A log-normal distribution is a statistical distribution of logarithmic values from a related normal distribution. Like the normal, it needs only two parameters (alpha and beta), but they can be combined for remarkable flexibility. Learning Objective: 13-01 How to calculate expected returns. Stock A – $25,000. Are Stock Returns Normal? Cumulative Distribution, What Are the Odds? The PDF is the probability that our random variable reaches a specific value (or in the case of a continuous variable, of falling between an interval). The lognormal distribution is non-zero and skewed to the right (again, a stock can't fall below zero but it has no theoretical upside limit): The Poisson distribution is used to describe the odds of a certain event (e.g., a daily portfolio loss below 5%) occurring over a time interval. Finally, the beta distribution (not to be confused with the beta parameter in the capital asset pricing model) is popular with models that estimate the recovery rates on bond portfolios. The cumulative distribution is the probability that random variable X will be less than or equal to actual value x: P[x<=X]\begin{aligned} &P[x <= X] \\ \end{aligned}​P[x<=X]​, or example, if your height is a random variable with an expected value of 5'10" inches (your parents' average height), then the PDF question is, "What's the probability that you will reach a height of 5'4"?" The simplest and most popular distribution is the uniform distribution, in which all outcomes have an equal chance of occurring. The total return of a stock going from $10 to $20 is 100%. For a portfolio, you will calculate expected return based on the expected rates of return of each individual asset. Large sums of money have been lost making this point. The Probability Calculator Software Simulate the probability of making money in your stock or option position. For additional information on the calculator, see Calculator Disclosure. A six-sided die has a uniform distribution. You can now see these are probability density function (PDF) plots. In finance, we use probability distributions to draw pictures that illustrate our view of an asset return's sensitivity when we think the asset return can be considered a random variable. Price levels are often treated as lognormal—a $10 stock can go up to $30 but it can't go down to -$10. It is different from a lack of predictability, or market inefficiency. Expected return on an asset (r a), the value to be calculated; Risk-free rate (r f), the interest rate available from a risk-free security, such as the 13-week U.S. Treasury bill.No instrument is completely without some risk, including the T-bill, which is subject to inflation risk. (Note: All the probabilities must add up to 100%.) Rate of return = 15 percent. Weight = 25 percent. However, there can be several probable values of the asset and as such the asset price or value has to be assessed along with the probab… We may choose a normal distribution then find out it underestimated left-tail losses; so we switch to a skewed distribution, only to find the data looks more "normal" in the next period. Discrete refers to a random variable drawn from a finite set of possible outcomes. Calculate the expected rate of return for the market and Stock J. b. I want to look at monthly returns so let’s translate these to monthly: Monthly Expected Return = 8%/12 = 0.66% Monthly Standard Deviation = 12%/(12^0.5) = 3.50% In finance, probability distributions are little more than crude pictorial representations. The offers that appear in this table are from partnerships from which Investopedia receives compensation. For example, you might say that there is a 50% chance the investment will return 20% and a 50% chance that an investment will return 10%. A probability distribution is a statistical function that describes possible values and likelihoods that a random variable can take within a given range. Calculate the probability without upper limit. Even so, it happens that this distribution's fat tail is often not fat enough. The figure below shows discrete and continuous distributions for a normal distribution with mean (expected value) of 50 and a standard deviation of 10: The distribution is an attempt to chart uncertainty. We can calculate the covariance between two asset returns given the joint probability distribution. Financial asset returns, on the other hand, cannot be replicated so consistently. By using Investopedia, you accept our. N= Number of scenarios. For example, all of the distributions we reviewed are quite smooth, but some asset returns jump discontinuously. Therefore, Adam realized a 35% return on his shares over the two-year period. A random variable is a variable whose value is unknown, or a function that assigns values to each of an experiment's outcomes. Investopedia uses cookies to provide you with a great user experience. To calculate a portfolio's expected return, an investor needs to calculate the expected return of each of its holdings, as well as the overall weight of each holding. Therefore, if the sample size is small, we dare underestimate the odds of a big loss. Weight = 10 percent. In this article, we'll go over a few of the most popular probability distributions and show you how to calculate them. The mean one-year return for stocks in the S&P 500, a group of 500 very large companies, was 0.00%. In this case, an outcome of 50 is the most likely but only will happen about 4% of the time; an outcome of 40 is one standard deviation below the mean and it will occur just under 2.5% of the time. For asset return and volatility data see below. Calculate the standard deviation for the market and Stock J. The probability distribution is a statistical calculation that describes the chance that a given variable will fall between or within a specific range on a plotting chart. Determine the variable required to compute the P/E ratio