Bid / Ask Curves

At the break in behavioural finance, I was speaking to a prop trader about the mechanics of the market. This reminded me of my short trading exercise in the Rotman Finance Lab with the Trading Simulation software.

In microeconomics, we discuss demand curves and how they are based on individuals with different levels of willingness to pay. So as the price increases due to a supply curve shift right (less supply), the quantity demanded decreases.

In markets, this is a little more transparent if you look at the bid / ask lists. These lists show the prices and volumes people are willing to buy and sell for. The other unique thing about the capital markets, is that there is actually a set number of securities (assuming that banks do not issue or buyback securities in the short term, supply is price inelastic based on total float) and that investors can be both buyers and sellers (short term suppliers and consumers) of securities. Actually, a better way to put it would be they can either hold or release securities (demand based relationship).

If their intrinsic value (IV) of a stock is above the current market price, they will buy the stock. If their IV is less than market, then they will sell. And in an exchange market, that is exactly the case (orders, unless removed before execution, are commitments to buy or sell at the stated price).

Shown here is an illustration of a “complete” market. This assumes that everyone’s IVs are included, that there are no hidden orders and that people’s opinions won’t change with the market price (a snapshot by nature). The current ask price is $8.00 and the bid is $7.75. As people’s sentiments change (or new investors are introduced into the market), orders to buy are satisfied at $8.00 and orders to sell are satisfied at $7.75. If all the potential sellers at $8.00 are taken up, then people can only buy the stock at $8.25 and the stock price goes up. Note that the differential between bid and ask is a proxy for market liquidity, as the lower the transaction fee to enter and exit a position the lower the cost of trading the security.

Also note that the steepness of the curve is a good proxy for potential volatility as well. Because if the slope of the curve is steep over a variety of prices, it means that the market doesn’t necessarily agree on the price. And if a few people cross the line from one side to another, the price can change quickly and dramatically (shown below):

Back from the Holiday

Well after a well deserved break, all the students are back.

First years are in their Negotiations class which odd for me as I didn’t do this last year due to the Middle East study tour, but now I see what it was like with the Atrium constantly being flooded by ambitious MBA students trying to get better deals in their exercises. There have also been requests for help with preparing for recruitment week which is coming up next week and some postings already up.

Even second years are at school, many having the clever idea of taking an intensive or two to lighten their final term course load.

Yesterday, we did a presentation for our ICP in Islamic Finance. Arash and I did a presentation on two comparable securities, one conventional and one Islamic and we showed they were strategically and operationally comparable (same industry, business model, enterprise value, capital structure, debt ladder, similar maturity, seniority and economic conditions, but different country and terms) and we analyzed the yield, adjusting for country risk and broke down the spread accounting for liquidity risk, minor maturity differences and increased cost of capital related to Sharia compliant terms.

This material will be used as part of Rotman’s new Executive MBA program class on Islamic Finance. While we aren’t quite finished with our work, the next step being to propose a term sheet for what the conventional financing would look like if it were Sharia compliant, I’m very happy with our progress and the insight we were able to bring into this new product class.

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.

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?

[LAIST] May 7th Visits – Rio de Janeiro

[LAIST Tour Begins, Fazenda Tozan, Churrascaria – Nova Pampa, Port of Santos, Deloitte, Embraer, Natura, Gol de Letra, Bom Bril, Agencia Click, Nextel Institute, May 6, Rio, Rio Weekend, Petrobras, PREVI]

Upon arriving at Rio late at night, we made a quick reconnasance of the area before calling it a night. The next morning, we were up and ready to go to our next set of meetings.

TV Globo

TV Globo is the largest group of media and entertainment companies in Latin America. They are focused on TV and entertainment, print and media and radio; telecommunications and distribution.
Because of their influence on the Brazilian society, they have been playing a unique role as educator. Although Brazil has language unity, there is a great deal of cultural diversity which plays a unique challenge to media broadcasters. In a growing economy, Brazil’s newspaper readership has been growing rather than falling, primarily because of the growing C class (lower middle class).
Brazil is divided into a class system (not well explained if it is a formal or informal class system – need to look into this more) where there are A1, A2, B1, B2, C, D and E rankings.

