Consider the data contained in the table below, which lists $30$ monthly excess returns to two different actively managed stock portfolios $($A and B$)$ and three different common risk factors $(1,2,$ and $3).($Note: You may find it useful to use a computer spreadsheet program such as Microsoft Excel to calculate your answers.$)$

Period Portfolio A Portfolio B Factor $1$ Factor $2$ Factor $3$

$11\mathrm{.}15\%0\mathrm{.}00\%0\mathrm{.}01\%-0\mathrm{.}96\%-1\mathrm{.}76\%$

$27\mathrm{.}686\mathrm{.}576\mathrm{.}790\mathrm{.}22-1\mathrm{.}21$

$34\mathrm{.}976\mathrm{.}014\mathrm{.}77-1\mathrm{.}491\mathrm{.}88$

$41\mathrm{.}200\mathrm{.}300\mathrm{.}680\mathrm{.}500\mathrm{.}24$

$5-1\mathrm{.}92-1\mathrm{.}55-2\mathrm{.}94-3\mathrm{.}604\mathrm{.}23$

$64\mathrm{.}202\mathrm{.}452\mathrm{.}78-3\mathrm{.}34-1\mathrm{.}49$

$7-0\mathrm{.}65-2\mathrm{.}52-2\mathrm{.}77-4\mathrm{.}49-1\mathrm{.}79$

$8-15\mathrm{.}55-15\mathrm{.}54-16\mathrm{.}05-5\mathrm{.}845\mathrm{.}60$

$95\mathrm{.}954\mathrm{.}085\mathrm{.}860\mathrm{.}01-3\mathrm{.}84$

$107\mathrm{.}646\mathrm{.}787\mathrm{.}21-3\mathrm{.}27-2\mathrm{.}88$

$117\mathrm{.}805\mathrm{.}435\mathrm{.}911\mathrm{.}33-3\mathrm{.}71$

$129\mathrm{.}584\mathrm{.}825\mathrm{.}97-0\mathrm{.}35-4\mathrm{.}97$

$135\mathrm{.}232\mathrm{.}723\mathrm{.}541\mathrm{.}09-6\mathrm{.}25$

$14-3\mathrm{.}16-0\mathrm{.}54-4\mathrm{.}12-5\mathrm{.}571\mathrm{.}61$

$155\mathrm{.}442\mathrm{.}563\mathrm{.}40-3\mathrm{.}88-3\mathrm{.}02$

$162\mathrm{.}397\mathrm{.}244\mathrm{.}452\mathrm{.}992\mathrm{.}80$

$17-2\mathrm{.}870\mathrm{.}14-2\mathrm{.}423\mathrm{.}413\mathrm{.}17$

$186\mathrm{.}473\mathrm{.}634\mathrm{.}783\mathrm{.}48-4\mathrm{.}34$

$19-3\mathrm{.}35-0\mathrm{.}69-3\mathrm{.}422\mathrm{.}000\mathrm{.}72$

$20-1\mathrm{.}17-4\mathrm{.}03-1\mathrm{.}30-1\mathrm{.}16-1\mathrm{.}31$

$21-1\mathrm{.}430\mathrm{.}11-2\mathrm{.}763\mathrm{.}21-3\mathrm{.}27$

$226\mathrm{.}025\mathrm{.}345\mathrm{.}83-6\mathrm{.}55-3\mathrm{.}20$

$231\mathrm{.}982\mathrm{.}343\mathrm{.}157\mathrm{.}79-8\mathrm{.}13$

$247\mathrm{.}147\mathrm{.}097\mathrm{.}747\mathrm{.}02-9\mathrm{.}08$

$25-4\mathrm{.}84-2\mathrm{.}83-4\mathrm{.}384\mathrm{.}16-0\mathrm{.}09$

$261\mathrm{.}10-1\mathrm{.}962\mathrm{.}4621\mathrm{.}58-11\mathrm{.}94$

$279\mathrm{.}075\mathrm{.}355\mathrm{.}22-16\mathrm{.}617\mathrm{.}87$

$28-4\mathrm{.}23-3\mathrm{.}05-6\mathrm{.}18-7\mathrm{.}468\mathrm{.}49$

$29-3\mathrm{.}32-0\mathrm{.}62-4\mathrm{.}29-5\mathrm{.}935\mathrm{.}31$

$303\mathrm{.}821\mathrm{.}824\mathrm{.}7113\mathrm{.}36-8\mathrm{.}68$

Compute the average monthly return and monthly standard return deviation for each portfolio and all three risk factors. Also state these values on an annualized basis. $($Hint: Monthly returns can be annualized by multiplying them by $12,$ while monthly standard deviations can be annualized by multiplying them by the square root of $12.)$ Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to three decimal places.

Portfolio A Portfolio B Factor $1$ Factor $2$ Factor $3$

Monthly:

Average

$\%$

$\%$

$\%$

$\%$

$\%$

Std Dev

$\%$

$\%$

$\%$

$\%$

$\%$

Annual:

Average

$\%$

$\%$

$\%$

$\%$

$\%$

Std Dev

$\%$

$\%$

$\%$

$\%$

$\%$

Based on the return and standard deviation calculations for the two portfolios from Part a$,$ is it clear whether one portfolio outperformed the other over this time period? Do not make any additional calculations to answer this question.

Portfolio A earned a

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return and a

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standard deviation than Portfolio B$.$ Therefore, it

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clear that one portfolio outperformed the other over this time period.

Calculate the correlation coefficients between each pair of the common risk factors $($i$.$e$.,1$ & $2,1$ & $3,$ and $2$ & $3).$ Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers to four decimal places.

Correlation between $1$ & $2$:

Correlation between $1$ & $3$:

Correlation between $2$ & $3$:

In theory, what should be the value of the correlation coefficient between the common risk factors? Explain why.

In theory the correlations should be

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because we want the factors to be

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$.$