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How can he return and standard deviation of a portfolio be determined?
Wiki User
∙ 14y ago
How can the return and standard deviation of a portfolio be deteremined
Wiki User
∙ 14y ago
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How do you calculate risk on a two-asset portfolio?
For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000
How is expected rate of return calculated from average rate of return on investment and standard deviation?
The expected rate of return is simply the average rate of return. The standard deviation does not directly affect the expected rate of return, only the reliability of that estimate.
How are variance and standard deviation used as measures of risk for both a security and a portfolio?
Risk reflects the chance that the actual return on an investment may be very different than the expected return. One way to measure risk is to calculate the variance and standard deviation of the distribution of returns.Consider the probability distribution for the returns on stocks A and B provided below.StateProbabilityReturn onStock AReturn onStock B120%5%50%230%10%30%330%15%10%320%20%-10%The expected returns on stocks A and B were calculated on the Expected Return page. The expected return on Stock A was found to be 12.5% and the expected return on Stock B was found to be 20%.Given an asset's expected return, its variance can be calculated using the following equation:whereN = the number of states,pi = the probability of state i,Ri = the return on the stock in state i, andE[R] = the expected return on the stock.The standard deviation is calculated as the positive square root of the variance.Note: E[RA] = 12.5% and E[RB] = 20%Stock AStock B
How do you calculate a coefficient knowing the expected rate of return and standard deviation?
It depends on what the underlying distribution is and which coefficient you want to calculate.
The Sortino Ratio?
I've written before about the Sharpe Ratio, a measure of risk-adjusted returns for an asset or portfolio. The Sharpe ratio functions by dividing the difference between the returns of that asset or portfolio and the risk-free rate of return by the standard deviation of the returns from their mean. So it gives you an idea of the level of risk assumed to earn each marginal unit of return. The problem with using the Sharpe Ratio is that it assumes that all deviations from the mean are risky, and therefore bad. But often those deviations are upward movements. Why should an investment strategy by graded so sharply by the Sharpe Ratio for good performance? In the real world, investors don't usually mind upside deviations from the mean. Why would they? These were the questions on the mind of Frank Sortino when he developed what has been dubbed the Sortino Ratio. The ratio that bears his name is a modification of the Sharpe Ratio that only takes into account negative deviations and counts them as risk. To me, it always made a lot more sense not to include upside volatility from the equation because I rather like to see some upside volatility in my portfolios. With the Sortino Ratio only downside volatility is used as the denominator in the equation. So the way you calculate it is to divide the difference between the expected rate of return and the risk-free rate by the standard deviation of negative asset returns. (It can be a bit tricky the first time you try to do it. The positive deviations are set to values of zero during the standard deviation calculation in order to calculate downside deviation.) By using the Sortino Ratio instead of the Sharpe Ratio you’re not penalizing the investment manager or strategy for any upside volatility in the portfolio. And doesn’t that make a whole lot more sense?
How do you calculate the standard deviation of the mean using Excel?
=stdev(...) will return the N-1 weighted sample standard deviation. =stdevp(...) will return the N weighted population standard deviation.
How do you calculate risk on a two asset portfolio?
For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000
How do you calculate risk on a two-asset portfolio?
For a two-asset portfolio, the risk of the portfolio, σp, is: 2222p1122112212222p11221212121212σ=wσ+wσ+2wσwσρorσ=wσ+wσ+2wwcovcov since ρ=σσ where σi is the standard deviation of asset i's returns, ρ12 is the correlation between the returns of asset 1 and 2, and cov12 is the covariance between the returns of asset 1 and 2. Problem What is the portfolio standard deviation for a two-asset portfolio comprised of the following two assets if the correlation of their returns is 0.5? Asset A Asset B Expected return 10% 20% Standard deviation of expected returns 5% 20% Amount invested $40,000 $60,000
How is expected rate of return calculated from average rate of return on investment and standard deviation?
The expected rate of return is simply the average rate of return. The standard deviation does not directly affect the expected rate of return, only the reliability of that estimate.
How do you compute the risk-adjusted return on an investment?
The risk-adjusted return is a measure of how much risk a fund or portfolio takes on to earn its returns, usually expressed as a number or a rating. This is often represented by the Sharpe Ratio. The more return per unit of risk, the better. The Sharpe Ratio is calculated as the difference between the mean portfolio return and the risk free rate (numerator) divided by the standard deviation of portfolio returns (denominator).
Annualized standard deviation?
http://www.hedgefund.net/pertraconline/statbody.cfmStandard Deviation -Standard Deviation measures the dispersal or uncertainty in a random variable (in this case, investment returns). It measures the degree of variation of returns around the mean (average) return. The higher the volatility of the investment returns, the higher the standard deviation will be. For this reason, standard deviation is often used as a measure of investment risk. Where R I = Return for period I Where M R = Mean of return set R Where N = Number of Periods N M R = ( S R I ) ¸ N I=1 N Standard Deviation = ( S ( R I - M R ) 2 ¸ (N - 1) ) ½ I = 1Annualized Standard DeviationAnnualized Standard Deviation = Monthly Standard Deviation ´ ( 12 ) ½ Annualized Standard Deviation *= Quarterly Standard Deviation ´ ( 4 ) ½ * Quarterly Data
The correlation between an asset's real rate of return and its risk as measured by its standard deviation is usually?