TV Globo mentioned that infrastructure remains the biggest challenge for Brazil, not just in terms of roads and rail, but rather in education in the form of schools and labs for students to learn.
TV Globo uses their Tela Nouvella’s (sophisticated versions of soap opera’s) to address social change. They often hire sociologists to address social issues that are currently on the minds of Brazilians addressing topics such as racism and . They treat this service as a charitable non-cash forgone revenue expense.

Vale

The next presentation was at Vale (recent acquirer of Inco) the largest producer and has the most reserves of iron ore in the world (2nd largest resource producer in the world). Their business is 35% based in iron ore, demonstrates stable demand and has recently successfully moved from a yearly pricing model to a quarterly pricing model.

We had a talk from a political analyst two was describing the broad range of international investments of Vale in different parts of the world including Asia Pacific, South America and Africa.
In the crisis period, 38% of their revenue was from China, their number one client, who was previously only accounting for 17.4% of their revenue previously (number one position in the past also).

The cycle for mining is usually 3 to 8 years for exploration followed by licensing and 4 to 5 years to open and build the mine and infrastructure required to develop the mine. Their required IRR is 12+% and they have 12 golden shares held by the government (similar to Embraer).
One of their largest challenges is relocating indigenous people, developing infrastructure and developing communities at mine sites. Once a mine’s resources are deleted, there is a large outflow of business which can potentially decimate at geography, so Vale is careful to build a legacy plan and invest in the community remain stable after their exit including schools and diversified industry.

Brookfield Brazil

Next we had a talk from the CEO of Brookfield Brazil, an asset management company with $100B USD AuM and $22B invested capital. They talked about the macro factors affecting investment in Brazil including the allocation of 4% of Brazilian GDP towards social development, allocating resource surpluses towards financial deficits versus social deficits and the challenges of moving from an “artificially fixed exchange rate” to a floating rate.

He also mentioned the rebirth of the consumer class in Brazil, or the so called D and E class to the C class and how Brookfield was capitalizing on commercial real estate development. Their strategy is to invest in tangible assets where there are high barriers to entry, predictable long term cash flows and they prefer to be operators rather than passive investors.

Their IRR is 12% and they tend to focus on quality of investments rather than increased marginal returns. Their strategy allows their mall properties to command the same sales per square foot as comparable US malls. The mall model is different in Brazil than what we are used to in NA. Rather than have high city density where consumers drive to malls or super centers in sub-urban areas, Brazil malls tend to be in the city, with high density, vertical and paid parking (a surprisingly large 12-15% of mall revenue) and demonstrate less dependency on large anchor stores (such as Walmart or Sears). Consumption growth is currently well above the GDP which is having a large effect on the financial and economic strategy of the country.

With their high 16.7% Tier 1 capital ratio in Brazil allowed many Brazilian asset management firms like Brookfield take advantage of depressed prices in the market as a result of the recent financial crisis. They prefer to avoid higher leverage, look for quality of earnings and a high level of liquidity which allowed them to take advantage of special situations.

With the acquisition of many new properties, they have boosted their CAGR to a whooping +119% (keep in mind that this is a result of massive acquisitions and actually investing more of their AuM). When investing, the look for different partners including: Institutional, sovereign, pension, endowment and family funds. We were told they were partnering with 2 Canadian Pension funds, 1 Asian sovereign fund and 2 European family offices. You can probably guess who the Canadian and Asian sovereign funds are.

They prefer partners who have the same market views and investing profiles: long term, stable predictable growth and high cash positions and liquidity (all attractive makings of a proper pension fund investment).

They also have a unique array of investments, including agriculture. They raise cattle as one of their primary investments and follow their operator strategy. What does this mean? They may be one of the few companies where cowboys who work in a company which complies with Sarb-Ox and is audited by Deloitte. The work environment creates a unique culture.

