Understanding Aggressive Revenue Recognition

While we normally look at items higher up on the I/S as being of higher quality (less prone to manipulation), there are still some issues which may cause analysts to take a closer look at some of the top line items. For instance, revenue is not immune to manipulation.

For example, a company that is looking to boost it's top line revenue might be more inclined to aggressively (through a variety of mechanisms) recognize revenue. However, with accrual accounting, there are many potential ways to detect some red flags with regards to changes in current practices by looking at the numbers.

First, let's decompose what revenue is actually composed of. Revenue is composed of two types of sales, cash sales and credit sales. Or expressed as:

Revenue = Cash Sales Collected + Δ A/R

Even if all sales contain some component of credit, the conversion implications as it relates to collecting debts will have a noticable effect on various ratios.

The most obvious among these is the Days Sales Outstanding (DSO) ratio:

DSO = (A/R) / Averages Sales per day = 365 * (A/R) / Sales

This is a familiar activity / operating ratio, because it is used to forcast A/R levels in the OWC schedule in a financial model and is the most obvious place to look to see if the active practices of the company have changed. It also plays a huge role in the Cash Conversion and Operating cycles.

Another interesting note is that with a constant of 365, this ratio tells the EXACT same story as the ratio (A/R) / Sales which offeres some insight into your company's policy with regards to percentage of credit extended per sale.

An alternative method is the portion of aggregated accrual attributed to revenue recognition method which is calculated as (A/R) / Δ in Net Operating Assets (or NOA).

However, note that the major components of NOA are Inventory and A/R (related to OWC which is similar but also includes A/P, prepaid expenses and other current / operating liabilities). Notice that when financial modeling, these items are modeled against ratios which incorporate I/S items such as Revenue, COGS, Operating expenses etc. Note that in turn, these items (COGS, Operating Expenses etc.) are usually modeled as a constant percentage of Revenue.

The end result? It doesn't matter which of the two ratios you use, they should both tell you the same story. If a company starts taking more aggressive revenue recognition through extending credit (and possibly risking having customers default on purchases), both of these ratios will increase as A/R as a % of sales increases faster than sales.

Defined Pension / Benefit Obligations

One of the interesting topics in the CFA Level II material is the mechanics for Defined Pension / Benefit Obligations. Previously, in the Rotman Finance I exam / CFA Level I material, I posted an example of the basic mechanics of how a pension plan would be valued (how much would be the PV of future benefit cash flows based on life expectancy and % of salary expectations and what rate of saving would be required to save the required FV to generate those future CF's).

However, if you notice, the "mechanics" of a pension plan are suspiciously similar to that of a bond. And that should come as no surprise. In the retirement or payout phase of retirement, it is as if the retiree is cashing out a fixed income investment (getting regular payments over time) or similar to amortizing a bond liability for the pension plan. However, when they are still "young and saving money" the pension plan is receiving regular payments overtime. The because the payments are regular and defined, they have all the characteristics of a bond.

This metaphor extends even further when you think about what the worker is doing. First a few contrasting scenarios:

Scenario 1: The worker makes a salary of $100k per year.

Scenario 2: The worker makes a salary of $70k per year, but has a defined benefit plan where the company contributes $30k per year into it.

In both of these scenarios the worker (assuming fair treatment) is being given the same value through salary (note also, the I/S in both scenarios reflects a $100k expense with regards to this worker... the only difference is that the $30k would be recognized as deferred wages or change in pension benefit non-cash expense on the CF/S).

However, let's take a closer look at that $30k. What is another way of looking at this? Well, another perspective is to say that the worker is deferring $30k of salary in the hope of future gain as realized through the defined pension benefit. In essence, the worker is loaning money to the company. Assuming that the DPO/DBO is as risk free as the company can guarantee (it is a contractual obligation) in terms of seniority of capital, this money actually ranks as quite senior (priority claim). This is a topic of particular interest with the recent financial crisis, especially as it related to Chrysler and it's recent financial trouble and relationship with the UAW / CAW.

This answers the next question: What is the appropriate discount rate for these funds? Well if you assume this obligation to be one of the most senior forms of claims against the company, it should have the most risk free rate the company can afford which is usually the same rating as it's highest quality bond.

