. Data and descriptive
To assess the difference in stock market performance in expansionary and restrictive monetary environments quarterly data of the TOPIX Index are obtained from Bloomberg for the period between 1960 and 2013.10 The third quarter of 1960 is chosen as the start date since this is when the first full
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12 series of rate changes occurs for which I could obtain returns of the TOPIX Index. Also, quarterly returns are chosen since these reach back in time further then monthly returns and hence span more episodes of expansionary and restrictive monetary policy environments. To define monetary environments the central bank target rates are obtained from the time-series data search section of the website of the Bank of Japan.11 The inflation rates are obtained from the Japanese Bureau of Statistics.12
Two types of data are used in the regression analysis performed in this paper, stock returns and monetary variables. All stock return data are obtained from FactSet for the period between October 1989 and August 2013. The universe of stock returns from which portfolios are constructed is defined as all listed Japanese equities with a price higher than 100 Yen and positive book-to-market ratio.13 Furthermore, a dynamic universe is used to ensure that there is no survivorship bias in the data. The value weighted return of the universe is used as the market return in this paper.
To investigate the cross-section of stock returns, the dependent variables are constructed as portfolios based on firm characteristics as in Fama and French (1993). This is done by sorting the universe of stocks by market capitalization and market value. The sorts by market capitalization and book-to-market value are placed in baskets with the quintiles of the sorts as cut off points. This process yields five baskets based on market capitalization (basket 1 refers to small companies and basket 5 refers to large companies) and five baskets based on book-to-market values (high book-to-market companies are placed in basket 5 and low book-to-market companies are placed in basket 1). By combining the baskets on market capitalization and book-to-market ratio a total of 25 portfolios can be constructed.14 The monthly returns series in Yen of these 25 portfolios in excess of the risk free rate are used in this paper as dependent variables for the regressions with the returns of the portfolios either being equal weighted or market capitalization weighted. In this paper the monthly uncollaterized call rate in Japan is used as the risk free rate.15
Table 1 provides an overview of the returns and standard deviation of the 25 portfolios. The data shows that small firms in general have higher returns than large firms with the largest return spread of 1.051%
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The central bank target rate series code is BJ’MADR1M and can be obtained from the Bank of Japan, http://www.stat-search.boj.or.jp/index_en.html
12 Japanese Ministry of Internal affairs and Communications, http://www.e-stat.go.jp/SG1/estat/ListE.do?bid=000001033702andcycode=0
defined as the Index of all items, less imputed rent. Quarterly growth in the index is then taken as inflation
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This to avoid penny stocks which can exhibit large swings biasing the overall returns. The SEC defines penny stocks as stock below $5 (http://www.sec.gov/answers/penny.htm) whereas in the U.K. penny stocks are viewed as stocks trading below 1 pound making the definition of a penny stocks as trading below 100 Yen an inclusive one
14
Before 1989 the coverage in FactSet becomes too narrow, making it hard to form 25 portfolios by book-to-market value and size. Appendix A provides an overview of the number of firms per basket
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13 per month between small and low book-to-market firms (0.734% monthly return) and large and low book-to-market firms (-0.317% monthly return) for the basket based on equal weighted returns.
Table 1. Average monthly returns and standard deviation in percentages of 25 portfolios sorted by book-to-market and Size. Portfolios are constructed by sorting Japan listed stocks in quintiles on market capitalization and book-to-market value. This yields five baskets (quintiles) ranging from the smallest (basket 1) to the largest (basket 5) stocks and five baskets (quintiles) ranging from low book-to-market stocks (basket1) to high book-to-market stocks (basket 5). Average returns and standard deviations are calculated between October 1989 and august 2013. Panel a shows equal weighted stock returns whereas panel b provides returns based on market capitalization weighted stock returns.
Panel a.