Getting a Job in Asset Management

Previously, I was asked to write a post about getting a job in the Asset Management industry. While I myself am not that well versed on the buy side, I interviewed and got advice from other people who know more than I and were successful in getting interviews / offers. This is of course, beyond what is expected in any capital markets job, and this is what they had to say:

Application Materials

As always, you have to get your initial application materials in order with the hope of getting that first round interview. At the application stage, asset management companies have been known to ask for typical materials such as resume, cover letter and transcript as well as:

• Writing samples
• Sample stock pitches

Networking

As always networking is an important part of getting that first interview. Before you start networking, you should already be very polished, particularly on the topics of:

• Their fund strategy and your style / fit
• Know their holdings and weightings
• Diversification - know the focus of the fund

To get this information:

• Hedge funds tend to be proprietary and it will be more challenging to get info
• Mutual funds holdings are generally public

Either way, go go onto Capital IQ / Bloomberg and find out as much as possible. Read manager's letter about their performance and strategy. Know their best performing success stories as well as their dog holdings. Know where their exposures are and what strategies they are using.

If you impress them at the outset with a networking or informational interview, that improves your chances of getting that first round interview.

Interview

For the interview, they will probably ask you a few fit questions. I've been told buyside will not ask you too much technical stuff on valuation (i.e. walk me through a DCF) because these are expected. If your resume doesn't show some experience in capital markets, I'm told you have a much lower chance of being interviewed.

Have a view of the market and ensure congruency in your view. A great piece of advice was to really understand the "off balance sheet items". The reasoning for this is because these are the items that are more difficult to value and provide you a potential differentiation advantage. If you are able to better interpret this information, this is your potential competitive advantage in the market.

Also, the "stock pitch" component of this interview is generally more intense than in other finance jobs. I've heard it described as the interview was just "10 stock pitches". Having said that, while most finance interviews usually require 2 longs and a short, it's been suggested that you have a mix of 10 long and short positions, with a mix of long and short companies and industries. Also, you have to make sure that there is congruency in your view as well as your story.

For instance, one example from an interview was: "I see that you've recommended this stock because you think the industry is strong. If that is true, why not buy an ETF of that industry rather than cherry pick stocks? What if the one or two companies you buy in that industry turn out to be dogs?"

Asset management is much more than just "buying and selling stocks" as any portfolio manager will tell you. There are many aspects that portfolio managers are responsible for in funds including:

• Risk Management and protection or hedging strategies
• Investment style
• Investment objectives and goals
• Liquidity requirements

It is important to comprehensively understand and prepare as much as possible so that you can maximize your chances of getting a successful result in your interviews.

Investment Challenge - 3rd Place

Yesterday, we participated in the Investment Challenge hosted by the Rotman Asset Management Association. Shree, Petar, Natalia and myself presented to a panel of judges from industry who critiqued our fund's performance, benchmark, goals, execution etc. There were teams from the Rotman MBA as well as the Masters of Financial Economics (MFE) program.

We made it to the final round and placed 3rd overall. More importantly, I learned a lot while in this competition about the practical side of asset management beyond the academic theory. And it is certainly more than just "trading stocks".

It was absolutely a pleasure to work with our team members. Shree is particularly passionate about asset management and it shows when you speak to him about stocks and what is happening in the economy. I learned a lot from him in terms of the practical side of asset allocation, risk management, company analysis etc.

I've been mentioning this to several people, but I think it is absolutely critical to participate in competitions and activities. Rotman does a decent job of trying to mix up the groups and have as much interaction as possible between the incoming 265 students every year. There is your 1st semester section of 65 people and team of 5, 2nd semester section of 65 people and team of 5, your 24 hour strategy comp team of 5 or 6, your markstrat team of 5 or 6 etc.

One of the most valuable experiences in the MBA is take advantage of these opportunities to work with smart driven people on interesting challenges and topics they are passionate about. Also, the open bars don't hurt.

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.

