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# Market Portfolio

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Your investment portfolio consists of \$15,000 invested in one one stock - Microsoft. Suppose the risk-free rate is 5%. Microsoft stock has an expeted 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 volatilty while having the same expected return as Microsoft?
b. What investment has the highest possible expected return while having the same volatility as Microsoft?

https://brainmass.com/economics/investments/299670

#### Solution Preview

Efficiency of the Market Portfolio
Your investment portfolio consists of \$15,000 invested in one 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?

The equation for the capital market line (CML) is
return on efficient portfolio = risk free rate + (return on market portfolio-risk free rate ) x ( volatility of portfolio / volatility of market portfolio)
or rp= rf + (rm-rf) x ( &#963;p/ &#963;m)

return on efficient portfolio = x * return on market portfolio + (1-x) * risk free rate
or rp= x rm + (1-x) rf

volatility of efficient portfolio = x * volatility of market portfolio
or &#963;p=x ...

#### Solution Summary

Under the CAPM assumptions finds:
1) investment that has the lowest possible volatilty while having the same expected return
2) investment that has the highest possible expected return while having the same volatility

\$2.19

## Assume the following variance-covariance matrix. What is the optimal weight of the two assets? Write the equation of the capital market line. Create a portfolio with 20% return. Describe that portfolio in terms of the holdings of stock A, B and the risk free asset.

Please disregard the short sale of stock. Instead, consider that you have purchased 100 shares of stock A.

Assume the following variance-covariance matrix:

Stock A B E(r)
A 0.09 12%
B 0.20 0.25 18%

There is unlimited borrowing and lending at the risk free rate of 8%.

a. What is the optimal weight of the two assets?
b. Write the equation of the capital market line.
c. Create a portfolio with 20% return. Describe that portfolio in terms of the holdings of stock A, B and the risk free asset.

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