finance 23013

Historically, stocks have delivered a ________ return on average compared to Treasury bills but have experienced ________ fluctuations in values.

higher, lower

You currently hold a portfolio of three stocks, Delta, Gamma, and Omega. Delta has a volatility of 30%, Gamma has a volatility of 20%, and Omega has a volatility of 20%. Suppose you invest 60% of your money in Delta, and 20% each in Gamma and Omega. What is the highest possible volatility (as a percent) of your portfolio? %

(.60)^2(.30)^2+(.20)^2(.20)^2 + (.20)^2(.20)^2 +2(.60)(0.20)(1)(.30)(.20) + 2(.60)(.20)(1)(.30)(.20) + 2(.20)(.20)(1)(.20)(.20) = square root = 26%

The standard deviation of returns of: I. small capitalization stocks is higher than that of large capitalization stocks. II. large capitalization stocks is lower than that of corporate bonds. III. corporate bonds is higher than that of Treasury bills. Which statement is true?

1, 3 are correct

If the returns on a stock can be characterized by a normal distribution with mean 12%, the probability that returns will be lower than 12% over the next period equals: 46%50% 33%25%

50 %

The volatility of Home Depot stock returns is 30% and that of General Motors stock is 30%. When I hold both stocks in my portfolio, the overall volatility of the portfolio is more information needed 26%. 28%. 30%.

A

The Ishares Bond Index fund (TLT) has a mean (average) and annual standard deviation of realized returns of 5% and 10%, respectively. If these are unbiased estimators of expected returns and future volatility, answer the following. (Round your answers to the nearest integer.) (a) What is the 68% confidence interval for the returns on TLT next year (as a percent)? % to % (b) What is the 95% confidence interval for the returns on TLT next year (as a percent)? % to % (c) What is the 99.7% confidence interval for the returns on TLT next year (as a percent)? % to %

A . (.05-1 x .10) , (.05+1 x .10) = (-5%,15%) B. (.05- 2 x .10), (.05-2 x .10) = (-15%,25%) C. (.05-3 x .10) , (.05-3 x .10) = (-25%,35%)

You are considering how to invest part of your retirement savings. You have decided to put $80,000 into three stocks: 50% of the money in GoldFinger (currently $25/share), 25% of the money in Moosehead (currently $80/share), and the remainder in Venture Associates (currently $2/share). None of the three stocks pay any dividends. Further, after one year, GoldFinger stock goes up to $30/share, Moosehead stock drops to $70/share, and Venture Associates stock rises to $3 per share. (a) What is the return on the portfolio as a percent? (Round your answer to two decimal places.) % (b) If you don't buy or sell shares after the price change, what is the market value (in $) of the portfolio? (Hint: To answer this question, you first need to determine how many shares of each stock you have purchased) $ What are your portfolio weights as percents at year-end? (Round your answers to two decimal places.) GoldFinger % Moosehead % Venture % (c) How many shares of each stock will you have to buy/sell to keep the portfolio weights the same? (Enter positive numbers for shares bought and negative numbers for shares sold. Round your answers to the nearest integer.) GoldFinger shares Moosehead shares Venture shares

A . Rp =Wg x Rg + Wm x Rm + Wv x Rv Rg = 30-25+0/25 = 5/25 =25% Rm = 70-80 + 0 /80 = -10/80 = -12.5% Rv = 3-2+0/2 = 1/2 = %50% Rp 0.50(.25)+.25(-.125)+.25(.50) = 21.88 B. Total Invest = 80000 G = .50 x 80000 = 40000/25 = 1600 M = .25 x 40000 = 20000 / 80 = 250 V = .25 x 4000 = 20000 / 2 = 10000 G = 1600 x 30 = 48000 M = 250 x 70 = 17500 V = 10000 x 3 = 30000 add G+M+V =95500 G = 48000/95500 = 50.26% M = 17500 / 95500 = 18.32% V = 30000/ 95500 = 31.41% C. G = 95500x.50 = 47750/30 = 1591.6 =1600-1591.6 = 8.4 shares sell M = 95500 x .25 = 23875/70 = 341.07 -250 = 90.07 buy V = 95500 x .25 = 23875/3 =7958.3 =10000-7958.3 = 2041.7 sell

Consider the returns for the past 5 months below (returns are in decimals). These past monthly returns are drawn from identical and independent distributions that are the same as those of monthly returns over the next year. 123450.04−0.040.030.07−0.02 (a) Calculate the expected return over the next month (as a percent). % (b) Calculate the standard deviation of returns over the next month (as a percent). (Round your answer to two decimal places.) %