The Calculus of Duration

We have been discussing bonds and spot rates in finance as a fairly "simple" investment vehicle (no default risk for government bonds and steady and predictable cash flows).

While I had technically learned the math behind bond duration, it was after the homework assignment that we were assigned in finance that I began to get a better understanding of exactly what this means and why it's important.

As I had mentioned before, duration is defined as the percent change in price for a given change in yield. You'll notice that the definition of the formula is strikingly similar to elasticity calculations.

However, rather that jump in at that level, let's talk about it from the first principles of calculus:

P = C + C/(1+y) + C/(1+y)^2 + C/(1+y)^3 + ... + C/(1+y)^n + M/(1+y)^n

Where P is the price of the bond, C is the coupon and y is the YTM and M is the face value. So far nothing new. But the next idea is to take the derivative of the Price, P, with respect to y to understand how the price will be affected for any give change in y. We can re-write the formula as:

P = C + C (1+y)^-1 + C (1+y)^-2 + C (1+y)^-3 + ... + C (1+y)^-n + M (1+y)^-n

dP/dy = - C (1+y)^-2 + -2 C (1+y)^-3 + -3 C (1+y)^-4 + ... + -n C (1+y)^-(n+1) + -n M (1+y)^-(n+1)
= -1/(1+y)[ C (1+y)^-1 + -2 C (1+y)^-2 + -3 C (1+y)^-3 + ... + -n C (1+y)^-n + -n M (1+y)^-n

Recall that dP/dy describes the change in P with respect to y. In order to get percentage change, we divide both sides by P. This gives us the term dP/dy * 1/P which is a precursor to understanding % change in P or modified duration:

dP/dy * (1/P) = (1/P)[ -1/(1+y)][ C (1+y)^-1 + -2 C (1+y)^-2 + -3 C (1+y)^-3 + ... + -n C (1+y)^-n + -n M (1+y)^-n]

There is a special definition for the monstrous summation term above called the Macaulay duration which is defined as:

Macaulay duration = [ C (1+y)^-1 + -2 C (1+y)^-2 + -3 C (1+y)^-3 + ... + -n C (1+y)^-n + -n M (1+y)^-n] / P

Modified Duration = -Maccaulay duration / (1 + y)
= dP/dy * (1/P)

That's a lot of complicated math with calculus. What is the value of this exercise? Well if you can understand how your bond liabilities will move with interest rates, you can construct a portfolio of bonds which can insulate (immunize) you from changes in the price due to changes in the yield even if the bond's structure you are using to immunize is not of the same construction as the original liability buy matching face values and durations.

Therefore any change in the percentage value of your liability will be offset by a similar change in the percentage value of your bond portfolio (a hedging asset).

Rotman Finance Association - Building My Prep Team

It seems the most popular clubs feel like they can have their kick off meetings late on Friday afternoon and still get pack rooms. Which they did. The two undisputed heavy weight champions in terms of clubs interest are the Management Consulting Association (MCA) and the Rotman Finance Association (RFA), both of which held their kick off meetings on consecutive Friday afternoons. Last week was MCA, this week was RFA (today).

The info session was a good primer for those with little or no background in finance as well as an introduction to the upcoming events. They emphasized some key points (which I've been talking to some of the Club Executives about) in terms of how to prepare for what amount to the most competitive and desired jobs available to MBAs. The RFA Exec made a good point, essentially: "All the skills you need to interview for summer jobs, you won't learn until it's too late. You're on your own." There's just too much going on too fast. It's really up to you to take the initiative. Keep in mind that if you went to Ivey (One year program), you'd be facing the same challenges except you'd be worried about full time rather than internships.

I'm currently in the process of putting together a team of people who are interested in investment banking and high finance. I offering to teach them what I know (learned over the summer and through CFA) in exchange for having serious partners for preparation in the same way we're building a case interview / competition team for consulting. The Analyst Exchange was very good in prepping me to discuss and build valuation, consolidated financial statement modeling, leveraged buy outs, mergers and acquisitions.

