"Calculating" the hedge ratio...?

When I teach The Spaulding Group's prep courses for the CIPM exams, I always advise candidates to carefully consider the Learning Outcome Statements in each study session, as these statements describe the subject matter that candidates are required to master. In particular, I tell the candidates to focus on the verbs in each statement (e.g., compare, contrast, state, calculate, describe), as I see these as really the centerpiece of each statement.

At the Expert Level, there is a Learning Outcome Statement in Study Session II that reads:

Calculate the hedge ratio (delta) of an option and conclude whether the option is in-the-money, at-the-money or out-of-the money

The word "calculate" has a fairly specific meaning in my mind, but I decided to consult with Merriam Webster:

transitive verb

• 1a : to determine by mathematical processes <calculate the rate of acceleration>
• 1b : to reckon by exercise of practical judgment : estimate <calculate the likelihood of success>
• 1c : to solve or probe the meaning of : figure out calculate his expression — Hugh MacLennan>

• 2a: to design or adapt for a purpose calculated the timing of his arrival for maximum impact>

• 3a : to judge to be true or probable b : intend calculate to do it or perish in the attempt — Mark Twain>

intransitive verb

• 1a : to make a calculation
• 1b : to forecast consequences
• 2a : count, rely

In checking the list of formulae for the Expert Level, I don't see a specific formula for the hedge ratio, and I don't see one in the assigned readings. Thus, I don't think "calculate" is what is intended - at least not in the common, every day usage of the word.

Having said that, it is important to understand the characteristics of the hedge ratio (of a call option) in certain situations:

• Hedge ratio is a function of stock price, term of the option contract, the expected variance of the underlying stock's price, and the risk-free rate
  
  
• If the underlying stock's price is considerably below the option's strike price (i.e., the option is deeply "out-of-the-money"), the hedge ratio approaches zero and it is not desirable to exercise the option.
  
  
• If the underlying stock's price is "at-the-money" (i.e., the stock price and the strike price of the option are approximately equal), the hedge ratio is close to .5, as it makes little difference if the stock is acquired via market purchase or by exercising the call option
  
  
• If the option is deep "in-the-money", the hedge ratio approaches 1, and it is advantageous to acquire the underlying stock by exercising the option.

Note that all of this describes call options only (i.e., options where the holder has the right to purchase the underlying security). Put options are not currently covered in the CIPM curriculum.

Note: The graphic above illustrates Bloom's Taxonomy, upon which the Learning Outcome Statements of the CIPM curriculum are based.

Did the Expert Level Just Get *More* Difficult?

Well, I'm not sure if it got harder... but certainly there is quite a bit more content?

I am in the process of updating the materials I use to teach The Spaulding Group's CIPM Prep Classes (Principles and Expert Levels), and in reviewing the 2011 curriculum, I see that some of the content has shifted from the Principles Level curriculum to the Expert Level curriculum.

I suppose that's a "good news / bad news" thing for new CIPM candidates. The good news is that the Principles Level curriculum is a bit lighter, content wise, as some subjects are now deferred to the Expert Level. But, the bad news, there's more information to master at the
Expert Level than there was in the past.

The following subjects have been removed from the Principles Level curriculum, and are now entirely covered at the Expert level:

• real estate
• private equity
• (most of) verification
• GIPS standards related to model portfolios
• GIPS standards related to switching of portfolios between composites
• GIPS standards related to measuring composite dispersion
• GIPS standards related to portability of past performance

In prior examination windows, I would characterize what was required of candidates for these topics as essentially learning the provisions at the Principles Level, and being able to apply the related guidance and interpretations (as well as deal with some additional calculations) at the Expert Level. Now all of this will be covered at the Expert Level.

While this change does not increase the overall content, it does make the Expert Level more "packed."

So, CIPM candidates, be aware! (Details can be found here.)

P.S. I have received some lighthearted flak from candidates for making this suggestion at conferences, but I wonder aloud again if it would be worthwhile for the CIPM Body of Knowledge to be covered in three (3) exams rather than two...

Is the S&P 500 actively managed?

