Put call forward parity problems

CFA Level I Derivatives
#1

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As we know
Synthetic protective put = Long risk-free asset (FV=F0(T)) + long forward contract + long put option (1)
Fiduciary call = long risk-free bond (FV=X) + long call option (2)
(1) = (2) <=> Long risk-free asset (FV=F0(T)) + long forward contract + long put option = long risk-free bond (FV=X) + long call option
<=> Long risk free bond = Long risk-free asset (FV=F0(T)) + long forward contract + long put option + short call option

I wonder that the question misses long risk-free asset (FV=F0(T)), doesn’t it?

#2

S + P = C + PV(X)

S(1+r)^t = F

PV(F) + P = C + PV(X)

PV(X) = PV(F) + P - C
Long forward, long put, short call

we know this
Fiduciary call = long risk-free bond (FV=X) + long call option (2)

but we don’t know this.
Synthetic protective put = Long risk-free asset (FV=F0(T)) + long forward contract + long put option (1)

#3

Didn’t get why we don’t know this - Synthetic protective put = Long risk-free asset (FV=F0(T)) + long forward contract + long put option.
Let’s say ST> X —
Payoff (1) = Long Forward + Long Put + Short Call
= ST-F0(T) + 0 + X-ST
= X-F0(T)
Payoff from Long Risk free Bond = X
If we take payoff from long risk free asset (F0(T)), than the payoff from (1) will match the payoff from Long Risk free Bond.

#4

Also, did you come across this question from the Institute Book -

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I think the answer should be Long Forward, Long Put, Long Risk Free Bond as we purchasing/investing at Rf and not borrowing at Rf

#5

The sign on X is negative, so that means short.

#6

Okay, yes I get it. I was thinking risk free bond as the risk free asset.
But then now the confusion is where the risk free asset went?
Synthetic protective put = Long risk-free asset (FV=F0(T)) + long forward contract + long put option.
Adding to this I think the main confusion is when we are writing this - F0(T)(1+r)^(-T) - what are we referring to? - I am seeing this as Long Risk Free asset. But as per the equation in this question - it seems long Forward. But essentially the price of Long Forward at Inception is Zero