A = 1/t (R1+R2+R3+R4+R5) 1/5(0.04-0.04+0.03+0.07-0.02) = 0.016 = 1.60 % B. = 1/t-1 (R1-R)^2+(R2-R)^2+(R3-R)^2+(R4-R)^2+(R5-R)^2 =1/4[(0.04-0.016)^2+(-0.04-0.016)^2+(0.03-0.016)^2+(0.07-0.016)^2+(-0.02-0.016)^2] = 0.00203 Square root 0.00203 = 4.51%

Suppose you invested $83 in the Ishares High Yield Fund (HYG) a month ago. Immediately after you received a dividend of $0.44 from the fund, you sold the shares for $84. A. What is the (monthly) return on your investment as a percent? (Round your answer to two decimal places.) B. What were your (monthly) dividend yield and percent capital gains yield on the investment as percents? (Round your answers to two decimal places.) dividend yield%capital gains yield% C. What is the relationship between return, dividend yield, and capital gains of a stock? A. Return from investment in the stock is the difference of dividend yield and the capital gain yield. B. Dividend yield is the sum of return from investment in the stock and the capital gain yield. C. Return from investment in the stock is the sum of dividend yield and the capital gain yield. D. There is no relationship between return on investment, dividend yield, and capital gains yield. E. Capital gain yield is the sum of return from investment in the stock and the dividend yield.

A calculate return (Pt-Pt-1+Ct)/Pt-1 or (84-84-1+0.44/84-1 84-83+0.44/83 = 1.73 B. Divided Yield Ct/Pt-1 =0.44/84-1 0.44/83 =53.01 Capital Gains] Pt-Pt-1/Pt-1 = 84-84-1/84-1 = 84-83/83 = 1.20 C. C. Return from investment in the stock is the sum of dividend yield and the capital gain yield.

Which of the following statements is FALSE? A. Almost all of the correlations between stock returns are negative, illustrating the general tendency of stocks to move together. B. Stocks in the same industry tend to have more highly correlated returns than stocks in different industries. C. Stock returns will tend to move together if they are affected similarly by economic events. D. With a positive amount invested in each stock, the more the stocks move together and the higher their correlation, the more variable the portfolio returns will be.

A.

You purchased Enron stock at a price of $42 per share. Its price was $28 after six months and $21 at the end of the year. A. What is the realized return over the first six months in percent? B. What is the realized return over the next six months in percent? C. What is the realized return over the entire year in percent?

A. 28-42/42 = -33.33 B. 21-28/28 = -25.00 C. 21-42/42 = -50.00

The last four years of returns for a stock are provided. 1234−8%+24%+12%+8% (a) What is the stock's average annual return as a percent? % (b) What is the standard deviation (volatility) of the stock's returns as a percent? (Round your answer to two decimal places.) %

A. 1/T (R1+R2+R3+R4) = 1/4 (-.08+.24+.12+.08) = .09 or 9% B. 1/t-1 (R1-R)^2 + (R2-R)^2 + (R3-R)^2 + (R4-R)^2 = 1/3[(-.08-.09)^2 + (.24-.09)^2 + (.12-.09)^2 + (.08-.09)^2 = 0.01746 square root 0.01746 = 13.22

Suppose you invest in 100 shares of Harley-Davidson at $50 per share and 300 shares of Yahoo at $20 per share. Over the next year, the price of Harley-Davidson increases to $80 and the price of Yahoo decreases to $10 per share. (a) What is your profit (in $) from the portfolio? $ (b) Using your answer in part (a), calculate the return on your portfolio (as a percent). % (c) What is the return on your investment in Harley-Davidson stock (as a percent)? % (d) What is the return on your investment in Yahoo stock (as a percent)? % (e) What are the weights (in decimals) of Harley-Davidson and Yahoo in the portfolio at the beginning of the year? (Round your answers to three decimal places.) Harley-DavidsonYahoo (f) A portfolio is a collection of assets. Therefore, the return of a portfolio can also be expressed in terms of the realized returns of each asset in the portfolio and the weight of each asset. Using this idea, compute the realized returns (as a decimal) of the portfolio (this is the approach used by investors and one that we will use for the remainder of the problems). (Round your answer to two decimal places.)

