Modeling a Down Payment as a Call Option

There was an interesting idea that came up in our discussion of Islamic Finance that got me thinking. While not directly related to what we were doing, someone mentioned the idea that a down payment was modeled like a call option which I thought was quite clever.

Consider this, you can:

• put down a payment for the right to purchase the asset
• elect to walk away from this right, forfeiting the down payment, or
• pay the *remaining amount* and purchase the asset at the appropriate time

This is very similar to a call option, with only one exception:

Note that in a down payment, you are paying the remaining amount, not the full amount of the asset. So if you were to use a call option to model down payment, you would have to adjust the strike price down by the premium (down payment) because the down payment is applied to the purchase price of the asset.

So imagine that the value of your asset changes after you’ve paid the down payment. If it goes up, you can continue your purchase (and possibly even sell your asset for a profit, assuming its liquid enough) or you can elect not to buy it if you’ve taken a huge bath (maybe even the market value dropped by more than the down payment amount).

Islamic Finance - International Consulting Project

A new initative at Rotman (although you wouldn't know it as it has simply exploded this year) is the International Consulting Project. Laura Wood, Director of International Programs, has started a new research type project that engages students to work with professors on international topics. Some countries involved are the G20, Middle East, Israel, Africa and potentially others.

I myself am participating in the Islamic Finance ICP with Walid Hejazi, the professor who leads the Middle East study tour.

Yesterday, we were invited to attend the kick off event for the Islamic Finance EMBA course which will be offered in Jan 2011. The keynote speaker was David Dodge, Senior Advisor, Bennett Jones and former Governor of the Bank of Canada. He spoke about the growing interest in Islamic finance and how there it is common for people to see Shariah compliant instruments as simply "no interest" and how this superficial understanding does not encompass the fundamental rational for the structure of these products.

I am looking forward to working with my four other colleagues on this research project to look at Islamic financial instruments.

Financial Management Presentation

Yesterday, my team had our presentation for Financial Management with Asher Drory, a professor notorious for not pulling any punches and generally holding all Rotman students to a very high standard. We didn't want to disappoint.

Our case was on securitization as a form of financing. The company was a collections company which bought bad loans for pennies on the dollar and made a profit by collecting on them. However, they were being squeezed on the margins due to banks beginning to charge more for the bad debts as well as the quality and collectability of the debts shrinking.

The company was also looking to grow, and had been previously financing its growth through the securitization of it's uncollected loans (in this specialized financial industry, loans are a form of inventory, rather than as a liability in a traditional company). However, the conditions of the security were almost exactly the same as debt (monthly interest payments and principal flowthrough).

Therefore, in order to properly understand the risk exposure in the company, rather than have the financing sit off the balance sheet, we made adjustments to show what the balance sheet would look like if they were financed with traditional debt (which is not an unreasonable assumption, given the type of business risk that they are exposed to through this financing is not dissimilar). The end result is that suddenly all their solvency ratios and coverage ratios are totally out of whack. Whereas before their company had reasonable ratios (debt to equity of about 0.8x), their ratios were now about 4 to 5x.

Financial Executives International Competition

On Wednesday we had Rotman’s internal competition for the Financial Executives International competition. I was part of a team of four, including Irina, Shree and Matt Literovich. The case was on Tiffany’s expansion into Japan and how they wanted to protect themselves from exchange risk. All the teams did a comprehensive analysis on the potential hedging options and the exposure. It was very humbling to see the caliber of work produced by our classmates in such a short period of time.

It was great to work with my team mates and our discussion on the financial strategy was highly enlightening. In the end, we looked at a variety of strategies including forward contracts, put options and collars.

Yesterday, we found out that we were selected to represent Rotman at the national competition which will be hosted by Ryerson on November 12th. Unfortunately, Irina will be unable to attend, but Fei has gratiously joined our team.