Book-to-Market Quintiles
Size Quintiles
low 2 3 4 high low 2 3 4 high
Average Return Standard Deviation small 0.734 0.662 0.536 0.528 0.658 small 9.436 7.618 7.109 6.555 6.495 2 0.079 0.066 0.225 0.261 0.444 2 7.950 6.919 6.717 6.499 6.508 3 -0.278 0.046 -0.017 0.150 0.456 3 7.883 6.914 6.428 6.444 6.734 4 -0.321 -0.089 0.187 0.290 0.375 4 7.019 6.375 6.143 5.997 6.635 big -0.317 0.035 0.212 0.444 0.260 big 6.216 5.654 5.431 5.749 6.909 Panel b. Book-to-Market Quintiles Size Quintiles
low 2 3 4 high low 2 3 4 high
Average Return Standard Deviation small 0.596 0.492 0.428 0.437 0.582 small 9.349 7.434 7.049 6.444 6.499 2 0.052 0.078 0.214 0.255 0.457 2 7.887 6.931 6.736 6.511 6.532 3 -0.307 0.025 -0.037 0.138 0.446 3 7.850 6.920 6.412 6.419 6.759 4 -0.314 -0.066 0.184 0.294 0.382 4 7.001 6.360 6.127 5.988 6.638 big -0.358 0.002 0.330 0.584 0.126 big 6.288 5.707 5.622 5.888 7.896
Also one can see a spread in the returns between value stocks and growth with higher returns for value stocks. This does not hold for the small stocks where the small and low book-to-market basket exhibits larger returns (0.734% per month) then the small and high book-to-market basket (0.658% per month). When looking at the volatility of the baskets you can see that in general small firms and growth firms exhibit higher volatility then large firms and value firms. The result of higher returns for value stocks and small stocks and lower volatility for large stocks and value stocks is in line with the findings of Fama and French (1993).
The independent variables used in the regression analysis are either return based or monetary policy factors.16 The return based factors used in this paper are based on, and constructed as, the factors of the three factor model (Fama and French, 1993) and the four factor model (Carhart, 1997). The four
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14 factors from these models are the market factor, the size factor, the value factor and the momentum factor. The market factor (MKT) is constructed by subtracting the risk free rate from the return of the market. To construct the size factor (SMB) and the value factor (HML) stocks are sorted by market capitalization and book-to-market value. Sorts by market capitalization are divided in two baskets classified small (S) and large (L) with the median of the sort as the cut of point. Sorts by book-to-market value are divided in three baskets classified as either Value (V), neutral (N) or growth (G) stocks with cut off points at the 30th and 70th percentile, where the highest ranked companies have the highest book-to-market value. These baskets combined lead to six different portfolios (3x2). The size factor is constructed by subtracting the average return of the three large portfolios (LV, LN and LG) from the average return of the three small portfolios (SV, SN and SG). The value factor is constructed by subtracting the average return of the two growth portfolios (SG and LG) from the average return of the two value portfolios (SV and SG). The momentum factor (MOM) is constructed in a similar fashion as the HML factor but in this case portfolios are sorted by market capitalization and returns over the last twelve months excluding the most recent month (t-12 till t-1).17 The sort by return over the period t-12 till t-1 is then divided in three baskets with cut off points at the 30th and 70th percentile with high return stocks ranking as the highest momentum stocks. The momentum factor is then constructed by subtracting the average return of the low momentum portfolios from the average return of the high momentum portfolios. Both dependent and independent portfolios are rebalanced on the 1st of October to ensure the accounting data related to the most recent book year can be used in the construction of the portfolios.18 All returns are in Yen to allow comparability with the monetary variables.
Graph 1 provides an overview of the cumulative return of the factors. One can see that the Market Factor has a negative return, which is in line with the overall trend in the performance of the Japanese equity market, defined as either the Nikkei 225 Index or the TOPIX Index, with returns still below the 1989 peak. Furthermore the graph shows that investing in the value factor would have multiplied ones money more then fourfold since 1989. There appears to be no strong size effect over the sample in Japan as shown by the side ways pattern of the SMB Factor. This is in line with Daniel, Titman and Wei (2001) who find size to be insignificant in Japan. Moreover, the negative cumulative return on the
17 t-12 till t-1 is chosen to exclude the one month reversal effect as discussed by Jegadeesh and Titman (1993) and performed by Carhart (1997) 18
15 momentum factor (MOM) portrays the same behavior as found in previous research (e.g. Fama and French, 2012).19
Graph 1. Overview of cumulative monthly returns of the Fama and French (1993) factors and the momentum factor (Carhart, 1997) as constructed for this paper. Factors are constructed using Japanese listed stocks between October 1989 and August 2013. Factors are rebalanced annually on October and are denominated in Yen. The market factor (MKT) is the excess return of the market over the risk free rate. SMB refers to a factor that proxies for firm size whereas HML refers to a factor that proxies for value stocks. The momentum factor is denounced by MOM. Factors are constructed using market capitalization weighted stock returns. The graph is depicted using a log scale.
