Consider a market consisting of one risk-free asset with A(0) = 10 and A(1) = 11 dollars, and one risky asset such that S(0) = 10 and S(1) = 13 or 9 dollars. On the x, y plane draw the set of all portfolios (x, y) such that the one-step strategy involving risky position x and risk-free position y

Question

Consider a market consisting of one risk-free asset with A(0) = 10 and A(1) = 11 dollars, and one risky asset such that S(0) = 10 and S(1) = 13 or 9 dollars. On the x, y plane draw the set of all portfolios (x, y) such that the one-step strategy involving risky position x and risk-free position y is admissible.

Accepted Answer

For a one-step strategy admissibility reduces to a couple of inequalities, V (0) ≥ 0 and V (1) ≥ 0. The first inequality can be written as

[latex]10x + 10y ≥ 0.[/latex]

The second inequality means that both values of the random variable V (1)
should be non-negative, which gives two more inequalities to be satisfied by x and y,

[latex]13x + 11y ≥ 0,[/latex]
[latex]9x + 11y ≥ 0.[/latex]

The set of portfolios (x, y) satisfying all these inequalities is shown in Figure S.7.

Question 4.2: Consider a market consisting of one risk-free asset with A(0...

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