We are all excited at the opportunity to represent our classmates and showcase Rotman talent as well as meet MBAs from all across Canada at the "Best-in-class" competition.

Flight of Fancy: What If...? A Market for Bid Points

One common theme I've heard is that MBA's are often upset when they don't get all the elective courses that they want. While I certainly can't complain, it brings up an interesting question: "What if someone like me was able to sell their bid points? What would I get for them? And how would you value them?"

For example, my course choices weren’t very restrictive, I got 500 points to bid on four courses, most of which I could have gotten with a zero bid. Whereas, Mr(s). Ambitious was trying to take TMP and Value Investing while going on Exchange (physically impossible, Value Investing is a year long course and Exchange means you are physically gone). If there existed a mechanism (and therefore a market) for me to transfer my points for a price, what would I get for them? What should they be worth? Clearly, there is currently some "market inefficiency" as we are both unsatisfied: Mr(s). Ambitious because they didn't get all the courses they wanted [net deficiency] and me because I didn't realize the full value of my bid points because I had more than I could use - [net surplus].

Well let’s make some assumptions:

• Rotman tuition is C$35k per year (let’s not include first year as it’s common, or you can adjust the value of points accordingly if you feel second year courses are more / less important)
• You take 10 elective courses in your second year
• You are given 1000 points with which to bid

A “book value” of the points would simply be C$35k / 1000 points or about $35 per point.

But keep in mind that when something is inherently useful, especially in a scenario where a few points margin can mean the difference between getting the course you really want versus having to settle for a less popular course, there can potentially be bidding wars from “oversubscription” (points trade at a multiple above their book value) especially if they were in limited supply.

While people are paying C$70+k to go to school, for a marginal $35 x 100 points (a rough approximation of the average points allocated per student / course) or $3500 you can get any course you want (including the highly coveted TMP and Value Investing – which includes a trip to visit Warren Buffet – one of the reasons why this course is so wildly popular).

If you could some how do it, you could see how much additional probability you have of getting into the classes you wanted and put a dollar value on how badly you wanted to be in that class (regression analysis), you can determine a price you’d be willing to pay to attend that class. For example: Would there be a correlation between the number of points you consumed to get into classes of your choice against your overall earning power once out of university (thinking along the lines of DCF to value bid points like common shares).

And also imagine if this market had a “market maker”. For example, the PSO will (create and) sell you points for a certain value (either regulated and pre-determined or floating with the market). Students could liquidate their points at market value and get money back or buy points of the market to be more competitive for course selection and the school could potentially get revenue from selling points.

And since you have a market with underlying assets, imagine if you created financial instruments for those assets (shorts, puts, and calls for bid points, futures).

And imagine if other schools had market systems (I’m told that bidding systems are not uncommon at other MBA schools), you could trade between these. Or even other programs!

Of course, these points would inherently have an “expiry” as to their value (you wouldn’t want to be holding (take delivery of) 5000 MIT Engineering points if you were going to Stanford Law School).

There are some interesting implications. For instance, a new ranking system for schools where the relative value of a course is determined by the market value (determined by students taking courses there) in real time with comparisons to year over year values. Example: Would an engineering calculus class go for more at Waterloo or Toronto? Could you couple this with flexibility between schools (accreditation programs) which allow students to take equivalent courses at other schools and what do you get?

It would be a more sophisticated and real-time version of tuition regulated by the market. Taken to the extreme, here is another idea: drop the original tuition completely and have students buy bid points for classes. And then what if you were able to connect this market to actual financial markets? An S&P Index of Undergraduate studies to benchmark the valuation of your individual class’ performance.

Another thought: If the value of courses in a particular faculty started to "overheat" would that be a leading indicator of oversupply of labour in a particular industry in 4 years time?

Bidding for Electives Begins Today

Bidding for elective courses in second year began today. I'm happy to report that I still have 500 points to bid (the rumor that I lost points for study tours is apparently untrue). However, I only have to take 4 courses this term (maximum and minimum). I'm trying to bundle them together all on Tuesday, Wednesday and Thursday so I can have a four day long weekend every week (and so far it seems possible).

