Question

Mr Runar Rikeman invests in US stocks. His home currency is the euro. In the beginning of a 15-year investment period, the direct foreign exchange quote against the US dollar was 1,02. The holding period return on the shares that were bought was 203,6 per cent in local US terms. In the end, the FX quote was 0,83. Compute the annualised rate of return in per cent from a euro point of view. Instructions: The answer is given in per cent using one decimal place. This means that a return of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign. Should there be intermediate steps in your calculations, please remember to keep a large number of decimal places in all intermediate calculations, as the final answer needs to be exact.

Answer 1

The annualized rate of return from Mr. Runar Rikeman's investment from a EUR perspective, after accounting for the local US return of 203.6% and the change in EUR/USD exchange rate from 1.02 to 0.83 over 15 years, is approximately 6.5%.

Step-by-step explanation:

To calculate the annualized rate of return from a EUR point of view, we take into account the holding period return (HPR) in local US terms and the change in the exchange rate. Given that the initial investment generated a 203.6% return in US terms, and the EUR/USD exchange rate changed from an initial rate of 1.02 to a final rate of 0.83, we first find the overall return in EUR terms by adjusting the USD return for changes in the foreign exchange rate. Subsequently, we annualize this return over the 15-year period.

The formula for computing the overall return in EUR terms is HPR_EUR = (1 + HPR_USD) × (End FX rate / Start FX rate) - 1. Using the provided numbers: HPR_EUR = (1 + 2.036) × (0.83 / 1.02) - 1 = 3.036 × 0.8137 - 1 ≈ 1.4704 or 147.04% total return in EUR terms over the 15 years.

To find the annualized rate of return in EUR terms, we use the formula: Annualized Return = (1 + Total Return)^(1/n) - 1, where 'n' is the number of years. Plugging the values in, we get: Annualized Return = (1 + 1.4704)^(1/15) - 1 ≈ 0.0652 or 6.52% when expressed as a percentage with one decimal place.