Reading 10: Common Probability Distributions

Question 1

What are discrete random variables?

Answer 1

A discrete random variable is any variable that has fixed values.

EX: stock market prices (you cannot have 20.01 vs. 20.001 because a stock price is based off of dollar values)

Question 2

So, then what is a continuous random variable?

Answer 2

So a continuous random variable is when the values are infinite. When we are talking about ROIs, there are multiple points between 20% and 20.9999%.

Question 3

What is a probability function?

Answer 3

A probability function is the function that gives the percent probability on the Y-AXIS for a random discrete event (x).

Question 4

What is a probability density function?

Answer 4

A probability density function is used for continuous random variables on the X-Axis.

Question 5

What is a binomial distribution?

Answer 5

A binomial distribution has 2 outcomes: SUCCESS/ FAILURE

SUCCESS= HEADS      P(HEADS)= .50
FAILURE= TAILS           P(FAILURE)= .50

EX: You flip a coin 10 times. You get heads 7 times out of 10 trials. The question is what is the probability of getting 7 successes and 3 successes?

P(X=7)= nCx * (p)^x * (1-p)^(n-x)

P(X=7)= 10C7 * (.5)^(7) *(1-.5)^(3)

P(X=7)= .1170 or 11.70%

Question 6

So, we know that understanding normal distribution is very important to knowing portfolio theory. What are the properties of normal distribution?

Answer 6

Properties of Normal Distribution:

1.) “x” is normal distributed with a mean (u) and SD (variance = SD^2)

2. ) Skewness is equal to ZERO (mean= median=mode)
3. ) Kurtosis=3

Question 7

What is the importance of the Z-score?

Answer 7

The Z-score just tells you how many standard deviations you are away from the mean. A Z=1 means that the z-score is 1SD away. A Z=-2 means you are -2 SD to the left away from the mean.

Question 8

There is a saying in finance called ROY’S SAFETY FIRST CRITERION. What is it used for and what is the benefit of it?

Answer 8

Step 1: How do you calculate the THRESHOLD RETURN

THRESHOLD RETURN= (FINAL EXPECTED AMOUNT
- INVESTMENT AMOUNT)/ (INVESTMENT AMOUNT)

EX: 120 Million dollar investment plan with 123 million dollar return. First calculate the threshold return?

Step 2: Plug in the threshold return to find SFR Ratio

SFR = (E(r)* - threshold return) / (Standard Deviation*)

Step 3: See which investment has the highest SFR Ratio to choose the best investment to invest in!!!