FINAN EXAM 5

If you receive a $2 dividend per share on your 100 shares, your total dividend income is ____.

$2 x 100

geometric average return: 11.14, 37.13, 43.31, -8.91, -25.26

((1.1114)(1.3713)(1.4331)(1-.0891)(1-.2526))^1/5-1 = 1.4870 ^1/5 -1 = YX 5 1/X = -1 = 0.0826 OR N=5 PV= -1 PMT=0 FV= 1.4870 CPT I/Y= 8.26% OVERALL AVG IS 11.48% GAR< ARITHMENTIC AVG

If the economy booms, Meyer&Co. stock will have a return of 21.3 percent. If the economy goes into a recession, the stock will have a loss of 13.6 percent. The probability of a boom is 62 percent while the probability of a recession is 38 percent. What is the standard deviation of the returns on the stock?

(.62*21.3)+(0.38*-13.6)= 8.038 .62(21.3-8.038)^2= 109.0459993 .38(-13.5-8.038)^2= 177.9171567?????

The Ibbotson SBBI data show that over the long-term, ___.

- small-company stocks generated the highest average return - T-bills, which had the lowest risk, generated the lowest return - small-company stocks had the highest risk level

Percent Return: Dividend Yield

DY= D(t+1)/Pt

What is the beta of the risk-free asset?

zero

You have a portfolio that is equally invested in Stock F with a beta of .95, Stock G with a beta of 1.37, and the market. What is the beta of your portfolio?

(1/3*.95)+((1/3*1.37)+(1/3*0) =.77

You purchased shares of stock one year ago at a price of $62.81 per share. During the year, you received dividend payments of $1.85 and sold the stock for $69.93 per share. If the inflation rate during the year was 2.23 percent, what was your real return?

(69.93-62.81+1.85)/62.81 =0.142811654 1+0.142811654)/(1+0.0223)-1= 11.79%(Approx).

Risk premium

- Excess return on a risky asset over the risk-free rate - Reward for bearing risk

You own a stock portfolio invested 15 percent in Stock Q, 25 percent in Stock R, 40 percent in Stock S, and 20 percent in Stock T. The betas for these four stocks are .78, .87, 1.13, and 1.45, respectively. What is the portfolio beta?

= 0.78*15% + 0.87*25% + 1.13*40% + 1.45*20% = 1.0765 = 1.08

What is unsystematic risk?

It is a risk that affects a single asset or a small group of assets

Risk

Risk is measured by the dispersion, spread, or volatility of returns.

Returns

• Total Return = Expected return + unexpected return R=E(R)+U • Unexpected return (U) = Systematic portion (m) + Unsystematic portion (ε) • Total Return = Expected return E(R) + Systematic portion m + Unsystematic portion ε = E(R) + m + ε

Geometric average

- Average compound return per period over multiple periods - Answers the question: "What was your average compound return per year over a particular period?"

Which of the following are true based on the year-to-year returns from 1926-2014?

- Common stocks frequently experience negative returns. - T-bills sometimes outperform common stocks.

Portfolio Variance

- Compute portfolio return for each state: RP,i = w1R1,i + w2R2,i + ... + wmRm,i -Compute the overall expected portfolio return using the same formula as for an individual asset - Compute the portfolio variance and standard deviation using the same formulas as for an individual asset

______ risk is reduced as more securities are added to the portfolio

- Diversifiable - Company-specific - Unsystematic

Which one of the following is defined as a bell-shaped frequency distribution that is defined by its average and its standard deviation?

Normal distribution

Return Variability

Normal distribution: - A symmetric frequency distribution - The "bell-shaped curve" - Completely described by the mean and variance

The risk premium for an individual security is based on which one of the following types of risk?

Systematic

What is the intercept of the security market line (SML)?

The risk-free rate

The calculation of a portfolio beta is similar to the calculation of:

a portfolio's expected return

In an efficient market ______ investments have a _____ NPV.

all; zero

The geometric average return is the average_______ return earned per year over a multiyear period.

compound

True or false: To get the average return, the yearly returns are summed and then multiplied by the number of returns.

false

The second lesson from studying capital market history is that risk is:

handsomely rewarded

The risk-return relationship states that a riskier investment should demand a ____________ return.

higher

An investment will have a negative NPV when its expected return is _______ ________ what the financial markets offer for the same risk.

less than

Variance & Standard Deviation example

look at able 1) E(r)-Expected Return = square this x p(i) 2) add them all together to get variance 3) take square root of variance

#3 Use the following returns for X and Y. a.Calculate the average returns for X and Y. b.Calculate the variances for X and Y. c.Calculate the standard deviations for X and Y.

look at pic

SML example

look at table A: 7.5+(12.0-7.5) 1.3 = 13.35% market required return E(R) is higher than the req return which means price is low and this stock is undervalued B: 7.5+(12.0-7.5).08= 11.1% E(R) is lower than the req return which means price is high and this stock is overvalued

