Question

You are planning to buy $10,000 worth of IBM and $30,000 worth of Apple stock. According to an analyst, the expected returns for next year are 7% for IBM and 10% for Apple, with a standard deviation of 16% for IBM and 30% for Apple. The correlation between the two stocks' returns is 0.42.

what is the portfolio weight ?
what is the expected return on the portfolio?
what is the standard deviation of portfolio returns ?
what is the sharpe ratio of this portfolio IF the risk free rate IS 4% ?

Answer 1

The portfolio weight is 25% for IBM and 75% for Apple, with an expected return of 9.25%. The standard deviation of portfolio returns and the Sharpe ratio require further calculations using the formula for portfolio variance and Sharpe ratio respectively.

Step-by-step explanation:

To calculate the portfolio weight of IBM and Apple stock, divide the value of the investment in each stock by the total investment:

The expected return on the portfolio is the weighted average of the individual expected returns:

(IBM weight * IBM return) + (Apple weight * Apple return) = (0.25 * 7%) + (0.75 * 10%) = 1.75% + 7.5% = 9.25%

The standard deviation of portfolio returns can be calculated using the formula:

Sqrt[w²(IBM)*(SD²(IBM)) + w²(Apple)*(SD²(Apple)) + 2*w(IBM)*w(Apple)*Corr(IBM, Apple)*SD(IBM)*SD(Apple)]

Where w = weight, SD = standard deviation, and Corr = correlation.

The Sharpe ratio is calculated as:

(Return of portfolio - Risk-free rate) / Standard deviation of portfolio

= (9.25% - 4%) / Standard deviation of portfolio

The precise value for the standard deviation and Sharpe ratio requires the use of the formula provided and plugging in the given standard deviations and correlation coefficient.

Answer 2

• The portfolio weight for IBM is 0.25 and for Apple is 0.75.
• The expected return on the portfolio is 8.5%.
• The standard deviation of portfolio returns is 23.73%
• The Sharpe ratio is 0.1875.

Step-by-step explanation:

To find the portfolio weight, we need to divide the value invested in a particular stock by the total value of the portfolio. In this case, the portfolio weight for IBM would be $10,000 / ($10,000 + $30,000) = 0.25, and the portfolio weight for Apple would be $30,000 / ($10,000 + $30,000) = 0.75.

The expected return on the portfolio can be calculated by multiplying the portfolio weight of each stock by its respective expected return and summing them up.

The expected return on the portfolio would be (0.25 * 0.07) + (0.75 * 0.10) = 0.085 or 8.5%.

The standard deviation of portfolio returns can be calculated using the formula: √((w1^2 * σ1^2) + (w2^2 * σ2^2) + (2 * w1 * w2 * ρ * σ1 * σ2)), where w1 and w2 are the portfolio weights, σ1 and σ2 are the standard deviations of the individual stocks, and ρ is the correlation between the two stocks' returns.

Plugging in the values, the standard deviation of portfolio returns would be √((0.25^2 * 0.16^2) + (0.75^2 * 0.30^2) + (2 * 0.25 * 0.75 * 0.42 * 0.16 * 0.30)) = 0.2373 or 23.73%.

The Sharpe ratio is calculated by subtracting the risk-free rate from the expected return on the portfolio and dividing it by the standard deviation of portfolio returns. In this case, the Sharpe ratio would be (0.085 - 0.04) / 0.2373 = 0.1875.