## Sunday, April 3, 2011

### CIPM Expert Level - Sample Exam Solutions, #5 and #6

One of the students in my CIPM Expert Level Prep Classes asked me to explain the solution to the questions #5 and #6 from the sample exam questions found on the CFA Institute's CIPM Program page (). The vignette and questions 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.

5. The total return of the portfolio’s UK equities segment expressed in base currency (USD) is closest to:

A. –8.8%.

B. –5.1%.

C. –3.1%.

6. The portfolio’s total return, expressed in base currency, is the sum of the capital gain, yield, and currency components of return. In this framework, the capital gain component of the entire portfolio’s total return is closest to:

A. 0.00%.

B. 1.00%.

C. 2.42%.

Solution to #5: First important point is to realize that total return is equal to change in value plus period income, divided by beginning value. This is the holding period return that is referred to multiple times in the Expert Level curriculum:

HPR = (EMV - BMV - D) / BMV

where HPR is the holding period return, EMV is the ending value, BMV is the beginning value and D is the period income.

The starting value of the UK equities is 3,000,000 GBP, which converts to 6,000,000 USD at the beginning of period exchange rate of 1 GBP = 2 USD.

The ending value of the UK equities is 2,880,000 GBP for the stocks, plus the dividend income of 180,000 GBP, for a total of 3,060,000 GBP. This converts to 5,814,000 USD at the end of period exchange rate of 1 GBP = 1.9 USD.

Thus, the total return of the portfolio's UK equities is (5,814,000 - 6,000,000) / 6,000,000. This amounts to a return of -3.1%.

Solution to #6: For this problem, we are focused on the capital gain component of the portfolio's total return. Thus, we ignore the income that was earned (as well as the currency component of the total return), and focus on the equities.

At the start of the period, there are two positions, the UK equities and the CA equities:

- the value of 3,000,000 GBP converts to 6,000,000 USD at the exchange rate of 1 GBP = 2 USD.

- the value of 5,000,000 CAD converts to 4,000,000 USD at the exchange rate of 1 CAD = .8 USD.

Thus the starting value of portfolio is 6,000,000 + 4,000,000 = 10,000,000 USD.

At the end of the period:

- the value of 2,880,000 GBP converts to 5,760,000 USD at the exchange rate of 1 GBP = 2.0 USD.

- the value of 5,300,000 CAD converts to 4,240,000 USD at the exchange rate of 1 CAD = .8 USD.

Thus the ending value of the portfolio is 5,760,000 + 4,240,000 = 10,000,000 USD.

Given that the starting value of the portfolio equals the ending value of the portfolio, it should be straightforward that the total return is 0.00%.

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Note... I made a correction to this post. The math was correct, but the explanation for the solution to #6 had an error. The exchange rates used to convert the local market values to base currency at the end of the period should be the beginning of period exchange rates. This eliminates the currency return from occurring, in order to isolate the capital gain component of the return.

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