I'm thinking of taking all the core IB courses in one go (so I can concentrate on electives at LBS) including: Corporate Finance, Financial Management, M&A and Options and Derivatives. Considering the sessions (date / time / profs) I want, I will have plenty of points (some courses requiring as few as 0 points).

I just need to confirm my selection with a few friends before placing my bid. Bidding ends one week after the open.

Valuing Commodities Companies - Looking at P/NAV

Recently, I've been trying to learn more about commodities companies building on what we've learned in class as well as discussions with colleagues. Especially as Canada is a strong resource based economy (with a currency heavily influenced by the price of oil, I'm told), it is important to understand how these companies are valued.

Shree was previously very kind to explain why commodities companies provide leveraged exposure to the underlying commodity. In fact, I'm told that this is the reason why companies trade a P/NAV multiples greater than 1.

When I inquired as to what exactly Net Asset Value (NAV) was composed of, I was told that it is essentially the Asset Value (value of the commodity "in the ground") netted by the cost it took to get that asset out of the ground. So if you had to take a snap shot of what that company was worth, you'd intuitively assume that the value of the company was it's NAV.

However, as Shree demonstrated, the markets are always moving and the price of the commodity which the company bases its value on will change. This produces option like behaviour in the price of the company. While not a perfect explaination, I was told to think of it this way:

The value of the company is related to it's NAV PLUS a premium associated with the volatility of the commodity and the probability that the price of that commodity will increase. This is analogous to Intrinsic Value (NAV) + Time Value of a call option.

Obviously, there are a host of complicated relationships related to volatility, future price expectations, supply and demand, hedging and speculation which make this basic generalization a little too simple. However, I think it serves as a good starting point for how to think about and model the price.

This is similar to what we learned in Finance II when our professor explained the example of land that contained 1M barrles of oil which could be extracted at a price of $70 per barrel when the market price of oil was $60 per barrel. While a naive NPV calculation at today's rates would imply a negative NPV, the potential for the price of oil to top $70 provides real value to the land.

Recursive Options? Calling a Call

We've been shown how equity near bankruptcy behaves like a call option in our Finance II class. We've also been told in some of our integrative thinking classes to consider the models for employee (CEO) compensation to reduce the principle-agent costs / issues resulting from the relinquishing of control from capital investment.

My question is this. Consider the following scenario:

A company is struggling. It's Enterprize Value is low (less than debt) making equity intrinsic value essential zero (or negative) trading like an option.

In order to turn the company around and restructure, the company fires it's current CEO and recruits a new one. In order to motivate the new CEO to turn the company around, the CEO is offered stock options (we'll assume unrestricted for now).

What scenario have I just decribed? The securities that the CEO is holding are essentially call options on call options. That is to say the CEO's derivative, the call option, has an underlying asset which also behaves as an option (the equity behaves like a call option).

... Now assume that the stock is a mining company (which behaves like an option relative to the underlying commodity).

I wonder how you would even begin to model how much these options are worth? While valuing options itself are already quite tricky using models like Black Sholes Martin, I wonder what model would be appropriate for a derivative with recursive properties.

Also, as a financial derivatives joke, I overheard one unfortunate soul ask this question: "Are management stock options calls or puts?"

Equity Near Bankruptcy (or NPV = 0) Behaving as Call Options

This might be one of the most brilliant finance things I've ever seen taught a few days ago by our finance prof. I've always been interested in options thinking about how they behave and how to value them (and with the current financial crisis, have been taking more looks at bankruptcy).

First consider an oil company which can extract oil out of the ground for $70 per barrel with 1M barrels in the ground. The current cost of oil is $60. It costs more to get the oil out of the ground than it does to sell it on the open market, so the project is negative NPV right?