Example: Portfolio Weights

look at table 1) % of Pf = dollar invested/ total dollar invested 2) E(Rj)= % of Pf x E(Rj)

Example: Expected Returns

look at table how to calculate expected return: recession P(i) x E(Ra) + neutral P(i) x E(Ra + Boom P(i) x E(Ra do same for Stock B

The second lesson from studying capital market history states that the _______ the potential reward, the _______ the risk

lower; lower greater; greater

Systematic risk is also called ______________ risk.

market

To get the average, or _______return, the yearly returns are summed and then divided by the number of returns.

mean

If you use a geometric average to project short-run wealth levels, your results will most likely be _______ .

pessimistic

True or false: It is possible for the unsystematic risk of a portfolio to be reduced almost to zero.

true

True or false: The dividend yield = Dt+1/Pt

true

True or false: The risk premium can be interpreted as a reward for bearing risk

true

The standard deviation for large-company stock returns from 1926 to 2017 is:

19.8%

The probability of a return being within ± one standard deviation of the mean in a normal distribution is approximately ___ percent.

68

If the market changes and stock prices instantly and fully reflect new information, which time path does such a change exhibit?

An efficient market reaction

Percent Return: Capital Gains Yield

CGY = P(t +1) − Pt P t% Return = DY + CGY % Return = Dt +1 + Pt +1 − Pt P

Which of the following are ways to make money by investing in stocks?

Capital gains Dividends

You have $250,000 to invest in a stock portfolio. Your choices are Stock H, with an expected return of 13.4 percent, and Stock L, with an expected return of 10.2 percent. If your goal is to create a portfolio with an expected return of 11.3 percent, how much money will you invest in Stock H? In Stock L?

Consider investment in H=$A Hence investment in L=(250,000-A) Portfolio return= Weights * Stock return 11.3= ((A / 250,000)*13.4) + (250,000-A)/250,000) * 10.2 (11.3*250,000) = 2,550,000-10.2A+13.4A 2825000=13.4A+2,550,000-10.2A x=(2825000-2,550,000)/(13.4-10.2) Invest in H =$ 85937.5 Invest in L = (250,000-H) =$164062.5

You own a portfolio that has $3,140 invested in Stock A and $4,300 invested in Stock B.Assume the expected returns on these stocks are 9 percent and 14 percent, respectively. What is the expected return on the portfolio?

Total value=(3140+4300)=$7440 Portfolio return=Respective return*Respective weight =(3140/7440*9)+(4300/7440*14) which is equal to =11.89%(Approx).

Risk-Return Tradeoff

Two key lessons from capital market history: - There is a reward for bearing risk - The greater the potential reward, the greater the risk

Which one of the following best exemplifies unsystematic risk?

Unexpected increase in the variable costs for a firm

The total dollar return is the sum of dividends and __________.

capital gains or losses

When a company declares a dividend, shareholders generally receive ____.

cash

The average return on the stock market can be used to ___.

compare stock returns with the returns on other securities

The ________return on a portfolio is a combination of the expected returns on the assets in the portfolio.

expected

A stock has an expected return of 11.4 percent, the risk-free rate is 3.7 percent, and the market risk premium is 6.8 percent. What must the beta of this stock be?

expected return= risk free rate + beta x Market risk premium 0.114= 0.037+beta x 0.068 0.114-.037= beta x 0.068 .007 = beta x 0.068 1.13= beta

In an efficient market, firms should expect to receive ______ value for securities they sell.

fair

True or false: Discounting a news item is the same as taking the present value of that item.

false

True or false: Historical return data indicates that as the number of securities in a portfolio increases, the standard deviation of returns for the portfolio increases.

false

True or false: The smaller the variance or standard deviation is, the more spread out the returns will be.

false: The larger the variance of standard deviation is, the more spread out the returns will be.

True or false: The standard deviation is the variance squared.

false: The standard deviation is the square root of the variance.

Security Market Line

• The security market line (SML) is the representation of market equilibrium • The slope of the SML = reward-to-risk ratio: (E(RM) - Rf) / βM • Slope = E(RM) - Rf = market risk premium - Since β of the market is always 1.0

The two potential ways to make money as a stockholder are through _______ and capital appreciation.

Dividends

what is systematic risk?

It is a risk that pertains to a large number of assets.

What is a risk premium?

It is additional compensation for taking risk, over and above the risk-free rate

What is an uncertain or risky return?

It is the portion of return that depends on information that is currently unknown.

Historical Risk Premiums

Large Stocks: 12.1 - 3.4 = 8.7% Small Stocks: 16.5 - 3.4 = 13.1% L/T Corporate Bonds: 6.4 - 3.4 = 3.0% L/T Government Bonds: 6.0 - 3.4 =2.6% U.S. Treasury Bills: * 3.4 - 3.4 = 0*

Unsystematic risk will affect

- firms in a single industry - a specific firm

a portfolio is invested in security A with E(Ra)=10% and security B with E(Rb)=30% what is the E(Rp) if: - half is in A and Half is in B - 1/4 is in A and 3/4 is in B

- half is in A and Half is in B 0.5x10+0.5x30=20 - 1/4 is in A and 3/4 is in B 0.25x10+0.75x30=25

The true risk of any investment comes from:

-surprises -unanticipated events

If the arithmetic average return is 10% and the variance of returns is 0.05, find the approximate geometric mean.

