The Japanese Stock Market Has a Sigma of 18%, When

question 8

Essay

The Japanese stock market has a sigma of 18%, when computed in yen. The U.S. stock market has a sigma of 17% in US$ and the US$/¥ exchange rate has a sigma of 6%. The correlation between the Japanese stock market and $/¥ currency movements is -0.1; in other words, the Japanese stock market tends to go up when the yen goes down. The correlation between the Japanese and U.S.
stock markets is equal to 0.4, measured either in local currency of in dollars.
a. What is the sigma of the Japanese market when expressed in dollars?
b. Using this number, calculate the sigma, in dollars, of a portfolio made up of 50% of Japanese stocks and 50% of U.S. stocks.

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Definitions:

Test-Retest Reliability

The consistency of an individual's scores on a test administered at two different times, used to assess the reliability of the test.

T-Scores

Standardized scores with a mean of 50 and a standard deviation of 10, used to compare individual scores across different tests.

Self-Actualizing Values

Values that prioritize personal growth, fulfillment, and achieving one's potential, reflecting the top of Maslow's hierarchy of needs.

Percentiles

A method of comparing raw scores to a norm group by calculating the percentage of people falling below an obtained score, with ranges from 1 to 99, and 50 being the mean.