Here’s another reader question about short interest rates:

Hi Dave,

I read a contribution you made on the Nasdaq website responding to a question about Hard to Borrow securities. As a follow up, I'm wondering about how the borrow rate for these stocks is determined. I understand it is dictated by supply & demand, and is freely floating, but is that to say you are taking on unlimited "rate risk" when you enter a short position? What's stopping your broker/owner of the shares from advertising a 20% borrow rate, for example, and then as soon as the shares get borrowed, jack the rate up to 10000% overnight? Furthermore, is there any way to see a rate change coming and close out the position ahead of it? I seem to recall something about not being assessed a HTB fee if the trade is made intraday...

Any help would be most appreciated!

Thanks,

CP

Hi CP,

The answer to both questions depends on the specific policies of your brokerage firm, so I'd recommend checking with them before initiating a short position.

In my experience:

A) The brokerage (or clearing) firm is likely to warn holders of short positions that they are becoming hard to borrow. With existing positions, if the party you borrowed the shares from sells them, the brokerage has to borrow new shares for you to remain short. If they are unable to find them, they will "buy you in" or close the short position. If they can get them but they carry a negative rebate, they'll pass that rate on to you, and maybe even more in fees. This generally doesn't happen overnight, however. More often, it's a gradual process as short interest in illiquid stocks increases.

B) Intraday short sales don't pay the short rate as long as the position is closed by the end of the day. You only pay if you hold the hard-to-borrow short overnight. This is fair because you also don't earn credit interest on the balance from a short sale on an easy-to-borrow stock if you close the position the same day.

Again, every firm is different, so contact your brokerage directly if you have questions.

I hope this was helpful.

-Dave

Dave,

Thanks so much for the response! I’ve enjoyed several of your articles. This is quite helpful; I figured there would be a rational explanation. Just wanted to make sure my brokerage couldn’t put me out of business with an undisclosed rate hike!

Best,

CP

P.S. Just as a quick follow up, what do you make of signing up for a securities lending program, buying all the hardest to borrow securities, and hedging with puts? If the theta decay of the puts was less than your share of the borrow rate, wouldn’t there be an arbitrage opportunity?

Chase,

I like your thinking, but the markets are too efficient for that to work. When you put a negative interest rate into an options pricing model, the value of the calls goes down and the value of the puts goes up. The time decay changes commensurately. The puts you would be buying are already greatly inflated in value.

It you own a stock that's hard to borrow and intend to keep it for a while, you should by all means take advantage of any opportunity to lend the shares for extra income, but you won't be able to protect it in a price-efficient manner by buying puts.

-Dave

Here’s the math behind that concept:

We know that call/put parity means that the call price, minus the put price, plus the strike, equals the forward price of the stock.

C – P + K = F

In a positive interest rate environment, the forward price of the stock is the current price, plus the cost of carrying the position at the risk-free rate until expiration. (Options pricing models use a single interest rate, even though traders experience a spread – they pay a higher rate to borrow to buy stocks than they collect on cash balances. Traders will generally use the midpoint of the two rates as their input.)

If the stock pays a dividend, dividends are subtracted from the cost of carry. With the exception of those that pay a very high yield, the cost of carry is generally positive. In general, the stocks that have big short interest and trade at high negative rates are either high-flying growth stocks or companies that are in trouble, neither of which generally pay a dividend. For simplicity’s sake, I’m going to assume there’s no dividend in the examples. I'm also going to use simple interest rather than compounded. The prices will be slightly different, but the concept remains the same.

Stock price:         $100

Risk-Free Rate:    3%

Time to expiration: 180 days

If the $95 put is worth $3, we can figure out the value of the call. First, we find the cost of carry.

$100 * (180/365) * 0.03 = $1.48, so the forward price of the stock is $101.48.

C – 3 + 95 = 101.48

Call price = $9.48

Here’s how those values change if the rate is negative 20%. (We’ll assume that the implied volatility hasn’t changed, so the 95 put still has $3 worth of volatility-related time value.)

$100 * (180/365) * - 0.2 = -9.86, so the forward price is 90.14.

Now the 95 call would be worth $3.53 and the 95 put would be worth $9.09.

This is why buying puts on stocks with negative short rates isn’t a good way to get short or hedge a long position. In arbitrage-free markets, the value of calls will be lower and the value of puts will be higher.

In our example, the price of the put more than tripled when the rate went to -20%.

Incidentally, if you’d like to experiment with changing volatilities, interest rates, dividends or any other component of an option’s price and observe the effect, there’s a free options pricing calculator app available at the OCC’s website. Options Calculator

-Dave

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