An overly theoretical approach to understanding margin of safety

Acquire options at negative cost

I’ll wind a circuitous — possibly tortuous — path toward understanding margin of safety from a different angle than is typically discussed.

Some basics

A transaction is an exchange of one thing for another between two parties. A contract is an agreement between parties made in order to facilitate some transaction. Let’s imagine the simplest possible contract. A agrees to invest $1 with B for immediate exchange of $1. In other words, investor A gives investor B a dollar, and B turns around and gives it right back to A.

A simple scenario

Because we’re discussing finance, let’s securitize this contract and turn it into a tradable security S with an open market and a clearinghouse to verify and consummate transactions between parties. So A, by doing nothing other than being a participant in this market and holding at least $1 in cash, now has at any time the option to buy this security at the quoted market price. And B, by being a participant in the market and owning this security S, has the option to sell S at the quoted market price. The market price consists of two components: the bid, determined by the price at which A is willing to buy; and the ask, the price at which B is willing to sell. When A and B agree on a single price, this becomes the market clearing price, which is the price at which a transaction occurs between the two consenting parties.

The value of any financial asset is the sum of discounted cash flows that the asset will produce over the course of its life, which is also called net present value. For security S, its lifespan consists of a single moment in time: the instantaneous exchange of one dollar for one dollar. It’s NPV is thus easy to calculate:

NPV = 1

Presumably, as in any market, there can exist prices for S at which transactions do not occur. Because A will always receive $1 in exchange for whatever is paid for S, we might assume that A would never pay a price above $1 for security S, and B would not want to sell at a price less than $1. For example, A may not want to buy S at a price of $1.01. By paying $1.01 and receiving only $1 in exchange, A has suffered a loss of capital in the amount of $0.01, or one cent. This loss may not be subjectively damaging to A’s finances, but the loss is, nonetheless, permanent. In other words, no matter how long investor A holds security S, A will forever be one penny poorer than had A never engaged in the transaction in the first place. Investor A did not suffer this loss because the security itself was at all risky in the conventional sense— in fact, that A would receive $1 for his investment was an absolute certainty — but A exposed himself to risk anyway by paying more for the security S than the sum of discounted cash flows it would ever produce.

Likewise, investor B can expose himself to the risk of capital loss by selling the security S below its net present value. If B sells S for only $0.99, he too will suffer permanent loss of capital by giving up something he owned that is worth one dollar in exchange for only 99 cents cash. B’s net worth, therefore, delines by one penny by selling security S for only 99 cents.

Notice that risk of capital loss is not at all related to whether or not S is what might be colloquially called a “good investment” or “bad investment”. If the investor looks to the asset itself to deliver value, then once the value of the security is established with a reasonable degree of confidence, the investor only needs to be concerned with paying a reasonable price for the security in order to avoid the risk of loss. In the scenario laid out, paying a reasonable price means any price that is less than or equal to the NPV of one dollar.

Receiving $1 in exchange for $1 obviously accomplishes nothing for either the buyer or the seller. But engaging in a transaction at any other price leaves one investor better off, and the other worse off. Contrary to our presumption above that transactions would not occur at a price other than $1, it is in fact only prices greater or less than $1 at which transactions would likely take place in a real market, because it is at these prices that buyers and sellers may feel that they can accomplish something.

All options have value

(for some reason, this lesson remains unlearned even by finance professionals)

What is accomplished by B for selling security S at less than $1? From time to time, B may prefer having cash to owning a security. For example, B is contemplating a large discretionary purchase, or needs to make a non-discretionary payment on a debt, and the recipient would not accept the security S in lieu of cash. In cases where B does not have sufficient cash to meet these other obligations, B must sell the security for cash, becoming a forced seller. Being in a position where B is forced to sell the security, this necessarily revokes the option of selling the security. If, at that time, the highest bidder in the market is then only willing to pay 99 cents for the security with a NPV of one dollar, then the option to sell security S can be said to have a value of one cent. In this line of reasoning, it’s not difficult to see how, at other times, this option to sell may have an even greater value; if for example the highest bidder in the market is only willing to pay 85 cents, then the option to sell at that time has a value of 15 cents. By being forced to sell, the seller B is giving away, for the price of zero, the option to sell at a price that would be preferable to B had he retained the option.

In a rational setting, it is tempting to think that no buyer would similarly be forced to relinquish the option to buy. In the case of the seller B, he is forced to sell because of external obligations. In the case of buyers, however, the option to buy at a price congruent with a rational evaluation of net present value is quite often relinquished by the buyer’s own free will. This often happens because the buyer perceives a value that is much higher than the actual value of the security he wishes to purchase — the mere fact that he wishes to purchase it already distorts a hitherto “informed judgment” of value.

Another phenomenon that could cause a buyer to give up his option to buy, and which occurs frequently enough to be well-documented, is that of social frenzy. This typically occurs when the quoted market price, itself, is mistakenly factored into the buyer’s assessment of value. A recent history of increasing market prices, whereby so-called financial experts as well as the general public are regularly bidding the price of the security to ever higher levels, can become linked to the value of the security itself in the mind of a buyer.