My goal is two fold. In terms of what I'm offering to give, I hope my Rotman counterparts and I can improve our odds to boost our recruitment and offer batting average (the other side of the hiring batting average) which I promised as my speech for Rotman 1st Year rep.

More selfishly, I want to find a group of dedicated people who I can potentially draw upon as teammates for investment challenges and (in the future) network contacts.

"10 years from now when we've all reached our potential, I want you to tell your executive assistant to take my call when I'm looking to find partners interested in doing a deal." ~ Josh Wong, 2009

Diversification and Correlation - Understanding Risk and Reward

Often you'll hear people quoting investment cliches: "Don't put all your eggs in one basket" "Diversify, diversify, diversify" but not really understand what they mean. Most will understand that if they only invest in one stock and it tanks that they can lose everything straight away (or hit it big). However, few understand the risk and benefits of diversification.

The CFA Level II material begins to go into the idea of correlation, one of my favourite topics in math. While I am often criticized for loving math a little too much (one colleague went so far as to say that I think math can "solve all the world's problems" whereas I would prefer to think of it as "math can describe most of the world's patterns"). I even said that "there is math to describe when math fails" and that in my opinion is statistics.

A Quick Primer on Correlation
Correlation is the idea of how closely to items move together (in finance, the most notable example is stock prices) and the strength of their linear relationship. Relationships measured in correlation can have a value between 1 (perfectly linearly correlated) and -1 (perfectly negatively linearly correlated). What does this mean in layman's terms?

With a correlation of 1, two stocks will move in perfect harmony. If one stock rises, the other stock will rise proportionally. With a correlation of -1, if one stock rises, the other stock will fall proportionally. A correlation of 0 implies no linear relationship (strictly speaking not independent, but independent variables will have a correlation of 0).

Correlations of less than 1 mean that they move in the same direction, but do not have a perfectly linear relationship (most stocks in the stock market) and do not move proportionally (sometimes one will move faster or slower than the other). I would propose that the only way to find a perfect correlation is to buy more of the stock (or short it for a -1 correlation). Obviously, correlation is a bit more complicated that this but this will do for now.

Risk and Return of a Portfolio
Now that we have a basic understanding of correlation, how can that help us understand diversification, risk and reward? Let's look at two stocks A and B with expected returns 15% and 10% and a correlation of .5. Let's say the stocks have std dev of 9% and 6% respectively and the risk free rate is 4% (therefore the Sharpe ratio is 1.22 and 1 respectively). A is riskier, but offers more marginal return per unit of investment risk.

There are four possible actions:

1. Long (buy) A - Correlation to Long A: +1
   
2. Short (sell) A- Correlation to Long A: -1
   
3. Long (buy) B - Correlation to Long A: +0.5
   
4. Short (sell) B- Correlation to Long A: -0.5
   

Note that if you only care about maximum returns you will allocate all your capital to action 1: Long (buy) A. It has an expected return of 15% so it has the highest growth potential. But note that it also has the highest risk profile (largest standard deviation). If you were more moderate, you would Long (buy) a combination of A and B (with an expected return of between 10 to 15% depending on allocation and a standard deviation between 6 to 9%).

The lower risk portfolio construction would be from some combination of stocks with negative correlation (example Long A, Short B or Short A, Long B) because if one ever went down, the negative correlation will imply that the other will go up (possibly by more, possibly by less). However, also note that if their movements are counter each other as is usually the case in a negative correlation, your profit potential becomes much less.

Diversified Portfolio
In this over simplified scenario, assume that a portfolio, evenly weighted between a Long A position and a Long A and Long B. If the both hit their growth targets their combined return is 12.5% (equally weighted average between 10 and 15% and std dev between 6 and 9%). This is less reward than just buying A, but also less risk.

Assume another evenly weighted portfolio between a Long A and Short B position has it's Long A hit +15% and it's counterpart, the Short B hits -10%. The portfolio only gains 5%. Conversely, if the Long A drops to -15% and the Short B rises to 10%, the portfolio only loses 5%. Whereas the movement in the individual stocks is much more pronounced, the portfolio is dampened from extreme gains and losses.

