Topics 1-3

Question 1

What is the varience of a linear function W of two variables?

Answer 1

Var(aX+bY) = a^2(var(X)) + b^2(Var(Y)) +2abcov(X,Y)

Question 2

What is the expectation of the linear operator W?

Answer 2

aE(X) +bE(Y)

Question 3

What is the formula for co variance of X and Y?

Answer 3

E(XY) -E(X)E(Y)

Question 4

How to show two events are independent?

Answer 4

P(X,Y) = P(X)P(Y)

Question 5

What is a forward contract?

Answer 5

It pre-commits a party to pay/receive the difference between the market price and a pre determined strike price at a given future date.

Question 6

What is a future contracts?

Answer 6

Exchange traded product which demands the continuous maintenance of margin to be held at a centralized clearing house.

Question 7

When would a future be preferred to a forward?

Answer 7

Futures are preferred when there is large counterparty risk and the two parties are not familiar with each other.

Question 8

How do you find the variance of a random variable Y?

Answer 8

Sum of (between n and i=1)

(The prob of event)(y-E(Y))2

Remember that E(Y) is often written as Mew Y.

Question 9

Give an example of a systematic risk.

Answer 9

Recession

Question 10

Give and example of an Idiosyncratic risk.

Answer 10

Having your bike stolen.

Question 11

What is the rate-of-return for an asset?

Answer 11

Ry = Y-Py/Py

Question 12

Prove that the random Variable Y can be expressed as; Var(Y) =E(y^2) -(E(Y))^2.

Also prove varience as a function.

Answer 12

See notes CH1, proof 1.2.

See notes proof 1.3.

Question 13

Write a simpler way of using Var (a+bY)

Answer 13

b^2Var(Y).

Question 14

What is the variance of r-o-r?

Answer 14

Var(ry)= Var(Y)/P^2y

Question 15

Prove that Cov(X,Y)= E(XY) - E(X)E(Y)

Prove the varience is a^2var(x) + b^2(VarY) for a linear function.

Answer 15

Proof 1.4 lecture1

Proof1.8