Problem: Selecting assets to meet a desired return at minimum variance.
(In the March, 1952, issue of Journal of
Finance, Harry M. Markowitz published an article called "Portfolio Selection".
In it, he demonstrated how to reduce the standard deviation of returns on asset portfolios
by selecting assets which don't move in exactly the same ways. At the same time, he laid
down some basic principles for establishing an advantageous relationship between risk and
return, and his work is still in use forty years later.)
From the historical data, you have calculated an expected return, the variance of the
return rate, and the covariance of the return between the different assets. Variance is a
measure of the fluctuation in the return - the higher the variance, the riskier the
investment. The covariance is a measure of the correlation of return fluctuations of one
stock with the fluctuations of another. High covariance indicates that an increase in one
stock's return is likely to correspond to an increase in the other. A low covariance means
the return rates are relatively independent and a negative covariance means that an
increase in one stock's return is likely to correspond to a decrease in the other.
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