Implication
There are times to over diversify and there are times to cherry pick. Arguably, in this recovering economy, it's easy to pick "sprouts in scorched earth". That is to say, most stocks are undervalued so it's not hard to pick "winners". This is a decent time to over diversify, because the general trend is to go up in value.

The worst time to over diversify is at the peak of the market, when most stocks are over valued. In this case, it is better to be very specific about your investments and be extra diligent in your homework (or find another asset class like fixed income - deleverage).

Weighted Averages

Another recurring mathematical theme in the CFA is the weighted average (probably because it is so universally useful). It appears in portfolio management, expected returns, WACC, indexing etc. It essentially takes the components of a group, takes the proportional weight of each and determines the value of the aggregate. Example:

S = (wα x vα) + (wε x vε) + (wρ x vρ) + ...
Where w is the weight of of each component expressed as a percentage of the whole and v is the value of each component.

For portfolio management, each component is an individual security's expected rate of return.

[Example] A portfolio is make of three stocks A, B and C. A has an expected return of 8% and makes up 20% of the portfolio. B has an expected return of 10% and makes up half of the portfolio. Finally C has a return of 12%. What is the expected return of the portfolio?

[Solution] E (Rp) = wA x E (RA) + wB x E (RB) + wC x E (RC)
= 8% x 20% + 10% + 50% + 12% x 30%
= 1.6% + 5% + 3.6
= 10.2%

For weighted average cost of capital (WACC), each component (debt, mezz and equity financing) of cost is weighted by proportion again:
[Example] A company issues bonds with at a cost of 4% which accounts for half of their capital. The required rate of return for their projects is 9% and they have an issue of preferred shares out for of 6%. They have twice as many common shares issued as preferred. If their tax rate is 30%, what is their WACC? Assuming that preferred shares are treated as debt, what is their total financial leverage ratio?

[Solution] Note in this case: we = 2wp and wd = 50%
wd = 50% = 100% - wp - we
wp = 16.7%
we = 33.3%

WACC = wd x kd x (1 - tax rate) + wp x kp + we x ke
= 50% x 4% x (1 - 30%) + 16.7% x 6% + 33.3% x 9%
= 1.2 + 1% + 3%
= 5.2%

Financial Leverage of Assets (FLA) = A / E
On a percentage basis:
A = wd + wp + we = 100%
FLA = 100% / 33.3%
= 3

[Example] An market weighted index is composed of three stocks A, B and C. A is worth $50 and composes 50% of the index. B is worth $10 and is 30% of the index. If C increases in value by 15%, what is the increase in the index?

[Solution] Initial Index = 100%
Final Index = 50% + 30% + 20% x (1.15) = 103%

The index increases by 3%

Asset Pricing Models, Pt 3 - SML

Asset Pricing Models [ 1 - 2 - 3 ]

The Security Market Line (SML) uses CAPM to determine if securities are relatively over or under valued as compared to the market portfolio.

The SML is a graph where the Y axis is expected return, E(R), and the X axis is systematic risk, β. The two points used to construct the line are when β = 0 at RFR and β = 1 at E (R mkt). The line is extended beyond β=1 and individual securities are superimposed as a scatter plot on the graph.
This line represents portfolios which are appropriately valued given their systematic risk relative to the market portfolio. Therefore, portfolios or securities that lie above the line have excessive returns (are undervalued) and securities that lie below the line have under performing returns (not enough returns for the given systematic risk, overvalued).

Notice in the example above:
Security A, Above SML, excess returns, undervalued - Decision: Buy
Security B, Below SML, underperforming returns, overvalued - Decision: Sell
Security C, At SML, equilibrium returns, appropriately valued - Decision: Hold

Using the SML helps identify securities which are mispriced so that the appropriate action can be taken.