This also raises an interesting point, if you were a lender or potential acquirer (through M&A or LBO) and you were analyzing a company with a defined benefit plan, would you consider the liability similar to debt? While it is not strictly a form of debt in the same way as a revolving credit facility, debenture, high yield bond, PIK or other, it noticably has many of the same characteristics (and is often modeled as a bond liability).

Non-Cash Expenses

A friend was asking me some questions about financial statements and modeling companies and it brought up an interesting question. What exactly are non-cash expenses? For example, when we calculate FCFF we normally just focus on depreciation, although technically depreciation is just a component of the broader category of non-cash expenses. The next most obvious non-cash related expense is deferred taxes.

This got me thinking about what else is included:

• employee stock compensation (appearing on the I/S as operating expenses in SG&A)
• deferred wages (possibly relating to a pension plan obligation or company matching scheme, also appearing in SG&A)
• restructuring charges
• impairment of good will
• amortization of intangible assets
• non-controlling interest

These are normally the cash flow items that appear right in the "adjustment for non-cash expenses" (or similarly named category in CFO) with depreciation and deferred taxs after NI but before operating working capital.

When we were doing financial modeling in NYC, this was the most common question people where people were confused and were asking each other as it related to what exactly was going on in the statement. Other items, like OWC, CFI or CFF were normally pretty straight forward.

With the CFA level II material, at least it is going over some of the more common items in detail which really helps when reviewing and reading F/S. It provides a bit of clarity as to exactly what is happening in the income statement and the real cash effects it is having on the operation of the company.

Purchasing Power Parity

Another example of exchange rate theory is the Purchasing Power Parity (PPP) condition. This model is similar to IRP in that it assumes that when purchasing commodities across borders that the same real price should be used regardless of currency.

For example.

• A widget costs $150 USD in the US
• The same widget costs £100 in the UK

What is the implicit FX rate between US dollars and pounds?

Well, you should be able to buy the same widget with either $150 USD or £100, so the implicit exchange rate (assuming PPP holds) is:

= $150 / £100

= $1.5 / £

Obviously, there are some HUGE assumptions required for this theory to hold. Minimal or zero transaction costs (including transportation, cross border tarrifs etc). In practice, it is probably more realistic to say that there is a threshold for which arbitrage probably won't happen in PPP because of the real costs incurred to handle transactions.

Also to be more accurate, rather than just use a "widget" it would be more appropriate to use a basket of goods to reflect a more broad use of the currency.

Interest Rate Parity Condition

The Interest Rate Parity condition that is in the CFA and discussed in our Global Managerial Perspective (GMP) class talks about.

Long story short, it says: Regardless of what financial mechanisms are used, two countries which are considered to be default free should generate the same real returns for the same period.

For example:
Today:

• You hold $1 USD
• The FX rate is 100 yen per USD
• The Japanse Bonds are yielding 5%

A year from now:

• FX rate is expected to be 103 yen per USD

What does IRP imply the interest rate on the US bond should be?

This can be graphically represented by:


The blue path shows how $1 USD is convered to Japanese Yen, held in a bond, and converted back at the new exchange rate back into USD. IRP states that whether this route is taken or if the USD is just held in a US bond (Red path) should make no difference. It should result in the same amount otherwise there is an arbitrage opportunity.

This is the solution. Note that the US bond rate is reverse engineered from the information given such that the end result produced in the red path is the same as the blue path.

You also note that there is a relationship which is defined by IRP. That is:

Japanese Bond Rate = US Bond Rate + [Appreciation / Depreciation of Foreign Exchange Rate]

Notice that this framework can have a blank in any one cell which can be derived using algebra if the other cells are filled in.

Sustainable FCFF (UFCF)

One of the most important measures of value for a company is Sustainable (Terminal) FCFF so I wanted to review some of the ideas which go into calculating it. As the finance saying goes:

"Turnover is vanity,
Earnings is sanity,
but Cash is reality"

Also, because Terminal Value represents somewhere between 70 to 80% of the calculated Enterprise Value in a DCF, the assumptions that go into developing and FCFF have a major impact on the final valuation.

