Hedge ratio for

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afranks1

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Looking at CFAI reading 53 problem question 2:
If call price is overpriced, we should sell the call and buy the underlying stock.
If call price is underpriced, we should buy the call and sell the underlying stock.
Looking at CFAI reading 53, problem question 3:
If put price is overpriced, we should sell the put and sell the underlying stock.
If put price is underpriced, we should buy the put and buy the underlying stock.
For these 4 situations, i get that we should sell the option when the option is overpriced, and buy the option when the option is underpriced.
But, can someone please explain the logic behind what we do with the underlying stock in these 4 situations? I don’t get it.
 
I haven’t a copy of the curriculum, but this appears to be an application of put-call parity:
Stock + Put = Call + Bond
This can be rearranged to create a synthetic call:
Call = Stock + Put – Bond
or a synthetic put:
Put = Call + Bond – Stock
In all cases, when one security is mispriced, you buy the cheap one and sell the dear one:
  1. If a call is underpriced (cheap): buy a call, sell a synthetic call (i.e., sell the stock, sell a put, buy a bond
  2. If a call is overpriced (dear): sell a call, buy a synthetic call (i.e., buy the stock, buy a put, sell a bond)
  3. If a put is underpriced (cheap): but a put, sell a synthetic put (i.e., sell a call, sell a bond, buy the stock)
  4. If a put is overpriced (dear): sell a put, buy a synthetic put (i.e., buy a call, buy a bond, sell the stock)
This does seem to contradict what you wrote; i.e., what you wrote sounds weird.
 
I agree with what you have written, and Schweser also says: “if option is overpriced, short the option and buy a fractional share of the stock for each option we shorted. If option is underpriced, purchase the option and short a fractional share of stock for each option share”.
So why in CFAI reading 53 (question 3B) is the answer saying if put is overpriced, sell put and short underlying?
And why in CFAI reading 53 (question 3C) is the answer saying if put is underpriced, buy put and buy underlying?
 
Sorry: I just figured out what’s going on. (Perhaps I should have tried harder to understand the title of the thread; some things take me a little longer than others.) This isn’t put-call parity stuff (my mistake; sorry); it’s delta hedging stuff.
The value of a call option increases as the price of the underlying increases, in a ratio of δ:1. So if call options are underpriced, you buy, say, calls on 1,000 shares, and sell 1,000 × δ shares. You’ve hedged the price change of your portfolio, and you make money when call options become fairly priced and you close out your position.
The other three follow the same idea (with the price of puts decreasing as the price of the underlying increases, of course).
(Note: if options are mispriced, I still think it makes more sense to profit using put-call parity than using delta hedging. Put-call parity is one transaction, with one transaction cost; delta hedging is dynamic, so it could involve many transactions (especially if the price of the underlying moves a lot), with correspondingly more transaction costs, which will erode the profit. (Actually, the profit doesn’t disappear; it’s simply redistributed to the securities brokers/dealers.))
 
I think i get it, am i correct in saying the point of the hedge ratio is to hedge your overall position no matter the move in price, so
if put is overpriced:
- sell put (will benefit when price increases)
- sell short underlying (will benefit when price decreases)
if call is overpriced:
- sell call (benefit when price decreases)
- buy underlying (benefit when price increases)
 
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