MODULE 5.1: PROBABILITY MODELS FOR PORTFOLIO RETURN AND RISK

Question 1

What is covariance

Answer 1

measure of how two assets move together.
example) answers questions like What is the relationship between the return for Stock A and Stock B?” or, “What is the relationship between the performance of the S&P 500 and that of the automotive industry?”

Question 2

What are the properties of covariance

Answer 2

• The covariance of a random variable with itself is its variance; that is, Cov(RA,RA) = Var(RA).
• Covariance may range from negative infinity to positive infinity.
• A positive covariance indicates that when one random variable is above its mean, the other random variable also tends to be above its mean.
• A negative covariance indicates that when one random variable is above its mean, the other random variable tends to be below its mean.

Question 3

Sample covariance formula

Answer 3

the sample covariance formula is similar to the population covariance formula but divided by (n-1) instead of n, where n is the sample size. This adjustment is made to create an unbiased estimator of the population covariance.

COV / n-1

Question 4

Covariance formula

Answer 4

covariance is the expected value of the product of the deviations of two random variables. The formula can be written as:

Cov(X,Y) = E[(X - E[X])(Y - E[Y])]

= multiplying two standard deviations!!!
CALCULATOR KEYS:
1. Enter statistical mode by pressing 2ND + DATA
2. Clear any existing data by pressing 2ND + CLR Work
3. Enter the first set of values (X) followed by ENTER after each value
1. enter the y values into y
4. After entering all pairs, press 2ND + STAT
5. keep entering 2nd + Enter until i find the LIN option
6. find Sx , find Sy, find r
1. multiply them together to get the covariance of two variables

Question 5

Answer 5

Expected value of P = 0.2 × 15 + 0.2 × 12 + 0.6 × 0 = 5.4%

Expected value of Q = 0.2 × 7 + 0.2 × 4 + 0.6 × 0 = 2.2%

Covariance = 0.2 × (15 − 5.4) × (7 – 2.2) + 0.2 × (12 – 5.4) × (4 − 2.2) + 0.6 (0 − 5.4) (0 − 2.2) = 18.72

Question 6

Answer 6

Question 7

Answer 7

Question 8

The correlation of returns between Stocks A and B is 0.50. The covariance between these two securities is 0.0043, and the standard deviation of the return of Stock B is 26%. The variance of returns for Stock A is:

Answer 8

= 0
.0331
2
= 0
.0011

Question 9

For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.10, Var(RA) = 0.18, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the variance of the return of a portfolio that is equally invested in the two assets?