Question

Exercises 12.C.1-12.C.6 are based on data from the table below, which presents information on five mutual funds focusing on Latin American firms.12 gross total net assets manager 1-year10-year beta expense ($ millions) tenure return avg. return (years) ratio MDTLX | 1.6% MBLTX| 2.4% MCLTX| 2.4% FLAT I 1.190 PRLAXİ 1.2% 232 17 70 3,700 2,400 25.6%| 15.5% | 9.9 | 27.0% | 15.2% | 9.1 5 | 30.5% | 15.2% | 9.1 | 26.2% | 13.9% | 7.7 36.0% | 17.0% |10.5 3 Exercise 12.C.I. For the gross expense ratio, compute (a) the median, (b) the mean, (c) the variance, and (d) the standard deviation. Exercise 12.C.2. For total net assets, compute (a) the median, (b) the mean, (c) the variance, and (d) the standard deviation. Exercise 12.С.З. For manager tenure, compute (a) the median, (b) the mean, (c) the variance, and (d) the standard deviation. Exercise 12.C.4. How do you think the 10-year average returns were computed from the previous 10 years' returns? Exercise 12.С.5. a. Compute the correlation between manager tenure and 1-year returns. b. Compute the correlation between manager tenure and 10-year average returns. e the relationships between manager tenure and returns over c. Summariz the two durations.

All parts to 12.C.5 please!

Answer 1

The given data, along with the median, mean, variance and std deviation for the 3 metrics are shown in the table below:

fund	gross expense ratio	total net assets ($ millions)	manager tenure (years)	1-year return	10-year avg. return	beta
MDLTX	1.60%	232	5	25.60%	15.50%	9.9
MBLTX	2.40%	17	5	27%	15.20%	9.1
MCLTX	2.40%	70	5	30.50%	15.20%	9.1
FLATX	1.10%	3700	2	26.20%	13.90%	7.5
PRLAX	1.20%	2400	3	36%	17%	10.5
Median	1.60%	232	5
Mean	1.74%	1283.8	4
Variance	0.0000398	2817075.2	2
Std Deviation	0.006308724	1678.41449	1.4142

12.C.1 to 12.C.3 calculated and shown above.

12.C.4)  The 10-year average returns were most likely calculated compounding the previous 10 year returns, i.e. taking the geometric mean of the previous 10 year returns as follows:

r = $\sqrt[n]{r1*r2*r3.....*r10}$

12.C.5)  

a) Correlation between manager tenure and 1-year returns = Cov(X, Y) / $\sigma_x \sigma_y$ = -0.2169

b) Similarly, Correlation between manager tenure and 10-year avg returns = 0.1758

c) Manager tenure and 1-year returns seem to be weakly negatively correlated. However, Manager tenure and 10-year avg returns seem to be weakly positively correlated. This suggests that as manager tenure increases, fund returns possibly get better, though the relationship isn't quite significant, suggesting there could be other factors (like investment skills, expense ratio management, market conditions, etc) which have more bearing on the fund's returns than the manager tenure.