R ECURSIVE P ORTFOLIO

In this section, we form recursive portfolios to identify performance persistence in mutual funds. We analyze performance of equally weighted (EW) quintile portfolios created by ranking the funds based on lagged the 24-month and 36-month alpha and corresponding t-statistic of alpha obtained from the Carhart 4-factor model. The EW portfolios are rebalanced after 3, 6, 12, and 24-month holding periods and this procedure is repeated over the whole time period. We examine performance of the EW quintile portfolios to identify how persistent these portfolios are in generating positive or negative alphas. We employ the Carhart 4-factor model to evaluate the risk-adjusted return of portfolios and then apply a bootstrapped method to test whether persistence or inconsistent performance arises due to luck or managers’ stock-picking abilities.

Tables 6 reports the results of the recursive portfolio method when funds are ranked and placed in the top to bottom quintiles based on their alphas. Panel A and B show the results based on 36 and 24 ranking periods, respectively, for quintiles 1 to 5, where the first quintile denotes the portfolios containing the best-performing funds, and the fifth quintile includes the worst-performing funds over the ranking period. We also construct 1-5 spread quintile, a hypothetical self-financing quintile² that represents the trading strategy of longing the best-performers and shorting the worst-performers. The column estimates are the Carhart 4-factor model alpha and Fama and French (2010) bootstrapped p-value³ of alpha for 3 to 24-month holding periods.

The bootstrapped p-value of alpha indicates if the true risk-adjusted return of quintiles

2It is a hypothetical portfolio since Norwegian mutual funds are not able to short-sell shares. Moreover, self-financing refers to zero investment trading strategy which is about longing past-winners and shorting past-losers. By adding spread portfolio, we are differentiating the estimates between top and bottom quintile.

3For the right tail of alphas bootstrapped p-value is equal to the percentage of simulated alphas that are greater than actual alphas and for the left tail of alphas the bootstrapped p-value is equal to the percentage of simulated alpha that is smaller than actual alpha.

portfolios is different from zero and whether it is generated by managerial skill (lack of skill) or luck to persistently over-perform (under-perform) over time.

The results in Table 6 indicate that there is no evidence of persistence in obtaining excess return over the benchmark for the top quintile of Norwegian mutual funds. The past-winner funds generate negative alpha in the holding periods up to 6 months for both 24-months and 36-months ranking period. This under-performance has a significant bootstrapped p-value at 5% level, suggesting that this negative return is due to the managers' lack of skill, not bad luck.

By looking at Panel A, we find a positive risk-adjusted return of 0.19% for the 24-month holding period; however, it is not statistically significant. The bootstrapped p-value implies that we fail to reject the null hypothesis that true excess return is equal to zero, indicating this excess return is produced by luck.

The results for bottom quintiles denote performance persistence for poor-performing funds in both Panels A and B. The excess return of the bottom quintile portfolio for all holding periods from 3 to 24 months is negative, with a significant bootstrapped p-value. It means that past-loser funds remain past-losers due to bad managerial skills. We reject the null hypothesis that persistence in underperforming is a result of bad luck. In panel B, for the shortest and the most extended holding period, 3 and 24 months, respectively, alpha is around -2%, which is the most significant magnitude among all holding periods.

Comparing the results in panel A and B, we find that for 24 months ranking period, the absolute value of negative alphas is greater than the value for the panel B for all holding periods in quintile 1 to 5. The significant excess returns in the spread quintile suggest that the difference between the best and worst funds' performance is meaningful; however, this trading strategy cannot be utilized by the Norwegian mutual funds' managers.

Table 6: Performance Persistence across Quintile Portfolios Formed on Lagged Alpha

This table shows annualized alphas and bootstrapped p-values from the Carhart 4-factor model for individual quintile portfolio (1 to 5), and for the spread portfolio (long in quintile 1 and short in quintile 5) using different lengths of ranking and holding periods. Quintile 1 represents the best-performing mutual funds portfolios, and quintile 5 represents the portfolios of the worst-performing mutual funds during the portfolio formation period. The portfolios are equally weighted of monthly returns, and the weights are rebalanced whenever a fund dies to eliminate survivorship bias. In Panel A (B), the alpha and bootstrap p-value of alpha are reported for portfolios of ranked mutual funds based on lagged 36 (24) months alpha and held for different holding periods (3, 6, 12, and 24-month periods). The bold p-values indicate significance at 5% confidence level. The procedure of ranking, portfolio forming, and holding repeated throughout the entire sample period (1998-2019).

Holding Period Table 7 represents the results of the recursive portfolio method when funds are ranked and placed in quintiles based on the t-statistics of alphas. Aligned with the findings in Table 6, the negative risk-adjusted returns for the top quintile suggest that past-winners do not remain winners in the next ranking period, and consequently, there is no evidence of persistence of the best-performers in obtaining an excess return. The alpha of the top quintile portfolios for the 36-months ranking period and 24-months holding period is equal to 0.29%; however, it is not significant at 5% confidence level, meaning that we fail to reject that true excess return is equal to zero.

The outcome of bootstrapped simulation in Table 7 displays persistence among past losers both in Panel A and B, but the magnitude of the absolute value of negative alphas is greater

with the 24 months ranking period. Besides, the alphas of the bottom quintile portfolio suggest that for the shortest and longest holding periods, 3 and 24 months, respectively, persistence in generating a negative risk-adjusted return is stronger. The p-value is significant at 5%

confidence level, which implies that weak performance is not due to bad luck, but because of bad managerial performance.

Comparing Tables 6 and 7, we find the results for both ranking approaches are almost similar, suggesting that past-winner funds are not able to repeat their performance in the consequent period neither in the short nor in the long term. While past-losers, especially in the bottom quintile, exhibit persistence in generating negative risk-adjusted returns throughout all holding periods.

Table 7: Performance Persistence across Quintile Portfolios Formed on the t-statistics of Lagged Alpha

This table reports annualized alphas and bootstrapped p-values of the Carhart 4-factor model for each quintile portfolio (1 to 5), and for the spread portfolio (long in quintile 1 and short in quintile 5) using different lengths of ranking and holding periods. Quintile 1 represents the portfolios of best-performing mutual funds, and quintile 5 represents the portfolios of worst-performing mutual funds during the portfolio formation period. The portfolios are equally weighted of monthly returns, and the weights are readjusted whenever a fund disappears to avoid survivorship bias. In Panel A (B), the alpha and bootstrap p-value of alpha are reported for portfolios of ranked mutual funds based on t-statistic of lagged 36 (24) months alpha and held for different holding periods 3, 6, 12, and 24-month periods. The bold p-values indicate significance at 5% confidence level. The procedure of ranking, portfolio forming, and holding repeated throughout the entire sample period (1998-2019).