First a recap of what composes FCFF (a slightly more educated view since my first encounter with this measure on the CFA Level I exam):

FCFF = NI + Dep - WCInv - Capex + Int (1-t)

To build up to FCFF, we

1. take NI from the Income Statement
2. add depretiation to get Cash Flow (CF) as a non cash expense (we'll ignore others like change in deferred tax liability for now although for a "sustainable" cash flow they'd net out at 0 anyways)
3. Subtract Working Capital Investment (change in working capital) to get Cash Flow from Operations (CFO)
4. Subtract Capex to get Free Cash Flow (FCF)
5. Finally, since we are looking for cash flows to all stakeholders (including debt holders) we add back the net value of debt after tax to get FCFF

Now let's break down each of these components. First of all, in real terms we'll project zero growth. However, some terms are susceptible to inflation growth (marginal nominal growth).

As a result, even with zero real growth, there will be some marginal incremental growth in WCInv and Capex to reflect this inflation. The best way to model it is as a percentage of sales according to the CFA.

FCFF = NI + Dep - WCInv - Capex + Int (1-t)

Another consideration is dividing up capex along two dimensions - 1. Maintenance capex and 2. Investment capex. Maintenance capex is defined as the capex required to maintain your operations. By definition, it is equal to depreciation. Therefore:

FCFF = NI + Dep - WCInv - [Maintenance Capex + Investment Capex] + Int (1-t)

= NI - WCInv - Investment Capex + Int (1-t)

Also, investment capex is related to expanding to new opportunities. However, again, since we are modeling a "sustainable" cash flow rather than a perpetually growing cash flow, investment capex is 0 by definition. This generates a further interesting result:

FCFF = NI - WCInv + Int (1-t)

Next I'd have a look at WCInv. If WCInv is stable, then it should produce a marginal change in the cash flow.

Note also that FCFF = FCFE + Int (1-t) + Net Principle Repayment

This shows that NI is a decent (though not perfect) proxy for sustainable FCFE and that by tacking on the interest net of tax effect, we can arrive at a good proxy for sustainable FCFF.

Choosing Courses

I'll probably be putting up more posts on technical finance concepts for the next little while. As it was when I was thinking of coming to Rotman, I used this blog to flush out and articulate ideas on what interested me. This was supposed to provide me with a voice and a place to review some of the ideas I was thinking about and help me decide (initially) whether I wanted to gun for Management Consulting or Finance.

Currently, we are in the process of picking what courses we want. Looking at the electives that might be offered next year (Balloting or "giving a heads up to the PSO regarding what we *might* take next year for scheduling purposes" was due last week) I'd want to take:

• Corporate Finance
• Financial Management
• M&A
• Options

However, as you can expect, these are some of the heavier finance courses. I was warned by every second year I met that it would be a bad idea to take more than three finance courses together in one term, regardless of how much we keen first years thought we loved finance. Especially any of the first three, which I'm told are the core courses for a "specialization" in Investment Banking.

So I find myself posting outloud again to both prep for the CFA exam as well as put some thoughts into writing for me to review as I select my electives for next year. Technically, with the credits I already have, I could get away with only taking three courses, but it seems like such a waste. A - We paid too much to come here to start taking "spares" and B - the profs are good and the topics are interesting. I guess it's just a matter of balancing workloads.

BATNA and Sharpe Ratios in M&A

While I missed the Negotiations class my classmates took for the Middle East Study tour, I was fortunate enough to have taken a Negotiations class at the Analyst Exchange in NYC where they explained concepts like BATNA (Best Alternative to a Negotiated Agreement) in a simulated negotiation environment.

Also, in ITP, we talked about the model for "rational experimentation", that is to say the formula which describes the logic between probability of successful outcomes versus the risk and initial investment required (looks suspiciously similar to an NPV calculation because it uses the same mathematical components with probability of success superimposed on the cash flow, similar to how the CFA teaches to account for risk).

With my last post on M&A and splitting synergies with the target's share holders, this got me thinking about what would be "rationally" fair in M&A negotiations. I thought about it and decided it might be a good idea to integrate the thoughts from the post below with the idea of a Sharpe Ratio (or more exactly, Roy’s Safety First Criterion – where we use a “minimum return” rather than risk free rate).