0.10 -1/2 * 0.05 = 7.5%

What are the arithmetic and geometric average returns for a stock with annual returns of 8 percent, 9 percent, -7 percent, and 16 percent?

1 .08 2 .09 3 -.07 4 .16 total .26 .26/4=.065= 6.50 ((1.08)(1.09)(1.07)(1.16))^1/4-1 = 6.16%

Variance, s.d geometric mean returns: -10% 24% 19%

1) attribute mean = (-10+24+19)/3 = 11% 2) variance = ((-10-11)^2+(24-11)^2+(19-11)^2)/3-1= 674/2= 337 3) sd: sq root 337= 18.36% 4) Geometric= ((.90)(1.24)(1.19))^1/3-1 = 9.92% GAR< ATTRIBUTE

Arrange the following investments from highest to lowest risk (standard deviation) based on what our study of capital market history from 1926-2014 has revealed as shown in Table 10.3:

1. Small company common stock. 2. Large company common stock. 3. Long-term corporate bonds. 4. Long term government bonds. 5. U.S. Treasury bills.

The arithmetic mean for large-company stock returns from 1926 to 2017 is:

12.1%

consider an asset with a beta of 1.2 a risk free rate of 5% and a market return of 13%. what is the reward to risk ration

13%-5%/1=0.08 expected return on asset 5%+(13%-5%)*1.2=14.6%

The probability of an outcome being at least 2 standard deviations below the mean in a normal distribution is approximately:

2.5%

What is the expected return of a security with a beta of 1.2 if the risk-free rate is 4 percent and the expected return on the market is 12 percent?

4%+1.2(12% - 4% )=13.6%

An asset has an average return of 9.99 percent and a standard deviation of 18.93 percent. What range of returns should you expect to see with a 68 percent probability?

9.99 +- 1 x 18.93 = 9.99-18.93 to 9.99+18.93 = -8.94% to 28.92%

With a normal distribution, the probability that we end up withing two standard deviations is about _______ percent.

95

Portfolio Risk Variance & Standard Deviation

Portfolio standard deviation is NOT a weighted average of the standard deviation of the component securities' risk - if it were there would not be a benefit to diversification

Which of the following types of risk is not reduced by diversification?

Systematic, or market risk

Example: Calculating Historical Variance and Standard Deviation

TABLE 1) calc returns up and divide by number of them 2) put avg in next colunm 3) diff: Take return - avg return 4) sqr deviation: take diff and square it 5) Variance: take sqr dev added up / # of observations -1 6) Standard dev: take variance squared

Efficient Capital Markets

The Efficient Market Hypothesis: - Stock prices are in equilibrium - Stocks are "fairly" priced - Informational efficiency If true, you should not be able to earn "abnormal" or "excess" returns Efficient markets DO NOT imply that investors cannot earn a positive return in the stock market

What is the slope of the security market line (SML)?

The market-risk premium

Which of the following are needed to describe the distribution of stock returns?

The mean return The standard deviation of returns

overreaction and correction

The price over-adjusts to the new information, but eventually falls to the appropriate price.

According to the capital asset pricing model (CAPM), what is the expected return on a security with a beta of zero?

The risk-free rate of return

What is the equation for total return?

Total Return = Expected Return + Unexpected Return

Total Risk = Stand-Alone Risk

Total risk = Systematic risk + Unsystematic risk - the standard dev is a measure of total risk • For well-diversified portfolios, unsystematic risk is very small ->Total risk for a diversified portfolio is essentially systematic risk The expected return (market required return) on an asset depends only on that asset's systematic or market risk.

True or false: The expected return is the return that an investor expects to earn on a risky asset in the future.

True

A stock had returns of 14.71 percent, 19.29 percent, −16.53 percent, 12.53 percent, and 26.56 percent for the past five years. What is the variance of the returns?

[0.1471 + 0.1929 + (-0.1653) + 0.1253 + 0.2656] / 5= 0.11312 or 11.312% [(0.1471 - 0.11312)^2 + (0.1929 - 0.11312)^2 + (-0.1653 - 0.11312)^2 + (0.1253 - 0.11312)^2 + (0.2656 - 0.11312)^2] / 4= 0.027109 or 0.02711

What is the Reward-to-Risk Ratio?

[E(RA) - Rf]/βA

A positive capital gain on a stock results from ___.

an increase in price

Some important characteristics of the normal distribution are that it is:

bell-shaped symmetrical

True or false: The surprise part of any announcement is the information the market uses to form the expectation of the return on the stock.

false: The surprise is the news that influences the unanticipated return on the stock.

