# Ben Graham would be proud

GM has proposed a restructuring plan that (a) will not be accepted by bondholders; (b) will make the company literally government-owned; and (c) will dilute existing shareholders by at least 100x.

Naturally, the stock popped 20% on this news. So just for fun, I decided to short it with a small position.

Except that did not work, because GM is so heavily shorted already that there are no shares available to borrow. Since I think I am so clever, I decided to try a synthetic short instead. A “synthetic short” means selling a call option and buying a put option with identical strikes and expirations; the return of such a combination is identical to shorting the stock. For example, I could use the September $3 call and the September$3 put. As I write, these trade for $0.25 and$2.38, respectively… Which would allow me to go short the synthetic stock at an effective price of $3 –$2.38 + $0.25 =$0.87.

Now that is a little strange, since the actual stock is trading above $2. If you know anybody who believes in efficient markets, show them this example and see what they say. Two instruments with literally identical underlying value are trading at prices that differ by a factor of 2.5. The only way to arbitrage the difference is to buy a synthetic long and short the stock… But as I mentioned, the latter is not currently possible, which is why this anomaly can persist. However, if you know anybody who is holding GM stock because they are praying for a miracle or whatever, you might suggest they sell the stock and buy a synthetic long position instead. From their point of view, that is free money. Personally, I believe our markets have become a heavily manipulated nightmare where 99% of the volume consists of computers trading with each other based on purely technical factors. As evidence, look no further than GM. Update After doing some more thinking and reading — something similar is happening with Citigroup, for instance — I see there is an economic difference between owning the actual stock and owning synthetic stock via options: If you own the actual stock, you can loan it out right now for a ridiculous rate of interest to people who seek to short it. You cannot similarly loan out synthetic stock, and this accounts for the price differential. Put another way, the stock price is being amplified by a factor of 2.5 because so many people are willing to pay a premium to short it. Welcome to wonderland, Alice. ### 5 comments to Ben Graham would be proud • snoopy Nemo, Can you recommend a good book/website to learn about options trading? • richfam If you read “The Panic of 1907″ you’ll read a story about financing and technicals. The fundamental value of stock can be more fleeting than the persistence of the price. But when these things crack (like GM will), it seems to happen all at once. Its all technical until its not. • inefficient.frontier Snoopy – Hull is classic textbook material if you want dead tree format; the Options Industry Council site is pretty helpful for beginners without trying to pitch you on opening an account, as many options-ed site will. Nemo’s lament follows from put-call parity, for European style exercise: call + PV[strike] = put + underlying. N.b.: “PV” means present value; these options expire in September 09, so say your broker pays you 1% for a time deposit from now till Sep09. Then the future value of your deposit is$1x(1+1%) = $1x(1.01) =$1.01. Going backwards (and assuming you can borrow at 1% over the same term as well) the present value of $1.01 would be$1. Just a way to say money is worth more tomorrow than today, assuming your broker’s [nominal] rates are more than 0%.

You want the synthetic position to isolate the underlying (GM stock), so move the put over and rearrange the put-call parity equation for:

call – put + PV[strike] = underlying.

Using closing prices on the 27th (GM closed at 2.04, the call at 0.23, the put at 2.30), a synthetic long would look like

+0.23 – 2.30 + PV[3] = 2.04,

where you bought a call, sold a put, and invest your $2.07 net credit (of the put sale less call purchase) in a zero-coupon bond that matures to$3 in Sep09. Something doesn’t smell right, but hold that thought; you want to instead be short the underlying, so sell the call, buy the put, and finance the $2.07 net debit with a zero maturing to$3 in Sep09:

-0.23 +2.30 -PV[3] = -2.04.

… but since 2.30 – 0.23 = 2.07, then PV[3] must be 4.11 for the equation to balance, meaning you can borrow $4.11 today to pay back$3 in September. But that implies a negative (nominal) discount rate, which makes no sense — no broker will pay you to borrow, so something else must be off.

It’s easiest to back up to the synthetic long: the right side (GM stock) is too big (priced too high), for the calls to be that cheap and/or the puts to be that expensive. Since the right side is too big given the left side, the easy arbitrage would be shorting the stock at $2.04 and using the short-sale proceeds to fund part of the net$2.07 debit (of a $2.30 put purchase offset by$0.23 from the call sale); the extra $0.03 of funding you borrow from your broker. You can work out the scenarios depending on whether GM expires above or below$3; in either case you come out ahead with a risk-free return that exceeds the negative rate implied above.

So what’s the catch? As Nemo points out, borrowing stock (as is required to sell short) can be difficult. People who might let you borrow their GM shares are people who plan to hold them for a long time; think pension funds, an S&P 500 index mutual fund or ETF, maybe the the UAW VEBA. Under the circumstances, they’ve probably lent out a lot of GM to other people who want to get short. And by the way, they (or their broker) might charge a fee for their troubles; suppose they read the papers, realize GM borrows are a hot ticket, and charge a very large fee (say, 15% annualized); that quickly eats up any arbitrage profits you can make from the synthetic.

But don’t tell John Hull; he’s a good guy, buy his book by all means.

• mittelwerk