S = (E[R] - Rf) / sigma

Where:

• E[R] is the expected return of the project
• Rf is the risk free rate (or in Roy's SFC, minimum return)
• sigma is the standard deviation of the investment

Obviously, there are some of the same undertones that we have learned from CML or CAPM. While I was thinking about Synergies and Premiums analysis of an M&A deal, it struck me that while there is some "risk" in the total Synergies achievable, the Premium is paid in advance and essentially risk free. Immediately, some of the same terminology which was used in the previous post suddenly rung a bell with regards to the Sharpe Ratio (from CFA Level I).

I would propose that the Sharpe ratio calculation can be used in an analogous manner for an M&A deal with synergies. For example:

• Expected Returns --> Synergies
• Risk Free Rate --> Premium
• Sigma --> some sort of volatility related to success of M&A deals to achieve expected returns

In fact, you can take this a step further and get:

• Synergies / EV as a proxy for M&A incremental ROA
• Premium / EV as a proxy for M&A minimum return

S = (Synergies – Premium) / (EV * sigma)

The formula would then calculate something very similar to marginal excess ROA or value creation per unit risk by the deal. Besides helping you understand your BATNA, this metric might also help you select acquisition targets from a financial perspective.

PVs of M&A - Premiums and Synergies Analysis

There was an interesting perspective for Mergers and Acquisitions in the CFA course readings. Rather than look at accretion / dilution, there was the alternate perspective of looking at doing a sort of NPV analysis of M&A and seeing who benefits and what the implications are.

Example: Look at two companies A (Acquirer) and T (Target). The companies are all equity and have 100 shares each. However, A is valued at $1000 and T is valued at $400. Synergies (defined as the PV of all future cashflows) is valued at $200. The premium is $100 and the deal is all cash. What is the value of the combined entity, C?

C = A - Outflows + Inflows

Outflows = T + Premium
Inflows = T + Synergies

C = A - (T + Premium) + (T + Synergies) // T's cancel - makes sense, lose T in cash, but gain T in value by way of acquisition

Therefore,
C = A - Premium + Synergies
= $1000 - $100 + 200
= $1100

For the original share holders of A, the new stock price would be:
$1100 / 100 shares or $11, a $1 increase in value!

Note that T shareholders got $500 for their 100 shares or $5 each, also a $1 increase.

This is an interesting result, the actual value of T doesn't really affect the value of A. This alternative focuses more on two of the most important financial points of information on an M&A deal: Premium and Synergies. Because A and T split the synergies evenly through the premium, they both benefit the same. This result holds for any porportion of split between A and T shareholders based on the portion of the Synergies represented by the premium.

Another way of looking at it is this: Synergies are the value created in an M&A deal. The Premium represents what is picked up by the current owners of the target, T, where as what remains (Synergies - Premium) represents the value picked up by the original shareholders of A (the acquirer).

While this is a unique perspective, it also lends itself to another interesting result:

Continuing the example from above, the stock price for A is $10 ($1000 EV / 100 shares) and the acquisition price for T is $5 (($400 + $100) / 100 shares). A plans to acquire T by issuing T's current owners 1 Share of A for every share of T (giving away a "$10" dollar share for two "$5" dollar shares). We get an interesting result. Suddenly, the Value of A is different:

C = A + Outflows - Inflows

HOWEVER:

Outflows = 0
Inflows = T + Synergies = $400 + $200

Suddenly, value of C is $1600. Wow! Seems like we got something for nothing. But wait a second! We need to issue more shares to T's owners. How many? Well:

$500 EV / $10 per share = 50 shares.

So what is the new price per share of A? Well:

$1600 / 150 shares = $10.67 / share

Why is it lower? Where did the creation of value go? Well because A "gave away" some of their share of the synergies by paying T shareholders with PRE-merger valuations of their shares. Essentially, they gave T share holders some of their share of the synergies BEYOND the premium paid upfront in A's stock.

Note that T's former owners are now holding $10.67 for every two shares or $5.33 for each of their T shares or a $1.33 premium per share (@100 shares, thats $133). Notice anything interesting? The total synergies are the same ($67 for A shareholders + $133 for T shareholders = $200 total synergies), but T has taken a bigger slice. In the theoretical space, it is a zero sum game.

