An Internal Rate of Return exercise...

A CIPM Expert Level candidate sent me the following question, asking what are the proper keystrokes to obtain the solution:

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?

First, I suggest that readers of this blog review my post from a few months ago suggesting a series of steps to solve internal rate of return problems. That post is here.

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 (TI BA II Plus calculator):

[CF][2nd][CLR WORK] Clears cash flow worksheet

-2225000[ENTER] Enters 2,225,000 as CF0

[down arrow] 0 [ENTER] Enters 0 as CF1

[down arrow] 3 [ENTER] The frequency of this flow is three times

[down arrow] -50000 [ENTER] Enters 50,000 as CF2

[down arrow] 1 [ENTER] The frequency of this flow is once

[down arrow] 0 [ENTER] Enters 0 as CF3

[down arrow] 1 [ENTER] The frequency of this flow is once

[down arrow] -40000 [ENTER] Enters 40,000 as CF4

[down arrow] 1 [ENTER] The frequency of this flow is once

[down arrow] 0 [ENTER] Enters 0 as CF5

[down arrow] 5 [ENTER] The frequency of this flow is five times

[down arrow] 2445000 [ENTER] Enters 2,445,000 as CF6

[down arrow] 1 [ENTER] The frequency of this flow is once

[IRR][CPT] 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%

Upcoming Webinar - Excel Tips & Tricks for Performance Professionals

Granted, CIPM candidates are not able to use Microsoft Excel during their examinations. But one of the points I make to candidates that attend our CIPM Exam Prep Classes is that I do strongly believe that Microsoft Excel (or a similar spreadsheet software product) can be used as a powerful study tool.

In today's world, we've seen more and more that people learn more when they have a tactile experience with their curriculum. Also, we are typically more accustomed to using spreadsheets to perform calculations than calculators. Thus, I encourage candidates to use spreadsheets during their study time for any calculations they are required to learn, especially in the areas of attribution and risk.

Thus, I want to mention that there is a great learning opportunity available to CIPM candidates (and performance professionals in general)! My colleague, Jed Schneider, CIPM, FRM will be conducting a webinar entitled Excel Tips and Tricks for Performance Professionals. Jed will be conducting the webcast along with another performance professional that I highly respect, Neil Riddles, CFA, CIPM.

We are seeing a very high number of people sign up for this event, and I believe it is one that candidates will not want to miss!

Carve-outs: the Possibilities for Periods after 1 Jan 2010

A CIPM Principles Level candidate emailed the following question to me:

I was wondering if you could answer this question for me:

For Session 8 Q&A 7 Composite definition, how can carve-outs, included in composites prior to January 1, 2010, without separately managed cash be included in the composites after January 1, 2010? Shouldn’t all carve-outs that don’t have separately managed cash be excluded including carve-outs with cash allocation starting January 1, 2010 even if they were in a composite before? Please clarify the sentence below:

“As a result some composites may include carve-outs (managed separately with their own cash balance) after 1 January 2010 and some may not.”

Perhaps the wording used in the curriculum is confusing here, but the statement is making the point that, for periods after 1 January 2010, some of a fim's composites may include carve-outs while other composites do not include carve-outs. Any carve-outs included in composites after 1 January 2010 must use cash actually managed cash for the carve-out.

Keep in mind that for periods starting on/after 1 Jan 2010, firms have the following options with respect to the use of carve-outs:

1) Stop using carve-outs: this would reduce composite assets going forward. Firms could continue to show carve-outs in their supplemental information, if desired. I'd recommend that if the firm goes with this approach, it is a significant event worthy of disclosure, in the context of GIPS provision 4.A.14.

2) Establish separate cash accounts: You would have cash accounts created for each asset class (e.g., for equities, fixed income, cash). Your accounting system would need to be able to direct cash into and out of each segment (e.g., for purchases, sales, income), appropriate to that asset class. Additionally, any account-level contributions / withdrawals will need to be allocated to these separate cash accounts.

3) Establish separate sub-accounts: If your accounting system will allow it, simply” create separate sub-accounts for each asset class. The accounting system would need to properly handle all cash movements into and out of these separate cash accounts (for trades, income). You would also need to handle allocation of external flows, and reconciliation may be a challenge.

4) Establish separate accounts: Most portfolio accounting systems should be able handle this approach. The accounting system would need to properly handle all cash movements into and out of these separate cash accounts (for trades, income). You would need to handle allocation of external flows. Reconciliation may be a challenge - the custodian wouldn't necessarily match your account level details. An ability to consolidate accounts would be needed. Client reporting might be impacted.

5) Stop complying with GIPS: this is definitely not a desirable or intended option for firms to take. But, a possibility!

Options are Physical Securities!

There are several ways that options differ from futures contracts. One of those ways in which they differ is that options are securities that must be acquired in exchange for physical cash. By contrast, in acquiring a futures contract position, one does not need to pay cash - they only obligate themselves to ultimately pay the cash value of the futures position at contract expiration.

