If I own some shares, but at the same time I am afraid of a market crash, should I buy OTM puts or ITM puts?
If you are planning to hedge your stocks by buying, say, a put on the SPY, it's an expensive way to go. SPY is 208 right now, and the Jan16 (five months out) put is $8.20 or 4% of the value. i.e. you'd need more than a 4% drop to just break even.
If you fear a 20% sized crash, 40 points or so, a $190 strike is at $3.37. And at SPY $168, you'd have $22 in return.
To generalize, it's out of the money that works best for your 'crash' concern. You still need to decide on the timing, go out to Dec17 and that $190 put is $16.53, as well as the risk/reward by choosing the strike price.
In general, broad based indexes tend to have lower implied volatility and therefore lower premium per day per $ hedged than stocks. If hedging a single stock, use its options. If hedging a portfolio, use the index.
Buying ATM index puts (SPY) as a portfolio hedge will cost you about 6–8% per year, even more when the market is frothy and implied volatility is higher. That’s a lot of drag on your portfolio which will have to appreciate that much in order to break even.
Premium decay is non linear so the premium paid per day is higher for near term options than long term. That means that you should buy further out in time. However, if the stock moves up and the stock gets further away from the put’s strike price, then the amount of protection diminishes (the put does not protect the appreciated amount). So buying too far out in time can be counter productive.
To your question. Risk and reward go hand in hand. If you want less risk, you must give up more reward. The further OTM the strike of your protective put is, the less it costs but the more you can lose due to the greater the distance down to the strike price. That's your 'deductible'. As with buying standard insurance, if you want a lower deductible, you buy a higher put strike price which means a higher premium cost.
Buying an ITM put greatly reduces the 'deductible' since it has a higher delta and a much lower amount of time premium. That's a good thing. The problem is that to the upside, you forego any profit equal to the cost of the put. For example, if XYZ is $100 and you buy a $110 put for $11, on an expiration basis, your position makes or loses nothing between $100 and $111. Your max loss to the downside is $1 (at or below $110). Above $111, the profit is $ for $ to the upside. This hedge is fine for a brief period of time but to me it makes no sense whatsoever for the long term.
IMO, a more efficient way to protect the stock is a long stock collar it but that involves a willingness to sell the stock at a higher price. For every 100 shares that you own, sell an OTM call and use the proceeds to buy an OTM put which defines a floor beneath which you cannot lose as well as a ceiling, above which you do not profit (unless you can roll the calls up and/or out later).
Collared long stock is equal to a covered call and a long put. A covered call is synthetically equal to a short put so if you make the substitutions, a collar is synthetically equal to a bullish call vertical spread. That’s what your risk graph looks like.
Collars can be structured for no cost. That is efficient. If you want to skew the risk graph to having more upside than downside, the call will be further OTM than the put and the collar will have a net cost. Skewing it in the opposite manner will generate a credit but the collar will have more downside loss potential than upside gain..
If you do collars 2–3 months out with a short call strike that is reasonably far enough OTM, there's a chance that the stock will appreciate and not be taken away by assignment by expiry. Then, add the next month's collar at higher strikes. Wash, rinse, repeat.
Whether you bought long puts or collared the position, my approach if the stock collapsed would be to roll the long puts down, pulling money out of the position and lowering the cost basis. But that's another story.
Caveat? Don't monkey with collars if you don't want to sell the stock.