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The Wall Street Put

August 5, 2012

“Wall Street”, by which we mean, of course, the people who work there and the industry that is commonly known as “Wall Street” (or “Bay Street” or “The City” and so forth) has only one job (by preference) and that is to make connections between the people (persons or companies) who have money with those who need  (or want) money. That is an elegant job, indeed, but there are also variations on that theme as we move from principle to supplicant to principle and we endeavour to make connections  between the people who need money (and come to Wall Street) and the people who have money (and prefer to live out of town).

In accounting terms, as credits and debits, one would describe these jobs as

      money → Wall Street → (money)

and

(money) → Wall Street → money

and Wall Street is very good at both of them. For example, a person or company that needs money (the bottom line, above) could be described as being short ($1 billion) and a person who has money as being long $1 billion and the whole transaction (or job) could be described as an option and, one would think, should earn an option return or premium that we can calculate.

The direction of the arrows is intentional but, in fact, the direction of the arrows can be reversed in both cases and described as leverage:

     money ← Wall Street ← (money)

and

(money) ← Wall Street ← money

so that, in effect, the person who has borrowed ($1 billion) is now lending it to the person who already has $1 billion, or, the more unlikely case, the person who has $1 billion is now lending it to the debtor, who has already borrowed ($1 billion). And Wall Street is also very good at that.

Finally, we can readily see that the following also obtains:

(money) → Wall Street → (money)

and

      money → Wall Street → money

so that the person who has borrowed ($1 billion) is lending it to another person who has borrowed ($1 billion) and the person who has $1 billion is now lending it to the person who already has $1 billion, and, in the absence of effective risk management (and enforceable guarantees), one could replace the word “lending” with “giving” in all cases. And Wall Street is also very good at that. Please see, for example, The Secret Life of a Portfolio Manager, July 2012, or Maximising Shareholder Value (LOL), August 2012.

We have, of course, understood the pricing of options very well for hundreds, if not thousands, of years and a policy of risk aversion to control for the possibility of investment loss or business failure can be enforced by calculating the parameters of the Put-Call Parity Equation:

C(t) + Dividends(t) + K×exp(-k(T-t)) = P(t) + S(t).

In this equation, which is required in the absence of theft or academically risk-free returns through frictionless arbitrage, K is the value (in money terms) of the underlying asset at time T (in years) and is known or agreed upon by the both the “buyer” (borrower or lender) and the “seller” (respectively, lender or borrower) and t is the time between now (time t=0) and time t=T and k=k(t) is the “force of interest” (an actuarial term) that could vary with time but might also be k=log(1+i) where i is an annualized “real rate of interest” for one year and includes an allowance for “inflation” if K does not.

S(t) is the value of the underlying asset which depends on which accounting equation we’re using at time t and the right-hand side of this equation defines a “protective put” P(t) with the value max(0, K-S(T)) at time t=T so that both sides of this equation have the value max(S(T), K) at time t=T absent “dividends” or “interest” that is paid to the principle (the lender) by the supplicant (borrower, whether of stocks or cash) between now and the time T.

The left-hand side of the equation defines a “fiduciary call” and ensures that the money for the strike price K will be available at the expiration time T and the call option, in addition to the time and fundamental value, C(t), has the value max(0, S(T)-K) at time T.

The “lender” or principle invariably buys the put, P(t), at time t=0 in order to close the deal, but who buys the allegedly offsetting call, C(t), from them and what is it? And how is Wall Street to be paid for connecting the lender and borrower and closing the deal or transaction? Moreover, the investor wouldn’t know that they have bought the put and paid for it either now or possibly later, unless they are told what it is and what it is supposed to do.

The first two cases are the simplest (but not necessarily the most common) and one can imagine the lender or buyer either approaching Wall Street because they want to make an investment, or Wall Street approaching the lender or buyer because they have something to sell.

If, then, we are prepared to pay S at time t=0 (now) in order to receive K at time T, we should also be prepared to buy the put, P, at time t=0 in order to guarantee that result. The cost of P can be determined from the list of publicly traded options and if none is available, we can ask our broker to underwrite one, especially if they are approaching us to make this deal. The cost and worth of the offsetting call option, C, can be determined in the same way and, hence, we can compute the “force of interest” and determine whether or not this is a good investment. That is, our capital is safe and the return exceeds the rate of inflation. Moreover, because we are long in S, we are selling C and that will, in general, partially offset the cost of P.

If that appears to be too hard then the alternative is to buy a lottery ticket and just hope for the best. It might also appear to be an expensive way to buy stocks or lend money. But that depends on Wall Street and the price of their commissions (and the same could be said of the other four “deals”, only more so) and one would hope that if investors were in fact fully informed about who gets what and when, the market would be a safer and more productive place for all of us, including Wall Street.

For example, our broker might call us and suggest that we buy 100 shares of AAPL Apple (Computer) Inc for $62,000 today ($620 per share); the expected dividend is $10.60 per share and the stock price is down from $640 in April, just four months ago (they say). Well, the November put at $640 is available for $5,500 today and the call at $2,500 so we can “do this deal” for the cost of three transactions (buy the stock, buy the put, and sell the call) and $65,000 in cash which is $1,000 more than what we will surely obtain in November.

Possibly, they will have a better idea for us, such as, for example, Why not buy the call from us at a higher strike price $680 for $5,500 (even though it lists at $1,400)? After all, they must like Apple and we don’t know anything about it except that the demonstrated quarterly volatility is $73 and the stock price could go either way in the next six months, couldn’t it?

Moreover, in principle, we can’t buy Apple without a better deal because it’s an (N) (please see the chart below) and has been since $350 in April of last year (when we last sold it) and we only buy and hold (B)’s, that is, the stock price (SP) should exceed the risk price (SF). So, yes, we’ll buy the stock and we’ll buy the put, but What are you going to give us for the call? For more on this, please see one of our previous Letters such as Stock Prices Are The New Pink, June 2012.

Disclaimer

Investing in the bond and stock markets has become a highly regulated and litigious industry but despite that, there remains only one effective rule and that is caveat emptor or “buyer beware”.

Nothing that we say should be construed by any person as advice or a recommendation to buy, sell, hold or avoid the common stock or bonds of any public company at any time for any purpose. That is the law and we fully support and respect that law and regulation in every jurisdiction without exception and without qualification to the best of our knowledge and ability.

We can only tell you what we do and why we do it or have done it and we know nothing at all about the future or the future of stock prices of any company nor why they are what they are, now.

The author retains all copyrights to his works in this blog and on this website. The Perpetual Bond®™ is a registered trademark and patented technology of The RiskWerk Company and RiskWerk Limited (“Company”) . The Canada Pension Bond®™ and The Medina Bond®™ are registered trademarks or trademarks of the Company as are the words and phrases “Alpha-smart”, “100% Capital Safety”, “100% Liquidity”,  ”price of risk”, “risk price”, and the symbols “(B)”, “(N)” and N*.

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