You decide to invest in a portfolio consisting of 24 percent Stock X, 45 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio? LOOK AT TABLE

https://www.chegg.com/homework-help/questions-and-answers/decide-invest-portfolio-consisting-24-percent-stock-x-45-percent-stock-y-remainder-stock-z-q42582770 5.37%

An efficient market is one in which any change in available information will be reflected in the company's stock price ___.

immediately

Dividends are the ______ component of the total return from investing in a stock.

income

An efficient market is one that fully reflects all available ______.

information

Stock prices fluctuate from day to day because of:

information flow

The capital gains yield can be found by finding the difference between the ending stock price and the initial stock price and dividing it by the:

initial stock price

Fred works for Apple. If he can make an excess profit from his knowledge of new products the company releases what can we say about market efficiency?

its not strong form efficient

If a study of a firm's financial information will not lead to gains in the market, then the market must be at least _____ efficient.

semi-strong form

The variance and its square root, the_______ , are the most commonly used measures of volatility.

standard deviation

Dollar & Percent Returns: Total percent return

the return on an investment measured as a percentage of the original investment. • % Return = $ Return/$ Invested

You've observed the following returns on Yamauchi Corporation's stock over the past five years: −10 percent, 24 percent, 21 percent, 11 percent, and 8 percent. The average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 4.1 percent. a. What was the average real return on the stock? b.What was the average nominal risk premium on the stock?

yr-----return 1 -.10 2 .24 3 .21 4 .11 5 .08 .540 avg return= .540/5 = 10.80% a) ((1+.1080)/(1+.031))-1 = 7.47 b) (.1080-.041)= 6.70%

Portfolio Beta

βp = Weighted average of the Betas of the assets in the portfolio Weights (wj)= % of portfolio invested in asset j

Common Misconceptions about EMH

• EMH does not mean that you can't make money • EMH does mean that: - On average, you will earn a return appropriate for the risk undertaken - There is no bias in prices that can be exploited to earn excess returns - Market efficiency will not protect you from wrong choices if you do not diversify - you still don't want to put all your eggs in one basket

Systematic Risk

• Factors that affect a large number of assets • "Non-diversifiable risk" • "Market risk" • Examples: changes in GDP, inflation, int rates

Interpretation of Beta

• Ifβ=1.0, • Ifβ>1.0, • Ifβ<1.0, • Most stocks have betas in the range of 0.5 to 1.5 • Beta of the market = 1 • Beta of a T-Bill =0

Market Equilibrium

• In equilibrium, all assets and portfolios must have the same reward-to-risk ratio • Each ratio must equal the reward-to-risk ratio for the market E(RA)−Rf/ βA=E(RM −Rf ) /βM

Portfolios

• Portfolio = collection of assets • An asset's risk and return impact how the stock affects the risk and return of the portfolio • The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets

2008: The Bear Growled and Investors Howled

• The S&P 500 lost 50% of its value from November 2007 through March 2009 - On the other hand, long-term Treasuries gained 40% during 2008 • A Global Phenomenon • Volatile in both directions - The S&P 500 doubled in value from March 2009 through February 2011

Arithmetic vs. Geometric Mean Which is better?

• The arithmetic average is overly optimistic for long horizons The geometric average is overly pessimistic for short horizons Depends on the planning period under consideration • 15 - 20 years or less: use arithmetic• 20 - 40 years or so: split the difference between them • 40 + years: use the geometric

Variance & Standard Deviation

• Variance and standard deviation measure the volatility of returns • Variance = Weighted average of squared deviations • Standard Deviation = Square root of variance

The Ibbotson-Sinquefield data shows that:

*long-term corporate bonds had less risk or variability than stocks *U.S. T-bills had the lowest risk or variability

#6 Consider the following table for different assets for 1926 through 2017. TABLE a.What range of returns would you expect to see 68 percent of the time for large-company stocks? b.What about 95 percent of the time?

- 68% of times, the values in a normal distribution would lie within + and - 1 standard deviation of mean. - 95% of times, the values in a normal distribution would lie within + and - 2 standard deviation of mean. Question a For 68%, the confidence interval will be within +1 and -1 of standard deviation. Lower level = 12.1% - (1 * 19.8%) = -7.70% Higher level = 12.1% + (1 * 19.8%) = 31.90% Question b For 95%, the confidence interval will be within +2 and -2 of standard deviation. Lower level = 12.1% - (2 * 19.8%) = -27.50% Higher level = 12.1% + (2 * 19.8%) = 51.70%

Unsystematic Risk

- = Diversifiable risk - Risk factors that affect a limited number of assets - Risk that can be eliminated by combining assets into portfolios - "Unique risk" - "Asset-specific risk" Examples: labor strike, part shortages

Announcements, News, and Efficient Markets

- Announcements and news contain both expected and surprise components - The surprise component affects stock prices Efficient markets result from investors trading on unexpected news - The easier it is to trade on surprises, the more efficient markets should be Efficient markets involve random price changes because we cannot predict surprises

Which of the following are examples of unsystematic risk?