Next to the return based factors three monetary factors are used in this paper; the central bank target rate, the monetary base and a variable constructed using Principle Component Analysis (PCA). The central bank target rate in Japan is the uncollaterized overnight call rate, which is also known as the interest rate for uncollaterized transaction overnight between financial institutions.20 The central bank targets this interest rate to influence the supply and demand for loans. Whenever the central bank wants to be more accommodative it lowers the interest rate and vice versa. The change in the central bank target rate is in the literature established as a good proxy for the overall stance of the central bank towards monetary policy (Bernanke and Blinder, 1992). To ensure robustness of the results the monthly percentage change in the monetary base is also used as a proxy. The monetary base of a central bank encompasses all reserves banks have at the central bank and all currency in circulation. When a central bank wants to influence the supply of loans by banks it can do so by managing the reserves the banks have at the central bank. It can increase the reserves when it wants to be more accommodative and decrease them when it wants to be more restrictive. Since both variables are used by the central bank to conduct monetary policy and since both variables reflect the stance of the central bank towards monetary policy they can be used as proxies for monetary policy. In the literature M1 and M2 are also
19 The factors constructed in this paper are in line with the factors constructed by Fama and French (2012) for Japan, see appendix B and C 20
As explained by the Bank of Japan at: http://www.boj.or.jp/en/about/outline/data/foboj07.pdf 0.1
1 10
91989 91990 91991 91992 91993 91994 91995 91996 91997 91998 91999 92000 92001 92002 92003 92004 92005 92006 92007 92008 92009 92010 92011 92012
16 commonly used to proxy for monetary policy. Since only year on year percentage changes in M1 and M2 are available for the sample these can not be used directly. Therefore, a variable is created using Principle Components Analysis (PCA) with the central bank target rate, the monetary base, M1 and M2 as inputs. This variable can be used as an additional robustness check. PCA statistically generates a variable that explains most of the variance in the factors used as inputs. The benefit of using a PCA variable is that I can use the M1 and M2 variables and that I have statistically generated an unanticipated factor. On the other hand it is hard to interpret a variable constructed using PCA.
Table 3. Correlation matrix of the independent variables. TR stands for the monthly change in the Bank of Japan target interest rate also known as the uncollaterized overnight call rate (the inter-bank overnight market interest rate). MB refers to the month on month percentage growth in the monetary base of the bank of Japan. M1 refers to the year on year percentage growth of the money supply in narrow sense whereas M2 refers to the year on year percentage growth in money supply in broad sense. PCA is a principal components analysis with TR, MB, M1 and M2 as input. ). The market factor (MKT) is the excess return of the market over the risk free rate. SMB refers to a factor that proxies for firm size whereas HML refers to a factor that proxies for value stocks. The momentum factor is denounced by MOM. Factors are constructed using market capitalization weighted stock returns and are in Yen. Figures displayed are the correlations between the independent variables and the significance of the correlation is shown below the correlation. Data for the self constructed factors are obtained from FactSet are for the period between October 1989 and August 2013.** indicates significance at the 1% level, * indicates significance at the 5% level of the null hypothesis that the correlation equals zero.
TR MB PCA M1 M2 MKT SMB HML MOM TR 1.000 --- MB -0.085 1.000 (0.153) --- PCA -0.809 0.294 1.000 (0.000)** (0.000)** --- M1 0.042 0.050 -0.016 1.000 (0.481) (0.395) (0.785) --- M2 -0.345 0.052 0.794 0.016 1.000 (0.000)** (0.378) (0.000)** (0.783) --- MKT 0.039 0.044 -0.082 -0.020 -0.119 1.000 (0.510) (0.455) (0.164) (0.736) (0.044)* --- SMB -0.090 -0.121 0.073 -0.028 0.079 0.007 1.000 (0.127) (0.040)* (0.216) (0.640) (0.183) (0.908) --- HML -0.034 0.003 0.016 0.008 -0.007 -0.369 0.000 1.000 (0.571) (0.961) (0.783) (0.897) (0.908) (0.000)** (0.995) --- MOM -0.035 0.112 0.029 0.002 -0.027 -0.282 -0.206 0.106 1.000 (0.551) (0.058) (0.624) (0.973) (0.646) (0.000)** (0.001)** (0.074) ---
17 significant in line with the sign one would expect the relation to have, since an increase in the central bank target rate and a decline in the monetary base are associated with a restrictive monetary stance of the central bank. Another relation that stands out is the significant negative correlation between the monetary base and the size factor. One would expect a positive correlation which means that smaller firms benefit from increases in the monetary base (Gertler and Gilchrist, 1994). Lastly M2 and the market factor are negatively correlated (-0.119). This is remarkable since one would expect a positive correlation since expansionary monetary policy should lead to higher stock market returns as previously argued in the literature review.
