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The model definitions are given below:. The next step in the analysis is to create sorted portfolios from which the Fama and French factor return series could be calculated. Other sorting choices might have been used; however, [ 19 ] finds no differences in model performance when testing differing sorting methods. My first data point is at the 31st of December , and the investment variable is calculated as in Eq.

The portfolios were sorted at the end of May each year, and therefore the first available return observation in the final analysis is the return of June , sorted according to accounting data at the end of fiscal year Thus, the time period for the actual analysis is June to May or months of return data. Fifty percent of the market cap was used as the breakpoint for size. The resulting groups are labelled with two letters.

The first letter describes the size group, small S or big B. Sorted portfolio groups to construct Fama-French factors. Regressions were run on three sets of 16 left-hand-side regression portfolios. Table 1 shows the constructed dependent variables. Construction of dependent variables: each notation of a dependent variable in this table shows the monthly excess return of the corresponding sorted portfolio.

For example, S1BM1 shows average of the monthly excess returns of stocks included in the smallest size and lowest book-to-market portfolio. Panels A through C in Table 2 show the average number of stocks in each of the regression portfolios.

A similar phenomenon can be observed in Panel B, where low operating profitability is a feature of smaller companies and high operating profitability is more often found in stocks with higher market capitalisations. In this section, I give descriptive statistics for the regression portfolios and explanatory factors used in the regressions.

In Table 3 , the standard deviations of monthly excess return of portfolios seem to be very high. One of the explanations is that portfolio groups include small numbers of stocks. The second explanation could be the economic crisis experienced in in Turkey. This crisis created very high volatility in the financial markets, and the daily change in stock market index viz.

In normal circumstances, I would expect the standard deviations to be half of the figures in Table 3. Average monthly excess returns and standard deviations for definitions of variables, see Section 4. Table 3 shows that big-sized portfolios tend to benefit from high book-to-market ratios. On the other hand, small portfolios tend to benefit from high profitability, while the effect is weak on big portfolios.

In Panel B, returns of portfolios sorted and grouped according to their size and profitability are given. In the Turkish stock market, the highest monthly returns coincide with the high profitability. As you will see in the remainder of the study, I think the most important factor determining the returns of stocks is profitability. The main message is that, even if a company is grouped in the smallest size, if its profitability is high, its return is expected to be high. But one peculiar result is that S4OP3, which represents a portfolio with low profitability and the biggest size, has a monthly excess return of 1.

One explanation could be that even if the biggest-sized companies have low profitability, if it is an aggressive investing company and the expectation of the market participants is positive, then a monthly average return of 1. As you may see in Panel C of Table 3 , big companies with aggressive investing have the highest returns. Factor spanning regressions are a means to test if an explanatory factor can be explained by a combination of other explanatory factors.

Spanning tests are performed by regressing returns of one factor against the returns of all other factors and analysing the intercepts from that regression. These results suggest that removing either the RM-Rf or SMB factor would not hurt the mean-variance-efficient tangency portfolio produced by combining the remaining four factors.

Factor spanning regressions on five factors: spanning regressions using four factors to explain average returns on the fifth June —May , months. Having presented the methodology and statistical results, in this part, I present an answer to important question if the estimated models can completely capture expected returns.

The GRS statistic is used to test if the alpha values from regressions are jointly indistinguishable from zero. If a model completely captures expected returns, the intercept should be indistinguishable from zero. Hence, the first hypotheses are:. Finally, average individual regression alphas and joint GRS regression f-values were used together in order to compare the performance between the tested models.

The GRS test was developed by Gibbons et al. The following regression defines the GRS test:. The GRS test is used in this study to determine whether the alpha values from individual model regressions are jointly non-significant and hence to find out if a model completely captures the sample return variation.

As intercepts from individual regressions approach zero, the GRS statistic will also approach zero. However, since the GRS statistic derives its results from comparing the optimal LHS and RHS portfolios, the resulting statistic is not strictly comparable between models. A set of several summary metrics were deployed in order to compare the performance of the asset pricing models.

