Reference no: EM133073650

You currently own a portfolio comprised of U.S. equities (90%) and gold (10%). The U.S. equity allocation is invested passively in the S&P 500Index. You expect these assets have the following characteristics:

Annual Return Annualized Volatility

S&P 500 Index 10% 20% Gold 6% 14%

Return correction of S&P 500 Index and gold: 10%

Risk free rate: 2%

You are considering reducing portions of your gold and U.S. equities allocations allocations and adding bitcoin to your portfolio. You expect bitcoin will return 30% p.a., but with a annualized volatility of 60%. You estimate the following correlations:

Correlation of U.S. equities to bitcoin: 40%

Correlation of gold to bitcoin: 50%

Correlation of a 50/50 basket of gold and bitcoin to U.S. equities: 25%

(i) You decide to reposition your portfolio to 85% U.S. equities, 7.5% gold, and 7.5% bitcoin. Is that idea advisable? [Hint: Begin by constructing and analyzing a "miniportfolio" that is 50% gold and 50% bitcoin]

(ii) You decide to recast your portfolio with the 85% equities, 7.5% gold, and 7.5% bitcoin allocation, but you want this new portfolio to have the same expected volatility as your original portfolio. You believe you can either invest in T-Bills or borrow them at the same rate, which is 2%. How would you adjust your portfolio to bring its expected volatility back to the expected volatility of your original portfolio? What would be the new asset allocations in your portfolio?

(iii) What is the expected return and Sharpe ratio of the portfolio in your answer to part (ii) immediately above?