Well what happens if the oil prices rise to $80 a year from now? Then with a return of 10% (assume that it takes a year to get the oil out), you can make $10 per barrel on 1M barrels. The NPV works out to be about $9.1M.

But there is some inherent risk in this position which relies on the price of oil moving up. Sound familiar? It is the exact same behaviour as a call option.If the value of oil drops, the land is worth nothing, but if the value of oil appreciates, the value of oil appreciates accordingly also. The analogy holds up if you replace Exercise Price with Extraction Cost.

Here is another example of option like behaviour: Companies near bankruptcy.

Scenario 1: Healthy
Net Debt = $5M
Enterprise Value = 11M (Enterprise value calculated based on DCF)
Market Cap = 6M

Scenario 2: Near Bankruptcy / Highly leveraged:
Net Debt = 5M
EV = 6M
Market Cap =1M

Scenario 3: Bankruptcy
Net Debt = 5M
EV = 4M
Market Cap = 0

Because of the nature of capital at risk for corporations, the equity cannot fall below zero. A company in this position might also take on excessive risk (deliberately stir volatility on extremely risky projects) because there is nothing to lose.

However, in the absence of that, a company's equity at or near bankruptcy will be have much like a call option. Because of this relationship, a vulture fund might use the Black-Scholes model could potentially apply as an appropriate valuation metric to value the time value of the equity.

Revisiting History - "Pricing the upside derivative"

Our finance professor, Kent Womack, was just describing the model for pricing derivatives and it is almost exactly what I suggested the best method for pricing options would be based on my intuition in January (and was the topic of my Peter Godsoe Scholarship Award in Financial Engineering). He even asked the same questions I was looking into when I was studying for the CFA exam regarding the profit profiles for different put options and call options and why you would enter into different positions.

In his slide, he even mentions the idea of the distribution of stock prices influencing the expected outcome. I think the only difference in our models is that he used a distribution called Geometric Brownian Motion. It's similar to my normal distribution assumption, however, it accounts for an upward drift (which I didn't account for). However, I wonder if it can be approximated with a shifted normal distribution (mean greater than zero).

Also, to actually determine his option price prof. Womack used simulations whereas my model was based more on mathematical calculations. I'm sure both methods to determine the price are acceptable as it's more the model for describing the final underlying price that is more important.

Another improvement from his model is the inclusion of the time value of money as he discounts the future gains back to the present value.

Islamic Finance

Additionally in this Middle East International Study Tour class, we had professor Mohammad Fadel come in and describe the details, mechanics and rational of Islamic Finance.

While most people are familiar with Islamic Finance as simply "not charging interest" there are many more details which make up the rich tapestry of Islamic Finance.


The first note is that conformity with Islamic finance is voluntary. I think this might have been a point many members of my class (myself chief among them) got hung up on. Especially when we asked questions about how this law affected goodwill for M&A, sale of IP or brand equity or options or sale of receivables.


Some of the key takeaways for understanding Islamic Finance include:

• a strong association with tangible assets
• a general prohibition against floating or uncapped risk elements
• an emphasis on partnership, ownership and charity

There are certainly going to be more study before I can even begin to understand the find details, but this is certainly an interesting consideration for global finance.

2x Gold Exposure Without Leverage?

Today was the first Rotman stock pitch competition where the second year students gave the first years a chance to practice their skills in valuing and pitching companies. It was an interesting experience for all of us and there were many lessons learned.

In talking to other people doing pitches for companies in different industries, there was a lot of learning between groups. I though I would write about some of the more interesting lessons.

This post is focused on gold (or mining exposure to raw materials). Gold and copper have very important attributes and characteristics which are highly correlated to the health and confidence of the economy, especially as it relates to Canada. As a result, most portfolios will have some exposure in these areas depending on the strategy. Gold is often used as a hedge against inflation, but copper is associated as a leading indicator for the health of the economy.