Why would A do this? A may not have enough cash on their balance sheet to entirely swallow T (they'd need T's full value in cash). Also, perhaps they are not entirely confident on being able to realize the synergies in the deal and are looking to share the risk with T's shareholders. Giving away stock might also incentivize some of T's current shareholders (aka current management) to stay, align their interests and realize the synergies.

George Soros - Breaking the Bank

We were discussing the notorious story of George Soros' shorting of the UK pound in our GMP class this morning.

The story begins with the UK joining Europe's Exchange Rate Mechanism (ERM), not exactly fixed but had a policy where the currencies were staying within an exchange rate band. This simultaneously existed with a carry trade scenario where the German government was offering a higher interest rate than the British Government so people were borrowing in pounds and lending in DMs.

George Soros foresaw the opportunity where people who were participating in carry trades with the British pound created an opportunity for currency deprectiation. He sold off all his positions and then proceeded to short the position. This aggressive "attack" position resulted in many other fund managers dumping pound denominated assets. On the "Black Wednesday", the Bank of England tried to fight back by raising interest rates up to as high as 15% that day, but it wasn't enough.

Also, this is compounded by the required draw of the UK's foreign reserves (another avenue to defend against currency depretiation) to prop up the currency would have resulted in a significant depletion which would not have benefited nor saved the currency (essentially paying out the speculators).

This reminds me of the scenario I experienced in the finance trading lab where I could see the ask list depleting very quickly (low number of orders). The Interest Rate Parity condition only holds if you have a player who is large enough to hold the position of the currency. In a scenario (often repeated in other markets) where people put a currency (or any financial instrument) under siege, it makes it difficult for players to hold their positions as they take massive losses.

Eventually, as the story concludes, the epilogue is that the UK bank decided to let go and allow the currency to depreciate. George Soros also made a reported $1B USD.

Exchange Rates - Currencies as Investment Instruments

Oddly, in my Global Managerial Perspective (an international economics course), we were discussing exchange rates and the professor brought up nominal and real exchange rates (nothing new really), but also introduced the idea of using a weighted average of currency exchange rates as a bench mark for appreciation. There are two neat ideas which I took away from this:

The first is that when currencies appreciate relative to one another (on a bi-lateral basis) it is often hard to tell what is happening. For example, the Canadian dollar flirting with parity to the US dollar in the last few years. Is this a result of the US recession and lack of confidence in their dollar? Or the fact that Canadian Exports are in high demand and driving up our dollar value? Or both? In putting together a weighted average of exchange rates against your currency, you can tell on a more clear individual basis if your currency is appreciating against your "basket", a proxy for global currencies and real Purchasing Power Parity growth.

The second idea is that this weighted average looks an awful lot like an index. Much of the language above encompasses the idea that it behaves like a portfolio of financial instruments. Having said that, I recognize that things like CAPM probably wouldn't work (considering that currencies are not return generating instrumentns) so a regression of gains over time from the currency to the "index" would probably be meaningless. In the same way that commodities (although they are assets - items that store value) are not investment assets in the same way other financial instruments are because they don't generate return.

As the CFA material mentions, the only real way to receive gains from non-income generating instruments (commodities and currencies) is to rebalance after a change in price of the underlying asset.

The Acumen

I've been exceptionally busy the last few weeks. Even though I've decided to place a moratorium on competitions, I’ve still found myself overwhelmed with the MBA and the CFA Level II material. One thing I’ve been trying to keep track of in my posts is the absolutely brilliant ideas I’m encountering, whether in the Rotman MBA or CFA Level II.

But lately, my ability to post and get work done has drastically dropped off. And I would like to think it’s not because I’ve gotten lazy, but rather because there is so much brilliant and interesting stuff going on that I can’t post it all.

And I think that is exactly the case. Example? ITP, a course that had many of us scratching our heads in the beginning has suddenly burst forth with ‘light bulbs’. For example, not too long ago, I was complaining about how “past performance does [NOT] predict future behaviour” in some cases but not others. For example, individuals (as social science will tell you) are predictable (past performance DOES predict future behavior) but this is not so in finance and capital market instruments (good luck buying a stock based on it’s past behaviour hoping for gains).

