Final answer:
The standard deviation of a portfolio cannot be calculated without specific data on individual stock standard deviations and their correlation. Standard deviation is used to measure the volatility of stock returns, and the formula for portfolio standard deviation requires the weights of the stocks, their individual standard deviations, and their correlation coefficient.
Step-by-step explanation:
The standard deviation of a portfolio consisting of different stocks can be determined using the portfolio standard deviation formula, which accounts for the proportion of each stock in the portfolio, the individual standard deviations of these stocks, and the correlation between them. However, to answer this question accurately, we need more information such as the individual standard deviations of stock x and stock y, as well as the correlation coefficient between these two stocks. Without this information, we cannot calculate the portfolio standard deviation.
When evaluating individual stock deviations and their contribution to the portfolio, we use the concept of standard deviation to measure the variability or risk associated with the stock's returns. For example, if stock x had a mean of 25 and a standard deviation of 2, then about 95 percent of its values would lie within two standard deviations of the mean, assuming a normal distribution.
To find the standard deviation of a portfolio, we generally use the following formula:
σp = √(w1²σx² + w2²σy² + 2w1w2σxσyρxy)
Where:
- σp is the portfolio standard deviation.
- w1 is the weight of stock x in the portfolio.
- w2 is the weight of stock y in the portfolio.
- σx is the standard deviation of stock x.
- σy is the standard deviation of stock y.
- ρxy is the correlation coefficient between stock x and y.
It is important to note that the weights should be in decimal form (e.g., 30% as 0.30), and the correlation coefficient ranges between -1 and 1.