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Problem $7-14$

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 $3$

$11\mathrm{.}08\%0\mathrm{.}00\%0\mathrm{.}01\%-1\mathrm{.}06\%-1\mathrm{.}60\%$

$27\mathrm{.}656\mathrm{.}696\mathrm{.}830\mathrm{.}39-1\mathrm{.}30$

$35\mathrm{.}006\mathrm{.}074\mathrm{.}84-1\mathrm{.}521\mathrm{.}95$

$41\mathrm{.}240\mathrm{.}350\mathrm{.}680\mathrm{.}490\mathrm{.}13$

$5-1\mathrm{.}94-1\mathrm{.}65-2\mathrm{.}88-3\mathrm{.}594\mathrm{.}33$

$64\mathrm{.}232\mathrm{.}422\mathrm{.}96-3\mathrm{.}37-1\mathrm{.}52$

$7-0\mathrm{.}72-2\mathrm{.}47-2\mathrm{.}77-4\mathrm{.}56-1\mathrm{.}82$

$8-15\mathrm{.}54-15\mathrm{.}56-16\mathrm{.}14-5\mathrm{.}935\mathrm{.}78$

$96\mathrm{.}024\mathrm{.}056\mathrm{.}040\mathrm{.}02-3\mathrm{.}75$

$107\mathrm{.}706\mathrm{.}727\mathrm{.}04-3\mathrm{.}27-2\mathrm{.}76$

$117\mathrm{.}715\mathrm{.}445\mathrm{.}881\mathrm{.}37-3\mathrm{.}73$

$129\mathrm{.}534\mathrm{.}906\mathrm{.}03-0\mathrm{.}39-4\mathrm{.}90$

$135\mathrm{.}352\mathrm{.}803\mathrm{.}521\mathrm{.}17-6\mathrm{.}14$

$14-3\mathrm{.}29-0\mathrm{.}61-4\mathrm{.}10-5\mathrm{.}611\mathrm{.}56$

$155\mathrm{.}502\mathrm{.}523\mathrm{.}36-3\mathrm{.}92-2\mathrm{.}99$

$162\mathrm{.}377\mathrm{.}274\mathrm{.}462\mathrm{.}802\mathrm{.}72$

$17-2\mathrm{.}770\mathrm{.}13-2\mathrm{.}483\mathrm{.}503\mathrm{.}03$

$186\mathrm{.}593\mathrm{.}704\mathrm{.}783\mathrm{.}43-4\mathrm{.}33$

$19-3\mathrm{.}39-0\mathrm{.}69-3\mathrm{.}412\mathrm{.}010\mathrm{.}61$

$20-1\mathrm{.}20-4\mathrm{.}09-1\mathrm{.}42-1\mathrm{.}25-1\mathrm{.}29$

$21-1\mathrm{.}580\mathrm{.}21-2\mathrm{.}623\mathrm{.}26-3\mathrm{.}08$

$225\mathrm{.}965\mathrm{.}375\mathrm{.}77-6\mathrm{.}51-3\mathrm{.}22$

$232\mathrm{.}092\mathrm{.}343\mathrm{.}257\mathrm{.}64-8\mathrm{.}13$

$247\mathrm{.}246\mathrm{.}997\mathrm{.}776\mathrm{.}96-9\mathrm{.}03$

$25-4\mathrm{.}77-2\mathrm{.}69-4\mathrm{.}424\mathrm{.}17-0\mathrm{.}21$

$260\mathrm{.}90-1\mathrm{.}972\mathrm{.}4521\mathrm{.}53-11\mathrm{.}94$

$279\mathrm{.}005\mathrm{.}285\mathrm{.}03-16\mathrm{.}617\mathrm{.}76$

$28-4\mathrm{.}24-3\mathrm{.}03-6\mathrm{.}23-7\mathrm{.}478\mathrm{.}49$

$29-3\mathrm{.}34-0\mathrm{.}66-4\mathrm{.}20-5\mathrm{.}925\mathrm{.}29$

$303\mathrm{.}921\mathrm{.}714\mathrm{.}6913\mathrm{.}32-8\mathrm{.}71$

Using regression analysis, calculate the factor betas of each stock associated with each of the common risk factors. Which of these coefficients are statistically significant at $5\%$ level of significance? Fill in the table below. Use a minus sign to enter negative values, if any. Do not round intermediate calculations. Round your answers for factor betas to three decimal places and answers for t$-$statistics to two decimal places.

bi t$-$statistic Significance

Regression for Portfolio A

$$onstant

$-$Select$-($Significant$/$ not significant$)$

Factor $1$

$-$Select$-$

Factor $2$

$-$Select$-$

Factor $3$

$-$Select$-$

Regression for Portfolio B $($significant$/$not significant$)$

$$onstant

$-$Select$-$

Factor $1$

$-$Select$-$

Factor $2$

$-$Select$-$

Factor $3$

$-$Select$-$

How well does the factor model explain the variation in portfolio returns? On what basis can you make an evaluation of this nature?

The factor models explain

$-$Select$-($well$/$bad$)$

as the

$-$Select$-($adjusted r$2,$ multiple r$,$ or intercept$)$

values in both regressions are

$-$Select$-($high enough, not high enough, low enough, or not low enough$)$

$.$

Suppose you are now told that the three factors used in the models represent the risk exposures in the Fama$-$French characteristic$-$based model $($i$.$e$.,$ excess market, SMB$,$ and HML$).$ Based on your regression results, which one of these factors is the most likely to be the market factor? Explain why.

$-$Select$-($factor $1,2,$ or $3)$

is the most likely candidate for the market factor, because it has a

$-$Select$-($large significant positive, large significant negative, small not significant negative, or small not significant postive$)$

effect on both portfolios.

Suppose it is further revealed that Factor $3$ is the HML factor. Which of the two portfolios is most likely to be a growth$-$oriented fund and which is a value$-$oriented fund? Explain why.

$-$Select$-($ Portfolio A$/$Portfolio B$)$

is the more likely candidate for the value$-$oriented portfolio as it has a

$-$Select$-($Positive$/$ Negative$)$

loading on this factor.

$-$Select$-($Portfolio A$/$Portfolio B$)$

is the more likely candidate for the growth$-$oriented portfolio as it has a

$-$Select$-($Positive$/$ Negative$)$

loading on this factor.