- Changes in management - Labor strikes

The Principle of Diversification

- Diversification can substantially reduce risk without an equivalent reduction in expected returns7477 - reduce the variability of return - Caused by the off set of worse-than-expected returns from one asset by better-than-expected returns from another - Minimum level of risk that cannot be diversified away = systematic portion

Forms of Market Efficiency: Strong-formEfficientMarket

- Information = Public or private - "Inside information" is of little use

Forms of Market Efficiency: Weak-formEfficientMarket

- Information = past prices and volume data - Technical analysis is of little use

Forms of Market Efficiency: Semi strong-form Efficient Market

- Information = publicly available information - Fundamental analysis is of little use

Which of the following are examples of a portfolio?

- Investing $100,000 in a combination of stocks and bonds - Investing $100,000 in the stocks of 50 publicly traded corporations - Investing $100,000 in a combination of US and Asian stocks

As more securities are added to a portfolio, what will happen to the portfolio's total unsystematic risk?

- It is likely to decrease. - It may eventually be almost totally eliminated.

What are the two components of risky return (U) in the total return equation?

- Market risk - Unsystematic risk

Risk-free rate

- Rate of return on a riskless investment - Treasury Bills are considered risk-free

Which of the following are examples of systematic risk?

- Regulatory changes in tax rates - Future rates of inflation

Arithmetic average

- Return earned in an average period over multiple periods - Answers the question: "What was your return in an average year over a particular period?"

Reward-to-Risk Ratio

- Reward-to-Risk Ratio: - = Slope of line on graph - In equilibrium, ratio should be the same for all assets - When E(R) is plotted against β for all assets, the result should be a straight line

Beta and the Risk Premium

- Risk premium = E(R)-Rf - The higher the beta, the greater the risk premium should be - CAPM defines the relationship between the risk premium and beta so that we can estimate the expected return

Which of the following are examples of information that may impact the risky return of a stock?

- The Fed's decision on interest rates at their meeting next week - The outcome of an application currently pending with the Food and Drug Administration.

The CAPM shows that the expected return for an asset depends on which three things?

- The amount of systematic risk - The pure time value of money - The reward for bearing systematic risk

Market Risk for Individual Securities

- The contribution of a security to the overall riskiness of a portfolio - Relevant for stocks held in well-diversified portfolios - Measured by a stock's beta coefficient, βj - Measures the stock's volatility relative to the market

Portfolio Expected Returns

- The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio - Weights (wj) = % of portfolio invested in each asset

Which of the following statements is (are) true about variance?

- Variance is a measure of the squared deviations of a security's return from its expected return. - Standard deviation is the square root of variance.

Percentage returns are more convenient than dollar returns because they:

- apply to any amount invested - allow comparison against other investments

What two factors determine a stock's total return?

- expected return - unexpected return

The systematic risk principle argues that the market does not reward risks:

- that are diversifiable - that are borne unnecessarily

Example: Calculating Total Dollar and Total Percent Returns - You invest in a stock with a share price of $25. - After one year, the stock price per share is $35 - Each share paid a $2 dividend What was your total return?

--------------Dollar----------------------% Div 2.00 2/25= 8% Cap Gain 35-25 = 10 $10/25= 40 % Total Return 2+10=12 $12/$25 = 48%

Portfolio Risk

1. Calculate Expected Portfolio Return in each state of the economy and overall (Slide 11-12) 2. Compute deviation (DEV) of expected portfolio return in each state from total expected portfolio return 3. Square deviations (DEV^2) found in step 2 4. Multiply squared deviations from Step 3 times the probability of each state occurring (x p(i)) 5. The sum of the results from Step 4 = Portfolio Variance take -3 -10 = dev -13% ^2 = .01663 x .25 = .00416, add them all up = var (square root var)

Expected Portfolio Return

1. Calculate expected portfolio return in each state: 2. Apply the probabilities of each state to the expected return of the portfolio in that state 3. Sum the result of step 2 step 1: P(i) x E(Ra) + neutral P(i) x E(Ra + Boom P(i) x E(Ra Step 2: take weighted avg Stock V 30% x -20% Step 3: overall expected return, take P(i) x portfolio %

The computation of variance requires 4 steps. Place the steps in the correct order from the first step to the last step.

1. Calculate the expected return 2. Calculate the deviation of each return from the expected return 3. Square each deviation 4. Calculate the average squared deviation

A dividend yield of 10% says that, for each dollar we invest, we get _______ cents in dividends.

10

You purchased a zero-coupon bond one year ago for $267.35. The market interest rate is now 5.3 percent. If the bond had 25 years to maturity when you originally purchased it, what was your total return for the past year? Assume semiannual compounding.