Asset Pricing Models [ 1 - 2 - 3 ]

Asset Pricing Models, Pt 2 - CAPM

Asset Pricing Models [ 1 - 2 - 3 ]

The Capital Asset Pricing Model (CAPM) is a familiar term for finance analysts and CFA candidates. It is a model which helps approximate the required rate of return for a given investment portfolio based on it's systematic risk (unsystematic risk is assumed to be diversified away).

CAPM: E(R) = RFR + β(Market Premium)
Market Premium = E(R mkt) - RFR
∴E(R) = RFR + β [E(R mkt) - RFR]

Beta, β, describes the systematic risk and is equal to 1 at the market portfolio. Beta of stocks are described as systematic risk relative to the market portfolio.

While this is a fairly simple result, the implications are quite important. The expected return determines the cost of equity as well as the required rate of return. It also helps identify if stocks are over / under valued when we use the Security Market Line (next post).

Asset Pricing Models [ 1 - 2 - 3 ]

Asset Pricing Models, Pt 1 - CML

Asset Pricing Models [ 1 - 2 - 3 ]

One thing that I initially found confusing was the Capital Market Line (CML) and the Security Market Line (SML). At first glance, they seem to be identical graphs, but let's take a closer look at each while understanding what each is used for.

The Capital Market Line starts of with a scatter plot of all securities with the Y axis being expected return, E(R), and the X axis being standard deviation of return. After calculating the correlations and creating a variety of different portfolios, another scatter plot is super imposed onto the graph. At this point, it should naturally become obvious that there is a curved relationship between the maximum expected return for any given standard deviation (starting with economies of scope and increasing utility to a point of diminishing returns). The curve describing the upper bound of this scatter plot is called the efficient frontier.

Then, on the Y axis itself (the point of no standard deviation, no risk) we have the risk free asset which earns returns at the risk free rate (RFR) typically denoted by US Treasury securities.

The CML is created by creating a line between RFR and the point on the curve for which the CML is tangential. The reason for this is that at any given point on the CML, movement up or down the line will result in a change in the Safety First Ratio (marginal utility of risk, since we are using RFR as the basis for comparison) and therefore the utility is maximized at the point where the CML touches the efficient frontier (in theory this should happen only once). Below is the completed graph:

Because the efficient market portfolio (EMP) represents the optimal mix of securities, the optimal positions based on risk (assuming lending and borrowing at RFR) is any position along the CML. Positions with standard deviations below the EMP are lending positions (being short the EMP and long the RFA). Positions beyond the EMP are borrowing positions (being long the EMP and short the RFA). Basically, it's adjusting your risk tolerance by leveraging or deleveraging the EMP.

Asset Pricing Models [ 1 - 2 - 3 ]

Sharpe and Safety First Ratios - Maximizing Investment Utility

I've often quoted the Sharpe ratio as a good metric to use in investments. This is because it mathematically calculates the marginal utility of different investment vehicles. Let's look at the underlying formula:

Sharpe Ratio = Excess return / risk = [R p - RFR] / σ p

Where:

• R p is the expected return on the portfolio
• RFR is the risk free rate
• σ p is the standard deviation of the portfolio

The Safety First Ratio is a special case of the Sharpe Ratio. For any given security, rather than use the RFR, some minimum required rate of return is substituted instead. This is often used in scenarios where an investor would like to make a minimum return but also capture the most utility possible.

Safety First Ratio = [R p - R min] / σ p

Where R min is the minimum required rate of return (constant cor comparison across securities).

Note that both of these measures have units of return (as a percentage) over standard deviation. Also note that Sharpe Ratio will always be higher than Safety First-Ratio for any given individual security (it doesn't make sense to get a return less than the risk free rate).

If you hold R min constant across all securities and Sharpe is always greater than Safety first, the security with the highest Sharpe ratio will always have a highest Safety First as well for any and all R min.

