Answer-first summary for fast verification
Answer: t = 9.70, reject
## Explanation To calculate the t-statistic for the alpha: **Formula:** t-statistic = alpha / standard error of alpha **Given:** - Alpha (α) = 1.24% - Standard error of alpha = 0.1278% **Calculation:** t = 1.24% / 0.1278% = 9.70 **Interpretation:** - With 60 monthly returns, degrees of freedom = 60 - 1 = 59 - For a one-tailed test at 1% significance level (α = 0.01), the critical t-value is approximately 2.39 - Since our calculated t-statistic (9.70) > critical t-value (2.39), we **reject** the null hypothesis **Conclusion:** The portfolio manager's claim that the probability of observing such a large alpha by chance is only 1% is **rejected** because the t-statistic of 9.70 is much larger than the critical value, indicating the alpha is statistically significant at well beyond the 1% level. The manager should actually get more credit than claimed!
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Based on 60 monthly returns, you estimate an actively managed portfolio alpha = 1.24% and standard error of alpha = 0.1278%. The portfolio manager wants to get due credit for producing positive alpha and believes that the probability of observing such a large alpha by chance is only 1%. Calculate the t-statistic, and based on the estimated t-value would you accept (or reject) the claim made by the portfolio manager.
A
t = 9.70, accept
B
t = 2.66, accept
C
t = 2.66, reject
D
t = 9.70, reject
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