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Why the value of correlation coefficient is always between -1 and 1?
Why the value of correlation coefficient is always between -1 and 1?
How gamma are members of the exponential family prove?
Think you've got this backwards. The exponential probability distribution is a gamma probability distribution only when the first parameter, k is set to 1. Consistent with the link below, if random variable X is distributed gamma(k,theta), then for gamma(1, theta), the random variable is distributed exponentially. The gamma function in the denominator is equal to 1 when k=1. The denominator will reduce to theta when k = 1. The first term will be X0 = 1. using t to represent theta, we have f(x,t) = 1/t*exp(-x/t) or we can substitute L = 1/t, and write an equivalent function: f(x;L) = L*exp(-L*x) for x > 0 See: http://en.wikipedia.org/wiki/Gamma_distribution [edit] To the untrained eye the question might seem backwards after a quick google search, yet qouting wikipedia lacks deeper insight in to the question: What the question is referring to is a class of functions that factor into the following form: f(y;theta) = s(y)t(theta)exp[a(y)b(theta)] = exp[a(y)b(theta) + c(theta) + d(y)] where a(y), d(y) are functions only reliant on y and where b(theta) and c(theta) are answers only reliant on theta, an unkown parameter. if a(y) = y, the distribution is said to be in "canonical form" and b(theta) is often called the "natural parameter" So taking the gamma density function, where alpha is a known shape parameter and the parameter of interest is beta, the scale parameter. The density function follows as: f(y;beta) = {(beta^alpha)*[y^(alpha - 1)]*exp[-y*beta]}/gamma(alpha) where gamma(alpha) is defined as (alpha - 1)! Hence the gamma-density can be factored as follows: f(y;beta) = {(beta^alpha)*[y^(alpha - 1)]*exp[-y*beta]}/gamma(alpha) =exp[alpha*log(beta) + (alpha-1)*log(y) - y*beta - log[gamma(alpha)] from the above expression, the canonical form follows if: a(y) = y b(theta) = -beta c(theta) = alpha*log(beta) d(y) = (alpha - 1)*log(y) - log[gamma(alpha)] which is sufficient to prove that gamma distributions are part of the exponential family.
A stock market analyst estimates that the odds in favor of a stock market going up are 8 to 1. What is the probability of the stock’s not going up in value?
If it has an 8 to 1 chance of going up in value, then there is also a 1 to 8 chance that it won't.
How is the interquartile range calculated?
Find the difference between the values for quartile 3 and quartile 1.
What is the probability of sun rising in east?
On earth it is 1/1 or a certainty
A US Treasury bill has a beta of 0 while the overall market has a beta of what?
Beta is the measure of a security's volatility compared to the volatility of the market as a whole. Therefore, the market as a whole has a beta of 1.
How can you measure volatility using beta?
Beta measures the volatility of a stock in relation to the overall market. A beta of 1 indicates that the stock moves with the market, a beta greater than 1 suggests the stock is more volatile than the market, and a beta less than 1 indicates the stock is less volatile than the market. Traders and investors use beta to assess the risk of a stock in comparison to the market.
Does beta measure nondiversifiable risk?
Yes, beta measures the sensitivity of an asset's returns to market movements, representing the nondiversifiable risk (systematic risk) of an investment. A beta of 1 indicates that the asset moves in line with the market, while a beta greater than 1 implies higher volatility, and a beta less than 1 indicates less volatility than the market.
If a stock has a beta equal to one?
A beta of 1 indicates that the security's price will move with the market.
If the required rate of return is 11 the risk free rate is 7 and the market risk premium is 4 what is the beta coefficient?
the beta is 1 the beta is 1
What does BETA?
A beta of less than 1 means that the security will be less volatile than the market. A beta of greater than 1 indicates that the security's price will be more volatile than the market. Want to know more CALL 0800 016 3909 (Toll Free)
What is a BETA number?
In finance, a beta number measures the volatility or risk of a stock relative to the overall market. A beta greater than 1 indicates that the stock is more volatile than the market, while a beta less than 1 suggests the stock is less volatile. It helps investors assess the potential risk and return of a particular investment.
What do you mean beta factor?
In finance, the beta (β or beta coefficient) of an investment indicates whether the investment is more or less volatile than the market. In general, a beta less than 1 indicates that the investment is less volatile than the market, while a beta more than 1 indicates that the investment is more volatile than the market. Volatility is measured as the fluctuation of the price around the mean: the standard deviation.now what does it mean beta factor ??BETA FACTORS:The beta of an investment is a relative measure of the systematic risk of an investment. In other words it measures the specific risk of the company's shares relative to the market as a whole. In general, the sign of the beta (+/-) indicates whether, on average, the investment's returns move with the market or in the opposite direction to the market. The scale or value of the beta indicates the relative volatility of the particular stock.A beta of +0.25 for instance, would indicate that on average, the investment's returns move one quarter as much as the markets do in the same direction. If the market rose by 10%, the investment would be expected to rise by 2.5% but on the other hand if the market fell by 10% the investment would be expected to fall by only 2.5%. A beta of -0.1 would indicate that on average, the investment's returns move one tenth as much as the market's do, but in the opposite direction. If the market rose by 10%, the investment would be expected to fall by 1%. Hence we can summarise a number of situations:If Beta > 1 this means that the investment's returns will move, on average, in the same direction as the market's returns, but to a greater extent.If Beta = 1 this means that the investment's returns will move, on average, in the same direction as the market's returns, and to the same extent.If 0 -1, to the same extent if Beta = -1, and to a greater extent if Beta < -1. In practice it is rare to find negative beta stocks since they go against the trend of the market. One possible sector that could consist of negative beta stocks is the gold industry that tends to go against the trend shown by equity markets.Beta factor analysis is a useful technique that has enabled many international investors to achieve satisfactory returns in the past. If one looks at the trends in world markets then one can see that in a bull market those investors that have followed a selective aggressive portfolio (i.e. including shares with beta factors of over 1 times) have generally outperformed the market.