5. Results
5.1 Monetary environments
The return and volatility characteristics of the Japanese Stock market index in different monetary environments are discussed in table 4. In Panel a one can see that for the full sample the average nominal return is 1.88% per month and 1.16% per month in real terms. Also, both the nominal and the real returns are significantly higher for the expansionary environments then for the restrictive environments as shown by the P-values that lie below the 5% significance threshold (and for the real returns below the 1% significance threshold). To account for outliers, within the sample that affect the overall outcome, the non-parametric Wilcoxon signed rank test is performed. As can be seen in panel a of table 4 this test also rejects the null hypothesis of equality in median returns between the two monetary environments for real returns. For the nominal returns the null hypothesis cannot be rejected since the Z-statistic of 1.95 is lower then the threshold Z-statistic of 1.96 (5% p-value). This shows that outliers in monetary environments for the nominal returns have some effect on the overall picture. The volatility, measured by the standard deviation of the returns, for the expansive period is lower (respectively 9.72% for the nominal returns and 9.60% for the real returns) then the restrictive period (10.62% for the nominal returns and 10.66% for the real returns). 21 Therefore, expansive monetary environments are associated with higher returns and lower volatility, hence the classic risk/reward explanation does not hold in this analysis. Panel b of table 4 shows a breakdown of returns for each expansionary or restrictive period. During the expansive environments only one period has negative returns for both the nominal and the real returns. In the restrictive environments only one positive return period is observed for the real returns and two for the nominal returns. These results are in line with the results presented by Jensen and Johnson (1995) who find similar outcomes for the United
21
18 States. Moreover, the results are in line with Conover, Jensen and Johnson (1998) who show that for the Japanese market volatility is lower in expansionary monetary environments compared to restrictive environments.
Table 4. Average quarterly returns and standard deviations in percentages of the TOPIX Index between 1960 and 2013. Returns are calculated as either nominal returns or real returns (returns corrected by the quarterly rate of inflation). Nominal and real returns are calculated over the full sample, over the sub sample for which the monetary environment was expansionary and for a subsample for which the monetary environment was restrictive. Expansive monetary environments are defined as a series of downward rate changes of the central bank’s target rate. The restrictive monetary environment is defined as a series of upward rate changes of the central bank’s target rate. A new series starts whenever a rate changes in the opposite direction of the previous rate change. Panel a provides an overview of the average returns over the full sample, expansionary subsample and the restrictive subsample. The T-statistic and the Wilcoxon Z-statistic and the respective p-values (in brackets) reported in panel a. are related to the null hypothesis of equality of averages and medians between the expansionary and the restrictive monetary environments. Panel b provides a break down of average nominal and real returns per series of either expansive or restrictive monetary environments. ** indicates significance at the 1% level, * indicates significance at the 5% level. SD refers to the standard deviation of the returns.
Panel a.
Full Sample Expansive Restrictive
Average SD Average SD Average SD T-Stat (P-val)
Wilcoxon Z-stat (P-val) Returns 1.879 10.039 2.763 9.723 -1.463 10.623 2.42 (0.016)* 1.95 (0.052)* Real Returns 1.162 10.041 2.281 9.597 -3.044 10.664 3.08 (0.002)** 2.57 (0.010)** Panel b.
Expansive Monetary Period Restrictive Monetary Period Start of Series Observations
Average Real Return
Average
Return Start of Series Observations
Average Real Return Average Return 30-9-1960 4 3.778 4.688 29-9-1961 5 -5.385 -3.918 31-12-1962 5 -2.490 -0.842 31-3-1964 4 -2.092 -0.614 31-3-1965 10 2.475 3.473 29-9-1967 4 2.981 3.999 30-9-1968 4 2.035 2.883 30-9-1969 5 -1.908 -0.430 31-12-1970 10 10.272 11.974 29-6-1973 8 -5.291 -1.010 30-6-1975 16 0.738 2.218 29-6-1979 5 -0.616 1.460 30-9-1980 35 4.851 5.236 30-6-1989 9 -2.795 -2.146 30-9-1991 60 0.230 0.259 29-9-2006 9 -4.552 -4.294 31-12-2008 20 2.199 2.280
Base case factor models
In Table 5 the results of the base case three factor model estimated over the 25 portfolios formed by market capitalization and book-to-market value are shown.22 The results reveal that the smaller portfolios load stronger on the size factor then the portfolios including larger companies, this is best seen by scanning through the 5x5 matrix of the beta coefficients related to the size factor (SMB) from top to bottom. The same holds for the value factor (HML) which loads stronger on the value portfolios (high book-to-market portfolios). This is best observed by looking at the beta coefficient of the HML factor from right to left. So it appears that the base case model shows the characteristics one would expect to find in the three factor model.
