Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084. 1. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio? 2. In addition to the funds A and B in the previous question, now you decide to include fund C to your portfolio. Its expected return is 10, its variance 0.0625, its correlation with A is 0.1050 and its correlation with B is 0.07. You want to achieve an expected return of 16% on your portfolio, with the minimum possible risk (measured by the standard deviation). Derive analytically (that is, without the help of solver, but trough calculus) the weights of such desired portfolio, and its standard deviation.
Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
Problem 3: You have access to two investment opportunities. Mutual Fund A, which promises 20% expected return with a variance of 0.36, and Mutual Fund B, which promises 15% expected return with a variance 0f 0.12. The covariance between the two is 0.084.
1. Suppose that you seek to construct a portfolio with an expected return equal to 18%. What proportions of your wealth should you invest in A and B? What is the standard deviation of such portfolio?
2. In addition to the funds A and B in the previous question, now you decide to include fund C to your portfolio. Its expected return is 10, its variance 0.0625, its correlation with A is 0.1050 and its correlation with B is 0.07. You want to achieve an expected return of 16% on your portfolio, with the minimum possible risk (measured by the standard deviation). Derive analytically (that is, without the help of solver, but trough calculus) the weights of such desired portfolio, and its standard deviation.
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