MODULE 4.1 PROBABILITY MODELS, EXPECTED VALUES, AND BAYES’ FORMULA

Question 1

Variance

Answer 1

measure hwo mucha. random variables values spread around it’s expected value - is calculated as the probability-weighted sum of squared deviations from the mean

Question 2

Variance calculation

Answer 2

SD = SQRT(VAR) so VAR = SD^2

Question 3

Standard Deviation

Answer 3

simply the positive square root of variance

Question 4

probability models properties

Answer 4

they are forward looking and they look at POPULATION

Question 5

Expected Value

Answer 5

weighted avg of the possible outcomes of hte variable

Question 6

calculate expected value

Answer 6

e(x) = probability of A x (A)…..

Question 7

calculate expected value, variance, SD, from a probability model where we get the probabilities and their returns

Answer 7

can use 2nd data and put in the returns and their probabilities –> PROBABILITIES NEED TO BE WHOLE NUMBERS HERE .

We then need to do 2nd ENTER until we find 1-Y. The n should be 100 for this

Question 8

What are conditional expected values and what are they used for

Answer 8

• contingent on the outcome of some other event
  
  • analysts would use this to revise their expectations when new information arrives

Question 9

Bayes Formula meaning

Answer 9

Bayes’ formula is used to update a given set of prior probabilities for a given event in response to the arrival of new information.

Question 10

Bayes Formula

Answer 10

updated probability = ( probability for new info / unconditional probability of new info ) x prior probability of event

• we start with our prior beliefs here and multiply it with the new info to incorporate our new evidence

Question 11

Answer 11

• E(X | Y = 1) = (0.2)(0) + (0.4)(5) + (0.4)(10) = 6
• E(X | Y = 2) =(0.1)(0) + (0.8)(5) + (0.1)(10) = 5
• E(X) = (0.3)(6) + (0.7)(5) = 5.30

Question 12

An analyst believes that Davies Company has a 40% probability of earning more than $2 per share. She estimates that the probability that Davies Company’s credit rating will be upgraded is 70% if its earnings per share (EPS) are greater than $2, and 20% if its EPS are $2 or less. Given the information that Davies Company’s credit rating has been upgraded, what is the updated probability that its EPS are greater than $2?

• also calculate if it’s EPS are less than 2

Answer 12

Question 13

Answer 13

The expected value if the overall market decreases is 0.4($60) + (1 – 0.4)($55) = $57.