Question

using technology, calculate the weighted mean of the rors for each portfolio. based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst? portfolio 3, portfolio 1, portfolio 2 portfolio 2, portfolio 3, portfolio 1 portfolio 1, portfolio 2, portfolio 3 portfolio 3, portfolio 2, portfolio 1

Explanation:

Step1: Recall weighted - mean formula

The weighted - mean formula is $\bar{x}_w=\frac{\sum_{i = 1}^{n}w_ix_i}{\sum_{i = 1}^{n}w_i}$, where $x_i$ are the values (RORs in this case) and $w_i$ are the weights (portfolio amounts).

Step2: Calculate weighted - mean for Portfolio 1

Let $x_1 = 7.3\%=0.073$, $w_1 = 1150$; $x_2 = 1.8\%=0.018$, $w_2 = 1825$; $x_3=-6.7\%=-0.067$, $w_3 = 1405$; $x_4 = 10.4\%=0.104$, $w_4 = 1045$; $x_5 = 2.7\%=0.027$, $w_5 = 1450$.
$\sum_{i = 1}^{5}w_ix_i=0.073\times1150 + 0.018\times1825-0.067\times1405 + 0.104\times1045+0.027\times1450$
$=83.95+32.85 - 94.135+108.68+39.15$
$=169.495$
$\sum_{i = 1}^{5}w_i=1150 + 1825+1405+1045+1450=6875$
$\bar{x}_{w1}=\frac{169.495}{6875}\approx0.02465 = 2.47\%$

Step3: Calculate weighted - mean for Portfolio 2

Let $x_1 = 7.3\%=0.073$, $w_1 = 800$; $x_2 = 1.8\%=0.018$, $w_2 = 2500$; $x_3=-6.7\%=-0.067$, $w_3 = 250$; $x_4 = 10.4\%=0.104$, $w_4 = 1200$; $x_5 = 2.7\%=0.027$, $w_5 = 1880$.
$\sum_{i = 1}^{5}w_ix_i=0.073\times800+0.018\times2500 - 0.067\times250+0.104\times1200+0.027\times1880$
$=58.4 + 45-16.75+124.8+50.76$
$=262.21$
$\sum_{i = 1}^{5}w_i=800 + 2500+250+1200+1880=6630$
$\bar{x}_{w2}=\frac{262.21}{6630}\approx0.03955 = 3.96\%$

Step4: Calculate weighted - mean for Portfolio 3

Let $x_1 = 7.3\%=0.073$, $w_1 = 1100$; $x_2 = 1.8\%=0.018$, $w_2 = 525$; $x_3=-6.7\%=-0.067$, $w_3 = 825$; $x_4 = 10.4\%=0.104$, $w_4 = 400$; $x_5 = 2.7\%=0.027$, $w_5 = 2225$.
$\sum_{i = 1}^{5}w_ix_i=0.073\times1100+0.018\times525-0.067\times825+0.104\times400+0.027\times2225$
$=80.3+9.45 - 55.275+41.6+60.075$
$=136.15$
$\sum_{i = 1}^{5}w_i=1100 + 525+825+400+2225=5075$
$\bar{x}_{w3}=\frac{136.15}{5075}\approx0.02683 = 2.68\%$

Step5: Compare the weighted - means

$3.96\%(Portfolio\ 2)>2.68\%(Portfolio\ 3)>2.47\%(Portfolio\ 1)$

Answer:

Portfolio 2, Portfolio 3, Portfolio 1