1000 x (1/(1+r)^n r= .053/2=.0265 n= (25-1)x2= 48 Price of zero coupon bond after 1 year: 1000 x (1/(1.0265)^48)= 284.95 Total return for the past year: (284.95-267.35/267.35)x100= 6.58%

A portfolio consists of $17,000 in Stock M and $27,900 invested in Stock N. The expected return on these stocks is 9.80 percent and 13.40 percent, respectively. What is the expected return on the portfolio?

12.04%

Treasury Bills yielded a nominal average return over 86 years of 3.5% versus an average inflation rate of 3.0% over the same period. This makes the real return on T-bills approximately equal to _____.

3.5%-3.0% = 0.5%

Roger Ibbotson and Rex Sinquefield presented year-to-year historical rates of return on______ types of financial investments.

5

You purchased 250 shares of a particular stock at the beginning of the year at a price of $104.32. The stock paid a dividend of $2.34 per share, and the stock price at the end of the year was $113.65. What was your dollar return on this investment?

Dollar return=(End value-Beginning value+Dividend)*250 shares =(113.65-104.32+2.34)*250 which is equal to =$2917.5

Factors Affecting Required Return

E(Rj)=Rf +(E(RM)−Rf)βj • Rf measures the pure time value of money • RPM = (E(RM)-Rf) measures the reward for bearing systematic risk • βj measures the amount of systematic risk

A stock has an expected return of 10.9 percent, its beta is .90, and the risk-free rate is 2.8 percent. What must the expected return on the market be?

Expected return = Risk-free rate + Beta(Expected return on the market - Risk-free rate) 0.109 = 0.028 + 0.90(Expected return on the market - 0.028) 0.109 - 0.028 = 0.90(Expected return on the market - 0.028) 0.081 = 0.90(Expected return on the market - 0.028) Expected return on the market - 0.028 = 0.081 / 0.90 Expected return on the market - 0.028 = 0.09 Expected return on the market = 0.09 + 0.028 Expected return on the market = 0.118 or 11.8%

What is the equation for the capital asset pricing model?

Expected return on security = Risk-free rate + Beta × (Return on market - Risk-free rate)

The risk-free rate is 2.8 percent and the market expected return is 12.5 percent. What is the expected return of a stock that has a beta of .92?

Expected return=risk-free rate +Beta*(MArket rate- risk-free rate) =2.8+0.92*(12.5-2.8) which is equal to =11.72%(Approx).

Expected Returns

Expected returns are based on the probabilities of possible outcomes

What is the definition of expected return?

It is the return that an investor expects to earn on a risky asset in the future.

You bought one of Rocky Mountain Manufacturing Co.'s 5.7 percent coupon bonds one year ago for $1,032.15. These bonds make annual payments and mature nine years from now. Suppose you decide to sell your bonds today, when the required return on the bonds is 5.1 percent. If the inflation rate was 3.5 percent over the past year, what would be your total real return on the investment?

N = 9; I/Y = 5.1; PMT = 5.7%*1000 = 57; FV = 1000; CPT PV= -1042.46 [$1042.46 + $57 - $1032.15] / $1032.15 = $67.31 / $1032.15 = 0.0652, or 6.52% [(1 + 0.0652) / (1 + 0.035)] - 1 = 1.0292 - 1 = 0.0292, or 2.92%

Which type of stock price adjustment time path occurs when there is a bubble (price run up) in the path followed by a decline after the market receives information about the stock?

Overreaction and correction

Diversifying a portfolio across various sectors and industries might do more than one of the following. However, this diversification must do which one of the following?

Reduce the portfolio's unique risks

On a particular risky investment, investors require an excess return of 7 percent in addition to the risk-free rate of 4 percent. What is this excess return called?

Risk premium

Return Variability Review: Standard deviation

SD(R) or σ - Square root of the variance - Sometimes called volatility - Same "units" as the average

Which one of the following is the most apt to have the largest risk premium in the future based on the historical record for 1926-2014?

Small-company stocks

What are the portfolio weights for a portfolio that has 185 shares of Stock A that sell for $64 per share and 115 shares of Stock B that sell for $49 per share?

Stock A: Market value: 185*64= $11,840 Portfolio Weights: 11,840/ 17,475= 0.6775 Stock B: Market value: 115*49 = $5,635 Portfolio Weights: $5,635/$17,475= 0.3225 Market Value total: $17,475 Portfolio Weights: $17,475/$17,475= 1.000

The SML and Required Return

The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM) E(Rj)=Rf +(E(RM)−Rf)βj E(Rj)=Rf +(RPM)βj Rf = Risk-free rate (T-Bill or T-Bond) RM = Market return ≈ S&P 500RPM = Market risk premium = E(RM) - Rf E(Rj) = "Required Return of Asset j"

Capital Asset Pricing Model

The capital asset pricing model (CAPM) defines the relationship between risk and return E(RA) = Rf + (E(RM) - Rf)βA If an asset's systematic risk (β) is known, CAPM can be used to determine its expected return

efficient market reaction

The price instantaneously adjusts to the new information.

