arbitrage profit. $($Hint: Assume that the zero$-$coupon bonds listed in Table $1$ are tradeable bonds. That is$,$ they can be bought or sold short in any quantity necessary.$)$ Calculate the riskless profit to be earned today per $$100$ face value of Bond A$.$

Be sure to clearly specify the quantity of each of the $$1$ face value Zero$-$Coupon bonds that should be bought or short$-$sold in the strategy for each $$100$ of face value of Bond A that is being short$-$sold or bought. Your strategy should generate a cash inflow $($risk$-$free profit$)$ at Time Zero, and net cash flows of zero at all future dates.

Guidance For Part $1($c$)$: You are asked to describe an arbitrage strategy, and calculate the risk$-$free profit at Time Zero per $$100$ face value at Time $1.$ To help discover the correct strategy:

Begin by taking the $$100$ Time$-1$ face value and discount it back one period to Time Zero using the one$-$period spot rate.

Next, compound the same $$100$ at Time $1$ into the future for one period $($i$.$e$.$ find its future value at Time $2)$ using the quoted forward rate of $5\%.$

Then take that future value just calculated in Step $2,$ and discount it back for two periods $($find its present value at Time Zero$)$ using the two$-$period spot rate.

$2$

Comparing these two present values you should be able to determine the correct borrowing & lending strategy. $($Assume that you can borrow or lend at any of the three rates: the one$-$period spot rate, the two$-$period spot rate, and the quoted forward rate of $5\%.)$ Your strategy should generate a net cash inflow $($the risk$-$free profit$)$ today at Time Zero, and zero net cash flows at Time $1$ and at Time $2.$

If you want to confirm your understanding $($you do NOT need to do this as part of the assignment$)$ change the problem by instead beginning with a $$100$ face value at Time $2.$ Find the present value of this $$100$ two ways:

Discount this $$100$ back two periods to Time Zero using the two$-$period spot rate.

Discount the same $$100$ back to Time $1$ using the quoted forward rate, and then discount that Time$-1$ value back one$-$period to Time Zero using the one$-$period spot rate.

Comparing these two present values you should be able to determine the correct borrowing & lending strategy. In general it will be the same as in the original setting of $$100$ face value at Time $1,$ but the risk$-$free profit at Time Zero will be different.