Bad5shah

A bond portfolio consists of four BB-rated bonds. Each has a probability of default of 24% and these probabilities are independent. What are the probabilities of all the bonds defaulting and the probability of all the bonds not defaulting, respectively?

A) 0.96000; 0.04000.

B) 0.04000; 0.96000.

C) 0.00332; 0.33360.

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For the four independent events where the probability is the same for each, the probability of all defaulting is (0.24)4. The probability of all not defaulting is (1 − 0.24)4.

Bad5shah

If X and Y are independent events, which of the following is most accurate?

A) P(X or Y) = (P(X)) × (P(Y)).

B) P(X | Y) = P(X).

C) P(X or Y) = P(X) + P(Y).

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Note that events being independent means that they have no influence on each other. It does not necessarily mean that they are mutually exclusive. Accordingly, P(X or Y) = P(X) + P(Y) − P(X and Y). By the definition of independent events, P(X|Y) = P(X).

Bad5shah

A company says that whether it increases its dividends depends on whether its earnings increase. From this we know:

A) P(both dividend increase and earnings increase) = P(dividend increase).

B) P(earnings increase | dividend increase) is not equal to P(earnings increase).

C) P(dividend increase | earnings increase) is not equal to P(earnings increase).

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If two events A and B are dependent, then the conditional probabilities of P(A | B) and P(B | A) will not equal their respective unconditional probabilities (of P(A) and P(B), respectively). Both remaining choices may or may not occur, e.g., P(A | B) = P(B) is possible but not necessary.

Bad5shah

If the outcome of event A is not affected by event B, then events A and B are said to be:

A) conditionally dependent.

B) mutually exclusive.

C) statistically independent.

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If the outcome of one event does not influence the outcome of another, then the events are independent.

Bad5shah

The events Y and Z are mutually exclusive and exhaustive: P(Y) = 0.4 and P(Z) = 0.6. If the probability of X given Y is 0.9, and the probability of X given Z is 0.1, what is the unconditional probability of X?

A) 0.33.

B) 0.40.

C) 0.42.

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Because the events are mutually exclusive and exhaustive, the unconditional probability is obtained by taking the sum of the two joint probabilities: P(X) = P(X | Y) × P(Y) + P(X | Z) × P(Z) = 0.4 × 0.9 + 0.6 × 0.1 = 0.42.

Bad5shah

Firm A can fall short, meet, or exceed its earnings forecast. Each of these events is equally likely. Whether firm A increases its dividend will depend upon these outcomes. Respectively, the probabilities of a dividend increase conditional on the firm falling short, meeting or exceeding the forecast are 20%, 30%, and 50%. The unconditional probability of a dividend increase is:

A) 0.333.

B) 0.500.

C) 1.000.

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The unconditional probability is the weighted average of the conditional probabilities where the weights are the probabilities of the conditions. In this problem the three conditions fall short, meet, or exceed its earnings forecast are all equally likely. Therefore, the unconditional probability is the simple average of the three conditional probabilities: (0.2 + 0.3 + 0.5) ÷ 3.

Bad5shah

An investor is considering purchasing ACQ. There is a 30% probability that ACQ will be acquired in the next two months. If ACQ is acquired, there is a 40% probability of earning a 30% return on the investment and a 60% probability of earning 25%. If ACQ is not acquired, the expected return is 12%. What is the expected return on this investment?

A) 16.5%.

B) 12.3%.

C) 18.3%.

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E(r) = (0.70 × 0.12) + (0.30 × 0.40 × 0.30) + (0.30 × 0.60 × 0.25) = 0.165.

Bad5shah

Jay Hamilton, CFA, is analyzing Madison, Inc., a distressed firm. Hamilton believes the firm’s survival over the next year depends on the state of the economy. Hamilton assigns probabilities to four economic growth scenarios and estimates the probability of bankruptcy for Madison under each:

Economic growth scenario	Probability of scenario	Probability of bankruptcy
Recession (< 0%)	20%	60%
Slow growth (0% to 2%)	30%	40%
Normal growth (2% to 4%)	40%	20%
Rapid growth (> 4%)	10%	10%

Based on Hamilton’s estimates, the probability that Madison, Inc. does not go bankrupt in the next year is closest to:

A) 67%.

B) 18%.

C) 33%.

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Using the total probability rule, the unconditional probability of bankruptcy is (0.2)(0.6) + (0.3)(0.4) + (0.4)(0.2) + (0.1) (0.1) = 0.33. The probability that Madison, Inc. does not go bankrupt is 1 – 0.33 = 0.67 = 67%.

Bad5shah

An analyst announces that an increase in the discount rate next quarter will double her earnings forecast for a firm. This is an example of a:

A) conditional expectation.

B) use of Bayes' formula.

C) joint probability.

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This is a conditional expectation. The analyst indicates how an expected value will change given another event.

LiquidAssets10

A conditional expectation involves:

A) refining a forecast because of the occurrence of some other event.

B) calculating the conditional variance.

C) determining the expected joint probability.

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Conditional expected values are contingent upon the occurrence of some other event. The expectation changes as new information is revealed.