Earlier this week, my boss, David Spaulding surmised on his blog about the possibility that the mere existence of indexes may be a reason for "above average" performance, as changes in index constituents often results in trading in the newly added stocks, which often causes their prices to rise.

The question of whether the Standard & Poor's 500 is actually a managed portfolio is addressed in one of the "Benchmarks" study session readings at the CIPM Expert Level. The reading, authored by Laurence B. Siegel, refers to some research done by Sandy Rattray and Pravin Manglani. The article on that research is not required reading for CIPM candidates, but it may be of interest, and can be found online here.

The GRAP attribution linking formula

At the Expert Level, CIPM candidates are required to learn a few of the more commonly used linking methodologies for smoothing the attribution effects that come from arithmetic models. The required methodologies include:

• Cariño

• Menchero

• GRAP
  

Of these methods, the GRAP method is my personal favorite because of it's simplicity... which may not be apparent looking at the formula! Upon first glance, the GRAP formula, which appears above, may seem intimidating for a couple of reasons:

• It uses three "series" one summation series a two multiplication series.
  
  
• The three series have different indexes (T=1 through N, t = 1 through T-1, and t = T+1 through N).

When teaching the GRAP method, I find that it is easier to explain what it does, effectively, rather than explaining the formula.

Consider a situation where we are linking together monthly attribution effects for the first six months of the calendar year (January through June). Let's consider how we obtain the "G" factor that we will use to smooth the attribution effects for the month of April. Basically, what the GRAP formula tells us is that:

• The excess return is the sum of the "smoothed" attribution effects
  
  
• We obtain the smoothed attribution effects by multiplying the original attribution effects by the "G" factor
  
  
• The G factor for a particular month is a combination of portfolio returns and benchmark returns for the periods being linked together.
  
  
• In our example, we are smoothing the attribution effects for April. This will be done by multiplying together:
  

1. the unitized portfolio returns for the months preceding April (January, February, March)
2. the unitized benchmark returns for the months coming after April (May, June)

Thus, the following formula yields the G factor that we can use to smooth the April attribution effects:


Thus, the GRAP formula is very easy to remember, and much simpler to use than the Menchero or Cariño methods.

GIPS: "in transition" assets

Recently I received a question from one of our verification clients regarding what I call "in transition" assets - basically accounts that are in the process of moving from one category to another with respect to the firm's GIPS compliant performance presentations. In answering, I thought that this is the type of interpretative question that could appear in some form on the CIPM Expert Level exam.

Basically, the so-called “in transition” assets must be part of the firm assets on the firm's performance presentations, but not part of composite assets. In particular, the points in time where you need to worry about these are at the end of the year, as GIPS provision 5.A.1.c (GIPS 2005) requires the presentation to include information on the amount of firm assets and composite assets at the end of each annual period.

Examples of “in transition” assets include:

• An account that was GIPS discretionary, but the client has indicated they are closing they are closing the account (thus discretion can be inferred to have been lost) but the account had not been fully liquidated/closed at the end of the year. For example, if a client called to say they were leaving the firm on December 17, 2009, but the account had not been liquidated until January 5^th. Assuming the period for performance calculations is monthly, the account is not part of its composite for the month of December, but is part of the firm assets.
  

• A new account to the firm, that will become GIPS discretionary, but has not met the inclusion requirements yet, based on the firm’s documented GIPS policies. For example, assume an account is opened on December 17, 2009, but the firm’s policy is to include new accounts in composites starting with the first full month under management. Thus, the account would not appear in the composite’s performance until the month of January 2010, but it would be part of the firm assets for the end of 2009.

• An account that is changing composites (either due to a change in client mandate or a composite redefinition; see GIPS provision 3.A.5), assuming the change occurs on December 17, 2009 but the firm’s or the new composite’s documented inclusion policy is to include the account in the new composite in the first full month under management (a la a new account). Such an account would not be part of composite assets for the month of December, would be reflected in the new composite’s return for January 2010, and be part of the firm assets for the end of 2009.

Similar logic should be applied to:

• Actual, discretionary, non-fee-paying accounts that the firm has elected to exclude from composites.

• Legally discretionary accounts that are GIPS non-discretionary accounts (based on the firm’s documented policy on discretion).