How are the unsystematic risks of two different companies in two different industries related?

There is no relationship.

Arrange the following investments starting from lowest historical risk premium to highest historical risk premium.

U.S. Treasury Bills, Long-term corporate bonds, large-company stocks, small company stocks

Return Variability Review: Variance

VAR(R) or σ2 - Common measure of return dispersion - Also called variability

What will the dividend income be on W number of shares of XYZ stock if XYZ distributes a $Y per share dividend?

W x $Y

A stock has had the following year-end prices and dividends: Year---Price----Dividend 1 $ 64.10 — 2 74.05 $ 1.10 3 67.61 1.25 4 76.25 1.45 5 82.70 1.60 6 93.15 1.75 What are the arithmetic and geometric returns for the stock?

Year---Price---Dividend--Returns 1 64.1 2 74.05. 1.1 17.24% 3 67.61 1.25 -7.01% 4 76.25. 1.45 14.92% 5 82.7 1.6 10.56% 6 93.15 1.75 14.75% Arithmetic Average Returns = 10.09% Geometric Average Returns = 9.71%

If you wish to create a portfolio of stocks, what is the required minimum number of stocks?

You must invest in stocks of more than one corporation.

Suppose a stock had an initial price of $87 per share, paid a dividend of $2.15 per share during the year, and had an ending share price of $98. a.Compute the percentage total return. b.What was the dividend yield? c.What was the capital gains yield?

a.percentage total return=(End value-Beginning value+Dividend)/Beginning value =(98-87+2.15)/87=15.11%(Approx). b.Dividend yield=Dividend/Beginning value =(2.15/87)=2.47%(Approx). c.Capital gains yield=(End value-Beginning value)/Beginning value =(98-87)/87=12.64%(Approx).

When a dollar in the future is discounted to the present it is worth less because of the time value of money, but when a news item is discounted, it means that the market:

already knew about most of the news item

The dividend yield for a one-year period is equal to the annual dividend amount divided by the ____.

beginning stock price

The CAPM can also be used for a portfolio by first determining the portfolio's

beta

The percentage change in the price of a stock over a period of time is called its ___________.

capital gains yeild

The geometric average rate of return is approximately equal to ___

compounding

The appropriate discount rate to use to evaluate a new project is the _____.

cost of capital

The minimum required return on a new project is known as the:

cost of capital

Historical return data indicates that as the number of securities in a portfolio increases, the standard deviation of returns for the portfolio:

declines

The total return percentage is the _________ yield plus the capital gains yield.

dividend

You purchased 260 shares of stock at a price of $46.56 per share. Over the last year, you have received total dividend income of $280. What is the dividend yield?

dividend yield =( (280/260) / 46.56 )*100 = 2.3 %

The total dollar return on a stock is the sum of the ____ and the _____.

dividends; capital gains

True or false: Percentage returns are difficult to use for comparisons because they depend on the dollar amount invested. True false question.

false

True or false: A well-diversified portfolio will eliminate all risks.

false: Even if the portfolio is well diversified, the investor is still exposed to systematic risk

True or false: Calculating the expected return is the last step in the computation of variance.

false: It is the first step.

True or false: Portfolio weights can be defined as the dollars invested in each asset.

false: It is the percentage of dollars invested in each asset.

True or false: Labor strikes are an example of systematic risk.

false: Labor strikes are an example of unsystematic risk.

True or false: Expected return and inflation are the two components of risky return in the total return equation.

false: Market risk and unsystematic risk are the two components of risky return in the total return equation.

True or false: Arithmetic and geometric averages are useful because they are not influenced by volatility.

false: More volatility in returns produces a greater difference between the arithmetic and geometric averages.

True or false: Because T-bills have low risk relative to common stocks, T-bills cannot outperform common stocks.

false: T-bills sometimes outperform common stocks.

True or false: Since the CAPM equation can be used only for individual securities, it cannot be used with portfolios.

false: The CAPM can also be used for a portfolio by first determining the portfolio's beta.

True or false: The geometric average rate of return measures the return in an average year over a given period.

false: The arithmetic average rate of return measures the return in an average year over a given period.

True or false: The calculation of the portfolio beta is similar to the calculation of the portfolio weights.

false: The calculation of the portfolio beta is similar to the calculation of the expected return.

True or false: The capital gains yield = (Pt+1 - Pt)/Dt

false: The capital gains yield = (Pt+1 - Pt)/Pt

True or false: The expected return of a portfolio is a combination of the weights of each asset in a portfolio.

false: The expected return on a portfolio is a combination of the expected returns on the assets in the portfolio.

True or false: The dividend yield minus the capital gains yield is the total return percentage.

false: The total return percentage is the dividend yield plus the capital gains yield.

True or false: The average return of a given period is typically not a good estimate of the returns over that same period.

false: Without any other information, you can use the average return from a time period as a "best guess" of the return in a given year from that same period.

