Practice Problems – Midterm I

1. Multiple Choice

This problem includes ten multiple-choice questions. Choose only one answer for each question. You do not have to explain why you have selected a particular one. If you feel that a question is ambiguous, feel free to write a justification for your answer on the test sheet.

  1. The return on stock A is 4%, on stock B is 8%, and on stock C is -6%. What is the return on an equally weighted portfolio of stock A, B, and C?

A)-5.5%

B)-1%

C)2%

D)4%

  1. An unbiased estimator is one in which

A) the expectation shrinks as the sample size gets large.

B) the variance shrinks as the sample size gets small.

C) the expectation equals the parameter being estimated.

D) the variance equals the parameter being estimated.

  1. Which of the following best indicates a type II error?

A) accepting a true null

B) rejecting a true null

C) accepting a false null

D) rejecting a false null

  1. Firms often acquire short term debt by issuing ______to the public.

A)banker’s acceptances

B)commercial paper

C)t-bills

D)certificates of deposit

  1. Which of the following describes a “best efforts” arrangement between an investment bank and client who wants to launch an IPO?

A)The bank acts as a broker in finding potential buyers for the IPO

B)The bank acts as a dealer, and buys the shares from the client

C)The bank issues the IPO through an auction market

D)The client must find a buyer through a direct search market

  1. A limit buy order is an order to

A)Buy a stock when the price rises above a certain level

B)Buy a stock when the price volatility falls below a certain level

C)Buy a stock when the price falls below a certain level

D)Buy a stock when the price volatility rises above a certain level

  1. The over-the-counter market is

A)NASDAQ

B)Located in New York

C)An informal network of brokers and dealers

D)Used only by small investors

E)None of the above

  1. The Federal Funds rate is

A)The rate charged by the Federal Reserve to borrow funds at the discount window

B)The rate banks charge each other for over night loans to meet reserve requirements

C)The rate charged by the US treasury to foreign central banks

D)The rate US agencies charge each other for loans to meet project demands

  1. A price-weighted index is composed of two stocks: A and B. The price of A is 20 and the price of B is 30. If the level of the index is initially 40 and stock A suddenly splits two for one, then the index divisor before the split was ______and after the split is ______.

A)1.00; 1.25

B)1.25; 1.50

C)1.25; 1.00

D)1.50; 1.00

E)2.00; 1.25

  1. If the outcomes for random variables x and y are governed by a joint discrete PDF, and x is independent of y, then we know

A)Joint probabilities are the products of the marginals.

B)Conditional expectations are equal to unconditional expectations.

C)The correlation is zero.

D)All of the above.

Free Response:

  1. Assume the market is semi-strong form efficient. Is it possible for the market to not be semi-strong form efficient? Is it possible for the market to not be weak form efficient? Explain.
  1. Historical annual returns (over the last 4 years) for stock ABC: {10%, 15%, 2%, 7%}

a)Estimate the expected return.

b)Estimate the variance and standard deviation of the return:

c)Assume over the last 4 years you had a portfolio with 30% of your equity in stock ABC and the rest in a risk-free bond earning 5%. What would have been the realized return each year on your portfolio over the last four years? (I am asking for four numbers.) Assume you rebalance at the end of each year to keep portfolio weights constant.

d)Use your answer from part (c) to estimate the expected return of your portfolio.

e)Verify stat rule #1.

  1. Suppose you expect the return on a stock over the next year to be either 0.18 with 70% probability or -0.15 with 30% probability. You have $10,000 of which $6,000 is invested in the stock and $4000 is invested in risk-free bonds which pay 7% annually.

a)Calculate the expected return of your portfolio.

b)Calculate the variance of your portfolio.

c)Calculate the standard deviation of your portfolio.

  1. You gather data on IBM stock over the last 5 years: {12%, 5%, -8%, 2%}. Test the null hypothesis that the true mean IBM return is zero.
  1. Use the following PDF to answer the questions below:

A)What is E[rA|rI]=10?

B)What is E[rA|rI]=-5?

C)Calculate the correlation between stock A and the Index fund.

  1. The following output is created by using Excel to estimate a regression where the return on IBM is the y or dependentvariable, and the contemporaneous return on the market is the x or explanatory variable:

Coefficients / Standard Error / T Stat
Intercept / 0.0852 / 0.0569 / 1.4983
X Variable 1 / 1.0786 / 0.0185 / 4.2520

A)What is the conditional expectation of IBM given that the return on the market portfolio is 10%?

B)Given that the total variance of IBM stock is 0.04, and the total variance of the market portfolio is 0.025, what fraction of IBM’s variance is explained by variation in the market?

C)Test the null hypothesis that the true slope coefficient in the regression is 1.0.

  1. You have placed a limit buy order with your broker at $40.

A)Assume your broker has sought to place the order on the OTC market. If the best ask your broker finds is 40.35, and the best bid is 39.30, should the order be executed?

B)Now assume your broker seeks to place your order on an exchange. If the lowest limit sell in the limit order book is currently 40.35 and the highest limit buy is 39.30, what happens to your order?

C)Repeat parts A and B above assuming you have placed a stop buy order with your broker at $40.

D)Repeat parts A and B above assuming you have placed a stop sell (stop loss) order with your broker at $40.

  1. Assume you own a portfolio with a standard deviation of 0.14. There are two assets in the portfolio. The first asset has a standard deviation of 0.30 and 45% of your portfolio is invested in this asset. The other asset has a standard deviation of 0.40, and 55% of your portfolio is invested in this asset. What is the correlation between the two assets?
  1. Given: E[X]=10, E[Y]=10, Var[X]=20, Var[Y]=40, Corr[X,Y]=0.90. If conditional expectations are linear functions, what is:

A)E[Y|X=3]?

B)E[X|Y]=3?

C)For what value, z, does E[X|Y=z]=E[Y|X=z]?

  1. Assume that the return for some stock is governed by the following continuous pdf:

where rS is the return from buying the stock

a)Verify that the area under the pdf is equal to 1.

b)What is the expected return?

c)What is the standard deviation?

d)If you buy this stock, what is the probability you’ll lose20% or more?

e)If you have 65% of your equity in this stock, and 35% in a risk-free bond that pays 4%, what is the expected return and standard deviation on your portfolio?

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