An Internal Rate of Return exercise - HP 12C keystrokes

In a previous post, I covered an internal rate of return sample exam question, and I covered the keystrokes used on one of the calculators that may be used on the CIPM exam, the Texas Instruments Business Analyst II Plus (TI-BA II Plus).

There is, of course, another financial calculator that CIPM candidates may use on the exams, and that is the Hewlett Packard 12C.  In this post, I will cover the keystrokes to do the exercise on the HP 12C.

Recall the particulars of the exercise:

The Millers deposited $50,000 into their account on 1 May 2005 and another $40,000 on 1 July 2005. The portfolio also received and reinvested dividends of $30,000 on 1 July, plus another $30,000 on 31 December. The Miller's investment adviser, Greenbush Investments, uses a daily pricing system that shows account values (inclusive of dividends and contributions) of $2,375,000 and $2,460,000 on 1 May and 1 July, respectively. The account was valued at $2,225,000 on 1 January 2005 and at $2,445,000 on 31 December 2005.  

What is the annual internal rate of return?

I also remind candidates that I covered the steps to calculating internal rate of return in this previous blog post.

Next, we should identify the important information in this problem; i.e., the cash flows that must be entered into the calculator - and those that should be ignored. The important cash flows are:

• the initial market value of $2,225,000 on 1/1/2005
• the contribution of $50,000 on 5/1/2005
• the contribution of $40,000 on 7/1/2005
• the ending market value of $2,445,000 on 12/31/2005

You can ignore the dividends that are described because they are "reinvested" - this means they remain in the portfolio and are not an external cash flow. If they were "not reinvested," that would mean that they should be treated as withdrawals at the time of payment... but that is not the case here.

You can also ignore the other valuations that are given. With internal rate of return calculations, only the initial value and the ending value are needed.

In order to enter this into your financial calculator, you will need to evenly space the cash flows (in time) and "zero fill" the empty periods. In this problem, you can assume monthly occurring cash flows if you treat the initial market value as being for 12/31/2004, and the contributions as occurring on 4/30/2005 and 6/30/2005 (rather than 5/1/2005 and 7/1/2005).

The "zero filled" cash flows will be on the following dates: 1/31, 2/28, 3/31, 7/31, 8/31, 9/30, 10/31 and 11/30.

Thus, the following keystrokes may be used on the HP 12C calculator: 

[f] CLEAR [REG]                     (clears the registry)

2225000 [CHS] [g] [CF0]         (enters -2,225,000 as CF0)

0  [g] [CFj]                                (enters 0 as CF1)                        

3  [g] [Nj]                                  (indicates that CF1 occurs three times)

50000 [CHS] [g] [CFj]              (enters -50,000 as CF2)

0 [g] [CFj]                                 (enters 0 as CF3)

40000 [CHS] [g] [CFj]             (enters -40,000 as CF4)

0  [g] [CFj]                               (enters 0 as CF5)                        

5  [g] [Nj]                                 (indicates that CF5 occurs five times)

2445000 [g] [CFj]                    (enters 2,445,000 as CF6)

[f] [IRR]                                   (computes the IRR)

At this point, the calculator should tell you the solution is 0.4636%. But, this is a monthly return, because the spacing of our cash flows was monthly. We now need to convert this to an annual return. To do this, do the following steps:

• divide by 100 (converting the percentage to a decimal)
• add 1 (creating a wealth relative)
• raise the result of the last step to the 12th power
• subtract 1
• multiply by 100

This should give you an annual return of 5.70%

Happy studying!

Will You Join the Superheroes of Performance Measurement?

 

Read all about the Superheroes of Performance Measurement here!

(and yes, that's me on the left!)

CIPM Open Question/Answer Session... Tomorrow!

Tomorrow, I will be hosting an open Q & A (question and answer) session for CIPM candidates.  This is a chance for you to ask questions as you are (hopefully) doing your final studying for October's exams!  The session is open to both Principles Level and Expert Level candidates.  No format, other than YOUR questions and MY answers!

To join the webcast, please follow this link!

Also, prior webcasts are available for purchase on The Spaulding Group's website.  You can purchase the webcast from Fall 2011 and Spring 2012 by following the links in this sentence.  As each session has different questions, they may all be of interest to candidates.


Happy studying!

Loyalty Only Goes So Far...

