= Harry Markowitz
{c}
<Harry Markowitz> developed <modern portfolio theory>, making the tradeoff between expected return and variability a mathematical allocation problem. His 1952 <Portfolio Selection by Harry Markowitz> emphasizes that the variability of a combination depends on relationships between its components, not just on each component considered alone.<Portfolio Selection by Harry Markowitz>[pp.79–82, expected return, covariance and portfolio variance]{ref}
For an original toy example, let two return <random variables> $X,Y$ each have <variance> one. Equal weighting gives
$$
\operatorname{Var}\!\left(\frac{X+Y}{2}\right)=\frac14\operatorname{Var}(X)+\frac14\operatorname{Var}(Y)+\frac12\operatorname{Cov}(X,Y).
$$
With zero <covariance> the result is $1/2$; with <covariance> one it is one. The calculation explains why counting assets alone does not determine diversification. <Expected values>, <covariance> estimates and allocation constraints supply distinct inputs to the optimization.
The 1990 economics prize recognized his theory of portfolio choice. The awarding academy's account identifies both the 1952 paper and his expanded 1959 treatment.<The Prize in Economic Sciences 1990 press release>[16 October 1990, Markowitz and portfolio selection]{ref}
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{title=<Harry Markowitz>}
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