Options contracts may be exchange listed or over-the-counter (OTC) - but in either case, they trade at some price. The cost basis of the option contract must then be deducted from physical cash at the time option positions are acquired. This is an important point to keep in mind when dealing with options at the CIPM Expert Level - your return calculations will not be correct unless you remember to reduce portfolio cash by the cost basis of the options traded.

Actual vs. Model Investment Management Fees

A CIPM candidate emailed me a question today regarding one of the exercises found in the Principles Level, in the interactive portion of the curriculum materials. This question is found in Study Session VII and is question 10:

Langerton Asset Management has complete historical information about the fees
incurred by the portfolios in the domestic large cap equity composite. Langerton
recently increased its investment management fees. To calculate net-of-fees composite
returns, Langerton must reduce the domestic large cap equity composite's gross-offees
returns by the:

a) highest investment management fee in the current fee schedule
b) actual investment management fees incurred by the portfolios in the composite
c) highest investment management fee incurred in each period by the portfolios in the composite

The exercise indicates to select the "best" answer.

The answer is b). But why?

Here is my interpretation:

- They indicated to select the "best" answer. This is an acknowledgment that more than one answer could be correct. It is also an indication that if more than one answer is correct, in the opinion of the question writers, one of the correct answers is more valid (i.e., better) than the rest of the correct answers.

- GIPS allows compliant firms to calculate net-of-fees performance in a couple of different ways: you may reduce the gross-of-fees return by actual management fees or, alternatively, you may reduce the gross-of-fees return by model management fees.

Unfortunately, there is no guidance at this time that explains what a model management fee is. Whenever the question of what is meant by model management fee is asked of me, I say the safest thing is to use the highest management fee.

Given this, either a) or c) could be correct answers, in my opinion. Both answers provide a means of calculating a model management fee.

Having said all of this, I think it is fair to say that GIPS does not indicate a preference for the use of actual management fees over model management fees. Thus it could seem that either approach is fine and equally valid. But, my interpretation here is that they expect candidates to understand that actual performance is better than estimated performance, and the use of model management fees is more of an estimate of performance results than the use of actual management fees. Thus, b) is the best answer, because it provides for a net-of-fees return that is the best representation of the actual net-of-fees return for the composite in question.

I welcome other interpretations on this, so please feel free to comment.

CIPM Expert Level - Sample Exam Solution #7

One of the participants in last week's webinar on CIPM Q & A asked me to explain the solution to the question #7 from the sample exam questions found on the CFA Institute's CIPM Program page (). The vignette and question follow below:


Longitudinal Asset Management is a US-based portfolio manager investing in international equities. One of the firm’s portfolios is invested entirely in Canadian and United Kingdom equities. At the beginning of an evaluation period, the market values of the portfolio’s Canadian and UK segments are 5,000,000 Canadian dollars (CAD) and 3,000,000 pounds sterling (GBP), respectively. At the prevailing exchange rates, one CAD equals 0.80 US dollars (USD), and one GBP equals 2.00 USD.
Excluding dividend income, at the end of the period the Canadian equities are valued at CAD 5,300,000 and the UK equities are valued at GBP 2,880,000. The CAD now equals 0.90 USD while the GBP now equals 1.90 USD. Dividend payments of CAD 100,000 and GBP 180,000, respectively, are received at the prevailing exchange rates on the last day of the period.

7. The currency component of the Canadian equities segment return in USD is closest to
A. 9.0%
B. 12.5%%.
C. 13.5%.


The relationship that you should understand to solve this question is that currency return is not simply the exchange rate return. Rather, exchange rate return compounds the local return components (capital yield and income yield). That is,

c = s * (1 + p + y)

where c is the currency return, s is the exchange rate return, p is the price return in local currency terms (i.e., the capital return) and y is the income return.

The exchange rate return is (0.9 - 0.8) / (0.8) = .125.

The capital return is (5,300,000 - 5,000,000) / 5,000,000 = 6% = .06.

The income return is 100,000 / 5,000,000 = 2% = .02.

Thus the currency component of the Canadian equities segment return is:

.125 * (1 + .06 + .02) = 13.5%

Steps for calculating IRR

The following steps may be used to calculate internal rate of return using one of the financial calculators (HP 12C and TI BA II Plus):

1. Identify all external cash flows, including beginning and ending market values, and arrange them in chronological order.

2. Arrange the cash flows so that they are evenly spaced with respect to time. The financial calculators expect cash flows to occur at a regular frequency, so the cash flows entered must be evenly spaced, with zero cash flows used to fill in any missing data. I will describe how this can be done below.

3. Create the present value equation, equating the sum of the present value of outflows (beginning market value and any contributions) with the sum of the present value of in-flows (ending market values, and any withdrawals). I recommend ordering cash flows on each side of the equation in chronological order, from the first through to the last.

4. Identify simultaneously occurring cash flows. These are cash flows that occur on the same date, including both outflows and in-flows. These will be netted for purposes of entry into the financial calculator.

5. Using the appropriate keystrokes, enter the cash flows into the financial calculator’s cash flow worksheet, and compute the IRR.

6. The solution obtained in step 5 will be an internal rate of return for the interval of the cash flow spacing (step 2). Using exponents, convert the internal rate of return to a return for the desired period.