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I am walking on this problem set and can really not get my head around question 8. Especially I don't understand what is meant by " - Since “short XPDR” strategy is the same as “write call, buy put, borrow PV(strike)” strategy, it therefore follows that “buy put, borrow PV(strike)” strategy is equivalent to “short XPDR and buy call”." I wanted to ask if somebody could maybe explain it in other words? :-/

Your help would be greatly appreciated.

7) Describe how to create a synthetic short using June options with strike price 30. 
Specifically, replicate the 40,000 short position in XPDR.

8) Writing a call is risky, and sometimes individuals do not receive permission (from 
their broker) to write a call. If you simply buy a June 30 put, but 
don’t write a June 30 call, you have not completely synthesized a short
position. Suppose you believe that, by June, the stub value of Metamor 
will converge  to the $12 per share figure mentioned on p. 5 of the 
case. In that case, what’s the most you could forgo by not writing a
call? That is, how much do you lose by being unable to write the call?
Would it be worth it to just buy the put alone (along of course with 
buying MMWW)?


Answer to 8) The most you could lose is the premium, $5.5. In the 
    best case scenario for you, the call options expires worthless and your 
    net profit on the call is $5.5. Thus if you believe the stub will be 
$12 in June, with perfect shorting you are going to get a profit of $12.71
(12+.71). By not writing a call, the worse you can get is:
12.71-5.5 = $7.21. So it is still worth it to just buy the put alone. Page 3
    Other comments.
    - Since “short XPDR” strategy is the same as “write call, buy put, 
    borrow PV(strike)” strategy, it therefore follows that “buy put, 
    borrow PV(strike)” strategy is equivalent to “short XPDR and buy 
    call”. In others words, failing to write the put is the same as 
    shorting one share of XPDR and then buying a call on XPDR.
    - If you can’t write a call, you can get closer to a synthetic 
    short position by buying a very out-of-the-money put. 
    Unfortunately, in this case there are no such puts trading, 
    the best we can do is the strike price of 35.
    - By failing to write the call, you could think of yourself as 
    insuring against the possibility that the spin-off is cancelled and 
    XPDR goes way up (remember, “buy put, borrow PV(strike)” strategy 
    is equivalent to “short XPDR and buy call”) . The price of this 
    insurance is $5.5.
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How about a hint rather than an exact answer? Put Call Parity concerns the relationship between the prices of European put and call options (with matched strike and expiration dates): $$ C - P = D(F-K) $$ where C and P are the current prices of calls and puts respectively, D is the discount factor, F is the forward price of the asset, and K is the strike price.

You can rewrite the equation above to get a the price of a negative call, just solve for $-C$.

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