Portfolio optimization involves three steps: asset allocation, security selection, and capital allocation. This question is about security selection. This question has two parts.

Part A: To simply the matter, assume your investable universe is two stocks, Pfizer (PFE) and Caterpillar (CAT), and a risk-free asset. PFE has an expected return of 15% with a standard deviation of 15%. CAT has an expected return of 12.5% with a standard deviation of 18%. The correlation of the two stocks is 0.1. The risk-free rate is 10%.

After you created the 90/10 risky portfolio, your manager looked at it and realize you didn't do your homework. So she asks you to seriously go through the mathematical steps in portfolio optimization. You did your homework this time following all the correct steps in finding the optimal weights. What is the optimal weights for PFE? Express it in % terms with 2 decimal points.

Part B:

To simply the matter, assume your investable universe is two stocks, Pfizer (PFE) and Caterpillar (CAT), and a risk-free asset. PFE has an expected return of 15% with a standard deviation of 15%. CAT has an expected return of 12.5% with a standard deviation of 18%. The correlation of the two stocks is 0.1. The risk-free rate is 10%.

After you find the optimal portfolio, you wonder whether all that effort is worth it. So you decide to check the Sharpe ratio of the newly created optimal portfolio. What is the Sharpe ratio? (Four decimal points)