Consider the expected returns and standard deviations below for a 20 US Treasury Bond ETF and an ETF based on near-dated bitcoin futures. The correlation coefficient of returns between these securities is -.2. Assume the risk-free rate is zero.

Market. Expected Return. Standard Deviation

UST 8%. 8%

BITC 25.5%. 32%

Build an investment opportunity set using portfolio weights of 10% increments of each security.

1. What is the Sharpe ratio of the optimum portfolio ?

2. What is the expected return on a portfolio of equality weighted holdings of each security ?

3. What is the standard deviation of a portfolio that holds 70% of the Bitcoin ETF?