(The picture at the top of this post is the cover from John Coltrane's album "Transition." Seemed a fitting reference from a few respects. First, the album came between Coltrane's quartet period of somewhat traditional jazz, and the last major period of his life which featured more experimental styles. Also, the album was released after Coltrane's death, when one might imagine that Coltrane was making his transition from his earthly life to his spiritual one!)

Why Do We Call it "Time-Weighted?"

Recently, my boss David Spaulding commented regarding the origin of the term "time-weighted return."

The CIPM curriculum at the Principles Level gives a description as to the origin of the name. Unfortunately, an original source is not cited. But, I remind candidates of this description given in the curriculum, as they are responsible for knowing this information.

I quote from the candidate reading, Chapter 12, Evaluating Portfolio Performance:

"The TWR derives its name from the fact that each subperiod return within the full evaluation period receives a weight proportional to the length of the subperiod relative to the length of the full evaluation period. That relationship becomes apparent if each subperiod return is expressed as the cumulative return over smaller time units."

The curriculum goes on to describe an example of a time-weighted return calculated for a month as follows:

• beginning value - 1,000,000
• contribution of 30,000 on the 5th of the month; market value at that time is 1,045,000
• contribution of 20,000 on the 16th of the month; market value at that time is 1,060,000
• ending value is 1,080,000

The two external cash flows break the month into 3 sub-periods, with returns as follows:

• rt,1 = [($1,045,000 − $30,000) − $1,000,000]/$1,000,000 = 1.50%
• rt,2 = [($1,060,000 − $20,000) − $1,045,000]/$1,045,000 = -0.48%
• rt,3 = ($1,080,000 − $1,060,000)/$1,060,000 = 1.89%

Thus, the time-weighted return for the month is the geometric linking of the subperiod returns: rtwr = (1 + 0.0150) × (1 + −0.0048) × (1 + 0.0189) − 1 = 2.92%

The reading goes on to point out that one could calculate a daily compounded return for each subperiod:

• period 1 corresponds to a daily compounded return of 0.30% for 5 days
• period 2 corresponds to a daily compounded return of -0.04% for 11 days
• period 3 corresponds to a daily compounded return of 0.13% for 14 days

Thus, the time-weighting, the curriculum indicates, corresponds to the exponent used to compound the daily returns:

rtwr = (1 + 0.0030)**5 × (1 + −0.0004)**11 × (1 + 0.0013)**14 – 1 = 2.92%

The Expanding CIPM Body of Knowledge

On next Friday (June 25th at 9:00 a.m. Pacific time), I will be hosting a webinar covering the changes (really, the additions) that have occurred to the Certificate in Investment Performance Measurement (CIPM) program since the first examination window.

As Dave Spaulding mentioned on his blog (Investment Performance Guy) today, Dave and I were "pioneers" as we were part of the first group to enroll for the exams and earn the certification. Back in 2004, The Spaulding Group and the Performance Measurement Forum formed a Blue Ribbon Committee that kicked off the process of developing a certification program for performance professionals. We have offered our training classes since the initial enrollment periods for the CIPM (then called CGIPS) exams. It has been very gratifying to teach our CIPM classes and see our students succeed with a significantly higher pass rate than the general population.

This particular webinar is actually targeted at CIPM certificants. As we learn at the Principles Level, the Body of Knowledge that is required to do our work well and serve our clients is constantly evolving. Also, certificants are required to update their body of knowledge by meeting a Mandatory Continuing Education requirement (MCE). We are offering the webinar to help certificants satisfy their MCD requirements.

To sign up, please contact Patrick Fowler.

"Failure to prepare is preparing to fail."

Last week, the world lost one of (in my opinion) the most influential teachers in sports (and elsewhere), the legendary Coach John Wooden, who led my alma mater, UCLA to an unsurpassed 10 national championships in men's college basketball. Coach Wooden (shown above with Lew Alcindor, who later changed his name to Kareem Abdul-Jabbar) is famous for many quotations, but one that applies to CIPM candidates right now is in the title of this blog post: "Failure to prepare is preparing to fail."

The examination window for the Fall 2010 period is now open (and has been since May 1st), yet the exams will not happen until October, which I'm sure seems to be far off in the future to some.