However, in order to make larger hedges in the market based on these commodities, portfolios will utilize instruments which promise 2x exposure to these materials. When I first heard this, I asked, "How is it possible to have 2x exposure without employing some form of leverage?"

As Shree explained to me, this is how it works:
Imagine gold is selling for $1000 per ounce.
Imagine a company can mine gold for $500 per ounce.
It's profit is $500 per ounce (and let's exclude all other costs for now, or assume that the $500 per ounce includes all expenses).

Now imagine gold rises in price to $1100 per ounce.
The company can still mine it for $500 per ounce.
The profit is now $600.

Gold has only gone up 10%, but the companies earnings have gone up 20%! It's a 2x exposure without any leverage.

Spot Rates and Bonds - Supply and Demand of Investment Vehicles

We were discussing Treasury strips for CI (Coupon Interest) and NP (Note Principle) bonds. We discussed ideas such as reconstituting bonds, arbitrage opportunities and pricing.

I had wondered before if when investment vehicles get "abstracted" (either with a derivative, in some form of aggregation etc), if it was possible to get supply and demand curves which differ from the original underlying asset.

Prof. Womack showed us the example of two otherwise identical treasury strips, both maturing in 2 years with the same $100 Face Value, but trading at nearly the same (but marginally different) prices. One was a CI strip with the ask yield at 5.78% with an ask price at $89/08 and the other was an NP strip with an ask yield at 5.79% with an ask price of $89/07.

Although these two investment vehicles have identical risk profiles, payment schedules etc. (for all intents and purposes, they are identical) they are trading at different prices. Prof. Womack described the different as being differences in supply and demand for investors who are interested in reconstituting bonds (for example). However, at the same time, since they are so related, they should trade at near identical values.

Bonds with Options

Before we start, let's take a look at the basic principles behind bonds. A bond's yield is dependent on to major factors, the coupon rate (payments made semi-annually unless otherwise specified, analogous to interest payments) and the face value (analogous to repayment of principle). The combination of these two factors determines the yield to maturity (YTM) which is analogous to IRR in NPV and DCF (your calculator can actually use the same function to compute both as the math is identical). The relationships between these components are fairly intuitive and predictable (ceteris paribus):

• The higher the coupon, the higher the yield
• The higher the face value relative to the present value, the higher the yield
• The higher the yield, the lower the present value (and vise versa, Price and yield have an inverse relationship)
  

Note during this discussion that many of the mechanics relating to the treatment of options as they relate to equities also apply in the world of bonds as it relates to the value of the option. However, just to reiterate and clarify, let's look at each class of bond option seperately.

Callable Bonds
A callable option allows the borrower to pay the lender a specified amount to exit the bond agreement (benefits the borrower at a lower interest rate). This effectively acts as a ceiling price for the bond:

1. If the yield drops,
   
2. the cost of borrowing goes down, and
   
3. the price of the bond goes up.
4. If it passes the ceiling, the borrower will call the bond and issue a new bond at the lower rate.

This puts a cap on the maximum value of the bond.

Notice that the call option always benefits the lender, and this flexibility is paid for by issuing the bond at a lower price than an otherwise comparable straight bond at any given price. The nominal spread is always larger to account for the option. An option adjusted spread (OAS) is often approximated to understand the performance of the bond, excluding the option.

Putable Bonds
A putable bond option allows the lender to take a specified amount to exit the bond (benefits the lender at a higher interest rate). This acts as a price floor for the bond.

1. If the yield rises,
   
2. the cost of borrowing goes up, and
   
3. the price of the bond goes down.
4. If it passes the floor, the lender will put the bond and buy a new issue at the higher rate.

The price of a putable bond is always greater than a straight bond at any price point because of the inclusion of the put option (benefiting the lender).

