Probability Concepts
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Question 1 of 13
1. Question
The probability that a particular junk bond will default is 3/8. What are the odds for a default of the bond?
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Question 2 of 13
2. Question
Based on the performance of the stock in the past 10 rate hikes, Susan estimates that the probability of the stock going down in the event of a rate hike is 0.8.
What kind of probability is this?
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Question 3 of 13
3. Question
Andy Seiko, CFA estimates that the probability of a recession happening next year is 30%. He also estimates that the probability of a drop of more that 10% in the stock index and a recession next year is 18%. What is the probability that the stock index will NOT drop more than 10% in the event of a recession?
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Question 4 of 13
4. Question
The probability of a stock consolidation for Fragrance Inc is 0.3. An analyst estimates that the likelihood of the stock going down in the event of a stock consolidation is 0.8. She also estimates that the probability is 0.4 if there is no consolidation.
What is the unconditional probability of the stock going down?
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Question 5 of 13
5. Question
The joint probability of the returns of assets X and Y are given in the table below.
Returns Y=8 Y=10 Y=13 X=-3 0.3 0 0 X=12 0 0.5 0 X=25 0 0 0.2 -
Expected return of X is %.
Expected return of Y is %.
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Question 6 of 13
6. Question
The joint probability of the returns of assets X and Y are given in the table below.
Returns Y=8 Y=10 Y=13 X=-3 0.3 0 0 X=12 0 0.5 0 X=25 0 0 0.2 Given E(X) = 10.1 and E(Y)=10.0, what is Cov(X,Y)?
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Question 7 of 13
7. Question
The covariance matrix between the returns of assets X and Y in a 2-asset portfolio is given below.
X Y X 9 7 Y 7 25 Given that the asset X forms 60% of the portfolio, and asset Y forms 40% of the portfolio, what is the standard deviation of the portfolio?
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Question 8 of 13
8. Question
Analysts predict that there is a 40% chance that the economy will experience a recession next year. The analysts also estimate that given a recession next year, the probability of the stock market underperforming this year is 0.7. Regardless of a recession, the probability of the stock market underperforming this year is 0.35.
Given that the stock market did NOT underperform this year, what is the updated probability of a recession next year?
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Question 9 of 13
9. Question
Rodrigues has 10 stocks in his portfolio. He wishes to sell off 4 of these stocks. How many ways can he sell them off if the sequence of sale is important?
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Question 10 of 13
10. Question
A fund manager company has 12 analysts. He wishes to divide them into 3 teams of equal strength. How many different combinations can there be?
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Question 11 of 13
11. Question
From a broad market of 320 stocks, a portfolio wishes to form a recommended list comprising 15 stocks with no particular order. Which formula is most appropriate to calculate the number of ways this list could be formed?
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Question 12 of 13
12. Question
The covariance matrix between the returns of assets X and Y in a 2-asset portfolio is given below.
X Y X 9 7 Y 7 25 What is the correlation between the returns of assets X and Y?
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Question 13 of 13
13. Question
Tick those which are true if events A and B are independent.
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