## Saturday, April 7, 2012

### Expert Level Sample Exam Question #6, revisited In a previous blog post, I covered the answers to two CIPM Expert Level sample exam questions, specifically, #5 and #6.  One current Expert Level candidate asked me to elaborate on the answer, asking which formula(e) in the curriculum could be used to obtain the answer.

I would say that the solution here does not relate directly to any specific single formula in the reading; rather, it relates to the relationships in the diagram on page 101 of your Virtual Bookshelf materials, and extending the concepts you have learned.

Recall the vignette that goes with these exercises reads as follows:

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.

Question #6 reads as follows:

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%.

Apologies for using different notation from your courseware, but Google blogspot does not cleanly support the use of superscripts and subscripts.

My notation here is as follows:

• Local market value at the start of the period is V(0).
• Local market value at the end of the period is V(1).
• Converted market value at the start of the period is V(0)*S(0).
• Converted market value at the start of the period is V(1)*S(1).
When investors buy foreign assets, they are exposed to two sources of return:

• Change in value of the asset in local currency; i.e, V(1) – V(0).
• Change in value of the foreign currency; i.e., S(1) – S(0).

Investors are also exposed to the compounding of these two sources of return:
[V(1) - V(0)]*[S(1) - S(0)].

If we want to examine the return due to the change in value of the asset in local currency, but in terms of the base currency, we assume the exchange rate during the period does not change (i.e., assume it remains fixed at S(0)), and apply that exchange rate to the change in value in local currency:
S(0)*[V(1) – V(0)] = S(0)*V(1) – S(0)*V(0).

So, back to my solution to item #6, at the start of the period and at the end of the period, there are two positions, the UK equities and the CA equities.  Assuming the exchange rate during the period stays fixed at S(0), the calculation of the base currency value at the end of the period (i.e., S(0)*V(1)) is obtained as follows:

• 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.

And, the calculation of the base currency value at the start of the period (i.e., S(0)*V(0)) is obtained as follows:

• 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.

Given the base currency amount is the same at the start and end of the period (assuming the spot exchange rate did not change), then the amount earned due to this is a total of 10,000,000 USD – 10,000,000 USD = 0 USD.  The solution asks for a return, so you could determine the denominator to divide by, but given that the denominator is 0 USD, you don’t need to bother – the return is 0.00%.

(Note, the correct denominator would be the 10,000,000 USD at the start of the period, based on the formula S(0)*V(0)).