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Your investment portfolio consists of $$15,000$ invested in only one stock$$Microsoft$.$ Suppose the risk$-$free rate is $5\%,$ Microsoft stock has an expected return of $12\%$ and a volatility of $40\%,$ and the market portfolio has an expected return of $10\%$ and a volatility of $18\%.$ Under the CAPM assumptions,

a$.$ What alternative investment has the lowest possible volatility while having the same expected return as Microsoft? What is the volatility of this investment?

b$.$ What investment has the highest possible expected return while having the same volatility as Microsoft? What is the expected return of this investment?