GRS statistics and average alpha values were used as the main two statistics in order to determine how good the different asset pricing models performed in explaining portfolio returns. In addition to these statistics, average absolute alpha spread was added for a more complete picture of the alpha results. Only five-factor model in Panel C has a p-value of 0. Both [ 19 , 22 ] pay specific importance of the absolute values of alphas. Keeping this in mind, my main conclusion from the model comparison tests follows.

Beware that, as discussed in [ 19 ], fGRS values between models cannot be strictly compared. The fGRS in [ 21 , 22 ] is used in comparisons between models only in combination with a comparison of average alpha values.

Fama and French [ 19 ] instead use the numerator of a GRS regression as a comparison value when choosing which factors to include in a model. In every panel of Table 5 , explanatory power measured by average R 2 clearly improves with the inclusion of more factors. For this reason, metrics for explanatory power are important in providing additional help to compare these types of asset pricing models.

The main conclusions from the performance comparison tests can be summarised as follows. A GRS test on the joint set of all tested portfolios clearly rejects all tested models as complete descriptions of average returns. The CAPM model elicits the lowest average absolute alpha values of the three tested models throughout all tests but shows a statistically insignificant fGRS value compared to other models.

Considering all the evidence in Table 5 , it is clear that the 5F-FF model shows the strongest performance out of the three models for the sample. In the following section, I provide alpha values from individual left-hand-side portfolio regressions, and I re-examine the alpha values from a different perspective.

In this part, I give individual regression alphas, the coefficients that were defined in Eqs. I concentrate on the significance of alphas. Significant alpha patterns between models are compared and further analysed by looking at regression slopes in Tables 6 — 8.

At the end of May each year, stocks are distributed into four size groups using sample quartile breakpoints. For the definitions of dependent variables, see Table 1. The highest number of significant alpha values belongs to 3F-FF model. In addition to this observation, in none of the models, RM-Rf has no statistically significant coefficient except in a few models see rows 13, 14 and 15 in Tables 6 — 8.

There is an interesting pattern in the results of the regression tables Tables 6 — 8. As the size of the companies in portfolios increases, more factors become statistically significant, and the explanatory power of the 5F-FF model rises.

Before I present the regression details, readers should be aware that in an OLS regression, R-squared values will always increase with the inclusion of more factors. In other words, correlation between explanatory variables, which are created from return differences, and dependent variables has to be highly correlated.

Hence, R 2 s in the equations become stronger and true. Sundqvist in [ 22 ] states that:. This might have been due to the fact that BIST Index, which approximates the monthly excess return of the market, is heavily financial stock weighted. However, using different market indices in all models did not improve the results more information on this issue is given in the discussion of the results in Table 7.

Stocks are independently allocated to four OP groups, using sample quartile breakpoints. The intersections of the two sorts produce 16 size-OP portfolios. The LHS variables in each set of 16 regressions are the monthly excess returns on the 16 size-OP portfolios. The 3F-FF regressions find larger intercept t-values on most portfolios compared to the 5F-FF regressions, of which three are more than five standard errors from zero.

I can find no exceptional characteristics that might shed light into the reasons behind the significant alpha value. However, as I already discussed above, this may be due to the fact that BIST Index is heavily financially sector stock weighted. From Table 6 it is easily seen that last four rows in the table excess monthly returns of the biggest-sized company portfolios are best explained by the 5F-FF model.

However, as can be seen from the t-statistics, when the company size gets smaller portfolios starting with the letter S1 and S2 , RMW and CMA variables have no effect on excess monthly returns of small-sized portfolios, while SMB and HML variables have significant t-statistics. Fama and French [ 19 ] note however that one should not expect univariate characteristics and multivariate regression slopes connected to the characteristic to line up. The slopes estimate marginal effects holding constantly all other explanatory variables, and the characteristics are measured with lags relative to returns when pricing should be forward-looking.

The dependent variables are the monthly excess returns of the portfolios sorted by size and profitability for the definitions of the variables, see Table 1. The results in Table 7 are not much different from the ones that are in Table 6. The best performing model is the 5F-FF model.

