Question $1$

The following is the Economist's article entitled How the "Magnificent Seven" misleads:

The reason was that shares in this group of tech giants$-$Alphabet, Amazon, Apple, Meta, Microsoft, Nvidia and Tesla$-$were acting as if they made up a

market of their own. By the start of June the S&P $500$ had risen by $12\%$ since the beginning of the year, but virtually the entire gain was down to these

seven stocks, with the other $493$ having collectively moved sideways. By July they were the biggest seven companies in the index. By late October the

Magnificent Seven had added $$3\mathrm{.}4$ trn $($or $50\%)$ to their combined market value since the start of the year, even as the other $493$ had lost $$1$ trn $(3\mathrm{.}8\%).$

Apple was the group's worst performer but had nevertheless seen its share price rise by $30\%.$

In other words, from January to October $2023,R_{\text{M}\text{a}\text{g}\text{n}\text{i}\text{f}\text{i}\text{c}\text{e}\text{n}\text{t}\text{S}\text{e}\text{v}\text{e}\text{n}}=50\%,$ and $R_{\text{O}\text{t}\text{h}\text{e}\text{r}}493$ Stocks $=-3\mathrm{.}8\%.$ During the same time, the return of S&P

$500$ was $9\mathrm{.}2\%.$ If the S&P $500$ is a value$-$weighted index $($and hence $R_{\frac{S}{\text{\&}}P500}=w{R}_{\text{M}\text{a}\text{g}\text{n}\text{i}\text{f}\text{i}\text{c}\text{e}\text{n}\text{t}\text{S}\text{e}\text{v}\text{e}\text{n}}+(1-w)R_{\text{O}\text{t}\text{h}\text{e}\text{r}493\text{S}\text{t}\text{o}\text{c}\text{k}\text{s}}),$ what was the weight

$w$ for the Magnificent Seven stocks above?

$24\mathrm{.}2\%$

$31\mathrm{.}5\%$

$38\mathrm{.}9\%$

$46\mathrm{.}2\%$