FRM Fun 21: bear call spread versus bear put spread, P1

[David Harper CFA FRM]

P1.T3 only.

Based on RiskNoob 's correction of my mistake here @ http://forum.bionicturtle.com/threads/p1-t3-211-option-trading-strategies-i-spreads.6104/

A bear spread (Hull Chapter 11) can be entered either

• with two calls (long call with higher strike plus short call with lower strike) or
• with two puts (long put with higher strike plus short put with lower strike).

Question: which bear spread produces an initial cash inflow rather than requires an initial cost, and (here is the real question): is not this cash inflow always superior; i.e., if we are bearish looking for capped down-side, why wouldn't we always choose the trade that returns initial income?

 

[Jas]

Call Bear spread always gives positive cash inflow at the start of the strategy.
Reason: Call bear means buy high K and sell low K - Also for calls the price varies inversely to K => higher K call will be cheaper to the lower K call => call we are buying is cheaper and call we are selling is costlier. Hence the initial cash inflow.
For Put Bear, the reasoning is similar to result in initial cash outflow.

However, the logic of which strategy to use depends on other factors rather than the initial cash inflow or outflow

• The payoff would differ between a similar call bear and a put bear. We would need to compare the market prices of the calls and puts to be used to check the payoff and decide on the particular bear spread which gives the higher payoff. This occurs due to the difference in the market prices.
• Another factor is the liquidity and availability of the particular calls or puts under consideration. We may be bearish at certain X levels, but at these levels maybe only the puts are liquid while the calls are not liquid.

 

[RiskNoob]

I agree with FeRMioN, and I could not find more answers from myself, so I search the web (thus I don't quality for this round):

http://www.tylerstrading.com/mail-time-call-vs-put-spreads/

It says traders prefer to take positions for out-of-the money options for bullish/bearish spreads (e.g. for bearish spreads, take short c1 and long c2 where K1 < K2 and current stock price is lower than K1 - which results initial cash OUTFLOW).

The link says (regarding the preference , 1st and 3rd one):
- Higher liquidity, smaller spread (as FeRMioN pointed from the above)
- Advantages to the spread holders for the early exercise (I am not quite so sure about this especially in the case of calls, since the position concerns both long and short calls)

RiskNoob

 

[ShaktiRathore]

1. Bear spread with two calls c1 and c2: long c1 and short c2 such that K1>K2
value of call=max(S-K,0)
also evident from BSM, call=S0N(d1)-Kexp(-rT)N(d2)
=>value is negatively related to exercise price so higher K implies lower call value.
so value of c2>c1=> if i pay x for c1 and get y for c2 than my net pay is y-x and since c2>c1=>y>x so there is a net pay.
Bear spread with two puts p1 and p2: long p1 and short p2 such that K1>K2
value of put=max(K-S,0)
also evident from BSM, put=Kexp(-rT)N(-d2)-S0N(-d1)
=>value is positively related to exercise price so higher K implies higher put value.
so value of p2<p1=> if i pay x for p1 and get y for p2 than my net pay is y-x and since p2<p1=>y<x so there is a net outflow of pay.
Hence the calls bear spread has net initial inflow of cash.
2. Regarding the second part as to why we don't always choose the bear spread of calls rather than puts because the former always has initial outflow. Initial outflow of cash does not necessarily mean that the overall profit from trading these strategies will be greater for calls bear spread than the put bear spread. Its possible that net payoff of puts is greater than net payoff for calls spread.In the end it depends on the future movement of stock price. What the investors might be interested is how much they make in the end and not what are the initial and intermediate cash flows which should be the case as is synonymous with the shareholders interest in final rate of return without concerning themselves with Dividends flow.
Fore.g. the value of call bear spread =max(S-K1,0)+max(S-K2,0)+initial flow
the value of put bear spread =max(K1-S,0)+max(K2-S,0)-initial flow
i) S>K1>K2=> the value of call bear spread=2S-(K1+K2)+initial flow
the value of put bear spread =0+0-initial flow=-initial flow
so investing in call bear spread is more profitable
ii)K1>S>K2=>the value of call bear spread=S-K2+initial flow
the value of put bear spread =K1-S-initial flow=K1-S-initial flow
now total profit of put spread is greater than call spread for,
K1-S-initial flow>S-K2+initial flow=>K1+K2-2S>2*initial flow(quite possible!!!)
iii)S<K2<K1=>the value of call bear spread=initial flow
the value of put bear spread =K2-S+K1-S-initial flow=K1+K2-2S-initial flow
now total profit of put spread is greater than call spread for,
K1+K2-2S-initial flow>initial flow=>K1+K2-2S>2*initial flow(quite possible!!!)
So in the end the cases ii and ii are always possible and that they provide more over cash inflow for put bear than the call bear, so there is no surety that the net cash flow is more for call spread than the put spread. In the end it does not matter whether there is an initial cash inflow or not what matters is what is the end profit as they say what matters is who wins in the end.

thanks