This shows that, at least in the Turkish case, market risk is not a preliminary and strong factor in determining monthly excess returns of portfolios. When one concentrates on alpha coefficients of the 5F-FF model, it is seen that only 3 of the 16 alphas are statistically significant.

One of the main messages of the results of the 5F-FF model is that as the size of the companies under investigation increases, the explanatory power of the model rises. It seems from the results of both Tables 6 and 7 that the best explanatory factor for the monthly excess returns of portfolios is the size factor. As the size of the companies in portfolios that have been sorted by size and profitability gets smaller, RMW and CMA become ineffective in determining the monthly excess returns of these portfolios see the coefficients of RMW and CMA in the first six rows of Table 7.

This result indicates that the CAPM and 3F-FF model are not the true definition of a model to explain the variations in monthly excess returns of portfolios. Stocks are independently allocated to four Inv groups, using sample quartile breakpoints. The intersections of the two sorts produce 16 size-Inv portfolios. The LHS variables in each set of 16 regressions are the monthly excess returns on the 16 size-Inv portfolios. Variations of the monthly returns of portfolios constructed by big-sized companies are best explained by the 5F-FF model.

However, CMA factor turns out to be insignificant when estimating the model for portfolios with relatively small-sized companies. This study adds to the asset pricing literature using the Turkish data. The best suited model but not perfect for the Turkish case is 5F-FF model. As seen elsewhere [ 17 , 19 , 20 , 21 , 22 , 23 ], as the number of explanatory variables increases in the regression portfolios, explanatory power of the equation increases, and the R 2 rises.

Besides testing all intercepts individually, we also tested whether all the pricing errors were jointly equal to zero. Gibbons et al. The 5F-FF model shows the strongest performance out of the three models for the sample.

This might be due to the fact that RMW and CMA factors add little in explaining the cross-sectional variations of portfolio returns in Turkey. Readers should be aware that correlation between explanatory variables, which are created from return differences as in the case of definition of Fama-French factors , and dependent variables has to be highly correlated. Consequently, our empirical results are reasonably consistent with [ 19 , 20 , 21 , 22 ] findings, and the 5F-FF model was found viable and superior to CAPM and 3F-FF model for the Turkish stock market.

Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3. Edited by Soner Gokten. Published: January 17th, Impact of this chapter. Variable definitions This subsection defines the variables needed in the factor creation process. The return period Fama and French use 6-month gap between the ends of the fiscal year and the portfolio formation date can be considered as convenient and conservative. Filtering data At the end of each year, I eliminated firms that have the following specifics: 1 negative book-to-market values were removed, and 2 the companies with yearly increase in their investment, as defined in Eq.

Construction of Fama-French factors The next step in the analysis is to create sorted portfolios from which the Fama and French factor return series could be calculated. The sorting process is as follows: 1 First of all, stocks are sorted according to their market cap to define small-sized and big-sized stocks. Regression portfolios and other data used in the regression analysis Regressions were run on three sets of 16 left-hand-side regression portfolios.

Table 1. Table 2. Average number of stocks in regression portfolios. Read More. Forex trading is an around the clock market. Benzinga provides the essential research to determine the best trading software for you in Benzinga has located the best free Forex charts for tracing the currency value changes.

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Range aka points. See more Scatterplot. Volume candles. Hollow candlesticks. Candle trend chart. Multiple Charts Layout. Multiple charts grid. Symbol sync. Aggregation sync. Date range sync. Indicators sync. Compare instruments. Amount of drawing tools. Magnet mode. Drawing mode. Amount of default indicators. Indicator templates. Price Scale. Automatic scale. Manual scale. Left scale. Percent scale.

Logarithmic scale. See more Countdown. Multiple scales. Inverted scale. Locked scale. Configurable default aggregations. N ticks aggregations. Date range. User-customizable aggregations in GUI. Arithmetic operators for custom series. N seconds aggregations. Timezone selector. Session breaks. Market data from your provider. Market data integrated out of box. Data export. Data loading by chunks. Instrument search. See more Events. Open positions.