I strongly urge candidates to begin studying for the CIPM exams as soon as possible. The curriculum is broad, and learning the material over time (rather than cramming in the final weeks before the exam) will help you obtain a deeper understanding of the material, and give you a greater chance of success (i.e., passing the exams). Do not underestimate the number of hours of study required. I have heard various quotes regarding the recommended study time for each exam level, but for most people I think those estimates are on the low side.

So, enhance your chance of success by starting your studies now - you'll be glad you did when you are taking the exam!

The Performance Professional... Like a Rolling Stone, Baby...

The image shown above is the album cover of the Rolling Stones' 1972 album, "Exile on Main St." Upon its initial release, this album, while enjoying substantial sales, received very mixed reviews from rock music critics. Time has viewed this album kindly, however, and the album now is generally considered to be one of the greatest rock albums of all time. The album was re-released yesterday in a remastered format with several previously unreleased demos and other features, creating quite a media buzz.

So what, you may be asking, do the Rolling Stones and this album have to do with performance measurement or the CIPM designation?

When I was growing up, for a long time my desired career choice was to become a rock radio DJ (fortunately, I did not pursue this path, as rock radio has essentially died and DJ has a completely different meaning in today's world). Thus, I like to reflect on music and related events and their broader meaning. A couple of thoughts come to mind with respect to the Rolling Stones that remind me of performance measurement.

First, when watching old interviews of the Rolling Stones, one of the things that is striking is the frequent comments that the members of the band did not set out with a plan to have a career doing rock music. They certainly did not intend to be playing music 10 years later, let alone 20, 30, 40 plus years later! Quite similar to performance analysts, really... virtually all of us that are doing performance measurement ended up doing so somewhat accidentally. Granted, the reasons we first opened our spreadsheets to calculate time-weighted returns are likely different from what drove Keith Richards to pick up a guitar... but, I think many of us share the fact that we didn't expect to be doing performance analysis 10 or 20 years later. How serendipitous for us, and Mr. Richards!

Perhaps more importantly, though, is the longevity aspect of the Rolling Stones career. People are fond of debating which band was the greatest ever - the Beatles or the Rolling Stones. I definitely favor the Beatles in that debate, as no other band (in my opinion) came close to extending rock music from a form of entertainment to a true form of artistic expression, at a critical juncture in time. But, at the same time, I think the greatest legacy of the Rolling Stones is their longevity and their professionalism. Don't be fooled by the guitars, the sneers, the leather... these guys go out on a regular basis and do what they do, and they do it well. Professionalism and doing one's job well, day-in and day-out, are so important to enabling a job that someone does to become a viable career. Musicians of many genres benefit because the Rolling Stones carry on, doing their work well.

And that is a lot of what the CIPM designation is about. Yes, we need to know how calculate returns, risk and attribution, just like a guitarist needs to know how to play certain notes, chords and techniques. But just as important, perhaps more important in the long run, is the professionalism that we bring to our daily work, and the ethics. That is how we add value to our niche and the broader investment industry, and doing so is in the long-term interest of us all.

So, see, you have more in common with Keith Richards than you might have thought...

An invite to see sample GIPS presentations

I'm taking some liberties here, as this is mainly John's blog, but knowing that most of the readers probably work for firms that claim compliance with the Global Investment Performance Standards, I thought you might find this invite of interest.

Many firms struggle with their Global Investment Performance Standards (GIPS(R)) policies and procedures; and even for those who feel theirs are pretty good, there is always an opportunity for improvement.

Here's an invitation: if you send me a copy of your policies and procedures (either PDF or Word format), I'll include it with those of others who respond, and then send all participants a complete collection. I advise you to remove your firm's identity from you materials before sending it to me as I will not do any editing (you're free, of course, to include your firm's identity in the materials).

If you wish to participate, please send it to DSpaulding@SpauldingGrp.com by May 31. Only those who participate will receive the complete set.

Principles & Expert: Repetition, Repetition, Repetition...

I suspect that most current CIPM candidates at both the Principles and Expert levels are about to sit for their exams this week - that's what the statistics tell us. (CFA Institute shortened the test taking window from two months to one month for this very reason, effective this period.)

