Verwenden Sie „expected value“ in einem Satz

1. Although some sceptics of this phenomenon have found similar patterns in secular books, their results were within statistically expected values

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2. So your Expected Value is 1,5 per trade

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3. is equal to the expected value of the return on the market

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4. the expected value of any security divided by its beta is equal to the expected value of

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5. If the random walk describes the price path, then over a large set of trades, you will discover that your win ratio is a little over 9 percent, leaving an expected value of zero

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6. If you try some other strategy—taking smaller profits, for instance—your win ratio will increase, but now the reward/risk ratio will also shift, again resulting in an expected value of zero

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7. But skilled traders find that they are compensated for these risks by quick profits and a good expected value over a large set of these trades

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8. When the probability of the loss is considered, a very tight stop often is a much larger loss in terms of expected value than a farther stop

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9. On average, we end up with $149,259, which is close to the theoretical $150,000 from the expected value equation

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10. So what conclusions can we draw from this? Well, first of all, math works—the theoretical expected value calculation gave a number very close to the mean of the terminal values, and the difference is easily explained by normal variation

11. However, this concept of expected value fails to capture the degree of variation possible within a positive expectancy framework

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12. Do not be misled by the sheer size of the winners, because, as you know by now, the extremely low probabilities associated with those outcomes moderate the expected value

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13. Mathematically, risk is part of the expected value function, and can be defined as:

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14. We can redefine the expected value equation like this:

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15. The job of a trader seeking to take consistent money out of the market can be simplified to making the E in this equation bigger than zero, or, more formally, to achieving a positive expected value over a large set of trades

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16. Any combination of the two that results in a positive expected value will make money in the absence of transaction costs

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17. The market’s reinforcement is not truly random; over a large number of trades, results do tend to trend toward the expected value, but it certainly can seem random to the struggling trader

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18. However, traders who would focus exclusively on fading moves need to deal with an important issue: with-trend trades are usually easier and offer better expected value than countertrend setups

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19. Note also that it is not necessary to calculate expected value in this analysis, as the trade means are equivalent to the expected values for each class of trade

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20. expectancy or expected value Mathematically, the expected payout of a scenario that has several possible outcomes is the sum of the probability of each outcome occurring times their payoffs

21. Second, there is no innate bias to high reward/risk trades; this ratio must be understood in the context of expected value

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22. As the option approaches its maturity date, an option contract’s expected value becomes more certain with each day

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23. 2: If X and Y are two independent discrete random variables, show that the expected value of X + Y is equal to the sum of the expected values of X and Y

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24. To find the mean or expected value of this binomial distribution, let us first note that the computation of the arithmetic mean can be simplified when there are a large number of ties by multiplying each distinct number k in a sample by the frequency fk with which it occurs;

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25. To find the expected value of our distribution using R, type

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26. 11: Show without using algebra that the sum of a Poisson with the expected value λ1 and a second independent Poisson with the expected value λ2 is also a Poisson with the expected value λ1 + λ2

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27. 13: Show that if Pr{X = k} = λke–λ/k! for k = 0, 1,2, … that is, if X is a Poisson variable, then the expected value of X = ΣkkPr{X = k} = λ

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28. Then we would want to make use of an estimate that minimizes the mean squared error, that is, an estimate that minimizes the expected value of (h – θ)2, which is equal to the variance of the statistic h plus (Eh − θ)2, where Eh denotes the expected value of the estimate when averaged over a large number of samples

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29. Compare with the empirical cumulative distribution functions of (1) a sample of 512 normally distributed observations with expected value 3

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30. Recall that if X and Y are independent, E(XY) = (EX)(EY), so that the expected value of the covariance and hence the correlation of X and Y is zero

31. “The expected value of Y is not larger than the expected value of X,” against a one-sided alternative, “The expected value of Y is larger than the expected value of X

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32. Now suppose, we’d stated our hypothesis in the form, “The expected values of Y and X are equal,” and the alternative in the form, “The expected values of Y and X are not equal

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33. If the means of the I populations are approximately the same, then changing the labels on the various observations will not make any difference as to the expected value of F2 or F1, as all the sample means will still have more or less the same magnitude

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34. 6: We saw in the preceding exercise that if the expected value of the first population was much larger than the expected values of the other populations, we would have a high probability of detecting the differences

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35. We saw in the preceding exercises that we can detect differences among several populations if the expected value of one population is much larger than the others or if the mean of one of the populations is higher and the mean of a second population is lower than the grand mean

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36. Suppose we represent the expectations of the various populations as follows: EXi = μ + δi where μ (pronounced mu) is the grand mean of all the popula­tions and δi (pronounced delta sub i) represents the deviation of the expected value of the ith population from this grand mean

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37. We will sometimes represent the individual observations in the form Xij = μ + δi + zij, where zij is a random deviation with expected value 0 at each level of i

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38. In the balance of the chapter, we shall consider three primary modeling methods: decision trees, which may be used both for classification and prediction, linear regression, whose objective is to predict the expected value of a given dependent variable, and quantile regression, whose objective is to predict one or more quantiles of the dependent variable’s distribution

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39. where Y is known as the dependent or response variable, X is known as the independent variable or predictor, f[X] is a function of known form, μ and β are unknown parameters, and Z is a random variable whose expected value is zero

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40. Suppose we have determined that the response variable Y whose value we wish to predict is related to the value of a predictor variable X, in that its expected value EY is equal to a + bX

41. The objective of the method is to determine the parameter values that will minimize the sum of squares Σ(yi − EY)2, where the expected value of the dependent variable, EY, is modeled by the right-hand side of our regression equation