Active orders. Basic order types market, limit, stop. Bracket orders. Custom chart colors. Custom font family. Custom colors for drawings and indicators. The same model was tested using international data [ 20 , 21 ], and they have found similar results. Data was collected for all available active and dead stocks in Istanbul stock exchange totalling observations.

The downloaded sample included a large amount of stocks, which were already dead at the beginning of the research period, as well as some missing data types and data errors, which ought to be removed.

This subsection defines the variables needed in the factor creation process. Market capitalisation or market cap was used as a measure of size for each stock and was calculated by multiplying the price P at the 31st of December each year with outstanding shares at the 31st of December for the same year. The price data was obtained from FDY.

Book equity was calculated as yearly total assets minus total liabilities from FDY. Operating profitability OP was calculated by dividing operating income by book equity following [ 22 ]. Finally, investment Inv was calculated as in Eq. It consists of stocks, which are selected among the stocks of companies listed on the national market excluding list C companies. Monthly returns for stocks are all calculated as natural log difference of monthly stock data.

Fama and French use 6-month gap between the ends of the fiscal year and the portfolio formation date can be considered as convenient and conservative. Hence, to ensure that all accounting variables are known by investors, I assume that all accounting information is made public by the end of May, and I use monthly returns from the beginning of June to the end of the following year in May. And, each year at the end of May, I sort the portfolios. Fama and French [ 15 , 16 ] used value-weighted returns in their study; however, they also stressed that equal-weighted returns do a better job than value-weighted returns in explaining returns by 3F-FF model.

Lakonishok et al. Hence, the equal-weighted monthly returns on each portfolio were used in this study. At the end of each year, I eliminated firms that have the following specifics: 1 negative book-to-market values were removed, and 2 the companies with yearly increase in their investment, as defined in Eq.

This would imply that the company in question lost half of its assets, or more than doubled its assets in the given year, which seems very unlikely during normal recurring circumstances. The model definitions are given below:. The next step in the analysis is to create sorted portfolios from which the Fama and French factor return series could be calculated. Other sorting choices might have been used; however, [ 19 ] finds no differences in model performance when testing differing sorting methods.

My first data point is at the 31st of December , and the investment variable is calculated as in Eq. The portfolios were sorted at the end of May each year, and therefore the first available return observation in the final analysis is the return of June , sorted according to accounting data at the end of fiscal year Thus, the time period for the actual analysis is June to May or months of return data.

Fifty percent of the market cap was used as the breakpoint for size. The resulting groups are labelled with two letters. The first letter describes the size group, small S or big B. Sorted portfolio groups to construct Fama-French factors. Regressions were run on three sets of 16 left-hand-side regression portfolios. Table 1 shows the constructed dependent variables. Construction of dependent variables: each notation of a dependent variable in this table shows the monthly excess return of the corresponding sorted portfolio.

For example, S1BM1 shows average of the monthly excess returns of stocks included in the smallest size and lowest book-to-market portfolio. Panels A through C in Table 2 show the average number of stocks in each of the regression portfolios. A similar phenomenon can be observed in Panel B, where low operating profitability is a feature of smaller companies and high operating profitability is more often found in stocks with higher market capitalisations.

In this section, I give descriptive statistics for the regression portfolios and explanatory factors used in the regressions. In Table 3 , the standard deviations of monthly excess return of portfolios seem to be very high.

One of the explanations is that portfolio groups include small numbers of stocks. The second explanation could be the economic crisis experienced in in Turkey. This crisis created very high volatility in the financial markets, and the daily change in stock market index viz. In normal circumstances, I would expect the standard deviations to be half of the figures in Table 3.

Average monthly excess returns and standard deviations for definitions of variables, see Section 4. Table 3 shows that big-sized portfolios tend to benefit from high book-to-market ratios. On the other hand, small portfolios tend to benefit from high profitability, while the effect is weak on big portfolios.