The highest Safety first, however, does not necessarily imply the highest Sharpe (depending on the R min). In this case, it is better to chose the one with the highest R p. Example:

Two Portfolios
RFR = 1%
R min = 4%
Portfolio A
E(R) = 10
σ = 6
Sharpe = [10% - 1%] / 6 = 1.5
Safety First = [10% - 4%] / 6 = 1

Portfolio B
E(R) = 6
σ = 2
Sharpe = [6% - 1%] / 2 = 2.5
Safety First = [6% - 4%] / 2 = 1

In this case, the two securities have the same Safety First Ratio, but security B has a higher Sharpe Ratio.

Asset Allocation - A Potential Key to Success

Let's assume that there are three asset classes: Equity, Fixed Income (Bonds), and Cash.

Generally, these three classes are generalized as follows:

Equity - Highest volatility, highest potential for growth and gains (let's say 8%)
Fixed Income - Moderate volatility, moderate gains (let's say 4%)
Cash - No volatility, Low to no gains, incredibly liquid (let's say 0%)

Let's also assume that you are relatively young and looking for growth (let's say 20's to 40's) and that you have 100k to invest. Your allocation might look something like this (numbers will vary based on your individual risk tolerance profile):

E - 50% - 50k
FI - 30% - 30k
C - 20% - 20k

Now let's say that things go according to plan and your portfolio next year becomes:
E - 50k * 108% = 54k (51.3%)
FI - 30k * 104% = 31.2k (29.7%)
C - 20k = (19%)

Your portfolio is now worth $105.2k. If you were to re-balance your portfolio, you'd move some of the value received from equities into fixed income class (.3% worth or ~$315.60) and cash (1% worth or about ~$1.052k). I think this is the most "true" definition of "profit taking" that we often hear about on stocks news shows, where a calculated reallocation of capital takes place from one class to another more liquid class (cash).

Having said that, how does this protect us from huge crashes (as I suggested they might in a previous post)? Well an indicator that a bubble is about to burst is when equity prices start going too high. However, if you notice, as equity prices start to get too high, you start to liquidate your position out of them (to a position which is more comfortable for your tolerance). You begin to take your gains out and put them in more stable instruments.

How about when prices fall? Say the equity component drops as well. If you follow the strategy, you will take money from your FI or C and bolster your E (in an attempt to profit from low prices). You can clearly see that the old adage "Buy low sell high" is built right into the strategy.

Although hardly a perfect strategy, we can improve it's effectiveness by looking at a few issues which arise:

Frequency of re-balancing - There are transaction costs involved with re-balancing portfolios (it might not be simple nor cheap to just sell equity class investments and buy fixed income instruments). Therefore, you might not be able to re-balance the portfolio every time there is a tiny bit of movement. However, re-balancing should take place at regularly defined time intervals (say a year), OR if a certain threshold is met (your equities gaining 20% in a day might be a good reason to reallocate funds).

Seeding your investments - Another way to "re-balance" is for people who regularly contribute to their investment portfolio through regular contributions (RRSP or just general savings). If your portfolio is misaligned, you can divert the funds you were planning on investing into the appropriate category. For example if you had the ratio mentioned above as a plan, but your portfolio was currently overweight in the FI class, you could put your savings directly into E to balance it out.

Redeeming your investments - If you are close to retirement and taking money out, you can take money out of a class which is overweight. Let's say that in retirement you want to move from the ratio mentioned above (50/30/20) into a ratio of 30/50/20, you might start by cashing out your equities first.

Granularization - When you have the opportunity to add (or remove) funds to (or from) a particular class, such as equity, you can use the same recursive thought process for which individual equities you want to buy more of. For instance, you can purchase more of a stock which is currently at a lower price relative to it's counter parts rather than try to buy a spread of stocks (if transactions would prevent that). Or you could buy more of a particular ETF.

Especially for people who want to be more active in their retirement planning, but aren't experts in investing, I'd rank this as a good strategy to use even right up to investors who would categorize themselves as moderate to highly experienced. Even investment firms will practice this in a more sophisticated way but having a variety of funds available to capitalize on different opportunities in the market (and can be classed by weigh in terms of how much capital exposure is allocated to them.)