Estimación de la demanda insatisfecha

To further investigate the impact of tournament behavior on the low-risk premiums as described with the second hypothesis, I next perform cross-sectional Fama and MacBeth (1973) regressions. The advantage of this method is that we can easily control for multiple other effects that might have impact on the relationship between tournament behavior and the low-risk premium. Therefore, I yearly regress the low-risk premiums on tournament behavior and other factors in the prior year that could potentially influence the results:

(5.24) 𝑍𝑟𝑖,𝑡= 𝑐𝑡+ 𝑏1𝑡𝑅𝐴𝑅𝐿𝑜𝑠𝑊𝑖𝑛𝑖,𝑡−1+ 𝑏2𝑡𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑉𝑎𝑟𝑖,𝑡−1+ 𝜀𝑖,𝑡.

Zri,tis again the standardized low-risk premium of asset category i in year t. The variable

RARLosWini,tis the tournament behavior in asset category i in year t and ControlVari,tis a

control variable for asset category i in year t.

I investigate four control variables. First, I control for the activeness of the market. The idea here is that the larger the mutual fund market of a particular asset category, the larger the low-risk premium. In case of strong tournament behavior in an asset category, but a relatively small mutual fund market, the impact on asset prices will likely be low. I use

two proxies for the activeness of the market in year t: 1) NFunds, which is the number of

mutual funds in a particular asset category and 2) PercMCap, which is the ratio of the total

net market value of the mutual funds in an asset category divided by the total market value

of that asset category.63 _{I proxy the latter by the total market cap of the individual securities}

in the universe of that asset category which I use to compute the low-risk premium. Second,

I control for the relative market volatility over the past 12 months ZMarketVol, which I

standardize by subtracting the sample mean of that asset category and divide it by its standard deviation. This makes volatility comparable across asset categories. The reason to include this variable is to investigate whether selecting relatively low-volatile asset categories could drive the higher low-risk premium. Last, I use the return-to-risk ratio of the

63 _{The market value data of mutual funds in the Morningstar database are often not continues series.} In case of a missing observation I take the last available market value in case of less than a year missing market values.

market of the asset category each year, labelled MarketReturnRisk. The idea is to investigate whether asset categories that have performed well are also the asset categories with a high low-risk premium. Table 5.6 presents the average coefficient estimates of the different

regression models together with the associated t-values which are corrected for

heteroscedasticity and autocorrelation using Newey and West (1987). Additionally, the table presents the average adjusted R-squared values of the regressions.

The resulting coefficient estimates of the base case regression in column (1) show a large and significant coefficient for tournament behavior. Columns (2) to (5) of Table 5.6 show the coefficient estimates when we augment the base case regression model with each of the four control variables. If the positive relation between tournament behavior and the low-risk premiums can be attributed to control variables, we should observe that augmenting the cross-sectional regressions of the low-risk anomaly on tournament behavior with control variables should lead to a significant decrease of the estimated coefficient of tournament behavior. In addition we should observe that the coefficient estimates of the control variables become significant. However, in almost all cases we observe that the coefficient estimate for RARLosWin remains significant and nearly unchanged. Only when controlling for market

volatility we observe a lower t-statistic for tournament behavior. Moreover, apart from

market volatility, none of the coefficient estimates for the control variables turns out significantly different from zero. The reason that the two proxies for the activeness of the market do not show up significantly, could be because I use only large and relevant asset categories, which have a relatively large mutual fund market.

The last row of the table shows the adjusted R-squared values. From the first column we observe that tournament behavior explains 8.90% of the variability of the low- risk premiums. We observe a moderate increase in explanatory power once control variables are added to the regression. When market volatility is added, the explanatory power increases to 12.20% (column 4). This means that still the majority of the variation is explained by tournament behavior. In case the return-to-risk ratio of the asset categories is added, we observe that the R-squared value increases to 17.80% (column 5), which is double that of the base case regression. This seems to suggest that the risk-return ratio of the categories can explain part of the variability of the low-risk premiums. However, the estimation coefficient shows that the relation between this control variable and tournament behavior is not statistically significant, while tournament behavior remains statistically significant.

TABLE 5.6. Fama-MacBeth regression results for the relation between low-risk premium and tournament behavior across asset categories

This table reports Fama-MacBeth regression results of low-risk premiums regressed on tournament behavior while controlling for other effects over the period January 1990 until December 2013. Each year the following regression is performed:

(5.24) 𝑍𝑟𝑖,𝑡= 𝑐𝑡+ 𝑏1𝑡𝑅𝐴𝑅𝐿𝑜𝑠𝑊𝑖𝑛𝑖,𝑡−1+ 𝑏2𝑡𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑉𝑎𝑟𝑖,𝑡−1+ 𝜀𝑖,𝑡,

where Zri,t is the low-risk premium of asset category i in year t where I standardize the low-risk premium by subtracting the asset category’s sample median annual low-risk premium and divide by the sample median standard deviation. The variable RARLosWini,tis the tournament behavior in asset category i in year t. The base case regression in Equation 5.24 is augmented with four control variables

ControlVari,tfor asset category i in year t. The four control variables: NFunds is the number of mutual

funds in a particular asset category; PercMCap is the ratio of the total net market value of the mutual funds in an asset category divided by the total market value of that asset category; ZMarketVol is the relative market volatility over the past 12 months standardized by subtracting the sample mean of that asset category and divide by the standard deviation; MarketReturnRisk is the return-to-risk ratio of the market of the asset category each year. The table presents the average coefficient estimates of the different regression models together with their t-values (second row) computed using Newey-West (1987) standard errors. In addition, the table shows the average adjusted R-squared values of the regressions.

All in all, the outcomes of the Fama-MacBeth regressions are consistent with the results based on the sorting test of the previous sub-section. It appears that the finding that the low-risk premium is positive related to tournament behavior is robust to the method that is used to investigate the relation between the two variables. Moreover, the relation is not affected by the activeness of the market, market volatility and risk-return ratio of the market.

(1) (2) (3) (3) (5) Constant -1.21 -1.26 -1.29 -1.09 -0.90 -2.12 -1.78 -2.11 -1.64 -1.86 RARLosWin 1.23 1.26 1.28 1.14 0.92 2.49 2.01 2.31 1.83 2.16 Nfunds 0.00 0.25 PercMcap 0.08 0.95 ZMarketVol -0.38 -3.23 MarketReturnRisk 0.06 0.66 Adj. R2 8.90% 11.90% 9.10% 12.20% 17.80%

I therefore conclude that there is also a positive relation between tournament behavior and the low-risk premium over the cross-section.