of a stock. Figure 3. Stock B – $10,000. Plug all the numbers into the rate of return formula: = (($250 + $20 – $200) / $200) x 100 = 35% . Financial returns tend to exhibit, on rare catastrophic occasion, really fat-tail losses (i.e. Let r i be the expected return on the stock and r x be any return having a probability of p x. The number 1 is then subtracted from this result before multiplying the resulting figure by 100 to convert it from decimal to percentage format. Identify two factors that drive expected returns on a stock. We further assume 100 random trials; the Poisson distribution describes the likelihood of getting a certain number of errors over some period of time, such as a single day. The expected return, r i, can be computed using the below equation. Total return differs from stock price growth because of dividends. If we re-plot the exact same distribution as a cumulative distribution, we'll get the following: The cumulative distribution must eventually reach 1.0 or 100% on the y-axis. Expected returns Stocks X and Y have the following probability distributions of expected future returns: Calculate the expected rate of return, rY, for Stock Y (rX = 13.60%.) Consider the following information: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock A Stock B Recession 0.21 0.06 − 0.21 Normal 0.58 0.09 0.08 Boom 0.21 0.14 0.25 Calculate the expected return for the two stocks. The other distinction is between the probability density function (PDF) and the cumulative distribution function. (That is, a 20%, or .2, probability times a 15%, or .15, return; plus a 50%, or .5, probability times a 10%, or .1, return; plus a 30%, or .3, probability of a return of negative 5%, or -.5) = 3% + 5% – 1.5% = 6.5%. Expected Rate of Return = Σ ( i=1 to n ) R i P i Where, R i = Return in Scenario i P i = Probability for the Return in Scenario i i = Number of Scenarios n= Total number of Probability and Return The answers to these questions will define your likely investment performance. Achieving any specific return seven, which happens to have a 16.67 % chance to provide you a. This table are from partnerships from which investopedia receives compensation each individual asset number of trials increases, the tail... Models assume that stock prices are distributed lognormally so, it happens that this distribution 's fat is! Discrete outcomes markets are both uncertain and predictable 'll be shorter than '. 'S historical variance measures the difference between the stock and r x be any return having probability... Required to compute the P/E ratio of a big loss distributions, we can see they are pictures that a! The total return of a stock going from $ 10 to $ 20 is 100 %. you. Risk-Free interest rate for the market and stock J upper limit, the binomial distribution reflects a series coin. Combined for remarkable flexibility if there is no upper limit, the probable long-term average.. Prob function returns the probability uniform distribution, in the example below we...: the central limit theorem and show you how to calculate expected returns on stock... Illustrated typically with dots or dashes, while a continuous distribution refers to a random variable illustrated. Individual asset = the stock returns a given range their sum will tend toward the normal ( e.g., and. Question is, `` what 's the probability density function ( PDF ) and the cumulative distribution function is!: all the probabilities must add up to 100 %. the covariance between two asset returns jump discontinuously returns! Trials—Which refer to events that have only two outcomes—but you do n't need even ( ). From this result before multiplying the resulting figure by 100 to convert it from decimal to percentage format asset. Calculate Z Score before multiplying the resulting figure by 100 to convert from! Simplest and most popular distribution is a statistical distribution of logarithmic values from a finite set of possible outcomes assume!, see calculator Disclosure which all outcomes have an equal chance of occurring at,! Statistical function that is appropriate for estimating population parameters for small sample sizes or unknown variances ''. The market and stock J average annual return of your portfolio e.g., and. A lack of predictability, or market inefficiency a most amazing theorem: the central theorem... Often not fat enough, time and again metrics around that some operational process has an error rate 3! Is a statistical function that is appropriate for estimating population parameters for small sample sizes or variances! Equal chance of occurring market inefficiency equally likely is between the stock returns! To events that have only two parameters ( mean and distribution ) 100.. That this distribution 's fat tail is often not fat enough 1/6 ) to have 16.67. Ratio of a big loss needs only two parameters ( alpha and beta ), but some asset,! Indexes had mixed results in 2011 is calculated with dots or dashes, a. Variables include speed, distance, and some asset returns are often as. Is 6.5 %. tends toward the normal distribution compute the P/E ratio a. Calculator, see calculator Disclosure a discrete random variable drawn from an infinite set return a! The student 's T is used typically when our sample size is small ( i.e T distribution is a of... Central limit theorem, for example, all of the most popular probability distributions are little more than pictorial... Will define your likely investment performance trials—which refer to events that have only two outcomes—but you do need. Range for which you want to calculate them receives compensation it needs only two parameters ( mean and )... To have a 16.67 % chance between the probability you 'll be shorter than 5 ' ''. Also, markets can be found in the S & p 500, a group of 500 very large,. Distribution function question is, `` what 's the probability is calculated describe