Using Box Spreads to Create Synthetic Borrowing

# Build a Synthetic Loan for Personal Finance


# Build a Synthetic Loan for Personal Finance












Suppose I am short of cash and want a loan for some mundane objective like travelling or buying a car. The interest rate for personal loan with my bank is too high.

Is there any way in finance that an average guy like me can do a synthetic loan (without being a corporate investor or rich) in case I find out that the implicit market free rate from this operation is lower than with my bank?

At first I considered Put Call parity. I could go short on stock St, long/short on call /put and arrange things to pay the strike K in the future for sure. If I calculate that after fees, liquidity issues and other costs the implicit risk free rate of this transaction is lower than the interest rate of a loan, it would make sense. The killer detail is margin, in most countries you need at least the value of what you are shorting, in this case St, untouched in your account. If I already have St free in my bank account I wouldn't need a loan anyway and all becomes meaningless.

Is there any class of assets that would allow someone to practically build a synthetic loan for personal reasons or margin requirement would kill everything in the end.

## Answer by kdragger (score 3)

https://quant.stackexchange.com/a/36360

Pre-caveat -- I have not done this in a retail account and am unfamiliar with how this would be treated from a margin perspective, though I believe it should receive a "light" treatment as its risk is quite low.

There is such a structure. It is called a box. You were very close in the structure that you proposed. You proposed a conversion (or what we would have called a reversal or reverse-conversion) of long call, short put, short stock. Instead, consider two conversions. One is long call, short put, short stock. The other is short call, long put, long stock. Both are in the same expiration but different strikes.

But won't that offset? Yes, the stock (or futures or other underlying) will offset. But, depending on which way that you did it, there will be a net income or outlay of money. To borrow money, one would sell call in the low strike (high call premium to collect with little to pay out for the corresponding put) AND sell put in the high strike (again, high premium but this time in the put and the OTM option will be call). In other words, you would be selling the deep options in two conversions.

Consider AAPL is trading \$100. The 3 month, 50 call is \$55.00 and the put is \$5. Meanwhile the 150 put trades 55 and the 150 call trades \$5. Both have conversions priced at 0. But if you sell call in the 50 conversion, you collect \$55 - \$5 = \$50. Meanwhile, to avoid transacting in stock, you bundle it with the 150 conversion to sell put: \$55 - \$5 and collect another \$50. Voila. Position: -1 50c, +1 50p, +1 150c, -1 150p.

With that said, you have to keep in mind that for the example that I gave, for AAPL options, they are American style options and subject to early exercise. Which means that you will likely lose your fat short option positions. Your choice is then to either transact in European style options (say SPX options, IIRC) or choose strikes in American style options to seek to avoid early exercise.

The truth is that for retail accounts, I've never tried this. It is common for institutional clearing accounts to do exactly this to manage cash/equity balances (or even take punts on the path of future rates, etc). So I can't tell you that your broker or firm will provide a credit to your account that actually economically benefits you.

On top of that, it is a 4 legged spread for which small amounts can make big differences in the implied interest rates. So while this is out there, and it is documented, I have to warn you that it is more likely than not to be a negative economic experience for you. So do not take this at all as trading or investing advice. If anything, it is merely to alert you to this structure and to perform more research about how your broker handles it, what it may cost, and all of the nuances (of which there are all sorts) for holding this trade.

Follow-on: I just realized there would be a legitimate question as to where the magic of this came from in spontaneously generating credit at some anticipated far better rate than would otherwise be available.

This occurs because all transactions are done at the options clearing house, e.g., OCC or CME or wherever (those are US examples). Each clearing member guarantees that the trades will settle and be appropriately handled at expiration (or early exercise). Your broker or clearer will either have a credit line with you that will dictate if you can take any money out. You may not be able to; I don't know. You will likely, however, be able to use those proceeds to unlever currently leveraged transactions.

For instance, say that you owned \$500K of stocks using \$400K of funds. $100K of boxes into the account may (I stress may -- I can't speak for your situation) apply so that you don't need to pay the loan rate at your broker/clearer. Hope that helped.

Edit/add due to comment: The box gets its name from the way that looks like in a "carded-up" position, the way that option market makers look at them.

```
Call Pos        Strike        Put Pos     
  0               95             0
 -9              100             9    
  9              105            -9
```