You find yourself in a difficult position. You CEO has asked you to help her rank these $6$ agencies in terms of currency forecasting expertise. You obtain the following information from your departments for the Mexican Peso value for $180$ days:

Current spot rate: $ $0\mathrm{.}0495/$MP $($MP $=$ Mexican Peso$)$

$180-$day forward rate: $ $0\mathrm{.}0500/$MP

$180-$day inflation rate in the US $=8\%$

$180-$day inflation rate in Mexico $=15\%$

Forecast of the $180-$day rate from agency $1$: $ $0\mathrm{.}1800/$MP

Forecast of the $180-$day rate from agency $2$: $ $0\mathrm{.}1025/$MP

Forecast of the $180-$day rate from agency $3$: $ $0\mathrm{.}0515/$MP

Forecast of the $180-$day rate from agency $4$: $ $0\mathrm{.}0492/$MP

Forecast of the $180-$day rate from agency $5$: $ $0\mathrm{.}0399/$MP

Forecast of the $180-$day rate from agency $6$: $ $0\mathrm{.}0486/$MP

The actual spot rate $180$ days from now: $ $0\mathrm{.}0899/$MP

Part a$)$: Can you rank the agencies in terms of their forecasting expertise? Make sure that you show all your workings for full credit. Provide a brief executive summary to be delivered to your CEO.

Part b$).$ What if the forward rate was biased and you had to use PPP rates to determine the synthetic forward? Calculate the new rankings based on this new information.