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When combining two investment portfolios with high Sharpe Ratios, would the resulting portfolio also have a high Sharpe Ratio? How about combining two investment strategies

When combining two investment portfolios with high Sharpe Ratios, would the resulting portfolio also have a high Sharpe Ratio? How about combining two investment strategies with high information ratios relative to S&P500 benchmark? Would the resulting portfolio have a higher IR? Please use examples or derive carefully your explanation.

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