Information Technology Reference
In-Depth Information
2.
Let
denote the weight of the
-th variable. The total score of stock
at time
,
,
, can be defined as:
,
∑
,,
,
(2)
where
is the vector of the weights of the input features. Given the scores for all
stocks, the ranking of a stock can be defined as:
,
,
,
(3)
where
is a ranking function so that
,
∈N
is the ranking of stock
at time
,
and
,
,
if
,
,
.
3.
Use rankings from step 2 to select the top-ranked
stocks as components of a
portfolio. The performance of a portfolio can be evaluated by averaging the actual
returns of the stocks in the portfolio, which is defined as:
,
(4)
∑
,
where
,
is the
-th ranked stock at time
;
is the actual return for a stock at
time
and
is the average return over all the
stocks in the portfolio at time
.
4.
Use the following two objectives to evaluate the performance of a stock selection
model.
•
The cumulative total (compounded) return:
,
∏
(5)
, of the stocks in a
where
is defined as the product of the average yearly return,
portfolio over
consecutive years.
as the measure of risk:
•
The standard deviation of
∑
,
(6)
σ
∑
,
(7)
;
is the average return of all the
stocks
where
is defined as the mean of
in the portfolio at time
.
5.
With return and risk, use the non-dominated sorting and crowding distance [4] to
calculate the scores for all portfolios, in which the ranking of a portfolio can be de-
fined as:
if
or
,
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