You may very likely be feeling the fatigue of studying these past several weeks, and need a strategy to keep you fresh with the information over the next few days without overloading your brains.

My recommendation to you at this point is that you sit down and recite (on paper) your formulae that you are required to know for the exam. Do this as many times as you can over the next few days.

Repetition is a key to success. For this particular blog post, I chose to include a picture of Coach John Wooden (UCLA, 10 national championships). All good coaches encourage their athletes to repeat things over and over (plays, footwork, drills). One reason is to build up muscle memory, so that the body (and brain) will do what it has practiced and is accustomed to, even when exhausted or faced with adversity.

When you are sitting for the exam, you want to respond to the questions like Kobe Bryant taking a last second shot with the game on the line and a hand in his face blocking his view of the basket. You want to respond like you have been there before, hundreds of times, and as if it is second nature to you (if not first nature!).

OK, maybe a last second shot in an NBA game is over-dramatic, but you get my meaning... repeat for success!

(and, if you are looking for a good study distraction, check out www.coachwooden.com !)

Expert Level: Reading the Vignettes

The structure of the Expert Level exam is 80 multiple choice questions based on 20 vignettes. Thus, for each vignette there are four questions. Each multiple choice question will have three possible answers.

Please consider this suggestion in light of your own specific test taking strategies, I suggest that you take the following approach to the vignettes:

1. Skim the vignette to get a general sense of the scenario and the subject areas touched upon.

2. Read the four questions that accompany the vignette.

3. Go back to the vignette and read it more carefully. Now that you know the questions, you will have a better idea of what to focus on.

When I sat for the Expert exam, it was in the first period that it was offered and I did not have the benefit of anyone's past experience. Thus, my first approach to the vignettes was to read them very carefully right off the bat, trying to understand them before I looked at the questions. This approach I found to ultimately be very time-consuming, and also frustrating when I discovered that there were occasionally questions that I could answer very quickly because they did not have to do with calculations (and in some cases had only a general connection to vignette).

I believe that if you follow the three steps above, you will use your time more efficiently during the exam. Unlike the Principles Exam, I think that most people will find they need most (if not all) of the allotted 3 hours to complete the exam. Every minute will count!

Principles Level: Setting up your calculator

(Note: this tip applies to Expert Level candidates as well, but I presume that if you passed your Principles Level exam you must have had the calculator set the way you expect it to work!)


I generally recommend that candidates make sure to check two settings in particular on their calculators prior to the exam:

- precision
- order of operations

With respect to precision, my recommendation is that you set the number of decimal places that your calculator uses to the maximum value possible. I think it is better for you to see the answer in as "pure" a form as possible, and then you can choose to round or truncate your result, as necessary. For the Texas Instruments BA II Plus, for example, you can set the number of decimal places anywhere from 0 to 9 places.

As for order of operations, keep in mind that there are two different methods:

- chain (essentially left to right)

- algebraic

The chain mode of operation means that the calculator will perform calculations as they are entered (i.e., a literal "left to right" mode).

The algebraic mode of operation uses the following hierarchy:

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

People often use the acronym PEMDAS (Please Excuse My Dear Aunt Sally) to help them remember the hierarchy under the algebraic mode. Another (less witty) form of the mnemonic device is BEDMAS (Brackets Exponents Division Multiplication Addition Subtraction). Use whatever works!

To illustrate the difference between chain mode and algebraic mode, consider the following expression: 3 + 5 * 4.

Under chain mode, the solution is 32. (Obtained by first adding 5 to 3 to get 8, then multiplying 8 times 4).

Under algebraic mode, the solution is 23. (Obtained by multiplying 5 times 4, then adding 3).

I hesitate to give a recommendation with respect to mode of operations - you should use whatever makes sense for you. Personally, I can't see why anyone would use the chain mode unless that is the way their brain works - and if it works, I don't see a reason to change.

Most financial calculators default to the chain mode, whereas scientific calculators tend to default to the algebraic mode. All of the "allowed" calculators for your CIPM exams are financial, of course. Thus, given that (I think) most people tend to think and use in algebraic mode, you probably need to change your calculator's settings to get it to work the way you want it to on the exam.

