Fight Finance

(a) Under priced and should be bought.

(b) Under priced and should be sold.

(c) Over priced and should be bought.

(d) Over priced and should be sold.

(e) Fairly priced and an arbitrageur would be indifferent to buying or selling them.

(a) Systematic variance of the underlying asset increases.

(b) Idiosyncratic variance of the underlying asset increases.

(c) Systematic, idiosyncratic or total variance of the underlying asset increases.

(d) Systematic variance of the underlying asset decreases.

(e) Systematic, idiosyncratic or total variance of the underlying asset decreases.

(a) Borrow $109.09 from the bank and lend $100 of it to your neighbour now.

(b) Borrow $100 from the bank and lend it to your neighbour now.

(c) Borrow $209.09 from the bank and lend $100 to your neighbour now.

(d) Borrow $120 from the bank and lend $100 of it to your neighbour now.

(e) Borrow $90.91 from the bank and lend it to your neighbour now.

(a) 1.336851119

(b) 1.782468159

(c) 1.836881513

(d) 1.969931972

(e) 2.030068028

(a) Basis risk makes hedges more risky.

(b) Basis risk can only lead to worse than expected effective dollar prices.

(c) Basis risk only occurs when the future is closed out early, before it matures.

(d) ‘The basis’ is defined as the underlying spot price less the futures price quote $(S_t - F_{t,T})$.

(e) The futures price of oil will tend to be higher than the spot price due to storage costs, so the basis will tend to be positive for hedgers who long futures contracts.

(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) Future portfolio values have a log-normal distribution. The mean (expected or arithmetic average) portfolio value in one year is $115,603,957.

(b) The median (50th percentile) portfolio value in one year is $115,603,957.

(c) The 90% confidence interval of continuously compounded portfolio returns over the next year $(r_{0 \rightarrow 1})$ is $-39.3456088\% < r_{0 \rightarrow 1} < 59.3456088\%$.

(d) The 90% confidence interval of portfolio values in one year $(V_1)$ is $\$67,472,095 < V_1 < \$181,023,395$.

(e) The annual 95% relative VaR is $48,131,863 and the absolute VaR is $32,527,905.