22
19
Table 5. Overview of the parameters of a time series regression of the following composition;
Where the dependent variable , represents a time series of value weighted returns for portfolio i, is the intercept for portfolio i. is
the time series of market returns in excess of the risk free rate. SMB refers to a factor that proxies for firm size whereas HML refers to a factor that proxies for value stocks. The respective coefficients for the factors are denoted as where k represents the respective factor to which
the coefficients belongs. The regression is performed over 25 portfolios and estimated using Newey-West standard errors. Portfolios are constructed by sorting stocks in quintiles based on market capitalization and book-to-market value. This yields five baskets (quintiles) ranging from the smallest (basket 1) to the largest (basket 5) stocks and five baskets (quintiles) ranging from low book to market stocks (basket1) to high book to market stocks (basket 5). All returns are monthly and in percentages over the period between October 1989 and August 2013. Reported T-statistics are for the null hypothesis that the respective coefficient deviates from 0. ** indicates significance at the 1% level, * indicates significance at the 5% level. The Wald test and the associated Chi2 statistic is for the null hypothesis that the 25 coefficients for the associated factor are significantly different from one and other ( ). The reported GRS Statistic (Gibbons, Ross and Shanken,
1989) is a test statistic of the significance of the joint deviation of the alphas from zero ( ).
Book-to-Market Quintiles
Size Quintiles
low 2 3 4 high low 2 3 4 high Wald Test
T-stat small 0.429 0.191 0.132 0.105 0.113 small 1.694 1.485 0.963 1.320 1.542 2 -0.018 -0.100 -0.045 -0.116 -0.050 2 -0.119 -0.912 -0.436 -1.510 -0.770 3 -0.365 -0.186 -0.350 -0.288 -0.109 3 -2.052* -1.763 -3.322** -3.258** -1.005 4 -0.280 -0.268 -0.097 -0.132 -0.156 4 -2.205* -2.155* -0.722 -1.141 -1.364 big -0.118 0.000 0.142 0.203 -0.557 big -1.679 -0.004 1.196 1.487 -1.534 T-stat
small 1.164 1.025 0.973 0.907 0.931 small 21.816** 30.915** 28.193** 59.739** 53.155** Chi2 Stat 200.617
2 1.047 1.006 0.997 0.999 1.014 2 32.914** 51.656** 40.920** 48.982** 58.856** P-Value 0.000**
3 1.117 1.050 1.022 1.044 1.124 3 39.945** 45.799** 51.618** 44.012** 57.521** 4 1.065 1.056 1.024 1.024 1.132 4 42.879** 36.038** 31.933** 45.668** 32.805** big 1.011 0.973 0.981 1.020 1.124 big 51.638** 40.353** 30.971** 39.621** 15.791**
T-stat
small 1.507 1.208 1.132 1.075 1.095 small 17.815** 29.577** 22.850** 30.591** 28.593** Chi2 Stat 5830.458
2 1.227 1.014 0.990 0.945 0.969 2 20.465** 30.162** 28.462** 29.332** 30.753** P-Value 0.000**
3 1.031 0.917 0.776 0.765 0.755 3 16.150** 14.854** 22.882** 18.159** 21.060**
4 0.648 0.515 0.482 0.474 0.547 4 12.716** 11.379** 9.813** 11.334** 8.545**
big -0.071 -0.142 -0.093 -0.017 0.181 big -2.209* -5.201** -2.178* -0.327 1.246
T-stat
small 0.059 0.355 0.360 0.434 0.682 small 0.441 5.677** 4.087** 11.012** 16.478** Chi2 Stat 1725.648
20
Table 6. Overview of the parameters of a time series regression of the following composition;
Where the dependent variable , represents a time series of value weighted returns for portfolio i, is the intercept for portfolio i and also
the pricing error of the asset pricing model for cases in which the left hand and the right hand side of the regression are both returns. The market factor (MKT) is the excess return of the market over the risk free rate. SMB refers to a factor that proxies for firm size whereas HML refers to a factor that proxies for value stocks. The monetary policy proxy in this regression is the month on month percentage change in the monetary base (MB). The monetary base is the sum of the reserves banks hold at the central bank and the currency in circulation. The respective coefficients for the factors are denoted as where k represents the respective factor to which the coefficients belongs. The
regression is performed over 25 portfolios and estimated using Newey-West standard errors. Portfolios are constructed by sorting stocks in quintiles based on market capitalization and book-to-market value. This yields five baskets (quintiles) ranging from the smallest (basket 1) to the largest (basket 5) stocks and five baskets (quintiles) ranging from low book to market stocks (basket1) to high book to market stocks (basket 5). All returns are monthly and in percentages over the period between October 1989 and August 2013. Reported T-statistics are for the null hypothesis that the respective coefficient deviates from 0. ** indicates significance at the 1% level, * indicates significance at the 5% level. The Wald test and the associated Chi2 statistic are for the null hypothesis that the 25 coefficients for the associated factor are significantly different
from one and other ( ).
