ADM 3352 Lecture Notes - Lecture 6: Tangent, Standard Deviation, Business Cycle

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1 Nov 2014

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From the standard deviations and the correlation coefficient we generate the covariance matrix (note that cov(rs,rb) = r. The minimum-variance portfolio is found by applying the formula w (s) = The mean and standard deviation of the minimum variance portfolio are. = [. 17392 . 0900 + . 82612 . 0225 + 2 . 1739 . 8261 . 0045]1/2 = 13. 51% 6-2 s: the proportion of stocks in the optimal risky portfolio is given by. S r ]cov(b,s) f r e(r ) f. The mean and standard deviation of the optimal risky portfolio are. E(rp) = . 4516 20 + . 5484 12 = 15. 61% p = [. 45162 . 0900 + . 54842 . 0225 + 2 . 4516 . 5484 . 0045]1/2 = 16. 54: the reward-to-variability ratio of the optimal cal is. If you require your portfolio to yield a mean return of 14 percent you can find the corresponding standard deviation from the optimal cal.

Related Questions

1. If we are able to eliminate all of the unsystematic or diversifiable risk in a portfolio then, what is the result?

a.

a risk-free portfolio
b.
a portfolio that has an expected return of zero
c.

a portfolio that contains only systematic risk

2. A portfolio consists 20% of a risk-free asset and 80% of a stock. The risk-free return is 4%. The stock has an expected return of 15% and a standard deviation of 30%. Whatâs the expected return of the portfolio?

a.
9.5%
b.
15.0%
c.
12.8%

d.
2%

3. The risk-free rate is 5% and the expected return on the market portfolio is 13%. A stock has a beta of 1.5, what is its expected return?

a.
12%
b.
19.5%
c.

17%

4. For what value of the correlation coefficient for the returns of a pair of stocks will the benefits of diversification the largest?

a.

1.0
b.

-1.0
c.

0.0
d.

0.5

5. Which of the following is an example of systematic risk?
a.
IBM posts lower than expected earnings.
b.
The overall stock market becomes more risky due to super fasting trading algorithms.
c.

Intel announces record earnings.

6. According to the CAPM (capital asset pricing model), the security market line is a straight line. The intercept of this line should be equal to

a.
zero
b.
the expected risk premium on the market portfolio
c.
the expected return on the market portfolio
d.
the risk-free rate

7. A portfolio has 40% invested in Asset 1, 50% invested in Asset 2 and 10% invested in Asset 3. Asset 1 has a beta of 1.2, Asset 2 has a beta of 0.8 and Asset 3 has a beta of 1.8, whatâs the beta of the portfolio?

a.
0.80
b.
1.06
c.
1.27

8. Suppose you can borrow and lend at the risk free-rate of 3%. Which of the following four risky portfolios has the best return relative to risk. (Hint: Calculate Sharpe Ratios the ratio of risk premium to standard deviation for each portfolio)

a.
portfolio with a standard deviation of 15% and an expected return of 12%
b.
portfolio with a standard deviation of 12% and an expected return of 9%
c.
portfolio with a standard deviation of 25% and an expected return of 18%
d.
portfolio with a standard deviation of 19% and an expected return of 15%

9. Which statements are TRUE regarding risk and return?

Statement I:
Diversification is the process of removing systematic risk from a portfolio.
Statement II:
In general, the greater the risk, the greater the return required by an investor.
Statement III:
Investors should focus on real returns if they are concerned about the purchasing power of their wealth.

a.
Statements II and III only
b.
Statement I only
c.
Statements I and III only
d.
Statements I and II only

10. The beta of the risk-free asset is:
a.

1.0
b.

0.5
c.

0.0
d.

-1.0

Please answer all of the following questions

1) In a CAPM framework, prohibiting short sales:

a. will prohibit investors from holding the market portfolio in equilibrium.

b. will make the security market line steeper.

c. will encourage investors to hold more riskless assets.

d. will not change the equilibrium.

2) The beta of an efficient portfolio:

a. must be 1 since an efficient portfolio is perfectly positively correlated with the market portfolio.

b. is proportional to 1, depending on the proportion invested in the market portfolio.

c. is equivalent to the portfolio's standard deviation, since standard deviation is the measure of risk for an efficient portfolio.

d. is always less than 1.

3) Which of the following is not a general conclusion of studies of stock prices?

a. The serial correlation in daily returns in U.S. stocks is positive.

b. The serial correlation in longer period returns (monthly, annual) in U.S. stocks is negative.

c. Filter rules greater than 1% generally do not make money.

d. Stocks that have done well in the past are also likely to do well in the future.

e. There are more runs in daily stock prices than we would expect to find under a random walk.

4) In case of a simple CAPM being used to estimate a time series data:

a. the mean of a residual risk should be equal to zero.

b. the regression coefficient should be equal to zero.

c. the difference between the market return and the riskfree rate of return should be equal to zero.

d. the beta of the portfolio should be equal to zero.