Principles Level: Macro Attribution (risk-free rate)

I received an email from a candidate that requested a repeat explanation of the answer to a question from our recent CIPM Q&A webinar, and I thought the answer is worth sharing with everyone here, as I would hate to see candidates waste their time with this particular item.

The question:

Macro Attirbution – Risk Free – how do we come up w/ fund value of 187,944,879 or 575,474 if none of below #s multiplied by .31% give # $575,474????

Exhibit 1-6

Michigan Endowment for the Performing Arts

Monthly Performance Attribution

June 20xx

Decision-Making Level (Investment Alternative)	Fund Value	Incremental Return Contribution	Incremental Value Contribution
Beginning Value	$186,419,405	—	—
Net Contributions	187,369,405	0.00%	950,000
Risk-Free Asset	187,944,879	0.31%	575,474
Asset Category	194,217,537	3.36%	6,272,658
Benchmarks	194,720,526	0.27%	502,989
Investment Managers	194,746,106	0.01%	25,580
Allocation Effects	194,816,599	0.04%	70,494
Total Fund	194,816,599	3.99%	8,397,194

The answer is: you don't. Or, rather, you can't. The reading that CFA Institute provides does not give you adequate information to calculate their value metric for the "risk-free asset" decision.

I refer you to the footnote at the bottom of page 35 in the "Evaluating Portfolio Performance" reading. The footnote indicates that the value metric of $575,474 "cannot be replicated... because the $950,000 net contribution... was not a single, beginning-of-the-month cash flow."

In other words, there was more than external cash flow and some of them did not occur at the start of the month, thus they did not grow at the risk-free rate of 0.31% for the entire month. They do not, unfortunately, give you all of the details of the external cash flows - they simply give you the answer; i.e., the value metric for the risk-free rate decision.

In our prep class, for simplicity, the example and exercise we cover assumes all cash flows occur at the end of the month, which enables candidates to calculate the metric themselves (and, presumably, gives them some comfort level that they understand this particular item.

A follow-up question that is often asked in our classes is what should the candidate do if presented with a problem with cash flows that do not occur at the start of the month. My answer is that you should prorate the growth at the risk-free rate accordingly. For example, assuming a 30 day month, if a cash flow occurred at the end of the 10th day, then the cash flow would grow at the risk-free rate for 2/3 of the month.

Expert Level - Common Themes #1: Standard Deviation, Downside Deviation and Tracking Error

It may seem that the list of formulae to memorize for the CIPM Expert Level exam is quite long, but three of the risk measurement formulas are essentially three different applications of the same formula.

Expert level candidates are responsible for knowing the formulae for the following risk statistics:

• standard deviation
• downside deviation
• tracking error

Consider the formulae for each of these:
If you accept and understand that the standard deviation formula measures variability in an account's historical returns, then downside deviation and tracking error are variations of that idea:

• Downside deviation uses the same formula as standard deviation, except that it measures variability in the downside (i.e., losing returns). Losing returns are defined as those that fall below the pre-defined target return T. Thus, T replaces the average return in the standard deviation formula. The other modification to the formula is that any observations that are at or above the target return are treated as having a distance from the target of zero. We still divide by the total number of observations, N.
  

• Tracking error measures the variability of the historical excess returns. Thus, tracking error uses the same formula as standard deviation (because it is, in fact, a standard deviation), but we are using the excess return in each period rather than the account's return in each period as the input data.

Given this, candidates have a couple of different ways to approach these formulae:

1. You can memorize the individual formulae
2. You can memorize the formula for standard deviation, and learn the three different applications for it.

Every candidate learns differently, but I recommend the latter approach be used, as it will give you a more comprehensive understanding of the material.

Principles Level: After-Tax Performance???

Hopefully the mental strains of preparing for the CIPM Principles Exam ***and*** getting ready for the I.R.S. tax man on April 15th is not too much for the Principles candidates out there!

I have received a couple of questions lately regarding the CIPM Principles curriculum and what one needs to know with respect to after-tax performance.

This post should also clarify the discussion on after-tax performance during our webinar yesterday.

