Question

The quarterly returns for a group of 59 mutual funds with a mean of 1.7​% and a standard deviation of 5.9​% can be modeled by a Normal model. Based on the model ​N(0.017​,0.059​), what are the cutoff values for the

​a) highest 20​% of these​ funds?

​b) lowest 40​%? ​

c) middle 80​%?

​d) highest 60​%?

Answer 1

(a) Corresponding to highest 20% funds, the critical z value = 0.8418

Thus, the required cutoff value = 0.017 + 0.8418*0.059

= 0.0667 = 6.67%

(b) Corresponding to lowest 40% funds, the critical z value = -0.253

Thus, the required cutoff value = 0.017 -0.253*0.059

= 0.0021 = 0.21%

(c) Corresponding to middle 80% funds, the critical z values are -1.2845 and 1.2845

Thus, the required cutoff values are (0.017 - 1.2845*0.059, 0.017 + 1.2845*0.059)

= ( -0.0588, 0.0928)

= -5.88% and 9.28%

(d) Corresponding to highest 60% funds, the critical z value = -0.253

Thus, the required cutoff value = 0.017 - 0.253*0.059

= 0.0021 = 0.21%