The standard deviation of return to the Indian stock market is 24.8% in local currency. The standard deviation of the Indian rupee against the Canadian dollar is 30.2%. Ignoring interactions between the Indian stock market and the value of the Indian rupee, what is the standard deviation of return of the Indian market to a Canadian investor?

Question

Quizplus · Accepted Answer

To calculate the standard deviation of the Indian market to a Canadian investor, we need to use the concept of covariance. 
Covariance = correlation coefficient * standard deviation of market * standard deviation of exchange rate
Since there is no information about the correlation coefficient, we assume it to be zero as there are no interactions between the Indian stock market and the value of the Indian rupee. 
Therefore, 
Covariance = 0 * 24.8% * 30.2% = 0 
Now, using the formula of total variance, 
Total variance = variance of market + variance due to exchange rate 
Variance due to exchange rate = (standard deviation of exchange rate)^2
Variance of market = (standard deviation of return to Canadian investors)^2
Therefore, 
(standard deviation of return to Canadian investors)^2 = (standard deviation of market)^2 + (standard deviation of exchange rate)^2 - 2 * covariance 
= (24.8%)^2 + (30.2%)^2 - 2 * 0 
= 0.153 
Standard deviation of return to Canadian investors = sqrt(0.153) = 0.391

The Standard Deviation of Return to the Indian Stock Market