Formulae for Exam

Question 1

VaR (%)

Answer 1

VaR = μ + Z * σ

μ = mean return, σ = standard deviation, Z = z-score

Question 2

No arbitrage price of stock

Given an exercise price, price of call and put.

Answer 2

S = PV(exercise price) + C - P

PV = present value, C & P = price of call and put respectively.

Question 3

VaR from 1-day to 10 days

Answer 3

10-day VaR = 1-day VaR * SQRT(10)

Question 4

Portfolio variance calculated using correlation matrix

(with weights/weighted volatility - wv listed horizontally)

Answer 4

Matrix multiplication using weighted volatility and correlation matrix.

{=MMULT(WV ARRAY,MMULT(CORRELATION MATRIX,TRANSPOSE(VW)))}

(shift+ctrl+enter) to force matrix multiplication

Question 5

Portfolio variance calculated using covariance matrix

(with weights - w listed horizontally)

Answer 5

Matrix multiplication using weights and covariance matrix.

{=MMULT(W ARRAY,MMULT(CORRELATION MATRIX,TRANSPOSE(W)))}

(shift+ctrl+enter) to force matrix multiplication

Question 6

Put-call parity for options with exercise prices 40 and 50 is expressed by?

Answer 6

C(40) – P(40) – S + PV(40) = C(50) – P(50) – S + PV(50)

Question 7

Formula used to show no arbitrage price of a put and call option with the same exercise price?

Answer 7

C(exercise price) – P(exercise price) = S – PV(exercise price) = 0

Plug in call & put price, spot price, present value of exercise price

Does the left hand (C-P) = the right hand (S-PV)?
If not, one of the portfolios is undervalued and could be exploited with an arbitrage trade.

Question 8

Work out yield on a bond?

Answer 8

(Face value / Price)-1

Do not -1 if you need the discount factor (as in PV). Or +1 to yield to get the discount factor.