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42. The term intercept stands for “intercept with the Y-axis,” since when f[X] and g[W] are both zero, the expected value of Y will be μ

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43. Linear regression techniques are designed to help us predict expected values, as in EY = μnn + βX

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44. What is the expected value for this proposition? There are 38 slots on the roulette wheel, each with equal probability, but only one slot will return $36 to the player

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45. The 5-cent difference between the $1 price of the bet and the 95-cent expected value represents the profit potential, or edge, to the casino

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46. Alternatively, the player would like to find a casino where he could purchase the bet for less than its expected value of 95 cents, perhaps 88 cents

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47. Thus far, the only factor we have considered in determining the value of a proposition is the expected value

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48. The player may now purchase the roulette bet for its expected value of 95 cents, and as before, if he loses, the casino will immediately collect his 95 cents

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49. The theoretical value of the bet is really the present value of its expected value, the 95 cents expected value discounted by interest

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50. How might we adapt the concepts of expected value and theoretical value to the pricing of options? Consider an underlying contract that at expiration can take on one of five different prices: $80, $90, $100, $110, or $120

51. What will be the expected value for this contract at expiration? Twenty percent of the time, the contract will be worth $80; 20 percent of the time, the contract will be worth $90; and so on, up to the 20 percent of the time, the contract is worth $120:

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52. At expiration, the expected value for the contract is $100

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53. Now consider the expected value of a 100 call using the same underlying prices and probabilities

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54. Then, given an exercise price, we can calculate the intrinsic value of the option at each underlying price, multiply this value by its associated probability, add up all these numbers, and thereby obtain an expected value for the option

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55. The expected value for a call at expiration is

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56. The expected value for a put is

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57. If the 100 call has an expected value of $6 at expiration, the theoretical value will be the present value of this amount

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58. Using these new probabilities, the expected value for the 100 call is now

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59. Note that the new probabilities did not change the expected value for the underlying contract

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60. Because the probabilities are symmetrical around $100, the expected value for the underlying contract at expiration is still $100

61. But as long as the expected value is equal to the forward price, there is no requirement that the probabilities be assigned symmetrically

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62. Nonetheless, the expected value for the underlying contract is still equal to $102

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63. Assign a probability to each possible price with the restriction that the underlying market is arbitrage-free—the expected value for the underlying contract must be equal to the forward price

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64. From the prices and probabilities in steps 1 and 2, and from the chosen exercise price, calculate the expected value of the option

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65. 83 profit? One possibility is that the price of the futures spread will return to its expected value of $17

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66. If the price of the spread does not return to its expected value, the trader can carry the entire position to maturity

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67. To see how spreading strategies can be used to reduce risk, recall our example in Chapter 5 where a casino is selling a roulette bet with an expected value of 95 cents for $1

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68. Using this approach, the expected value for a call option is the sum of the intrinsic values multiplied by the probability associated with each underlying price

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69. If we can answer these questions, the difference between the average value of the stock above the exercise price and the likelihood of paying the exercise price should equal the option’s expected value

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70. The expected value for a call option is the difference between these two numbers

71. Taking the average value of the stock we will receive at expiration and subtracting the average amount we will pay at expiration gives us the expected value for the call

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72. The expression SertN(d1) – XN(d2) represents the expected value of the option at expiration

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73. If we must pay for the option today, the theoretical value is the present value of the expected value

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74. Multiplying the expected value by e–rt yields the familiar form of the Black-Scholes model

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75. , the forward price is equal to the exercise price), for each percentage point of volatility, the expected value for the option is equal to the exercise price multiplied by 0

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76. If the exercise price is 100, the expected value is 0

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77. Lastly, this is an approximation for the expected value

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78. Putting everything together, for an exactly at-the-forward European option, the expected value at expiration is approximately3

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79. For example, if volatility is 18 percent, what is the expected value of a three-month (t = ¼) at-the-forward option with an exercise price of 65?

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80. If, in our example, we raise the volatility to 40 percent and increase the time to expiration to two years, the approximation for the expected value is

81. Finally, the present value of the option’s expected value at expiration is changing as time passes

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82. This leads to what is sometimes referred to as the 40% rule: the expected value of an at-the-forward option is equal to approximately 40% of one standard deviation, where one standard deviation is equal to F× σ√t

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83. The theoretical value of the call is the present value of the expected value

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84. The expected value of the option at C2,2 is therefore know that there is a 41 percent chance that the stock will move down in price, in which case the option will be worth 5

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85. The expected value of the option at C2,2 is therefore

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86. 95 were 25 percent), if we do a little math (multiplying the potential profit or loss by the likelihood of that profit or loss to calculate an expected value), we find that the difference in likelihoods doesn’t make up for the difference in outcomes

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87. Since stock prices reflect the expected values of discounted future cash flows, it is a mathematical identity that low earnings yields (high P/E ratios) reflect some combination of low discount rates and/or high expected earnings growth rates

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88. Computation of this criterion requires two parameters: the expected value of the underlying asset price and the variance of the normal distribution of the stock price logarithm

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89. For portfolios created shortly before the expiration (up to 20 days), the difference between the actual and the expected value changes were high, positive, and rather stable (low dispersion)

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90. 1 to calculate the expected value of the combination’s profit at the moment of expiration

91. ” Similarly, we can formulate other “expected value” criteria based on the integration of different functions by lognormal distribution

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92. Statistical arbitrage is an imbalance in expected values

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93. So diversifying broadly helps protect us against surprises and bad guesses, and best work towards an acceptable expected value

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