5) The fact that superior returns can not be made by selling stocks that cut dividends is evidence of:

a. weak-form efficiency.

b. semi-strong-form efficiency.

c. strong-form efficiency

6) Which of the following is an implication of market efficiency?

a. Resources are allocated among firms that put them to the best use.

b. No investor will do better than the S&P 500 in any time period.

c. No investor will do better than the S&P 500 consistently after adjusting for risk.

d. No investor will do better than the S&P 500 consistently after adjusting for risk and transactions costs.

7) Which of the following is an attribute of futures contract?

a. There are no limits on the size of the position that any investor can take in financial futures markets.

b. Futures contracts are marked to the market on a daily basis

c. Margins for futures are more relative to other types of markets.

d. Almost all futures positions are settled by delivery.

Question 5

The coefficient of variation is a better measure of risk than the standard deviation if the expected returns of the securities being compared differ significantly.

True

False

Question 6.

In portfolio analysis, we often use ex post (historical) returns and standard deviations, despite the fact that we are interested in ex ante (future) data.

True

False

Question 7

Typically, debentures have higher interest rates than mortgage bonds primarily because the mortgage bonds are backed by assets while debentures are unsecured.

True

False

Question 8

If two firms have the same current dividend and the same expected growth rate, their stocks must sell at the same current price or else the market will not be in equilibrium.

True

False

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Question 9

Which of the following is the best measure of the wealth of a firm's stockholders?

The firm's Net Income during the past year

Expected Earnings per Share during the coming year

Book Value (or Net Worth) as recorded on the balance sheet

The price of the firm's stock on the open market

Flag this Question

Question 10

Consider the following firms:

	Net Income	Stock Price at	Stock Price at
	this year	Beg of Year	End of Year
Firm A:	$10,000,000	$20	$10
Firm B:	$(10,000,000)	$10	$20

The manager of Firm A is doing a better job than B

The manager of Firm B is doing a better job than A

Neither manager is doing a good job

Both managers are doing a good job

Question 11

A company has the following income statement. What is its net operating profit after taxes (NOPAT)?

Sales $1,000
Costs 700
Depreciation 100
EBIT $ 200
Interest expense 50
EBT $ 150
Taxes (40%) 60
Net income $ 90

Question 12

Carter Corporation has some money to invest, and its treasurer is choosing between City of Chicago municipal bonds and U.S. Treasury bonds. Both have the same maturity, and they are equally risky and liquid. If Treasury bonds yield 6 percent, and Carter's marginal income tax rate is 40 percent, what yield on the Chicago municipal bonds would make Carter's treasurer indifferent between the two?

Question 13

If a firm's current ratio is less than 1.0, it indicates that:

The firm had negative net income for the year

The firm will be unable to pay its shortterm loans which come due this year

Current Assets are less than Current Liabilities

The firm is insolvent

Question 14

A firm which has a relatively large amount of cash and receivables in its current assets accounts and a relatively small amount of current liabilities would be considered:

Question 15

In November 2011 you bought 100 shares of Microsoft stock for $35.375 a share. In November 2013 you sold your stock for $92.5625 a share. What was your average annual rate of return on your Microsoft investment? (disregard dividends and commissions)

Question 16

You deposit $2,000 in a savings account that pays 10 percent interest, compounded annually. How much will your account be worth in 15 years?

Question 17

You can earn 8 percent interest, compounded annually. How much must you deposit today to withdraw $10,000 in 6 years?

Question 18

Calculate the required rate of return for Mercury, Inc., assuming that the real rate of interest is 3 percent, investors expect a 5 percent rate of inflation in the future, and they expect the rate of return on the overall stock market to be 13 percent. Mercury has a beta of 2.0.

Question 19

Which is the best measure of risk for an asset held in isolation? Which is the best measure for an asset held in a diversified portfolio?

Variance; correlation coefficient

Standard deviation; correlation coefficient

Beta; variance

Coefficient of variation; beta

Beta; beta

Question 20

You have three stocks in your portfolio. $10,000 is invested in a stock with a beta of 1.50 and $15,000 is invested in a stock with a beta of 1.00, and $25,000 is invested in a stock with a beta of 0.50. What is the beta of your portfolio?

Question 21

A corporate bond with a $1,000 face value pays a $50 coupon every six months. The bond will mature in ten years, and has a nominal yield to maturity of 9 percent. What is the price of the bond?

Question 22

The Jones Company has decided to undertake a large project. Consequently, there is a need for additional funds. The financial manager plans to issue preferred stock with a perpetual annual dividend of $5 per share and a par value of $30. If the required return on this stock is currently 20 percent, what should be the stock's market value?

Question 23

A share of common stock has just paid a dividend of $2.00. If the expected long-run growth rate for this stock is 15 percent, and if investors require a 19 percent rate of return, what is the price of the stock?

Question 24

A stock is not expected to pay a dividend over the next four years. Five years from now, the company anticipates that it will establish a dividend of $1.00 per share (i.e., D5 = $1.00). Once the dividend is established, the market expects that the dividend will grow at a constant rate of 5 percent per year forever. The risk-free rate is 5 percent, the company's beta is 1.2, and the market risk premium is 5 percent. The required rate of return on the companyâs stock is expected to remain constant. What is the current stock price?

ADM 3352 Lecture Notes - Lecture 6: Tangent, Standard Deviation, Business Cycle

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