Options Review, Pt 5 - Options Strategies

[Options Review Series 1 - 2 - 3 - 4 - 5]

One of the reasons why I enjoy options strategies so much is that it is a relatively clear cut way of showing how derivatives can be repackaged to create new instruments. What do I mean? For example, looking at the six different positions listed (Long Underlying, Short Underlying, Long Call, Short Call, Long Put, Short Put) you can see that there are a variety of different profiles which can be created.

Two which the CFA Level I exam seems to like to focus on are Protective Puts and Covered Calls. What are they? Let's look at Protective Puts first:

Protective Put
A Protective Put is someone who wants unlimited upside potential with some downside protection. This is a strategy which allows the portfolio to appreciate, but also protect against some downside if the asset loses value.

Protective Put = Long Underlying + Long Put

Conceptually, it's owning a stock with the option to sell it if the price gets too low. Sound great right (unlimited upside with no downside)? What's the catch?

Like all options, assuming (or removing) risk upfront also comes with an upfront cost. That is to say the catch is that there is an immediate downside in the form of the premium placed on the Long Put.

Consider this position the equivalent of gambling insurance (like in Black Jack when the dealer shows an Ace). If you buy the insurance and the dealer shows a 10 or face card, you max your loss out at your insurance, but if not, you can still get upside. [Odds actually state that you shouldn't use insurance, but perhaps gambling itself is a flawed analogy with negative expected returns.]

Protective Put = Long Underlying + Long Put = Long Call

You'll notice that if you add a Long Underlying with a Long Put, the profile of the new "Protective Put" position is identical to a Long Call. Below the excise price, the gains of the Long Put are offset by the losses of the Long Underlying. Above the excise price, the Long Put is worthless and the Long Underlying appreciates.

Covered Call
So what is a covered call? A covered call is someone who wants to write a call option (Short Call), but also wants to have stock on hand (be "covered") in case that call is executed in-the-money. Think of it as writing a call option with insurance.

Covered Call = Short Call + Long Underlying

What does the profile look like? Well below the excise price, the call is worthless and the underlying is losing value. Above the excise price, the call appreciates in value as fast as the underlying to cancel each other out.

This translates into limited upside and unlimited downside. Seems like a pretty raw deal. So why would anyone enter this position? Again, the answer is the premium. By assuming unlimited downside risk with a capped break-even upside profile, the incentive comes in the form of an upfront fee (the premium).

Covered Call = Short Call + Long Underlying = Short Put

Resolution:
The point I would like to highlight here is that with these six pieces, you can construct (or reconstruct) any profile position you would like. Below are the most obvious examples (in synthetic positions, Long and Short bond positions are assumed to have a face value at the excise price in order to balance the profiles by generating value related to X at expiration):

• Synthetic Long Call: Long Put + Long Underlying + Short Bond
  
• Synthetic Long Put: Long Call + Short Underlying + Long Bond
• Synthetic Long Underlying: Long Call + Long Bond + Short Put
• Synthetic Long Bond: Long Put + Long Underlying + Short Call

Note that all counter party (reversed) positions can be determined if all the positions of which they are composed are reversed (ex. Synthetic Short Call: Short Put + Short Underlying + Long Bond).

Since each option profile is constructed using simple arithmetic, they are commutative and associative. Therefore reversing each component position will reflect a reversing of the portfolio of options as a whole.

[Options Review Series 1 - 2 - 3 - 4 - 5]

Options Review, Pt 4 - Put Options

[Options Review Series 1 - 2 - 3 - 4 - 5]

Now let's look at Put Options. Put options are the options to "put" (sell) options in the market at a given price. They become more valuable as the stock drops (If you have the right to sell something at X even though it's only worth St) and the value is (X - St). It has similar features to short selling (Short the Underlying Asset) but it's value is capped at X (limited upside potential).

If the market price goes above X, the put option is worthless (why use a put to sell an asset at a price lower than what you can get for it in the market?). So for any price above X, the value is zero. For each dollar below the strike price, the intrinsic value goes up a dollar.

