Perform the same calculations in the case when the index increases from 890 to 920.

Question

Perform the same calculations in the case when the index increases from
890 to 920.

Accepted Answer

The return on the index will be [latex]3.37\% [/latex]. For [latex]r_F = 1\% [/latex] this gives the futures prices [latex]f(0, 3)≅916.97 [/latex] and [latex]f(1, 3)≅ 938.49. [/latex] If the beta coefficient for a portfolio is [latex]β_V = 1.5 [/latex], then the expected return on this portfolio will be [latex]μ_V≅4.56\% [/latex]. To construct a portfolio with [latex]β_{\widetilde{V}} = 0[/latex] and initial value V (0) = 100 dollars, supplement the original portfolio with [latex]N≅ 0.1652 [/latex] short futures contracts (observe that N is the same as in Example 6.4).

If the actual return on the original portfolio during the first time step
happens to be equal to the expected return, then its value after one step will be [latex]V (1) ≅ 104.56[/latex] dollars. Marking to market requires the holder of [latex]N≅ 0.1652[/latex] short forward contracts to pay $3.56. As a result, after one step the value of the portfolio with forward contracts will be [latex]\widetilde{V}(1) \cong 104.56 − 3.56 = 101.00 [/latex] dollars, once again matching the risk-free growth.

Question 6.11: Perform the same calculations in the case when the index inc...

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