Which of the following necessarily imply a violation of the no-arbitrage princip
ID: 3300409 • Letter: W
Question
Which of the following necessarily imply a violation of the no-arbitrage principle? Assume T > 0 and elementof > 0. (a) A portfolio which has zero value today, always non-negative value at T, and positive value at T for some sample outcomes omega with P({omega}) > 0. (b) A portfolio which has zero value today and expected positive value at T. (c) A portfolio which has value - elementof today and zero value at T. (d) A portfolio which has value elementof today and expected positive value at T. (e) A portfolio which has zero value today and value elementof at T. (f) A portfolio which has zero value today and positive value at T for some sample outcomes with positive probability. (g) A portfolio which has zero value today, always non-negative value at T, and positive value at T for some sample outcomes. (h) A portfolio which has zero value today, always non-negative value at T, and expected positive value at T.Explanation / Answer
(a) In this scenario, it is possible to acquire the portfolio with zero cost and incur a probability of getting a higher than zero returns. However this is not certain because there are certain sample outcomes where portfolio is zero. So this does not imply necessarily violation of no arbitrage principle.
(b) In this scenario, it is possible to acquire the portfolio with zero cost and incur a probability of getting a higher than zero returns. However this is not certain because there may be certain sample outcomes where portfolio is zero or negative with only the expected value positive. So this does not imply necessarily violation of no arbitrage principle.
(c) In this scenario, it is possible to acquire the portfolio and additional get inward cash flow with zero cost. In the future he can then transfer the portfolio to others for zero cost. So this does imply necessarily violation of no arbitrage principle as he is able to make a profit of without any risk.
(d) ) In this scenario, it is possible to acquire the portfolio with non-zero cost and incur a probability of getting a higher than zero returns. However this is not certain because there may be certain sample outcomes where portfolio is zero or negative with only the expected value positive. So this does not imply necessarily violation of no arbitrage principle.
(e) In this scenario, it is possible to acquire the portfolio at zero cost. In the future he can then transfer the portfolio to others for inward cash flow of . So this does imply necessarily violation of no arbitrage principle as he is able to make a profit of without any risk.
(f) In this scenario, it is possible to acquire the portfolio with zero cost and incur a probability of getting a higher than zero returns. However this is not certain because there may be certain sample outcomes where portfolio is zero or negative. So this does not imply necessarily violation of no arbitrage principle.
(g) In this scenario, it is possible to acquire the portfolio with zero cost and incur a probability of getting a higher than zero returns. However this is not certain because there may be certain sample outcomes where portfolio is zero. So this does not imply necessarily violation of no arbitrage principle.
(h) In this scenario, it is possible to acquire the portfolio with zero cost and incur a probability of getting a higher than zero returns since expected value is higher than zero. However this is not certain because there may be certain sample outcomes where portfolio is zero. So this does not imply necessarily violation of no arbitrage principle.
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