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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 500 Index. Your investment advisor recommends you sell all of the gold position and replace it with a similar sized positioning bitcoin. You gather the following data: S&P 500 Gold Bitcoin
Historical Annual Return: 12% 7% 50%
Historical Annualized Volatility: 20% 15% 80%
Return Correlation of Gold to the S&P 500 Index: 15%
Return Correlation of Bitcoin to the S&P 500 Index: 30%
Risk Free Rate: 1%
(i) Assuming this historical data is the best predictor of future outcomes, is your advisor's recommendation sound?
(ii) Assuming all of the other assumptions remained unchanged, and ignoring any coefficient of risk aversion considerations, at what level of correlation between bitcoin and the S&P 500 would you be indifferent between choosing to retain your current portfolio and substituting it for the new portfolio?
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