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Portfolio Analytics

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Definitions

Portfolio Weights

As before, assume that the investor is able to invest in a riskless asset

and

risky assets

,...,

.
Definition. By investor’s discounted wealth we imply his/her wealth, measured in units of

.
Having at his disposal at time

the amount of discounted wealth

,the investor distributes his wealth among assets

,...,

according to proportions

,...,

. The above means that in

-th asset the
investor puts a share

of his total wealth, i.e. amount

Amounts

,...,

should satisfy the condition

,therefore for full determination of portfolio structure at time

it is sufficient to provide the amounts

,...,

only . Then

Definition. Vector

of dimension

refers to a vector of proportions or weights of a portfolio at time

.
Definition. Stochastic process

is a Portfolio Strategy.

Note. In general, SmartFolio operates with portfolio strategies, whose weights are constant in time. At the
time of writing the only exceptions are “Inaction Region” Portfolio Strategies, used when proportional
transaction costs are present in the market, and Portfolio Insurance Strategies, used to satisfy specific
constraints put on wealth dynamics. An economic ground for using portfolio strategies with constant weights
is given here.

It will be assumed further, that weights of portfolios are constant in time. Such portfolios will be associated with the vectors of weights

Types of Portfolio Weights Structures

Consider the portfolio

Long-Only Portfolio

Fully Invested Portfolio

or equally

Long-Only Fully Invested Portfolio

and

Zero-Invested Portfolio

or equally