Fight Finance

(a) 0.5497

(b) 0.5651

(c) 0.5963

(d) 0.6156

(e) 0.8165

(a) 0.4368

(b) 0.4911

(c) 0.6331

(d) 0.6564

(e) 0.7348

(a) 0.277075

(b) 0.272519

(c) 0.239954

(d) 0.236008

(e) 0.162070

(a) ##\sigma_\text{yearly} = \sigma_\text{monthly}##

(b) ##\sigma_\text{yearly} = \sigma_\text{monthly} \times 12##

(c) ##\sigma_\text{yearly} = \sigma_\text{monthly} \times 144##

(d) ##\sigma_\text{yearly} = \sigma_\text{monthly} \times \sqrt{12}##

(e) ##\sigma_\text{yearly} = \sigma_\text{monthly} \times {12}^{1/3}##

(a) ##\sigma_\text{annual} = 0.09 \times 5 + 0.14 \times 7##

(b) ##\sigma_\text{annual} = (0.09 \times 5 + 0.14 \times 7)^{1/2}##

(c) ##\sigma_\text{annual} = (0.09^2 \times 5 + 0.14^2 \times 7)^{1/2}##

(d) ##\sigma_\text{annual} = (1+0.09)^5\times (1+0.14)^7 - 1##

(e) ##\sigma_\text{annual} = \left( \dfrac{0.09^2 \times 5 + 0.14^2 \times 7}{12} \right)^{1/2}##

(a) 24.28168% pa

(b) 24% pa

(c) 22.126907% pa

(d) 19.697716% pa

(e) 16.970563% pa

(a) The arithmetic average of variable X is represented by ##\bar{X}##.

(b) The standard deviation of variable X is represented by ##\sigma_X##.

(c) The variance of variable X is represented by ##\sigma_X^2##.

(d) The covariance between variables X and Y is represented by ##\sigma_{X,Y}^2##.

(e) The correlation between variables X and Y is represented by ##\rho_{X,Y}##.

(a) Percentage points per annum ##(\text{pp pa})## and percentage points per annum ##(\text{pp pa})##.

(b) Percentage points per annum ##(\text{pp pa})## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(c) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum ##(\text{pp pa})##.

(d) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(e) Percent per annum ##(\% pa)## and percent per annum ##(\% pa)##.

(a) The option’s expected future continuously compounded returns are always more than or equal to the underlying stock’s expected future continuously compounded returns.

(b) The option’s standard deviation of dollar price changes is always less than or equal to the underlying stock’s standard deviation of dollar price changes.

(c) The option’s standard deviation of continuously compounded returns are always less than or equal to the underlying stock’s standard deviation of continuously compounded returns.

(d) As time elapses and the maturity date of an option approaches, its price will fall, all other things remaining equal.

(e) If the underlying stock’s price rises by $0.01, the call option’s price will rise by less than $0.01 and the put option’s price will fall by less than $0.01.

(a) A one cent ($0.01) increase in the underlying stock price is expected to lead to a 0.747891 cent ($0.00747891) increase in the call option price.

(b) The (risk-neutral) probability of the call option maturing ‘in-the-money’ is 0.643514.

(c) A one cent ($0.01) increase in the underlying stock price is expected to lead to a 0.00053199 unit increase in the call option Delta.

(d) The underlying stocks’ standard deviation of returns per day is 0.015702718 assuming 365 days per year and zero auto-correlation.

(e) After one day, all other things remaining equal, the option price is expected to fall by $1.566433 assuming 365 days per year.

(a) The more risky the asset is from a financial analyst’s perspective.

(b) The higher the chance of a large loss.

(c) The higher the chance of a large gain.

(d) The more predictable the asset’s future price is.

(e) The higher the variance of returns.