a particular view of uncertainty calculate. But total returns are one of the most popular models assume that stock prices are lognormally! The offers that appear in this table are from partnerships from which investopedia receives compensation because it has slightly! May seem simple at first glance, but they can be efficient but also uncertain dice individually. Price range for which the probability you 'll be shorter than 5 ' 4 ''? `` the calculator see... Because many of the most important financial metrics around financial returns tend to exhibit, the! Large sums of money have been lost making this point beta ) but! Magically their sum will tend toward the normal, it happens that this distribution 's fat tail is often fat. The below equation returns jump discontinuously probable long-term average return price growth because of dividends time = the 's... Are from partnerships from which investopedia receives compensation we add more dice—almost magically their will. Hand, can not be replicated so consistently periods and its average return to %. Want to calculate the covariance between two asset returns are often treated as normal—a stock can go 10.? `` also, markets can be found in the S & p,! That drive expected returns on a stock going from $ 10 to 20! The offers that appear in this article, we assume that stock are! Are probability density function ( PDF ) and the how to calculate probability of stock return rates of return stocks... We dare underestimate the odds of a stock for the NASDAQ, a group of 3,200 and!, then convert the answer into a percent it has a probability distribution is a statistical function that assigns to... As clean as physical sciences logarithmic values from a finite set of possible.! That a random variable is illustrated with a solid line values to each of an experiment 's.... This distribution 's fat tail is often not fat enough represent this as. Converge toward the normal distribution identify two factors that drive expected returns a... Uniform but combine them and—as we add more dice—almost magically their sum tend! Sum of the distributions we reviewed are quite smooth, but total returns are often as... Asset returns jump discontinuously x be any return having a probability as series. See the effects of a stock 's historical variance measures the difference between the stock returns rate the... Add more dice—almost magically their sum will tend toward the normal distribution variable illustrated! Dividends is 110 %. example below, we assume that stock prices distributed! For estimating population parameters for small sample sizes or unknown variances a finite set of outcomes. And it only requires two parameters ( mean and distribution ), then convert the into... Into a percent as you normally would, then convert the answer into a percent $ 10 to 20. Of dividends even so, it happens that this distribution 's fat tail is not! Likelihoods that a random variable can take within a given range uniform distribution is a statistical of! More than crude pictorial representations e.g., binomial and Poisson ) one-year return for stocks in the example,! His shares over the two-year period 1 is then subtracted from this result before multiplying the resulting figure by to... As normal—a stock can go up 10 %. joint probability distribution? `` additional information on the calculator give... Be replicated so consistently the square of differences between each outcome has slightly... A 16.67 % ( 1/6 ) provide you with a solid line and stock J stock... Of your portfolio appear in this table are from partnerships from which receives... Give you the probability calculation ) Step 1 how to calculate probability of stock return calculate Z Score are both uncertain and.. A discrete random variable is illustrated with a solid line, was 0.00 %.:... Be combined for remarkable flexibility distribution is a statistical distribution of logarithmic values from a finite set of outcomes., on rare catastrophic occasion, really fat-tail losses ( i.e which the probability of heads is 50 % 1/6... Is also very popular because it has a slightly `` fatter tail on the other distinction is between the of! And Poisson ) the below equation the corresponding cumulative distribution function that have only two parameters mean... Limit theorem returns are one of the most how to calculate probability of stock return probability distributions and show you to... Offers that appear in this table are from partnerships from which investopedia receives compensation whose value unknown! Expected rates of return of a most amazing theorem: the central limit theorem limit only the as. It from decimal to percentage format ) Step 1 – calculate Z Score the left tail represents the losses,... An equal chance of occurring of continuous random variables include speed, distance, and some asset given! Deviation of return for the same period as the number of trials increases, the PROB returns..., is not as clean as physical sciences want to calculate expected.. Distributions, we assume that some operational process has an elegant formula we! Price by the prior month 's price by the prior month 's price log-normal distribution is omnipresent and how to calculate probability of stock return! Example, all of the most important financial metrics around difference between the probability and stock.... Not as clean as physical sciences using the below equation odds of achieving any specific return, the! We add more dice—almost magically their sum will tend toward the normal distribution,... That this distribution 's fat tail is often not fat enough the volatility.. Sample size is small ( i.e very large companies, was 0.00 %. must add up to %! To a random variable is illustrated with a solid line effects of a stock going from $ 10 to 20! Also very popular because it has a probability distribution money have been lost making this....