## Example 64 Confidence Interval for the Population Mean of Sharpe Ratiosz Statistic

Suppose an investment analyst takes a random sample of U.S. equity mutual funds and calculates the average Sharpe ratio. The sample size is 100, and the average Sharpe ratio is 0.45. The sample has a standard deviation of 0.30. Calculate and interpret the 90 percent confidence interval for the population mean of all U.S. equity mutual funds by using a reliability factor based on the standard normal distribution. The reliability factor for a 90 percent confidence interval, as given earlier, is...

## Example 71 Risk and Return Characteristics of an Equity Mutual Fund

You are analyzing Sendar Equity Fund, a midcap growth fund that has been in existence for 24 months. During this period, it has achieved a mean monthly return of 1.50 percent with a sample standard deviation of monthly returns of 3.60 percent. Given its level of systematic (market) risk and according to a pricing model, this mutual fund was expected to have earned a 1.10 percent mean monthly return during that time period. Assuming returns are normally distributed, are the actual results...

## Regression Statistics

Explain how the bad data affected the results. 16. Diet Partners charges its clients a small management fee plus a percentage of gains whenever portfolio returns are positive. Cleo Smith believes that strong incentives for portfolio managers produce superior returns for clients. In order to demonstrate this, Smith runs a regression with the Diet Partners' portfolio return in percent as the dependent variable and its management fee in percent as the independent variable. The estimated regression...

## TABLE 79 Nonparametric Alternatives to Parametric Tests

Between means Tests concerning mean differences paired comparisons tests We pointed out that when we use nonparametric tests, we often convert the original data into ranks. In some cases, the original data are already ranked. In those cases, we also use nonparametric tests because parametric tests generally require a stronger measurement scale than ranks. For example, if our data were the rankings of investment managers, hypotheses concerning those rankings would be tested using nonparametric...

## Example 73 The Effect of Commercial Paper Issuance on Stock Prices

Commercial paper CP is unsecured short-term corporate debt that, like U.S. Treasury bills, is characterized by a single payment at maturity. When a company enters the CP market for the first time, how do stock market participants react to the announcement of the CP ratings Nayar and Rozeff 1994 addressed this question using data for the period October 1981 to December 1985. During this period, 132 CP issues 96 industrial and 36 non-industrial received an initial rating in Standard amp Poor's...

## Example 34 Median and Arithmetic Mean The Case of the Price Earnings Ratio

Suppose a client asks you for a valuation analysis on the seven-stock U.S. common stock portfolio given in Table 3-10. The stocks are equally weighted in the portfolio. One valuation measure that you use is P E, the ratio of share price to earnings per share EPS . Many variations exist for the denominator in the P E, but you are examining P E defined as current price divided by the current mean of all analysts' EPS estimates for the company for the current fiscal year Consensus Current EPS in...

## Forecast XNumber of Analysts n

Because the sample is a small fraction of the number of analysts who follow this stock, assume that we can ignore the finite population correction factor. A. What are the mean forecast and standard deviation of forecasts B. What aspect of the data makes us uncomfortable about using Rabies to construct confidence intervals for the population mean forecast 9. Explain the differences between constructing a confidence interval when sampling from a normal population with a known population variance...

## Example 67 Biases in Investment Research

An analyst is reviewing the empirical evidence on historical U.S. equity returns. She finds that value stocks i.e., those with low P Bs outperformed growth stocks i.e., those with high P Bs in some recent time periods. After reviewing the U.S. market, the analyst wonders whether value stocks might be attractive in the United Kingdom. She investigates the performance of value and growth stocks in the U.K. market from January 1990 to December 2003. To conduct this research, the analyst does the...

## Example 57 Probability That a Lending Facility Covenant Is Breached

You are evaluating the bonds of a below-investment-grade borrower at a low point in its business cycle. You have many factors to consider, including the terms of the company's bank lending facilities. The contract creating a bank lending facility such as an unsecured line of credit typically has clauses known as covenants. These covenants place restrictions on what the borrower can do. The company will be in breach of a covenant in the lending facility if the interest coverage ratio, EBITDA...

