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A portfolio is 30% invested in stocks with a standard deviation of returns of 20%, and the remainder is invested in bonds with a standard deviation of returns of 12%. The correlation of bond returns with stock returns is 0.6. Calculate the standard deviation of returns for the portfolio. https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244135

https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244135

The initial market value of a portfolio was $100,000. One year later the portfolio was valued at $90,000 and two years later at $99,000. The geometric mean annual return excluding any dividend income is closest to: https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244122

(Ending value / beginning value) ^ 1/n

Annual returns on energy stocks are approximately normally distributed with a mean of 9% and standard deviation of 6%. Construct a 90% confidence interval for the annual returns of a randomly selected energy stock and a 90% confidence interval for the mean of the annual returns for a sample of 12 energy stocks. (https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244156)

A 90% confidence interval for a single observation is 1.645 standard deviations from the sample mean. 9% ± 1.645(6%) = -0.87% to 18.87% A 90% confidence interval for the population mean is 1.645 standard errors from the sample mean.

Consider a practice exam that was administered to 36 Level I candidates. The mean score on this practice exam was 80. Assuming a population standard deviation equal to 15, construct and interpret a 99% confidence interval for the mean score on the practice exam for 36 candidates. (https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244156)

At a confidence level of 99%, zα/2 = z0.005 = 2.58. So, the 99% confidence interval is calculated as follows: Thus, the 99% confidence interval ranges from 73.55 to 86.45.

An analyst estimates a stock has a 40% probability of earning a 10% return, a 40% probability of earning a 12.5% return, and a 20% probability of earning a 30% return. The stock's standard deviation of returns based on this returns model is closest to: https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244135

Expected value = (0.4)(10%) + (0.4)(12.5%) + (0.2)(30%) = 15% Variance = (0.4)(10 − 15)2 + (0.4)(12.5 − 15)2 + (0.2)(30 − 15)2 = 57.5 Standard Deviation = Square route of 57.5 = 7.58

Jane Acompora is calculating equivalent annualized yields based on the 1.3% holding period yield of a 90-day loan. The correct ordering of the annual money market yield (MMY), effective yield (EAY), and bond equivalent yield (BEY) is: https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244113

MMY < BEY < EAY No calculations are really necessary here since the MMY involves no compounding and a 360-day year, the BEY requires compounding the quarterly HPR to a semiannual rate and doubling that rate, and the EAY requires compounding for the entire year based on a 365-day year. A numerical example of these calculations based on a 90-day holding period yield of 1.3% is: the money market yield is 1.3% × 360 / 90 = 5.20%, the bond equivalent yield is 2 × [1.013182.5/90 − 1] = 0.0531 = 5.31%, which is two times the effective semiannual rate of return, and the effective annual yield is 1.013365/90 − 1 = 0.0538 = 5.38%. Calculating the semiannual effective yield using 180 days instead of 182.5 does not change the order.

What is the level of significance, or "significance level"? https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244163

The significance level is the probability of making a Type I error (rejecting the null when it is true) and is designated by the Greek letter alpha (α). For instance, a significance level of 5% (α = 0.05) means there is a 5% chance of rejecting a true null hypothesis. When conducting hypothesis tests, a significance level must be specified in order to identify the critical values needed to evaluate the test statistic.

What is a type one error, and what is a type two error? https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244163

Type I error: the rejection of the null hypothesis when it is actually true. Type II error: the failure to reject the null hypothesis when it is actually false.

An investment manager has a pool of five security analysts he can choose from to cover three different industries. In how many different ways can the manager assign one analyst to each industry? https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244135

We can view this problem as the number of ways to choose three analysts from five analysts when the order they are chosen matters. The formula for the number of permutations is: 5 x 4 x 3 = 60 On the TI financial calculator: 5 2nd nPr 3 = 60. Alternatively, there are 5 2nd nCr 3 = 10 ways to select three of the five analysts, and for each group of selected analysts, there are 3! = 3 × 2 × 1 = 6 ways to assign them the three industries. Therefore, there are 10 × 6 = 60 ways to assign the industries to the analysts.

What is the power of a test? https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244163

While the significance level of a test is the probability of rejecting the null hypothesis when it is true, the power of a test is the probability of correctly rejecting the null hypothesis when it is false. The power of a test is actually one minus the probability of making a Type II error, or 1 - P(Type II error). In other words, the probability of rejecting the null when it is false (power of the test) equals one minus the probability of not rejecting the null when it is false (Type II error). When more than one test statistic may be used, the power of the test for the competing test statistics may be useful in deciding which test statistic to use. Ordinarily, we wish to use the test statistic that provides the most powerful test among all possible tests.

The most commonly used standard normal distribution reliability factors are: (https://www.kaplanlearn.com/education/course/node/25593915?nodeId=4244156)

zα/2 = 1.645 for 90% confidence intervals (the significance level is 10%, 5% in each tail). zα/2 = 1.960 for 95% confidence intervals (the significance level is 5%, 2.5% in each tail). zα/2 = 2.575 for 99% confidence intervals (the significance level is 1%, 0.5% in each tail).