In Panel B, returns of portfolios sorted and grouped according to their size and profitability are given. In the Turkish stock market, the highest monthly returns coincide with the high profitability. As you will see in the remainder of the study, I think the most important factor determining the returns of stocks is profitability. The main message is that, even if a company is grouped in the smallest size, if its profitability is high, its return is expected to be high.

But one peculiar result is that S4OP3, which represents a portfolio with low profitability and the biggest size, has a monthly excess return of 1. One explanation could be that even if the biggest-sized companies have low profitability, if it is an aggressive investing company and the expectation of the market participants is positive, then a monthly average return of 1. As you may see in Panel C of Table 3 , big companies with aggressive investing have the highest returns.

Factor spanning regressions are a means to test if an explanatory factor can be explained by a combination of other explanatory factors. Spanning tests are performed by regressing returns of one factor against the returns of all other factors and analysing the intercepts from that regression. These results suggest that removing either the RM-Rf or SMB factor would not hurt the mean-variance-efficient tangency portfolio produced by combining the remaining four factors.

Factor spanning regressions on five factors: spanning regressions using four factors to explain average returns on the fifth June —May , months. Having presented the methodology and statistical results, in this part, I present an answer to important question if the estimated models can completely capture expected returns. The GRS statistic is used to test if the alpha values from regressions are jointly indistinguishable from zero.

If a model completely captures expected returns, the intercept should be indistinguishable from zero. Hence, the first hypotheses are:. Finally, average individual regression alphas and joint GRS regression f-values were used together in order to compare the performance between the tested models. The GRS test was developed by Gibbons et al.

The following regression defines the GRS test:. The GRS test is used in this study to determine whether the alpha values from individual model regressions are jointly non-significant and hence to find out if a model completely captures the sample return variation. As intercepts from individual regressions approach zero, the GRS statistic will also approach zero.

However, since the GRS statistic derives its results from comparing the optimal LHS and RHS portfolios, the resulting statistic is not strictly comparable between models. A set of several summary metrics were deployed in order to compare the performance of the asset pricing models. GRS statistics and average alpha values were used as the main two statistics in order to determine how good the different asset pricing models performed in explaining portfolio returns.

In addition to these statistics, average absolute alpha spread was added for a more complete picture of the alpha results. Only five-factor model in Panel C has a p-value of 0. Both [ 19 , 22 ] pay specific importance of the absolute values of alphas.

Keeping this in mind, my main conclusion from the model comparison tests follows. Beware that, as discussed in [ 19 ], fGRS values between models cannot be strictly compared. The fGRS in [ 21 , 22 ] is used in comparisons between models only in combination with a comparison of average alpha values. Fama and French [ 19 ] instead use the numerator of a GRS regression as a comparison value when choosing which factors to include in a model. In every panel of Table 5 , explanatory power measured by average R 2 clearly improves with the inclusion of more factors.

For this reason, metrics for explanatory power are important in providing additional help to compare these types of asset pricing models. The main conclusions from the performance comparison tests can be summarised as follows. A GRS test on the joint set of all tested portfolios clearly rejects all tested models as complete descriptions of average returns.

The CAPM model elicits the lowest average absolute alpha values of the three tested models throughout all tests but shows a statistically insignificant fGRS value compared to other models. Considering all the evidence in Table 5 , it is clear that the 5F-FF model shows the strongest performance out of the three models for the sample.

In the following section, I provide alpha values from individual left-hand-side portfolio regressions, and I re-examine the alpha values from a different perspective. In this part, I give individual regression alphas, the coefficients that were defined in Eqs. I concentrate on the significance of alphas.

Significant alpha patterns between models are compared and further analysed by looking at regression slopes in Tables 6 — 8. At the end of May each year, stocks are distributed into four size groups using sample quartile breakpoints.

For the definitions of dependent variables, see Table 1. The highest number of significant alpha values belongs to 3F-FF model. In addition to this observation, in none of the models, RM-Rf has no statistically significant coefficient except in a few models see rows 13, 14 and 15 in Tables 6 — 8. There is an interesting pattern in the results of the regression tables Tables 6 — 8. As the size of the companies in portfolios increases, more factors become statistically significant, and the explanatory power of the 5F-FF model rises.