Book-to-Market Quintiles
Size Quintiles
low 2 3 4 high low 2 3 4 high
Wald Test T-stat small 0.421 0.198 0.107 0.121 0.104 small 1.738 1.495 0.785 1.462 1.363 2 -0.018 -0.088 -0.022 -0.103 -0.053 2 -0.126 -0.803 -0.205 -1.281 -0.812 3 -0.353 -0.151 -0.319 -0.265 -0.106 3 -2.025* -1.484 -2.952** -2.973** -0.992 4 -0.259 -0.222 -0.042 -0.114 -0.156 4 -2.058* -1.849 -0.331 -1.005 -1.321 big -0.107 -0.007 0.147 0.210 -0.517 big -1.517 -0.064 1.241 1.621 -1.455 T-stat
small 1.163 1.026 0.971 0.908 0.931 small 22.061** 30.731** 28.358** 59.222** 53.286** Chi2 Stat 201.246
2 1.047 1.007 0.998 0.999 1.014 2 32.644** 51.026** 40.089** 48.370** 58.616** P-Value 0.000**
3 1.117 1.052 1.024 1.045 1.124 3 39.687** 46.161** 50.970** 43.845** 56.579**
4 1.066 1.058 1.027 1.025 1.132 4 42.808** 35.621** 31.456** 45.241** 32.626**
big 1.011 0.972 0.981 1.021 1.126 big 51.661** 40.207** 30.893** 39.886** 15.817**
T-stat
small 1.508 1.207 1.137 1.072 1.096 small 18.065** 29.861** 22.745** 30.457** 28.696** Chi2 Stat 5744.012
2 1.227 1.012 0.986 0.943 0.970 2 20.957** 30.570** 28.737** 29.429** 31.770** P-Value 0.000**
3 1.029 0.910 0.770 0.761 0.755 3 16.169** 15.265** 22.809** 18.295** 20.894**
4 0.644 0.506 0.471 0.471 0.547 4 12.497** 11.595** 10.106** 11.490** 8.712**
big -0.073 -0.141 -0.094 -0.018 0.173 big -2.281* -5.252** -2.237* -0.363 1.231
T-stat
small 0.059 0.356 0.359 0.435 0.681 small 0.434 5.688** 4.013** 11.101** 16.419** Chi2 Stat 1721.059
2 -0.066 0.173 0.327 0.540 0.781 2 -0.612 2.300* 4.329** 8.857** 17.692** P-Value 0.000**
3 -0.042 0.259 0.473 0.683 0.923 3 -0.384 4.353** 6.220** 10.028** 13.460**
4 -0.129 0.330 0.480 0.742 0.936 4 -1.608 3.466** 4.859** 8.701** 11.524**
big -0.355 0.098 0.427 0.765 1.282 big -7.282** 1.245 5.720** 8.540** 7.291**
T-Stat
small 1.204 -1.085 4.115 -2.632 1.457 small 0.171 -0.424 1.048 -0.850 0.635 Chi2 Stat 21.991
21 Furthermore, in almost all regressions in table 5 the three factors load significantly on the 25 portfolios. From the Wald test it follows that for all three factors in table 5 the null hypothesis of equality of beta coefficients per factor ( , is rejected. This means that the exposures of the size and
value factors are different across portfolios sorted on size and book-to-market value. Moreover, since the three factor model presented in table 5 (and the four factor model in appendix J), has returns on both sides of the equation it can be interpreted as an asset pricing model with the intercept, alpha, as the average pricing error. In five of the 25 regressions the null hypothesis that alpha is equal to zero is rejected, which indicates that the asset pricing model as depicted in table 5 does a good job in pricing assets in the individual regressions since most alphas do not significantly deviate from zero. To further investigate this statement the GRS Statistic is provided, with a F-statistic of 1.884 and a P-value of 0.008. This indicates that the null hypothesis, associated with the GRS Test, that the alphas are jointly equal to zero is rejected hence the three factor model does not price assets fully in the cross-section of stock returns. In the appendix the four factor model is also presented which yields similar results, with a GRS Statistic of 1.876 and P-value of 0.008. Therefore, with the additional momentum factor the model is still rejected as capturing all the risks to which the portfolio returns are exposed (See Appendix K and J). 5.2 Fama-Macbeth models
22 consistency of the monetary policy proxies. Also, from theory and from the evidence presented in table 4, a positive correlation between the monetary base and stock returns and a negative correlation between the target interest rate of the central bank and stock returns is expected, since an expansionary monetary stance is associated with higher asset returns and vice versa. In table 6, therefore, I would expect to find positive beta coefficients for the monetary base. Instead the opposite is shown in the table since all three significant beta coefficients are negative. Furthermore, even though not significant, for 18 out of the 25 regressions the sign of the beta coefficient is negative. This is counter intuitive to what has previously been argued theoretically and shown empirically (table 4). These results are robust for different monetary proxies and for different model specifications.23