There was good news in the media this morning, as the United States Internal Revenue Service (IRS) awarded a former UBS employee in the amount of $104 million USD for "whistle-blowing" regarding activities at UBS that assisted some of the firm's clients in hiding assets from the IRS.  The $104 million USD reward is reputed to be the largest ever given for whistle-blowing.

This announcement comes on the heels of the SEC issuing its first ever whistle-blowing award (a much smaller sum of $50,000 USD) to someone who helped stop "multi-million dollar fraud" from occurring.

I am reminded when I read these stories of Provision IV.A of the Standards of Professional Conduct, which CIPM candidates are required to know and interpret as part of the ethics component of the CIPM Curriculum.  This provision reads:

In matters related to their employment, Members and Candidates must act for the benefit of their employer and not deprive their employer of the advantage of their skills and abilities, divulge confidential information, or otherwise cause harm to their employer.

It is important to understand that loyalty only goes so far - as covered persons (those bound by the CIPM Code of Ethics and Standards of Professional Conduct), we are not required to put our employer's interest beyond our own in all situations.  Two key situations are mentioned in the readings place limitations on loyalty.  One deals specifically with whistleblowing, and the other deals with personal interests.

With respect to whistleblowing, from page 143 in the CIPM Principles VitalBookshelf readings:

• Whistleblowing. A member’s or candidate’s personal interests, as well as the interests of his or her employer, are secondary to protecting the integrity of capital markets and the interests of clients. Therefore, circumstances may arise (e.g., when an employer is engaged in illegal or unethical activity) in which members and candidates must act contrary to their employer’s interests in order to comply with their duties to the market and clients. In such instances, activities that would normally violate a member’s or candidate’s duty to his or her employer (such as contradicting employer instructions, violating certain policies and procedures, or preserving a record by copying employer records) may be justified. Such action would be permitted only if the intent is clearly aimed at protecting clients or the integrity of the market, not for personal gain.

The picture above shows Marlon Brando in "The Godfather" film - certainly, he commanded a high level of loyalty by persons under his watch.  It may seem with companies of the stature of UBS and similar firms that the loyalty they "encourage" is similarly intimidating.  But the Code and Standards call upon us as performance professionals to do what is ethically correct - and whistleblowing may be necessary in some scenarios, in order to do what is ethically correct.

On the other point, personal interests, from page 141 in the CIPM Principles VitalBookshelf readings:

• This standard is not meant to be a blanket requirement to place employer interests ahead of personal interests in all matters. The standard does not require members and candidates to subordinate important personal and family obligations to their work. Members and candidates should enter into a dialogue with their employer about balancing personal and employment obligations when personal matters may interfere with their work on a regular or significant basis.

Happy studying!

GIPS and return calculations: TWR vs. IRR - When Do We Use Each?

CIPM Expert Level candidates must know what return calculations are required by the Global Investment Performance Standards (GIPS(r)), and in which circumstances. 

Most of the time, time-weighted return (TWR) is required, but in some cases a since inception internal rate of return (SI-IRR) must be used. 

But what are the specifics?  Here is a breakdown:

• Generally speaking, i.e., if the real estate provisions of GIPS and the private equity provisions of GIPS do not apply (sections I.6 and I.7, respectively), then time-weighted returns are required by GIPS provision I.2.A.2.
• Total returns (i.e., that include gain/loss and income/expense) must be used (provision I.2.A.1).
• Either gross-of-fees or net-of-fees may be used, as long as clearly labelled (provision I.5.A.1.b).
• Gross is recommended (provision I.5.B.1).

• If the private equity provisions of GIPS (section I.7) apply, then since-inception internal rate of return is required (provision I.7.A.3).
• Total returns (i.e., that include gain/loss and income/expense) must be used (provision I.2.A.1).
• Both gross-of-fees and net-of-fees must be presented (provision I.7.A.21).

• If the real estate provisions of GIPS apply (section I.6), then time-weighted returns are required (provision I.2.A.2).
• In addition to total returns (which reflect gain/loss and income/expense) required by provision I.2.A.1), component returns must be presented (provision I.6.A.9).  Component returns are the capital return (gain/loss) and the income return (income/expense).
• Either gross-of-fees or net-of-fees may be used, as long as clearly labelled (provision I.6.A.14).