Before I present the regression details, readers should be aware that in an OLS regression, R-squared values will always increase with the inclusion of more factors. In other words, correlation between explanatory variables, which are created from return differences, and dependent variables has to be highly correlated.

Hence, R 2 s in the equations become stronger and true. Sundqvist in [ 22 ] states that:. This might have been due to the fact that BIST Index, which approximates the monthly excess return of the market, is heavily financial stock weighted. However, using different market indices in all models did not improve the results more information on this issue is given in the discussion of the results in Table 7. Stocks are independently allocated to four OP groups, using sample quartile breakpoints.

The intersections of the two sorts produce 16 size-OP portfolios. The LHS variables in each set of 16 regressions are the monthly excess returns on the 16 size-OP portfolios. The 3F-FF regressions find larger intercept t-values on most portfolios compared to the 5F-FF regressions, of which three are more than five standard errors from zero.

I can find no exceptional characteristics that might shed light into the reasons behind the significant alpha value. However, as I already discussed above, this may be due to the fact that BIST Index is heavily financially sector stock weighted. From Table 6 it is easily seen that last four rows in the table excess monthly returns of the biggest-sized company portfolios are best explained by the 5F-FF model.

However, as can be seen from the t-statistics, when the company size gets smaller portfolios starting with the letter S1 and S2 , RMW and CMA variables have no effect on excess monthly returns of small-sized portfolios, while SMB and HML variables have significant t-statistics.

Fama and French [ 19 ] note however that one should not expect univariate characteristics and multivariate regression slopes connected to the characteristic to line up. The slopes estimate marginal effects holding constantly all other explanatory variables, and the characteristics are measured with lags relative to returns when pricing should be forward-looking.

The dependent variables are the monthly excess returns of the portfolios sorted by size and profitability for the definitions of the variables, see Table 1. The results in Table 7 are not much different from the ones that are in Table 6. The best performing model is the 5F-FF model. This shows that, at least in the Turkish case, market risk is not a preliminary and strong factor in determining monthly excess returns of portfolios.

When one concentrates on alpha coefficients of the 5F-FF model, it is seen that only 3 of the 16 alphas are statistically significant. One of the main messages of the results of the 5F-FF model is that as the size of the companies under investigation increases, the explanatory power of the model rises. It seems from the results of both Tables 6 and 7 that the best explanatory factor for the monthly excess returns of portfolios is the size factor. As the size of the companies in portfolios that have been sorted by size and profitability gets smaller, RMW and CMA become ineffective in determining the monthly excess returns of these portfolios see the coefficients of RMW and CMA in the first six rows of Table 7.

This result indicates that the CAPM and 3F-FF model are not the true definition of a model to explain the variations in monthly excess returns of portfolios. Stocks are independently allocated to four Inv groups, using sample quartile breakpoints. The intersections of the two sorts produce 16 size-Inv portfolios. The LHS variables in each set of 16 regressions are the monthly excess returns on the 16 size-Inv portfolios. Variations of the monthly returns of portfolios constructed by big-sized companies are best explained by the 5F-FF model.

However, CMA factor turns out to be insignificant when estimating the model for portfolios with relatively small-sized companies. This study adds to the asset pricing literature using the Turkish data. The best suited model but not perfect for the Turkish case is 5F-FF model. As seen elsewhere [ 17 , 19 , 20 , 21 , 22 , 23 ], as the number of explanatory variables increases in the regression portfolios, explanatory power of the equation increases, and the R 2 rises.

Besides testing all intercepts individually, we also tested whether all the pricing errors were jointly equal to zero.

TKE INDICATOR is created by Dr Yasar ERDINC (@yerdinc65 on twitter) It's exactly the arithmetical mean of 7 most commonly used oscillators which are: RSI. TKE INDICATOR is created by Dr Yasar ERDINC (@yerdinc65 on twitter) It's exactly the arithmetical mean of 7 most commonly used oscillators. It remains unclear whether the CCs will be used as reserve currency in the future and how the major central banks will react to it.