# MATHEMATICS

Q1)

Returns on stocks X and Y are listed below:

 Period 1 2 3 4 5 6 7 Stock X 8% 0% 3% -2% 5% 12% 7% Stock Y 5% -2% 4% 7% 1% 12% -3%

What is the correlation of returns on the two stocks?

Note that the correct answer will be evaluated based
on the full-precision result you would obtain using Excel.

Q2)

Returns on stocks X and Y are listed below:

 Period 1 2 3 4 5 6 7 Stock X 4% 7% -2% 40% 0% 10% -1% Stock Y 2% -5% 7% 4% 6% 11% -4%

Consider a portfolio of 10% stock X and 90% stock Y.

What is the mean of portfolio returns?

Q3)

Returns on stocks X and Y are listed below:

 Period 1 2 3 4 5 6 7 Stock X 4% 7% -2% 40% 0% 10% -1% Stock Y 2% -5% 7% 4% 6% 11% -4%

Consider a portfolio of 10% stock X and 90% stock Y.

What is the (population) standard deviation of portfolio returns?

Note that the correct answer will be evaluated based
on the full-precision result you would obtain using Excel.

Q4)

Summary statistics for returns on two stocks X and Y are listed below.

 Mean Variance Stock X 3.41% 0.003000 Stock Y 5.25% 0.004000

The covariance of returns on stocks X and Y is 0.001800. Consider a portfolio of 20% stock X and 80% stock Y.

What is the mean of portfolio returns?

Q5)

Summary statistics for returns on two stocks X and Y are listed below.

 Mean Variance Stock X 2.85% 0.005000 Stock Y 5.91% 0.006000

The covariance of returns on stocks X and Y is 0.002800. Consider a portfolio of 30% stock X and 70% stock Y.

What is the variance of portfolio returns?