When the noise trader sentiment deepens in period 2, is the value of the portfolio constructed in

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Question:

When the noise trader sentiment deepens in period 2, is the value of the portfolio constructed in period 1 the same as the size of the fund in period 2? Explain.
What are the positions of the fund portfolio constructed in period 2 when the noise trader sentiment deepens? What are the adjustments of the portfolio made by the arbitrageurs in period 2 in this case? What are the motivations for these adjustments? Are these motivations consistent with the market conditions?
What is the value in period 3 of the portfolio constructed in period 2 when the noise trader sentiment deepens? What are the gains or losses due to the price movements?

Do the arbitrageurs have gains or suffer losses overall from period 1 to period 3 if the noise trader sentiment deepens in period 2?

If q = 0.5, we have the following in the model:

D1 = 0.1743 and p1 = 0.8743;

If noise trader pessimism deepens in period 2, then F2 = 0.1766 and p2 = 0.7766;

If noise trader sentiment recovers in period 2, then F2 = 0.23 and price returns to V =1.

Comparing this case (q = 0.5) with the previous case q < 0.35, is the asset price in period 1 more or less efficient? Explain the reason.