A financial scientist studying the effect of different

A financial scientist studying the effect of different strategies has serious concerns about the use of historical data for back-testing and thus prefers to test strategies using new data from the market as it becomes available. To reduce the lead time, multiple strategies were followed for 10 months and tested simultaneously using a two-way ANOVA. One set of treatments relates to risk-reduction strategies and the other focused on maximizing returns. One portfolio followed an index tracking strategy to provide a baseline against which to assess the others. Each portfolio’s Sharpe ratio [(Returni – risk-free rate) / volatility] was calculated to provide a standard metric for assessment. Results of this test appear below:

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Risk-reduction strategies

146.5679

9

16.28532

0.799124

0.617328

1.905914

Return-enhancing strategies

870.2418

3

290.0806

14.23431

8.72E-09

2.629707

Interaction

726.4466

27

26.90543

1.320255

0.135013

1.516813

Within

7336.427

360

20.37897


What follow up steps are necessary to determine which (if any) of the return-enhancing strategies worked? What technique could you use to reduce the probability of committing a type 1 error when determining which (if any) offer a higher Sharpe ratio?


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