• If the composite in question is a closed-end real estate composite, then both time-weighted returns and since inception internal rates of return must be presented.
• For closed-end real estate composites,  with respect to time-weighted returns, the general requirements for real-estate composites must be met; i.e., calculation of total return, capital return and income return, which may be shown either gross- or net-of-fees (provisions I.2.A.2, I.2.A.1, I.6.A.9 and I.6.A.14).
• Firms must present the net-of-fees since-inception internal rate of return (provision I.6.A.23).
• If the firm shows gross-of-fees since inception internal rate of return, it must be shown for the same periods ;for which the net-of-fees SI-IRR is presented.

So, as you can see, it can become a bit involved when trying to determine whether to use TWR or SI-IRR, what is required vs. what is recommended, and is it a net- or gross-of-fees return that should or must be used.  The above bullets should spell out all of the scenarios.

Hope this helps!

Campisi Fixed Income Attribution - Price Contribution Explained

The CIPM curriculum does not give much of an explanation of bond pricing in relation to interest rates, so here is a brief primer.

Price change on bonds can be explained by how interest rates change during the period.

Bonds are a lending agreement:  the purchaser is the lender, and the issuer of the bond is the borrower.  The coupon rate on the bond is the interest rate on the loan. 

When interest rates rise over an evaluation period, that means that the cost of borrowing for bond issuers has increased.  But it also means that newly issued bonds are more attractive to investors than existing bonds of the same time to maturity.  Because existing bonds are less attractive due to rising interest rates, their price drops, making their market value drop over the period - which resullts in a negative rate of return.

Conversely, if interest rates drop over an evaluation period, existing bonds look more attractive, making their price rise, thus their market value increases and they have a positive rate of return over the period. 

That is the inverse relationship between bonds and interest rates.  When rates rise, bond prices drop, and vice versa.

The Treasury (or risk-free) yield curve is the basis for bond prices.  On the X-axis is time to maturity, and on the Y-axis are the interest rates.  Thus, the combination of interest rates at various times-to-maturity create a curve.  Thus, how the yield curve changes over the period of evaluation gives us information we can use to approximate price change due to changes in interest rates.

Price change can be approximated by the following equation:

Thus, the portion of return that is due to price change over the evaluation period is equal to the change in interest rates over the period  multiplied by the negative of duration.  Or, said differently, we need to know the price change for a given bond or set of bonds.  Let's say we are talking Treasury bonds (i.e., risk free bonds).  That price change corresponds to how much interest rates changed during the period for a particular point on the risk-free yield curve that is equal to the duration of the bond in question.  For Treasury bonds of a given duration, how much did interest rates change during the period (i.e, from the start of the period T, to the end of the period T+1).

The yield curve could change over the period in different ways.  When there is a parallel shift in the yield curve, interest rates change by the same amount over the evaluation period at all points on the yield curve (i.e., at all time-to-maturity/duration points)

Or, there may be some sort of structural change in the yield curve over the evaluation period where the change in interest rates is different at one time-to-maturity or duration compared to at other times-to-maturity or duration:

Thus, if we know how much interest rates changed over the evaluation period for a particular time-to-maturity or duration, we can quantify how much return occurred for bonds of that duration that corresponds to that change in interest rates.

If we are talking about a class of bonds or a portfolio of bonds, we can use the market value weighted average of the durations of the individual bonds in the class or portfolio, and use the change in interest rates that corresponds to that.

In a subsequent blog post, we'll apply this concept in the Campisi model for attribution.

Happy studying!

Sample Rate of Return Exercise - Cash Flow Timing

A Principles Level candidate emailed me the following problem, and asked me about how to interpret the timing of the cash flows:

In this case, given that they tell you that the fair valuations are inclusive of the flows, my interpretation would be that the timing of cash flows is end of day.  Thus, your sub-period returns would be based on this assumption as follows:

 

The first sub-period return is:

The second sub-period return is:

The third sub-period return is: 

The return for the month is then the geometrically linked sub-period returns:

(1+1.8182%)*(1+6.40%)*(1+7.6923%) – 1 = 16.67%.

Note:  in previous years, there was a Learning Outcome Statement that explicitly required candidates to know how to calculate sub-period returns when cash flows were at the start or end of the period.  In this exam window, the Learning Outcome Statements have been rephrased, so this is no longer explicitly stated, BUT, your reading still contains the discussion that covers these scenarios (see page 257) and this is a normal dilemma faced by performance analysts on an on-going basis.  Return calculations will be different depending on whether cash flows are assumed to be at the start or end (or during) an evaluation period.  Performance analysts must be able to interpret the data accordingly and calculate returns.