What does beta mean in reference to mutual funds?
AnswerbetaA quantitative measure of the volatility of a given stock, mutual fund, or portfolio, relative to the overall market, usually the S&P 500. Specifically, the performance the stock, fund or portfolio has experienced in the last 5 years as the S&P moved 1% up or down. A beta above 1 is more volatile than the overall market, while a beta below 1 is less volatile.general market fluctuations, which affect all the securities present in the market, called market risk or systematic risk,second, fluctuations due to specific securities present in the portfolio of the fund, called unsystematic risk.The Total Risk of a given fund is sum of these two and is measured in terms of standard deviation of returns of the fund.Systematic risk, on the other hand, is measured in terms of Beta, which represents fluctuations in the NAV of the fund vis-Ã -vis market. The more responsive the NAV of a mutual fund is to the changes in the market; higher will be its beta. Beta is calculated by relating the returns on a mutual fund with the returns in the market. While unsystematic risk can be diversified through investments in a number of instruments, systematic risk can not.Also read http://www.mutualfundplan.com/2008/08/measurement-of-risk-return-in-mutual.html for more details about various Risk measurement tools..
What is the beta of a Aggressive portfolio?
The beta of an Aggressive portfolio is typically higher than 1, indicating that the portfolio is expected to be more volatile than the overall market. This means that when the market moves up or down, the Aggressive portfolio is likely to experience larger price fluctuations. Investors in Aggressive portfolios are seeking higher returns but also accept higher risk.
Why should investors use beta?
IN THE FIELD of investing, the term the 'beta' of a stock or share is an indicator of the movement of that stock's share price in relationship to the movement of share prices in the market as a whole. It is a comparative measure of an individual stock's past price volatility.If a particular stock has a beta of 1 this means that the movement of its price has exactly matched the general movement of all prices in the market, i.e. there was an extremely close relationship with percentage value movements of the stock and that of the market.But if a stock has a beta of 0 (zero), the movement of its price in the market has been seen to be the opposite to that of the general movement of prices in general in the market as a whole.Therefore investors should give careful attention to the beta of a stock they are considering investing in.ALTHOUGH the past is no sure guide to the future, market analysis attempts to spot trends -in the hope that, just maybe, the past IS a guide to the future!Based on the assumption that a stock's beta (of past performance) is a good guide to its potential future performance, an investor who wants to 'run with the market' might choose a stock with the highest beta, i.e. the closer to 1 the better. They therefore expect, based on the past, that the stock's price will correspondingly rise when general market prices rise. On the other hand, the investor must expect the stock's price to fall when general market fall, and by a similar percentage.But a stock with a beta of 0 (zero) closely counter-matches the market, and when markets have fallen, the beta 0 stock has risen by the same percentage, and when markets have risen, the beta 0 stock has fallen by a similar percentage.AN INVESTOR who wants to 'beat the market', especially in a falling market economy, will look for stocks with low betas, but of course, they also run the risk of their stock losing value when the market is rising!An investor who wants to take a more cautious/conservative approach, the middle-way, may choose a stock that falls partway between (a) 'responding with the market, one way or another!, and (b) being 'independent of the market'. In this case they might select a stock with beta of 0.5 which might better suit their expectations and attitude to risk.MORE INFORMATION: CALCULATING THE BETAThe beta is computed using regression analysis. In our simple examples we have basically compared a beta of 1 with a beta of 0. However, if a stock's price responds with the market but shows co-related increases/falls that are actually 50% greater than that of the market, they will have a beta of 1.5And if the stock still rises and falls with the market but its percentage increases and falls are double that of the market, it will have a beta of 2.CONCLUSIONYou can see, then, that the beta is a very interesting and important measure of a stock's past performance (in 'price' terms) in relationship with the stock market as a whole. But is the past a good guide to the future? It seems that the jury is still out on that one!For more information, see Related links below.
Beta?
In my last post I discussed an investment metric known as alpha. Alpha is a gauge of risk-adjusted returns provided by a portfolio manager. Alpha isn’t the only measure of a stock or portfolio’s risk profile. Another one is called beta. Beta measures a stock’s volatility in comparison to the overall market. A beta value of 1 is assigned to the overall market. So a stock that has a beta of one would be considered to move in lockstep with the overall market. If the market were to go up by 10%, the stock should also move by the same amount in the same direction. A stock that moves less than the overall market would have a beta less than one. A beta greater than one indicates a stock that moves in the same direction as the overall market but in more extreme swings. Beta can be a good figure to use in rule-of-thumb investment decisions but it does have one serious drawback of which investors should be aware. Beta is calculated based on historical price movements relative to the market. Because of this method of calculation it doesn’t take into account any new information about the underlying fundamentals of the company. Due to this limitation, beta should never be used in a vacuum. Remember, statistics like alpha and beta can provide guideposts to help you evaluate an investment manager or the risk of a particular stock but they shouldn’t be relied upon to replace the hard work of fundamental analysis. It is the key things going on with a company’s balance sheet and income statement that are the true underpinnings of the stock’s valuation. Keep this in mind when evaluating stocks or portfolios and you’ll be in good shape. I’m not saying that statistics like alpha and beta should be ignored; they’re great tools. Just don’t let them be the only tools you use when making investment decisions.