The profit profile for a long put position is as follows:

Long Put Profit = (X - St) - Call Premium, while X > St
- Call Premium, otherwise

Break Even point, St when Long Put Profit = 0
St = X - Call Premium

Note, whenever you are Long the option (regardless of what type of option), you pay the premium because you gain "flexibility" to exercise the option. If you are ever short an option you take the premium to assume the risk that the counter party will execute the option when it's "in-the-money".

Now the profile of a Short Put:

Short Put Profit = Call Premium - (X - St), while X > St
Call Premium, otherwise

Break Even point, St when Short Put Profit = 0
St = X - Call Premium

[Options Review Series 1 - 2 - 3 - 4 - 5]

Options Review, Pt 3 - Call Options

[Options Review Series 1 - 2 - 3 - 4 - 5]

Next, let's look at the intrinsic value of call options (St - X). I choose calls over puts because they have similar profit characteristics to longs with "downside protection". A call option is the option to "call" (purchase) a stock at a given price (the Excise price, X).

If the market price of the underlying asset is less than X, the call option is worthless (why use a call to buy an asset at a price higher than what you can get it for in the market?). So for any price below X, the value is zero. For each dollar beyond the strike price, the intrinsic value goes up a dollar.

In a Long Call position, the holder pays the premium to the counter party so therefore the entire graph shifts down by the amount of the premium.

It's profit profile for a long position is as follows:

Long Call Profit = (St - X) - Call Premium, while St > X
- Call Premium, otherwise

Break Even point, St when Long Call Profit = 0
St = X + Call Premium

Now let's look at the short call position. Remember that between any two opposite positions (Long and Short) the graph is reflected against the X-axis (reflecting a zero-sum game profit between two parties - you can't make something from nothing).

So inversely, being short a call means that you get the call premium, but can lose money if the market price goes up. And the profile is as follows:

Short Call Profit = Call Premium - (St - X), while St > X
Call Premium, otherwise

Break Even point, St when Short Call Profit = 0
St = X + Call Premium

A few quick notes:
Notice that a premium is required so that both Long and Short positions have both a profit and loss scenario. If either position doesn't have a profit scenario, then no party will not enter into that position. However, the profit scenario of one becomes the loss scenario of another.

The Break Even point is the same for Long and Short positions (no one comes out on top).

[Options Review Series 1 - 2 - 3 - 4 - 5]

Options Review, Pt 2 - Fundamentals

[Options Review Series 1 - 2 - 3 - 4 - 5]

Next let's look at Options. They are instruments which give you the flexibility ("option") to undertake an action if you feel it is beneficial.

The value of options are composed of two components, the intrinsic value and the time value.

Intrinsic value is the easiest to understand. It is the difference in value between the excise price and the current market price. If you option allows you to execute the option at price X, and the market price for the underlying asset is St, there is a intrinsic profit / loss potential of (St-X) and profit or loss would depend on which side of the transaction you are on (long or short). More on this later. Options have special words for profit or loss based on the intrinsic value. If the holder of an option (the Long position) earns a profit based on the current position of the option (St - X), the option is said to be "in-the-money". If the opposite is true, the option is said to be "out-of-the-money".

Regarding time value of options, there are generally two types of options. American and European. Here are some key points:

• American options can be exercised at anytime.
  
• European stocks can only be exercised at expiration.
  
• The flexibility of American style options makes them more attractive and therefore equal to or more valuable under every circumstance than their European counterparts. This is a tip for removing incorrect answers in the CFA exam.
  
• The time value of an option is always greater than zero.
• Time value of an option increases as the stock volatility increases (options are protection against volatility)
  

Option Value = Intrinsic Value + Time Value

Note that even if Intrinsic Value drops to zero, the Time Value must always be positive therefore the Option Value must always be positive. If by expiration, an option is not used, it expires and becomes worthless. The lowest possible price allowable for an option is 0. It cannot become negative.