And ITP has taken this exact point and, in our latest team assignment, asked us to investigate why this is. How “predictable” individuals (with their behaviour well defined) in a group produce slightly unexpected results. And the effect this has on our perception of what we learn in finance classes as it relates to theoretical concepts (CAPM comes to mind at the top of this list, but is closely accompanied by the idea of bubbles and crashes in the stock market, a very timely topic).

You can imagine that I am very excited. Suddenly, I am being given the vocabulary to describe in practical terms what we’ve been taught in textbooks. One of the reasons why I came to the MBA program was to help me structure my thoughts so that I could package them and deliver them to someone in a more digestible format.

While I was fortunate to have known many brilliant minds at McMaster Engineering, in my work life, I felt like I wanted to further develop my business skills to speak the same language as my colleagues and be able to use descriptors outside of the Engineering dictionary so we could understand each other, work together and accomplish amazing things. It was one of my goals coming into Rotman: I thought I was pretty clever. But I wanted to develop my business acumen.

Non-Leveraged Accretive Mezzanine Financing

I was looking over my CFA Level II materials for corporate finance this weekend when I looked at the CFA's definition of different types of risk. For instance:

Sales (Business / Industry risk)
- Operating Expenses (Operating Leverage)
- Interest Expense (Financial Leverage)
_____________
Cash flow

The definition of any type of leverage (operational or financial) is increasing your fixed cost component but reducing your variable component.

It got me thinking, is it possible to have an instrument which doesn't increase leverage and solvency ratios, but also provides accretion for common equity holders? For instance, if you want to deleverage, the general strategy is to purchase debt with equity (which results in dilution because cost of equity is higher than cost of debt due to risk concerns etc). I don't know if this is possible, but I asked myself about a preferred share with very particular characteristics.

Fixed income instruments (coupon paying bonds, dividend paying preferred shares) increase the fixed payments required which technically increase leverage.

Accretive
Is it possible to have a preferred share that, rather than paying a fixed predetermined dividend (similar to dividend yield based on price), that pays a percentage of net income (similar to a stated dividend payout ratio). Because it is more senior than common equity, the cost of this capital would be less than the cost of equity (accretive if used in a refinancing / capital restructuring).

No Leverage
But the payout would also be variable based on NI meaning that it isn't technically leverage according to the CFA definition (plus it would be classed as equity rather than debt on the books). If earnings are low, the payout is low. If the earnings are high, payout is high. It rises and falls as a variable component rather than a stated fixed component.

The problem with this model of an instrument is that I don't think you could get a "senior" level instrument to payout variable to net income with a cost of capital less than common equity because they technically face the same level of risk (percent of NI).

Also, because earnings can be manipulated, perhaps the payout would work if it was stated as a percentage of EBT or some other higher quality form of earnings? At first I thought EBITDA, but then I realized that doesn't make sense. It would have to be paidout after EBIT (because interest should be a more senior form of financing and paid first). However, EBT is often modeled with a fixed tax rate to go to NI (so a % of EBT is really a % of NI since tax rate is usually constant).

Perhaps it could be payed out as a % of EBITDA which is paid out after interest?

This would justify the instrument being more senior and paying a lower cost of capital.

The 4 C's of Credit

I have some friends who are looking at trying to gain positions in Fixed Income so I thought I would have a quick review of the 4 C's of Credit. They are:

1. Character - The management team's record, strategy and internal controls
2. Capacity - Ability to meet debt obligations
3. Collateral - Assets pledged to back the loan
4. Covenants - Restrictions on activities as well as maintenance

Recall that in bankruptcy, there is a hierarchy to how remaining capital, collateral and other assets are distributed relative to tranches. However, in restructuring "everyone gets a haircut".

Also, when building credit ratings, there are various ratios that are looked at, particularly:

• Profitiability Ratios
• Liquidity Ratios (Short Term Solvency)
• Capitalization (Leverage) Ratios (Solvency)

CFA Level II - Study Begins

I was studying for the CFA Level II on Sunday and I noticed that some of the topics covered in the Equity Analysis portion were items that I was pondering earlier including: alternate method of including the value of risk in DCF, inflation as a reasonable proxy for long term sustainable growth in a GGM or DDM, the constant relationship between ROE, k, PE, Dividend payout / retention, growth rate etc.

