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

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 13% with a standard deviation of 18%. The correlation of the two stocks is 0.1. The risk-free rate is 10%.

You realize PFE is strictly more preferable than CAT due to higher expected return with lower risk and decide to get lazy on optimization. Say, you decide to allocate the vast majority of your risky portfolio in PFE and put just a little into CAT just to check the diversification box. You decide you want 90% PFE and 10% CAT for your risky portfolio and call it good. What is the Sharpe ratio of this portfolio?

Note: This question expects a number with 4 decimal points. Try to keep as many decimal points as possible for intermediate steps in your calculation and round to 4 only in the very end. Or use Excel to avoid the rounding issue altogether.