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Free CFA-Level-I Exam Braindumps (page: 233)

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PDF with 3963 Questions

You can enter a derivative contract that will pay $100 at the end of a year if the price of corn exceeds $3 per bushel, or $50 if it is equal to $3 per bushel or lower. The probability that corn will exceed $x by the end of one year is 50%. The current price of the contract is $60, and interest is 5% per year. What is the optimal strategy?

  1. Sell the derivative contract short if corn prices rise.
  2. Invest $60 at 5% until the end of the year.
  3. Buy $3 per bushel worth of corn futures.
  4. Enter into the derivative contract for a cost of $60.

Answer(s): D

Explanation:

Enter into the derivative contract for a cost of $60, for the expected payoff is 0.50 * $100 + 0.50 * $50 = $75.
That is a 25% return on your investment in one year, greater than the 5% that could be made by investing the $60 at interest. This is an example of the investment consequences of inconsistent probabilities. The present value of the contract should be $75/1.05 = $71.43. Thus, an arbitrage opportunity is present. On an expected value basis, you can buy an asset worth $71.43 for only $60.



An investment of $100 grows in four years to $345. The investor observes that the annual arithmetic rate of return and the geometric rate of return were the same over this period. The annual arithmetic rate of return must be ________.

  1. 40.33%
  2. 33.93%
  3. 34.32%
  4. 37.84%
  5. 36.29%

Answer(s): E

Explanation:

If the annual geometric rate of return is r, then 100 * (1 + r)^4 = 345. This gives r = 36.29%. Note that the only way the mean will be equal to the geometric mean if every year, the stock experienced a return of 36.29% per year.



A sample of the monthly amounts spent for food by families of four receiving food stamps approximates asymmetrical distribution. The sample mean is $150 and the standard deviation is $20. About 95 percent of the monthly food expenditures are between what two amounts?

  1. None of these answers
  2. $110 and $190
  3. $205 and $220
  4. $85 and $105
  5. $100 and $200

Answer(s): B

Explanation:

About 95% of the observations lie between plus and minus two standard deviations from the mean.



A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that 8 have relief within a few minutes?

  1. None of these answers
  2. 0.168
  3. 0.667
  4. 0.001
  5. 0.231

Answer(s): E

Explanation:

This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: n!(p^r)[q^(n-r)]/r!(n-r)!.
Here n = 12, r = 8,p = 0.7 and q = 0.3. Therefore we have 12!(0.7^8)(0.3^4)/8!4! = 0.231.






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