The correlation between an asset's real rate of return and its risk (as measured by its standard deviation) is usually:
What is the standard deviation of a treasury bill that has a expected return of 10.5?
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What is the purpose of finding the standard deviation of a data set?
The purpose of obtaining the standard deviation is to measure the dispersion data has from the mean. Data sets can be widely dispersed, or narrowly dispersed. The standard deviation measures the degree of dispersion. Each standard deviation has a percentage probability that a single datum will fall within that distance from the mean. One standard deviation of a normal distribution contains 66.67% of all data in a particular data set. Therefore, any single datum in the data has a 66.67% chance of falling within one standard deviation from the mean. 95% of all data in the data set will fall within two standard deviations of the mean. So, how does this help us in the real world? Well, I will use the world of finance/investments to illustrate real world application. In finance, we use the standard deviation and variance to measure risk of a particular investment. Assume the mean is 15%. That would indicate that we expect to earn a 15% return on an investment. However, we never earn what we expect, so we use the standard deviation to measure the likelihood the expected return will fall away from that expected return (or mean). If the standard deviation is 2%, we have a 66.67% chance the return will actually be between 13% and 17%. We expect a 95% chance that the return on the investment will yield an 11% to 19% return. The larger the standard deviation, the greater the risk involved with a particular investment. That is a real world example of how we use the standard deviation to measure risk, and expected return on an investment.
How do you measure the risk of a single asset?
The total risk of a single asset is measured by the standard deviation of return on asset. Standard deviation is the square root of variance. To measure variance, you must have some distribution/ possibility of asset returns. However, the relevant risk of a single asset is the systematic risk, not the total risk. Systematic risk is the risk that cannot be diversified away in a portfolio. Systematic risk of an asset is measured by the Beta. Beta can be found using Regression (between market return and asset's return) or Covariance formula.
Sharpe Investing?
Have you heard of the Sharpe Ratio? The Sharpe Ratio is a measure of the risk-adjusted return of an asset or a portfolio of assets.The Sharpe Ratio can be used to compare investment strategies or managers, taking into account the amount of risk exposure each has in relation to their returns.William Forsyth Sharpe created the ratio in 1966. He would later develop the Capital Asset Pricing Model (CAPM) for which he would win the Nobel Prize in Economics.The Sharpe Ratio is calculated by dividing the difference between the average return for the portfolio and the risk-free rate of return by the standard deviation of returns for the portfolio.The formula looks like:S(x) = (Rx – Rf) / StdDev(x)Where x = portfolio, Rx = average returns of portfolio, Rf = risk-free rate of return, and StdDev(x) = the standard deviation of returns for x.So how do you go about using this tool? First, it’s important to remember that, just like any other number derived from a formula you use to evaluate investments, The Sharpe Ratio can act as a guide, but should not be used in a vacuum. There are always many things to consider when investing.The Sharpe ratio can give you some idea of the efficiency of a portfolio by showing the amount of return generated per unit of risk assumed.The higher the Sharpe Ratio the better relationship of reward to risk the portfolio is deemed to have.Because the Sharpe Ratio takes volatility of a portfolio into account in its analysis its use is helpful when comparing different investment strategies or managers.All other things being equal (i.e. rate of return, constant risk-free rate) the strategy or manager exhibiting the highest return with the lowest amount of risk (as measured by standard deviation) would be the better choice.
What do understand by 'Portfolio risk?
One important point about the estimation of standard deviation is the distinction between individual securities and portfolios.Standard deviations for well-diversified portfolios are reasonabily steady across time, and therefore historical calculations may be fairly reliable in projecting the future. Moving from well-diversified portfolios to individual securities, however, makes historical calculations much less reliable. Fortunately, the number one rule of portfolio management is to diversify and hold a portfolio of securities, and the standard deviations of well-diversified portfolio may be more stable.Something very important to remember about standard devitaion is that it is a measure of the total risk of an assset or a portfolio, including, therefore both systamatic and unsystematic risk. It captures the total variability in the assest or portfolio's return, whatever the source of that variability.In summary, the standard deviation of return measures the total risk of one security or the total risk of a portpolio of securities. The historical standard deviation can be calculated for individual securities or portfolios of securities using total returns for some specified period of time.This ex post value is useful in evaluating the total risk for a particular historical period and in estimating the total risk that is expected to prevail over some future period.The portfolio risk is not simply a measure of its weighted average risk. The securities that a contains are associated with each other.The portfolio risk also considers the covariance between the returns of the investment.