If the dispersion of returns on a particular security is very spread out from the security's mean return, the security ____.

highly risky

#3 a. Calculate the expected return for the two stocks. b.Calculate the standard deviation for the two stocks.

https://www.chegg.com/homework-help/questions-and-answers/consider-following-information-rate-return-state-occurs-probability-state-economy-stock-st-q42847326?trackid=ef008df2fd3a&strackid=394792f0b4d7

#4 a. Your portfolio is invested 25 percent each in A and C and 50 percent in B. What is the expected return of the portfolio? b-1.What is the variance of this portfolio? b-2.What is the standard deviation of this portfolio?

https://www.chegg.com/homework-help/questions-and-answers/consider-following-information-rate-return-state-occurs-state-probability-economy-state-ec-q41437089

More volatility in returns produces ______ difference between the arithmetic and geometric averages.

large

Systematic risk will ____ when securities are added to a portfolio.

not change

If you use an arithmetic average to project long-run wealth levels, your results will most likely be _______.

optimistic

If investors are risk averse, it is reasonable to assume that the risk premium for the stock market will be:

positive

Normally, the excess rate of return is _____.

positive

The security market line (SML) shows that the relationship between a security's expected return and its beta is ______.

positive

The risk _____ can be interpreted as the reward for bearing risk.

premium

Assuming markets are (only) weak form efficient, investors can make excess profits from______ information?

public or private

Historically, the real return on Treasury bills has been:

quite low

An unrealized gain is treated the same as a realized gain when computing the total ______

return

The arithmetic average rate of return measures the ____.

return in an average year over a given period

The excess return is the difference between the rate of return on a risky asset and the ______ rate.

risk free

If an asset has a reward-to-risk ratio of 6.0%, that means it has a __________ of 6.0% per unit of _______.

risk premium; systematic risk

Historical Average Returns

simple, or arithmetic average Using the data in - Table 10.1: - Sum the returns for large-company stocks from 1926 through 2014, you get about 10.77/89 years = 12.1%. • Your best guess about the size of there turn for a year selected at random is 12.1%.

Using capital market history as a guide, it would appear the greatest reward would come from investing in _______.

small-company common stock

The standard deviation is the ______ of the variance.

square root

Dan is a chemist for ABC, a major drug manufacturer. Dan cannot earn excess profits on ABC stock based on the knowledge he has related to his experiments if the financial markets are:

strong form efficient.

Efficient Market Hypotheses

strong: public and private info semistrong: public info weak: security market info

The _____ is the news that influences the unanticipated return on the stock.

surprise

The true risk of any investment comes from ____________

surprises

Even if the portfolio is well diversified, the investor is still exposed to _____ risk.

systematic

The return expected on an investment depends only on the asset's _____ risk.

systematic

Beta tells us the amount of ________ risk of an asset or portfolio relative to ______.

systematic; an average risky asset

For a risky security to have a positive expected return but less risk than the overall market, the security must have a beta:

that is > 0 but < 1.

To determine the appropriate required return for an investment, we can use _______________

the Security Market Line

Two ways of calculating average returns are _______ and _______.

the arithmetic average the geometric average

The geometric average rate of return is approximately equal to ___.

the arithmetic mean minus half of the variance

A portfolio can be described by its portfolio weights which are defined as _____________________.

the percentage of dollars invested in each asset

delayed reaction

the price partially adjusts to the new information; eight days elapse before the price completely reflects the new information

The average risk premium on long-term government bonds for the period 1926-2014 was equal to:

the rate of return on the bonds minus the T-bill rate.

Dollar & Percent Returns: Total dollar return

the return on an investment measured in dollars • $ Return = Dividends + Capital Gains • Capital Gains = Price received - Price paid

If the standard deviation of a portfolio is __________?

the square root of the variance

The standard deviation is ___.

the square root of the variance

Geometric average < arithmetic average unless all the returns are equal

true

Roger Ibbotson and Rex Sinquefield conducted a famous set of studies dealing with rates of return in U.S. financial markets.

true

The weights of the securities held in any portfolio must equal 1.0.

true

True or false: A capital gain on a stock is counted as part of the total return whether or not the gain is realized from selling the stock.

true

True or false: A capital loss is the same thing as a negative capital gain.

true

True or false: According to the capital asset pricing model (CAPM), the risk-free rate of return is the expected return on a security with a beta of zero.

true

True or false: Adding securities will reduce unsystematic risk only. Systematic risk is unaffected by diversification.

true

True or false: The normal distribution is completely described by the average and standard deviation.

true

True or false: Unsystematic risk is specific only to a single company or industry.

true

Average returns can be calculated:

two diff ways

The square of the standard deviation is equal to the ____.

variance

The normal distribution is completely described by the _______ and ________.

variance or standard deviation mean

If a study of past stock prices and volume to find mis-priced securities will not lead to gains in the market, then the market must be at least _____ efficient.

weak-form

The efficient markets hypothesis contends that _____________ capital markets such as the NYSE are efficient.

well-organized