The following Learning Outcome Statements (LOS) were dropped from the CIPM curriculum, effective in the Spring 2010 exam window:

• Calculate anticipated tax rates
• Calculate pre-liquidation returns, including adjustments for nondiscretionary realized taxes
• Calculate the benefit of tax loss harvesting

Thus, calculation of after-tax returns is not required.

Having said that, the following LOS remain part of the curriculum (as part of Study Session II):

• Explain the major issues surrounding after-tax performance measurement
• Evaluate approaches to after-tax benchmark selection
• Compare and contrast the pre-liquidation and mark-to-liquidation methods for calculating after-tax performance

This change was announced to the CIPM Prep Providers back in November 2009, and the details can also be found at following link: https://www.cfainstitute.org/cipm/curriculum/curriculum_updates.html

Expert Level: Calculating the Sterling Ratio

One of the questions asked during yesterday’s webinar has to do with the calculation of the Sterling Ratio:

Hello,

Attached are the screenshots to the Example and Solution in the courseware that I was referring to, which seems to be using a different methodology than what the reading material (and John) described. I’m just wondering which methodology we should be using for the exam, since the two methodologies will yield vastly different results.

Thanks.

The Sterling Ratio is covered in the "Risk" study session at the Expert Level of the CIPM curriculum. The question raised is Exercise LOS 2I from the CFA Institute's interactive courseware. I am not at liberty to include the screen shots here, but I will describe how I arrive at the solution.

The formula for the Sterling Ratio is: CompoundAnnualizedRoR / abs(AverageYearlyMaximumDrawdown – 10%)

The Sterling Ratio may be calculated as follows:

1. Geometric linking of the first year’s monthly returns results in an annual return of
-18.00%.

2. Geometric linking of the second year’s monthly returns results in an annual return of 15.99%.

3. Geometric linking of the third year’s monthly returns results in an annual return of 12.00%.

4. Geometric linking of the three annual returns results in a cumulative return of 6.53%.

5. Annualizing the cumulative return over the 3 year period results in a return of 2.13%.

6. The maximum drawdown in year 1 occurs from the start of the year through month 8. Geometrically linking the returns over this timeframe gives a drawdown (D1) of 22.24% (note that the negative is implied).

7. The maximum drawdown in year 2 occurs in month 17, which is a drawdown (D2) of 2.56%.

8. The maximum drawdown in year 3 occurs over months 29 and 30; geometric linking of the returns over those months indicates a drawdown (D3) of 3.98.

9. By adding D1, D2 and D3 and dividing the sum by 3, we get an average annual drawdown of 9.59% (again, note that the negative is implied).

It is at this point that the exercise solution seems to be in conflict with the reading entitled “Measuring the Volatility of Hedge Fund Returns” by Douglas S. Rogers and Christopher J. Van Dyke. I quote the authors:

“The challenge with the Sterling ratio is that if the average yearly maximum drawdown for any of the managers analyzed is less than the arbitrary 10%, then the denominator becomes negative and comparison with other managers with positive denominators is meaningless.”

Keep in mind that we are dealing with drawdowns, which are, by nature, negative numbers. Any negative number would be less than the “arbitrary 10%.” Thus, the statement the authors make would be pointless, unless they are referring to the absolute value of the drawdown being less than 10%.

Given my interpretation, the next steps to take to obtain the Sterling Ratio would be:

10. The numerator of the Sterling ratio is the annualized return of 2.1323%, and the denominator is abs[abs(-9.59) minus 10.00] which is equal to 0.41%. Thus the Sterling Ratio is 2.1323 / 0.41 = 5.20.

The solution to the exercise, however, shows the answer the last steps as follows:

11. The numerator of the Sterling ratio is the annualized return of 2.1323%, and the denominator is abs[-9.59 minus 10.00] which is equal to 19.59%. Thus the Sterling Ratio is 2.1323 / 19.59 = 0.11.

Quite a bit of difference in the answers! I believe this is the discrepancy in methodology that the candidate is referring to.

I believe the correct approach is to do step 10 rather than step 11. But, having said that, I will check with a couple of sources and let everyone know what I find out!