While options sound fantastic (they always have positive value) don't forget that an upfront premium is needed to purchase the option. As we will see in the next post, this creates more balanced (and realistic) scenarios for profit and loss.

[Options Review Series 1 - 2 - 3 - 4 - 5]

Options Review, Pt 1 - Underlying Asset

[Options Review Series 1 - 2 - 3 - 4 - 5]

While it would appear to be a misnomer for the inaugural post to start with underlying asset, I wanted to show a few graphs and tools related to movement in the underlying asset in today's posts about derivatives to build a foundation on which to describe other option based derivatives. Using the tools and short graphs presented in today's series, there should not be any learning outcome statement (LOS) on the CFA Level I exam relating to options based derivatives which can't be tackled.

Let's start with the position most people are familiar with: Being Long the underlying asset (buying something).
Obviously, as the value (St) goes up, so does the value of the asset. And if St is greater than S0 (purchase price), then you've made a profit. If it goes down below S0, you've taken a loss.

Long Underlying Asset Profit = St - S0

Now let's look at short selling. Short selling is the exact opposite of being long the underlying asset. In short selling, you borrow the stock from a broker, sell it on the open market, and repurchase it later in the hopes that the price will drop (rather than go up).

Short Underlying Asset Profit = S0 - St

A few interesting notes about short selling. Unlike being long a security which technically involves only two parties (yourself and the market), being short also includes the broker who lends you the stock. In being short a stock, all dividends paid by the stock while you hold it need to be paid by you to the broker. It's as if the broker still has it (they own it even if they don't currently hold it).

Interestingly, if you add the two graphs together, (Long Underlying Asset and Short Underlying Asset) there is no profit. The profit area under one graph cancels the loss area of the other. That is to say, the profit in the Long is the loss of the Short and visa versa.

Now capitalists being what they are, there is a fee which is associated with incentive for the broker for you to perform this action, but this is outside the scope of CFA Level I.

Also note that shorting is only permitted on "upticks" or flat prices where the previous tick was an uptick. What does this mean? Consider the following 5 prices in order: [52, 51, 53, 53, 50]

Short selling is not permitted on the:

• 2nd tick (a downtick from 52 to 51)
• last tick (a downtick from 53 to 50)

Short selling is permitted on the:

• 3rd tick (an uptick from 51 to 53)
• 4th tick (a flat tick at 53, preceded by an uptick from 51 to 53)

I did wonder, however, if you had an uptick followed by a series of flat ticks if you were still able to short sell. I would assume the answer is yes, since the underlying reason is to prevent short sellers from aggressively depressing the stock price, but this is also outside of the CFA Level I curriculum.

[Options Review Series 1 - 2 - 3 - 4 - 5]

The Irony of Arbitrage, Efficient Markets and Equilibrium

Inevitable yet paradoxically unreachable. Like the Greek myth of Tantalus, eternal temptation without satisfaction. Proponents of the efficient market hypothesis (EMH) state that it is impossible to exploit the markets. This reflects an interesting conundrum for would be arbitrageurs who look for inefficiencies to create abnormal profits.

One the one hand, they need to vigourously search for arbitrage opportunities to exploit. However, the harder they look collectively, the less there are. This leads to a sort of equilibrium, and a self fulfilling prophecy and would probably make an interesting case for game theory.

However, as a model for human behaviour, I find it incredibly interesting / ironic that there are a number of situations for which this type of model applies.

As I have previously written in a variety of posts, I feel as if any intrinsically unstable situation will eventually result in a recovery to it's equilibrium, however, it requires triggers and intervention in order to manifest. It requires a sort of perverse vigilance to the contrary.

Perverse in the sense that in order to maintain belief that equilibrium is inevitable simultaneiously requires a belief that the current situation is never in equilibrium. It's very paradoxical in the sense that the intended goal is assumed to be inevitable yet unreachable.