Table 7. Overview of the risk premia per factor for multiple regression settings for the period between October 1989 and August 2013. Risk premia are calculated using the static Fama-Macbeth regression technique (Fama and Macbeth, 1973). In the table the first column shows the type of regression being performed the two base regressions are either the three factor model (Fama and French, 1993) denoted as FF or the four factor model (Carhart, 1997) denoted as CH. Each base regression is then supplemented by one of three monetary variables, the central bank target rate (TR), the monetary base (MB) or a variable constructed using principle components analyses (PCA). The Fama and French (1993) factors are the risk premia denoted with either MKT for the market factor, SMB for the size factor or HML for the value factor. The additional Carhart (1997) Factor for momentum is denoted as MOM. The monetary policy factor is denoted as MONPOL and varies across regressions depending on which type of monetary policy proxy is used. The first row of the table provides the respective risk premium each column belongs to. T-statistics are calculated as follows:
where the average time series risk premium for regression i and factor k is divided by the standard deviation of the time series risk premium obtained from the cross-sectional regression at each point in time divided by the square root of the number of observations, t. ** indicates significance at the 1% level, * indicates significance at the 5% level. Panel a provides risk premia based on market capitalization weighted returns and the risk premia in panel b are based on equal weighted returns. Risk premia are denoted as monthly returns in percentages. Panel a. Risk Premia T-Stats FF 0.976 -1.112 0.236 0.487 1.628 -1.591 1.082 2.962** FF TR 0.297 -0.407 0.202 0.485 -0.101 0.490 -0.586 0.931 2.952** -2.638** FF MB 0.785 -0.813 0.176 0.506 0.038 1.324 -1.181 0.811 3.084** 3.975** FF PCA 0.778 -0.882 0.231 0.497 0.702 1.363 -1.325 1.058 3.023** 1.962* CH 0.312 -0.395 0.194 0.545 1.654 0.585 -0.614 0.892 3.392** 2.372* CH TR -0.352 0.295 0.161 0.542 1.638 -0.102 -0.644 0.458 0.744 3.378** 2.351* -2.653** CH MB 0.695 -0.721 0.172 0.514 0.837 0.037 1.287 -1.109 0.794 3.214** 1.106 3.261** CH PCA 0.242 -0.309 0.195 0.546 1.521 0.472 0.519 -0.517 0.843 3.258** 2.337* 1.430 Panel b.
Risk Premia T-Stats
FF 0.717 -1.043 0.425 0.601 1.377 -1.604 1.859 3.595** FF TR -0.154 -0.099 0.327 0.597 -0.113 -0.289 -0.154 1.456 3.576** -3.288** FF MB 0.710 -0.949 0.366 0.591 0.018 1.365 -1.480 1.628 3.542** 2.428* FF PCA 0.587 -0.873 0.400 0.606 0.501 1.177 -1.412 1.766 3.620** 1.545 CH 0.733 -1.063 0.429 0.601 0.081 1.524 -1.722 1.846 3.595** 0.125 CH TR -0.097 -0.173 0.339 0.597 -0.067 -0.113 -0.200 -0.290 1.491 3.576** -0.103 -3.282** CH MB 0.996 -1.293 0.413 0.588 -0.392 0.022 1.996* -2.030* 1.788 3.532** -0.576 2.662** CH PCA 0.647 -0.950 0.413 0.607 -0.051 0.521 1.385 -1.591 1.790 3.620** -0.078 1.579 23
24 negative risk premium for the central bank target rate in the sense that in both cases investors require higher returns for more exposure to monetary policy.
Graph 2 provides a graphical overview of the selected asset pricing models including and excluding monetary policy proxies. In the graph the actual returns of the portfolios are displayed (y-axis) versus the predicted returns from the asset pricing model. One can see that when the monetary policy is added to the asset pricing model, the dots move somewhat closer to the regression line that minimizes the sum of the squared errors. Also the adjusted R2 of the cross-sectional regression which is represented by the regression line in the graph is higher when the monetary policy proxy is included, increasing from 0.449 to 0.613 for the three factor model. This provides evidence that by adding the monetary policy factor in the standard asset pricing frameworks, assets are priced more precisely. The Graph also shows that certain groups of portfolios are less well modeled then others. Portfolio 51, which consists of small growth stocks is persistently badly priced regardless of which model is used. Furthermore, the large firms, recognizable by having a 5 as the second number are priced gradually worse moving from growth to value stocks. Value stocks, recognizable by a 1 as the first number, are priced well by the model each being very close to the regression line.
