A Popular Value-Weighted Index Is Constructed Out of Shares in the Two

question 78

Multiple Choice

A popular value-weighted index is constructed out of shares in the two companies, shown in the table below. On Day 1 you construct a portfolio that mimics the index with 15% invested in Company 1 and 85% invested in Company 2. On Day 2, what trades do you need to make in order to adjust your portfolio weights so that your portfolio earns the same return as the index from Day 2 to Day 3? $$\begin{array} { | c | c | c | c | c | } \hline & \text { Company 1 } & \text { Company 1 } & \text { Company 2 } & \text { Company 2 } \\\hline \text { Day } & \text { Price } & \begin{array} { c } \text { \# of Shares } \\\text { Outstanding }\end{array} & \text { Price } & \begin{array} { c } \text { \# of Shares } \\\text { Outstanding }\end{array} \\\hline 1 & 6.62 & 400 & 10.00 & 1,500 \\\hline \mathbf { 2 } & 7.53 & 400 & 10.54 & 1,500 \\\hline \mathbf { 3 } & 8.82 & 400 & 11.07 & 1,500 \\\hline\end{array}$$

• A)Buy more of Company 1 and buy more of Company 2
• B)Buy more of Company 1 and sell some of Company 2
• C)Sell some of Company 1 and sell some of Company 2
• D)Sell some of Company 1 and buy more of Company 2
• E)Make no trades

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Definitions:

Simultaneous Game

A game theory concept where players choose their strategies and make their moves at the same time, without knowledge of the others' choices.

Nash Equilibrium

A concept in game theory where no player can benefit by changing strategies while the other players keep theirs unchanged; it represents a state of mutual best responses.

Simultaneous Game

A strategic interaction where all participants make decisions or moves at the same time without knowledge of the others' choices.

Best Response

In game theory, the strategy that yields the highest payoff for a player, given the strategies chosen by other players.