Fight Finance

(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) $\min(S_0 - K, 0)$.

(b) $\min(K-S_0, 0)$.

(c) $\max(S_0-K, 0)$.

(d) $\max(K-S_0, 0)$.

(e) $\max(K, S_0)$.

Will the price of an out-of-the-money put option on equity or if the standard deviation of returns (risk) of the underlying shares becomes higher?

Two call options are exactly the same, but one matures in one year and the other matures in two years. Which option would you expect to have the higher price, the option which matures or , or should they have the price?

Two at-the-money put options are exactly the same, but one matures in one year and the other matures in two years. Which option would you expect to have the higher price, the option which matures or , or should they have the price?

(a) The geometric average of the gross discrete returns (GAGDR) equals 1.04075 which is 104.075%.

(b) $\exp \left( \text{GAGDR} \right) = \text{AALGDR}$. The natural exponent of the GAGDR equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(c) $\text{GAGDR}^T = \left( P_T/P_0 \right)$. The GAGDR raised to the power of the number of time period that it's measured over equals the ratio of the first and last prices.

(d) $\text{GAGDR} = \exp \left( \text{AALGDR} \right)$. This is always true, regardless of the distribution of the prices or returns. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithm of the gross discrete returns (AALGDR).

(e) $\text{AAGDR} \approx \exp \left( \text{AALGDR} + \text{SDLGDR}^2/2 \right)$. This is only approximately true and depends on the distribution of the prices and returns. It's asymptotically true as the time period that the returns are measured over reaches infinity.

(a) The returns $r_\text{t monthly}$ are continuously compounded monthly returns and are likely to be normally distributed, so the mean, median and mode of these continuously compounded returns are all equal to 1% per month.

(b) The annualised average continuously compounded return is $\bar{r}_\text{cc annual}=12×0.01=0.1=12\%\text{ pa}$. The annualised standard deviation is $\sigma_\text{annual} = \sqrt{12}×0.05=0.173205081=17.32\%\text{ pa}$.

(c) Over the next 10 years the mean, median and mode continuously compounded 10 year returns will all equal $0.01 \times 12 \times 10 = 120\%$.

(d) Over the next 10 years the expected mean gross discrete 10 year return is $e^{(0.01 - 0.05^2/2)×12×10} = 2.857651118$ and the median gross discrete 10 year return is $e^{(0.01 + 0.05^2/2)×12×10}=3.857425531$.

(e) If the current price of the CBA shares is $75, then in 10 years they’re expected to have a mean value of $75×e^{(0.01 + 0.05^2/2)×12×10} = 289.3069148$ and a median value of $75×e^{0.01×12×10}=249.0087692$.

(a) Firm A is less risky than Firm B. Firm A would have a higher credit rating.

(b) Firm A has the absolute advantage issuing bonds in both the fixed and floating coupon bond markets.

(c) Firm A has a comparative advantage issuing bonds in the floating coupon bond market.

(d) The net benefit from the swap available to Firm A is 0.25%.

(e) The swap rate between Firm B and the Bank would be 2.5% pa.