a-1. A well diversified portfolio has ÏpM=Î²Ï ==1.5(0.20) 0.30 View Answer. (a). There is not enough information to answer this question. It is a measure of total risk of the portfolio and an important input in calculation of Sharpe ratio. The Sharpe Ratio is a measure of risk-adjusted return, which compares an investment's excess return to its standard deviation of returns. Percentage values can be used in this formula for the variances, instead of decimals. Another area in which standard deviation is largely used is finance, where it is often used to measure the associated risk in price fluctuations of some asset or portfolio of assets. Quick SolveIgnore the T-bill, since that is 0Weight the Standard Deviation of the Risky Portfolio 8. Depending on weekends and public holidays, this number will vary between 250 and 260. Standard Deviation70% of 27%.7 * 27% = 18.9 9. The Sharpe Ratio is commonly used to gauge the performance of an investment by adjusting for its risk. The standard deviation of portfolio A is 24%, and its beta is 0.8. In other words s = (Maximum â Minimum)/4.This is a very straightforward formula to use, and should only be used as a very rough estimate of the standard deviation. It equals the weighted-average of the beta coefficient of all the individual stocks in a portfolio.. She wants a portfolio with an expected return of at least 14% and as low a risk as possible, but the standard deviation must be no more than 40%. be described with just two parameters â the mean and the standard deviation â and allows us to make probabilistic statements about sampling averages. The standard deviation of the resulting portfolio will be _____. This minimizes the volatility of the portfolio. Then, he calculates the portfolio standard deviation: Portfolio standard deviation = Portfolio variance0.5 = 0.00400.5 = 0.0629 = 6.29% A high standard deviation indicates greater variability in data points, or higher dispersion from the mean. Standard Deviation for the Stock y = 20%. the standard deviation is 20%. Choose the investment below that represent the minimum risk portfolio. Standard deviation is a statistical measure of diversity or variability in a data set. This quiz is incomplete! While variance and standard deviation of a portfolio are calculated using a complex formula which includes mutual correlations of returns on individual investments, beta coefficient of a portfolio ⦠A low standard deviation indicates that data points are generally close to the mean or the average value. Correlation coefficient between X and Y = +1.0. 8. The picture shows variance, and standard deviation is the square root of variance. 100% investment in stock X A. more than 18% but less than 24% B. equal to 18% C. more than 12% but less than 18% D. equal to 12% The sum of all variances gives a, which is the square of the standard deviation. Here's a sweet example to try: calculate variance and standard deviation of stock L and U, observe which is more volatile, and which has a higher expected return. Portfolio Standard Deviation Video 23) Most financial assets have correlation coefficients between 0 and 1. Bear Stearns' stock price closed at $100, $105, $56, $30, $2 over five successive weeks. III. Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The sample standard deviation is a descriptive statistic that measures the spread of a quantitative data set. For a portfolio that is 60% X and 40% risk-free asset: I. the expected return is 8.5% II. 10th - ⦠The only calculation required by the student is the expected return on the portfolio when funds are equally divided between the two stocks. holding too much of the risk-free asset. Standard deviation is most widely used and practiced in portfolio management services, and fund managers often use this basic method to calculate and justify their variance of returns in a particular portfolio. 100 investment in stock Y. Portfolio standard deviation is the standard deviation of a portfolio of investments. What is the sample standard deviation for the data given:5, 10, 7, 12, 0, 20, 15, 22, 8, 2. Standard deviation is a measure of the dispersion of data from its average. The standard deviation indicates a âtypicalâ deviation from the mean. Expected return for the stock k X =16%. Because it is easy to understand, this statistic is regularly reported to the end clients and investors. You put the rest of you money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. It shows how much variation or "dispersion" there is from the "average" (mean, or expected value). Example The following information about a two stock portfolio is available: Given the following information, what is the standard deviation of the returns on a portfolio that isinvested 35 percent in both stocks A and C, and 30 percent in stock B?rate of return if state occursstate of Probability of state stock a stock b stock cboom .20 16.4% 31.8% 11.4%Normal .80 11.2% 19.6% 7.3% 7. The annualized standard deviation of daily returns is calculated as follows: Annualized Standard Deviation = Standard Deviation of Daily Returns * Square Root (250) Here, we assumed that there were 250 trading days in the year. f = 0, the standard deviation of the clientâs portfolio is given by Ï c = .7Ï p = .7×.28 = 19.6% . Answer: TRUE. the standard deviation of the return difference between the portfolio and the benchmark. Standard Deviation for the Stock X = 12%. The standard deviation of a two-asset portfolio We can see that the standard deviation of all the individual investments is 4.47%. 10.10% b. Play this game to review Statistics. What is the sample standard deviation for the data given: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2 Preview this quiz on Quizizz. The standard deviation of a portfolio: A. is a weighted average of the standard deviations of the individual securities held in the portfolio. While variance is a common measure of data dispersion, in most cases the figure you will obtain is pretty large. If the standard deviation of returns of the market is 20% and the beta of a well-diversified portfolio is 1.5, calculate the standard deviation of the portfolio: A) 30% B) 20% C) 10% D) none of the above A. Let Ï B denote the standard deviation of the portfolio before hedging and Ï A denote the standard deviation of the portfolio after hedging. 83% average accuracy. Expected return and standard deviation are two statistical measures that can be used to analyze a portfolio. It is a popular measure of variability because it returns to ⦠If a test question asks for the standard deviation then you will need to take the square root of the variance calculation. This is the lowest standard deviation portfolio possible. Standard deviation is a widely used measurement of variability or diversity used in statistics and probability theory. One of the most basic principles of finance is that diversification leads to a reduction in risk unless there is a perfect correlation between the returns on the portfolio investments. Standard Deviation Example. a. Standard Deviation of Portfolio: 18%; Thus we can see that the Standard Deviation of Portfolio is 18% despite individual assets in the portfolio with a different Standard Deviation (Stock A: 24%, Stock B: 18%, and Stock C: 15%) due to the correlation between assets in the portfolio. Standard DeviationFirst, calculate the variance.This is easy, since standard deviation of a t-bill is 0. using the Sharpe measure. The market portfolio has a standard deviation of 10 percent. 1 (d). the standard deviation is 12%. A group of data items and their mean are given. That return is (.5)(.12) + (.5)(.2) = .16 = 16%. The crux of this problem is the calculation of the standard deviation of the portfolio consisting of the The use of standard deviation in these cases provides an estimate of the uncertainty of future returns on a given investment. The standard deviation of the market-index portfolio is 20%. The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. Covariance is a measure of how two variables change together, but its magnitude is ⦠Expected return for stock Y = 22%. 0.8 (b). D) the standard deviation of the return of the actively-managed portfolio. Answers to 12(a)Mean Expected Return = 14%Standard Deviation = 18.9% 10. 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