In an upcoming blog post, I will cover this subject in greater detail.

Happy studying!

Campisi Fixed Income Attribution - Income Contribution Explained

Recall from my previous posting, the steps to executing the Campisi fixed income attribution model are:

1. Decompose the benchmark return into:
   - income contribution
   - Treasury contribution (i.e., price change due to changes in Treasury rates)
   - spread contribution (i.e., price change due to changes in the average spreads of a risky bond class
    
2. Decompose the index portfolio return into:
   - income contribution
   - Treasury contribution (i.e., price change due to changes in Treasury rates)
   - spread contribution (i.e., price change due to changes in the average spreads of a risky bond class
3. Calculate the index portfolio spread change.  This is the change in interest rates that will be used to calculate the spread contribution of the portfolio (more on this in a subsequent blog post).
4. Decompose the portfolio return into:
   - income contribution
   - Treasury contribution (i.e., price change due to changes in Treasury rates)
   - spread contribution (i.e., price change due to changes in the average spreads of a risky bond class
   - security specific contribution
5. Calculate the attribution effects as the value added contributions:
   - income effect = portfolio income contribution minus the benchmark income contribution
   - Treasury effect = portfolio Treasury contribution minus the benchmark Treasury contribution
   - spread effect = portfolio spread contribution minus the benchmark spread contribution
   - selection effect = portfolio selection contribution (note - the benchmark has no selection contribution)

The first step under items 1, 2 and 4 above are to calculate an income contribution (for the benchmark, index portfolio and portfolio, respectively).

The income contribution is how much of the return comes from the income paid by the bonds in the portfolio or benchmark.  We express this income contribution as a rate of return, which has a numerator and a denominator.  The formula for this contribution is simply:

For example, in your reading, the portfolio's weighted average coupon is 7.118% and the  portfolio's weighted average price is 98.1.  Thus, the contribution of income to the total return of the portfoli may be calculated as:

To say it differently, out of the portfolio return of 0.31%, the portion that comes from income is the weighted average coupon divided by the weighted average price which is 7.26% in total.  Thus, obviously the sum of the other contributions must be negative.

The income contribution can also be calculated from money amounts:

Essentially, the income contribution is a form of current yield, comparing interest earned by the manager's portfolio to the market value invested to earn that income. 

Given, then, that the portfolio return may be decomposed into income and price change, we have decomposed the income portion of the return.  All remaining elements are part of the price change component.  We'll tackle that subject next!

Happy studying!

Correction to Exercise on Sample Exam (Principles Level)

Last week, when I was teaching The Spaulding Group's CIPM Exam prep class for the Principles Level, a student asked me for help with a question on a sample exam from CFA Institute.  The question read:

Which of the following is most likely not a requirement of the GIPS standards for Presentation and Reporting?

a.       Annualizing returns for periods of less than one year.

b.      Presenting the total return for the benchmark for each annual period.

c.       Presenting the percentage of composite assets represented by non-fee-paying portfolios.

The sample exam stated that “b” was the correct answer, and the explanation states that the answer choice of “b” is not a requirement.

I indicated to the class that this appeared to be an error, as presenting the total return for the benchmark as of the end of each annual period is definitely required by GIPS provision I.5.A.1.e.   It seemed to me that the choice of "a" was the correct answer as we must never annualize returns of less than a year (GIPS I.5.A.4).

I later learned that the candidate that asked the question had a copy of an old sample exam, and that the question had been reworded as follows on the most recent copy of the sample exam:

           Which of the following is most likely a requirement of the GIPS standards for Presentation

           and Reporting?

          A.      Annualizing returns for periods of less than one year.

          B.      Presenting the total return for the benchmark for each annual period.

          C.      Presenting the percentage of composite assets represented by non-fee-paying portfolios.

This time, the answer key indicated that "C" was the correct response.   While it is true that item "C" is a requirement, it is also true that item "B" is a requirement, based on GIPS provision I.5.A.1.e, as I indicated above.

To end this long story, I contacted CFA Institute, and they indicated that this is indeed an error, which will be corrected.    Thus, I wanted to pass this on to candidates who may have been perplexed by this question.  And if you are a Principles Level candidate and were perplexed by the question, don't feel bad... I passed this by my Expert Level class students last week, and an interesting debate ensued with views all over the map.  So, sometimes this stuff is not so easy!