Question

Your portfolio consists of a full investment in just one stock, Eriksson. Suppose this stock has an expected return of 18% and volatility of 31%. Suppose further that the tangency portfolio has an expected return of 16% and a volatility of 22%. Also, assume that the risk-free rate is 5%. What is the lowest possible volatility of an alternative investment that has the same expected return as your investment? What are the portfolio weights of this alternative investment on each one of its elements? You need to explain how you got to your final answers in all cases in order to get points for this question.

Answer 1

We know that expected returns of portfolio=weight in asset 1*returns of asset 1+weight in asset 2*returns o asset 2

Let w be the investment in tangency portfolio and 1-w be the investment in risk free rate
Given, returns=18%
Hence,
w*16%+(1-w)*5%=18%
=>w=(18%-5%)/(16%-5%)=1.181818182

Weight of tangency portfolio=1.181818182

Weight of risk free rate=1-1.181818182=-0.181818182

This means borrow 0.181818182 at risk free rate and invest own as well as borrowed money in tangency portfolio

Standard deviation or volatility=weight of tangency portfolio*standard deviation of tangency portfolio=1.181818182*22%=26.000%