using technology, calculate the weighted mean of the rors for each portfolio. based on the results, which…

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