The buyer might also put himself at additional disadvantage by placing himself in competition with other buyers if the security is perceived to be scarce. If supply of the security from sellers is perceived to be limited, buyer might think that even if the NPV of the security itself is higher than the quoted market price, the buyer might feel confident that he can re-sell the security to another market participant at a yet-higher price, who he thinks would also perceive the security scarce at some future time, and factors in this confidence into his own assessment of what he is willing to pay for the security.

If the pattern persists for long enough and, even worse, he might gain personal first-hand knowledge of another market participant successfully executing a trade of re-selling a security for a higher price than it was purchased for, providing a concrete anecdote of successfully extracting more value from his ownership of the security than the security itself will ever produce. In this case, where the opportunity for profit seems probable, and the supply of the security seems scarce, these facets might conspire in the mind of a buyer to make him feel he has no choice but to pay whatever the market asks at that time. In this way, by delegating his own assessment of underlying value to other market participants and placing himself in direct competition with other buyers for a resource perceived as scarce, he relinquishes his option to buy at a price that is consistent with his own assessment of the value of the security.

Option to sell = NPV minus selling price

Option to buy = NPV minus purchase price

The option to buy, and the option to sell, both have non-zero value at all times where the quoted market price is not equal to NPV. And because securities often do not trade on markets at their NPV, the market often implicitly assigns non-zero values to options to buy and sell that all market participants possess.

A buyer who would exercise their option to buy a security from a seller at a price equal to its NPV is not giving up or receiving any value from his option to buy nor the seller’s option to sell. On the other hand, a buyer who exercises the option to buy from a seller who is forced to sell a security for less than its NPV (i.e. a seller who has given away their option to sell for free) allows the buyer to also acquire the value of the seller’s option at a price of zero. If the buyer A buys security S (which has NPV = $1) for 60 cents from seller B, buyer A proves that B’s option to sell was worth 40 cents at that moment in time wherein the seller B’s ask was reflected in a quoted market price of 60 cents.

In these terms, buying below NPV can be characterized as an immediate profit by acquiring the seller’s valuable option to sell at a price of zero; and selling above NPV can likewise be characterized as an immediate profit by acquiring the buyer’s valuable option to buy at a price of zero.

Time value of options

There exist specialized options exchanges, where buyers and sellers can transact options with one another directly without needing to own the underlying asset. However all options available for sale directly have expiration dates, and they decay as time passes, which is to say they lose their value over time. If unexercised at the expiration date, they expire and are assigned a new value of zero, which means that their former value is permanently irrecoverable. In other words, an expired option causes a permanent loss of capital.

The options of market participants to buy and sell securities never expire, irrespective of how they were acquired, and their value does not decay. If a buyer buys a security from a seller, the buyer now possesses the value of the seller’s option to sell (or, suffers a loss of capital if the buyer pays more than NPV, as described above). In any case, the value of that option never expires, whether it is positive or negative.

Getting back to Margin of Safety

The Margin of safety is a fundamental concept in investing that has been discussed at length by Ben Graham, Warren Buffet, Seth Klarman in his eponymous book, and many others. I won’t rehash these discussions here. To summarize the idea, it can be lazily stated as “paying less for something than what it is really worth”. Like many other things in investing, it sounds easy and obvious, but also vague. I will try to make it more concrete by connecting it to the previous discussion on options.

As shown in the previous sections, paying more than its NPV for any security represents a permanent loss of capital by transferring the value of the option to buy to the seller and charging nothing for it. Likewise, paying less than NPV for any security represents an increase in capital, by receiving for the cost of zero the value of the seller’s option to sell.

Applying the margin of safety in practice involves three important principles:

1. It is impossible to know exactly what the NPV of a security is. Discount rates, terminal values, and other arithmetic assumptions can affect the calculated NPV, as well as informed judgment of the soundness of the underlying asset that the security represents.

2. It is usually possible to discern when a security is significantly overpriced where the market price represents a large (~2x or more) premium to an informed judgment of its NPV.

3. It is usually possible to discern when a security is wildly underpriced where the market price represents a large (~50% or more) discount to an informed judgment of its NPV.

“Informed judgment” does not imply a perfect and precise analysis. (I may expand on exactly what this does mean in another article). In general, it implies only that the investor reasonably understands the future prospects of the business, and can use this understanding to independently determine a reasonable estimate of the cash flows it will produce over time without being influenced by other market participants.

It’s clear from principle #2 that an investor does not want to pay significantly more than a security’s NPV — this guarantees that the investor is worse off than before, because they will suffer a permanent loss of capital. That is, the buyer pays $1 and receives less than $1 of discount cash flows in return for his investment. This is not merely risky, it is destructive.

It’s also clear in principle #1 that paying something close to NPV is risky, since it’s not possible to know exactly what the NPV is. The investor might be better off, but might not be. This is a gamble that introduces additional risk that is not necessary.

Sellers regularly offer securities at prices that, even if in their own internal P&L shows a profit to the seller, nonetheless represent a transfer of option value to the buyer. Margin of safety, in this context, can be thought of as acquiring an option at negative cost. Put another way, the investor earns a return at the time of purchase, rather than at the time of sale.

Taking into account principles #1 and #3, along with everything discussed above, the only reliable way to avoid the risk of permanent capital loss, and with a prospect of acquiring an option at negative cost, is to buy a security only when offered by a seller at a significant discount to an informed judgment of its net present value.