I'm very excited to be starting my study for the CFA Level II. Already, I'm learning a lot and getting confirmation and validations on some of the ideas I had pondered earlier as well as correction on some misconceptions.

So far, I'm particularly impressed with the integration of macro economic factors on valuations and approximating growth rates and factor variables in valuations via economic indicators (GDP growth, inflation, CPI etc). I am absolutely fascinated at the interplay and relationships for how different disciplines of study interact and how the mechanics of economics and strategy affect the mechanics of finance. Also, I think that the topics covered are pragmatic and absolutely brilliant in terms of applying theory in practice.

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).

Burning Hot - Getting Ready for the Rotman MBA

I've recently (Sunday) returned from NYC from my internship in finance and hit the ground sprinting. I've only recently moved into my new house and the internet situation isn't what I'd like (so I apologize for not having any CFA Level II posts up yet).

I haven't quite craked open my books yet, but rest assured they are forthcoming. I've already started to received my Rotman books and course materials. Classes start on Sept 8th so I have two weeks to get sorted out (between Rotman Pre-MBA classes and events).

Expect a great deal of content to appear over the next few days as my situation improves.

Does the CFA Exam Get Harder Every Year?

This is a question I've been asked a lot recently by friends and colleagues who are looking to boost their credentials in a very competitive job market. While many are coming out of school (Undergrad or MBA) and looking for an edge, some are thinking about the timing of when to write the exam.

While competitive tendencies would suggest that writing sooner would be beneficial, school and work schedules don't necessarily permit the allocation of study time required. Conversely, potential candidates are worried that if they put it off, the CFA exam will get harder and harder.

While it is true that the curriculum changes from year to year, and possibly that the most recent exam is much different from the exams given a decade ago, the most recent exam and associated curriculum only had incremental changes from the previous year (remember, I wrote Dec 2008 and June 2009... And got sent to years worth of books for two years worth of curriculum fees).

The only real changes I've noticed between the curriculum from year to year is that they added a VERY brief section on Game theory and Nash equilibrium. If I'm not mistaken, there was only one question on the 2009 exam, and even then I'm guessing that because it is so obviously new, it was probably one of those questions which will not count and will be evaluated for future inclusion in other tests.

With the introduction of the game theory section, however, there was an incredibly large optional section (which, by the way, is incredibly interesting reading, especially for those interested in business strategy as a science, rather than an over used buzz word). It doesn't seem like the basics of financial physics has really changed all that much.

Having said that, I would not be surprised if:

• More of the "optional" material slowly starts creeping into becoming mandatory
• More of the Level II material slowly starts creeping into Level I
• More of the Level III material slowly starts creeping into Level II
• There is more material added to Level III
  

But this is no different than how our school curriculum teaches subjects earlier and earlier. Calculus used to be taught mostly at the university level but has crept into high school. In the same way, I don't think there is anything to fear, when it comes to the CFA program. However, although the physics of finance don't change, this makes a compelling argument for continuing education and keeping your skills sharp.

Capitalists being what we are, always looking for that edge, I'm sure someone will eventually be interested in providing the service to teach you how to one-up your competition.

CFA Level II Candidate

As I've been proud to mention before, I've passed my Level I CFA exam this June. Recently, I registered for the Level II exam and my books recently arrived at my home in Toronto. As I'm finishing my internship here in New York, I'll be heading home next weekend. My plan is to begin burning through as much of those books as possible as a primer for my MBA (I've never really read the "suggested reading lists" since elementary school because I always found them to be busy work to calm down nervous over achievers rather than anything useful).

There are a lot of events happening in the week I return to Toronto (which is also the week before school officially starts), however, my goal is similar to my goal in the weeks leading up to the CFA Level I exam (for those of you who remember, I was trying to post 2 to 3 questions / related topics per day).

I will be registering for a CFA prep course with Passmax again, but I'll have to decide what my time commitment and allocation can be outside of my MBA classes which promise to be quite involved (even potentially "free" time will be allocated to extracurricular activities).

Also, in the week following my departure from my internship, I will see what work is cleared for release which I can talk about and discuss what I've been doing for the past summer.