We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. With asset prices undergoing a multiplicative random process , we derive approximate analytical results for the optimal investment fractions under various constraints . We show that , when returns and volatilities of the assets are small and borrowing is forbidden , the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. When short positions are also forbidden, only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is explored in detail.
We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns , we derive approximate analytical results for the optimal investment fractions in various settings . We show that when mean returns and volatilities of the assets are small and there is no risk-free asset , the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is explored in detail.
R
With asset prices undergoing a multiplicative random process
For lognormally distributed asset returns
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under various constraints
in various settings
R
, when
when mean
R
borrowing is forbidden
there is no risk-free asset
R
When short positions are also forbidden,
Since in the investigated case the Kelly approach forbids short positions and borrowing, often