5.3 Comparison of Asset Pricing Models
25
Graph 2. Overview of the predicted returns generated using the Fama-Macbeth regression technique (Fama and Macbeth, 1973) for several regression models versus the actual returns from the 25 portfolios constructed by market capitalization and book-to-market value. Above each graph the associated regression model is depicted, on the left hand side the two base case models are shown; the three factor model (panel a) and the four factor model (panel c). On the right hand side similar models are shown with the addition of a monetary policy proxy. The monetary policy proxy in this regression is the month on month percentage change in the monetary base (MB). The betas are estimated over the period between October 1989 and august 2013 using time series regression with Newey-West standard errors. Lambdas are calculated from cross-sectional regressions at each moment in time using the betas from the time series regression as independent variables. The dots in the graphs represent the combination of actual and predicted average monthly returns in percentages. Each dot represents a portfolio with the first number referring to value (1 equals value stock, 5 equals growth stock) and the second number referring to size (1 equals small, 2 equals large). R2 and adjusted R2 for the regression lines are presented in the right bottom corner of each graph.
Panel a. Panel b. Panel c. Panel d. 11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 51 52 53 54 55 R² = 0.518 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 -0.60 Act -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 u al R e tu rn s
Predicted Returns adj R2=0.449
11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 51 52 53 54 55 R² = 0.677 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 -0.60 Act -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 u al R e tu rn s
Predicted Returns adj R2=0.613
11 12 13 14 15 21 22 23 24 25 31 32 33 34 35 41 42 43 44 45 51 52 53 54 55 R² = 0.576 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 -0.60 Act -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 u al R e tu rn s
Predicted Returns adj R2=0.491
26 Table 8 provides an overview of all the models and the associated F-statistics and P-values of the GRS test for each model. In the table several models have significance levels above the threshold 5% significance level, this means that for these models the null hypothesis that the alphas are jointly zero can not be rejected (i.e. these models price the assets relatively accurate). When the monetary base is added to the model, in the case of value weighted returns, the model’s GRS P-value becomes 14.16%. Furthermore, by adding the central bank target rate as the monetary proxy the null hypothesis of zero pricing error cannot be rejected in three of the four regression settings (for all models but the value weighted three factor model). The risk premium associated with the monetary base seems to have a stronger impact for value weighted stocks then for equal weighted stocks. This could indicate that larger firms are better priced when the monetary base is included then smaller firms. The alpha coefficients in the table show that in general the addition of a monetary policy proxy leads to a smaller average pricing error. The PCA variable leads to the largest reduction in alpha for the value weighted portfolios, moving from 0.434 for the plain three factor model to 0.397 with the addition of the PCA variable. For the equal weighted portfolios the central bank target rate has the largest impact with a reduction from 0.331 for the four factor model to 0.291 for the same model with the central bank target rate included.
Table 8. An overview of the GRS Statistics for time series regressions using the time series of risk premia generated in the Fama-Macbeth technique (Fama and Macbeth, 1973) as independent variables. By using the time series of risk premia in a basic time series regression alpha (the intercept) of the time series regression becomes the pricing error. The GRS Test (Gibbons, Ross and Shanken, 1989) is used to test the significance of the joint deviation of the 25 alphas from 0. The F-statistic and P-value associated with the GRS Test are presented per regression setting. The base case regressions are the three factor model (FF) (Fama and French, 1993) and the four factor model (CH) (Carhart, 1997). The base case regressions are expanded upon using three monetary policy proxies; the month on month change in the central bank target rate (TR), the month on month percentage change in the monetary base (MB) and a variable constructed using Principle Component Analysis (PCA) using TR, MB and the year on year percentage change in M1 and M2 as inputs. The column with α as heading provides the average pricing error of the model in percentages per month. *next to the P-values indicate that the average pricing errors (alpha’s) are not significantly different from 0 at 5% significance level, ** indicates insignificance at 1% level. All regressions are performed using Newey-West standard errors.
F-Stat P-Value α F-Stat P-value α Value Weighted Equal Weighted
FF 1.913 0.007 0.437 1.743 0.018* 0.329 FF TR 1.720 0.020* 0.421 1.480 0.070** 0.310 FF MB 1.328 0.142** 0.421 1.616 0.035* 0.322 FF PCA 1.813 0.121* 0.397 1.718 0.021* 0.313 CH 1.594 0.397* 0.313 1.737 0.019* 0.331 CH TR 1.388 0.108** 0.292 1.469 0.074** 0.292 CH MB 1.281 0.172** 0.370 1.592 0.040* 0.355 CH PCA 1.539 0.052** 0.291 1.711 0.021* 0.317