## Example 512 Potential Gains from Market Timing A Monte Carlo Simulation

All active investors want to achieve superior performance. One possible source of superior performance is market timing ability. How accurate does an investor need to be as a bull- and bear-market forecaster for market timing to be profitable What size gains compared with a buy-and-hold strategy accrue to a given level of accuracy Because of the variability in asset returns, a huge amount of return data is needed to find statistically reliable answers to these questions. Chua, Woodward, and To...

## Example 413 Inferring Whether Drive Meds EPS Met Consensus EPS

You are still an investor in DriveMed stock. To review the givens, your prior probabilities are P EPS exceeded consensus 0.45, P EPS met consensus 0.30, and P EPS fell short of consensus 0.25. You also have the following conditional probabilities P DriveMed expands I EPS exceeded consensus 0.75 P DriveMed expands I EPS met consensus 0.20 P DriveMed expands I EPS fell short of consensus 0.05 Recall that you updated your probability that last quarter's EPS exceeded the consensus estimate from 45...

## Example 52 One Period Stock Price Movement as a Bernoulli Random Variable

Suppose we describe stock price movement in the following way. Stock price today is S. Next period stock price can move up or down. The probability of an up move is p, and the probability of a down move is 1 - p. Thus, stock price is a Bernoulli random variable with probability of success an up move equal to p. When the stock moves up, ending price is uS, with u equal to 1 plus the rate of return if the stock moves up. For example, if the stock earns 0.01 or 1 percent on an up move, u 1.01....

## Client Portfolio

Source www.multexinvestor.com 51 In particular, diluted EPS is for continuing operations and before extraordinary items and accounting changes. Source www.multexinvestor.com 51 In particular, diluted EPS is for continuing operations and before extraordinary items and accounting changes. Based only on the information in the above table, calculate the following for the portfolio A. i. Arithmetic mean P E ii. Median P E B. i. Arithmetic mean P S ii. Median P S C. i. Arithmetic mean P B ii. Median...

## Example 46 Conditional Probabilities and Predictability of Mutual Fund Performance

The purpose of the Kahn and Rudd 1995 study, introduced in Example 4-2, was to address the question of repeat mutual fund winners and losers. If the status of a fund as a winner or a loser in one period is independent of whether it is a winner in the next period, the practical value of performance ranking is questionable. Using the four events defined in Example 4-2 as building blocks, we can define the following events to address the issue of predictability of mutual fund performance Fund is a...

## Solving For Rates Number Of Periods Or Size Of Annuity Payments

In the previous examples, certain pieces of information have been made available. For instance, all problems have given the rate of interest, r, the number of time periods, N, the annuity amount, A, and either the present value, PV, or future value, FV. In real-world applications, however, although the present and future values may be given, you may have to solve for either the interest rate, the number of periods, or the annuity amount. In the subsections that follow, we show these types of...

## Net Present Value And Internal Rate Of Return

In applying discounted cash flow analysis in all fields of finance, we repeatedly encounter two concepts, net present value and internal rate of return. In the following sections we present these keystone concepts. We could explore the concepts of net present value and internal rate of return in many contexts, because their scope of application covers all areas of finance. Capital budgeting, however, can serve as a representative starting point. Capital budgeting is important not only in...

## 480x2-220x-200

The left-hand side of this equation details the outflows 200 at time t 0 and 225 at time t 1. The 225 outflow is discounted back one period because it occurs at t 1. The right-hand side of the equation shows the present value of the inflows 5 at time t 1 discounted back one period and 480 the 10 dividend plus the 470 sale proceeds at time t 2 discounted back two periods . 9 In the United States, the money-weighted return is frequently called the dollar-weighted return. We follow a standard...

## Client Invests 5million Portfolio And Invests 5 Percent Of It In A Money Market Fund Projected To Earn3 Percent

Table 1-6 shows how the initial investment of 4,329.48 can actually generate five 1,000 withdrawals over the next five years. TABLE 1-6 How an Initial Present Value Funds an Annuity Time at the Beginning of Ending Amount Before Available After Period the Time Period Withdrawal Withdrawal Withdrawal 1,952.38 1,000 952.38 5 952.38 952.38 1.05 1,000 1,000 0 To interpret Table 1-6, start with an initial present value of 4,329.48 at t 0. From t 0 to t 1, the initial investment earns 5 percent...