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# backsperad vs straight long options

Discussion in 'Options' started by hedgex, Sep 1, 2009.

1. ### hedgex

I am trying to compare ratio backspreads vs naked long options. It easier to work on puts since puts have an upper bound for the gain that is the strike price when the stock drops to 0.

I want to compare the fund efficiency: the maximum gain over money put in.

With a naked long put, the max gain the the strike and the price of the put is the cost: Kb/Pb, strike of the buy over the buy price.

With a backspread, suppose the ratio is 1:2 and the credit/debit is 0. The max gain is Kb and the margin requirement is (Ks-Kb), which is the money tied up, the effective cost, or the investment.

The ration is Ps/Pb = Nb/Ns, where N is the number of contracts bought or sold. The return on investment of the backspread is delta*Kb(Ps-Pb).

The ratio of returns on investment of the backspread over the long put is therefore simply the delta between the two strikes. That is, as far as return on investment is concerned, the backspread underperforms the naked put since delta < 1.

Has someone arrived at a similar conclusion?

Probably: MaxGain=Ks=Kb-(Ks-Kb)?

3. ### JJacksET4

To keep it simple without all the math, a simple put often would be better in a max gain scenario, but what about other times?

Instead of using formulas, just look at a simple example - XYZ at \$50

50 put - \$400
45 put - \$200

Buy 50 put - \$400 - max value = \$5000 = \$4600 gain and 12.5 folding the max risk.

Put Ratio Backspread (sell 1 50 / buy 2 45s) = max value = \$4000 (\$9000 - \$5000). Max risk was \$500 - so 8 times max risk. No money was spent, however \$500 would be required for margin.

Now look at what are the odds of the max risk? In the put purchase nearing expiration, any price over \$50 will result in max loss of \$400.

With the Put Ratio Backspread, the max loss area is only around the \$45 area. Large upward movement which will result in a likely max loss for the put purchase will result in a likely breakeven for the PRBS.

So like usual (always?) there is a trade off.

JJacksET4

4. ### spindr0

Some corrections:

The maximum gain on a put is the strike less the premium received

The maximum gain on a 2:1 put backspread is the lower strike less the difference in strikes +/- the premium received/paid

OR

2X the lower strike minus the upper strike +/- the premium received/paid

The backspread is going to underperform to the downside (toward zero) because there's a loss from the higher strike sold down to the lower strike bot. Simple as that.

If you look at strategies in isolation (just to the downside), then the backspread is inferior in terms of ROI. But will the expected profit be lower as well???

All of this reminds me of the brilliant science student who derives the exact equation for titration of the chemistry experiment but can't light the match (g). Ya still have to get the timing and direction right,

5. ### spindr0

And to add another 2 cents, backspread not very desirable unless done for a credit.

Typo: MaxGain=Kb-(Ks-Kb) if net credit/debit=0

Hi Spin Dr:
Would it be true and correct to say that with a relatively small size of movement (say, less than 1 StdDev), a backspread trade getting in the right direction and catching turns at the right timing could be still a losing trade?

PS: How do you apply spin on options trading? Do you actually mean Monitoring/ Adjusting a trade frequently, due to long-term trading dynamics? I'm just curious!

8. ### hedgex

Ok, guys, I set up simulations to study the choice of strikes on the risk and return rate. All in all, the result is surprising to me: deep ITM put backspreads gives the highest return on investment. Here come the details.

Constants: IV=50, S=25, price range=20:30, duration=60d
Variables: Ks, Kb
Relationship: spreads are all 0-cost, or Ps*Ns = Pb*Nb

Ks Kb ratio maxGain MaxLoss mrgn
25 24 1.33 0.32 1 1
25 23 1.84 0.52 2 2
27 25 1.61 1.06 2 2
27 26 1.26 0.54 1 1
30 29 1.18 0.59 1 1
30 inf 10 30 30
25 inf 5 25 25

The highest ROI occurs when you short 30 Put and buy 29 Put: the gain is 54% when the stock drops to 20. OTM spreads returns no more than 32%.

9. ### spindr0

Absolutely fascinating! With a stock at 25, what would the premiums be for two ITM puts (short 30 Put buy 29 Put) that can result in a 1:2 backspread that costs zero?

10. ### spindr0

Would "spin" be defined as...

1) Circular movement around an axis?
2) A short trip?
3) To give a verbal account of?
4) To turn in circles?

And what is the definition of "catching turns at the right timing" ?

All pertinent information greatly appreciated so that we can hone in on an unequivocally precise answer.

#10     Sep 2, 2009
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