A. Beginning Investment + Dividend- Ending Investment + Dividends 100 x 50 = 5000 + (300 x 20) = 11000 100 x 80 = 8000 + (300 X 10) = 8000 + 3000 beg = 11000 - end = 11000 = 0 B. Capital Gains/ Mv = 9000 - 9000 / 9000 = 0% C. R = Price ending - Price Beg. + D / Po = 80-50+0/50 = 30/50 = 60% D = 10-20+0/20 = -10/20 = -50% E. HD =50(100) = 5000/11000 = 45.45% Yah = 20(300) = 6000/11000 = 54.545% F. Rp=W1xR1+W2xR2 = 0

Suppose you purchased Heico Corp. (HEI) stock on September 30, 2013 for $66.75. On December 31, 2013, right after you received a dividend of $0.48 per share, you sold the stock for $57.98. The company underwent a 5:4 stock split on October 23, 2013. Calculate your realized return (as a percent) over the quarter. What were your quarterly dividend yield and capital gains yield (as percents) from your investment? (Round your answers to two decimal places.) Realized Return %? Dividend Yield %? Capital Gains Yield %?

A. MVend = 57.98 x (5/4) = 72.48 0.48 x (5/4) = .60 Total Return = Total Profits/Amount Invested = 72.48-66.75+.60/66.75 = 9.48 B Dividend Yield = Total Dividend Recieved/ Total Investment = 0.60/66.75 = .89 C. Capital Gains Yield = Total Capital Gains/Total Investment = 72.48-66.75/66.75 =8.58

Greg purchased 871 shares of Bear Stearns and Co. at a price of $84 per share one year ago. Today, the company was acquired by JP Morgan at a price of $10 per share. A. What is Greg's profit/loss (in $) from the investment? B. What is the return on his investment as a percent? (Round your answer to two decimal places.) C. Using your answer in part (b), calculate Greg's profit/loss (in $) if he had purchased 2,131 shares. (Round your answer to the nearest integer.)

A. MVend = 871 x 10 = 8710 MVbeg = 871 x 84 = 73164 Profit/ year =MVend-MVBeg+income = 8710-73164 = -64454 B. Return = profit/amount Inv. -64454/73164 = -88.10 C. MV 2131 = 2131 x 84 = 179004 Profit = Return x Amount Inv. -88.10 x 179004 = -157703

Suppose you invest $20,000 by purchasing 200 shares of Abbott Labs (ABT) at $20 per share, 200 shares of Lowes (LOW) at $40 per share, and 100 shares of Ball Corporation (BLL) at $80 per share. Over the next year Ball has a return of 12.5%, Lowes has a return of 20%, and Abbott Labs has a return of −10%. (a) What is the weight of each of three stocks—Abbott Labs, Lowes, and Ball Corporation—in your portfolio at the beginning of the year (as percents)? Abbott Labs % Lowes % Ball Corporation % (b) What is the return on your portfolio over the year (as percents)? % (c) What is the total profit (capital gains + income received) you made on your portfolio during the year (in $)? $

A. Market Value Abb = 200 shares x 20 = 4000 Low = 200 shares x 40 = 8000 BLL = 100 shares x 80 = 8000 W Abbott = 4000/20000 = 20% Lowes 8000/20000 = 40% BLL = 8000/20000 = 40% B. Rp =w1xr1 + w2+r2 + w3 + r3 =.25(-.10)+.40(.20)+.40(.125)=10.5% C. Total Profit(loss) = Return x amount invested .105x20000= 2100

The table below provides the year-end stock prices along with dividend information for North Air, West Air, and Tex Oil from 2004-2010. Assume dividends are paid at year-end. YearNorth AirWest AirTex OilYear-endStock PriceDividendsper shareYear-endStock PriceDividendsper shareYear-endStock PriceDividendsper share2004$100.00$50.00$50.002005$120.00$1.00$54.00$0.50$49.00$0.002006$155.00$1.00$64.00$1.34$46.00$0.552007$164.00$1.85$67.00$1.48$49.00$1.142008$153.00$2.80$64.00$1.66$58.00$1.292009$147.00$2.94$59.00$1.80$74.00$1.402010$157.29$2.94$74.90$1.80$77.78$1.40 (a) What is the average annual return (as a percent) for each stock? North Air %West Air %Tex Oil % What is the volatility of return (as a percent) for each stock? (Round your answers to two decimal places.) North Air %West Air %Tex Oil % (b) You invest 33% of your money in North Air, 14% in West Air, and 53% in Tex Oil in each period. Assume that the average annual realized returns and past volatility of each stock are unbiased estimators of their expected returns and future volatility. What is the portfolio's expected return and the standard deviation of returns (as percents) next year? The correlation between the returns of North Air and West Air is 62%, correlation between the returns of North Air and Tex Oil is −92.33%, and the correlation between the returns of West Air and Tex Oil is −71.33%. (Round your answer for standard deviation to two decimal places.) expected returns %standard deviation %

A. Northair 2005 Return = 120 - 100 + 1/100 = 21% northair 2006 return = 155- 120 + 1/120 = .30 northair 2007 return = 164 -155 + 1.85 / 155 =.07 north air 2008 return = 153-164+ 2.80 /164 =-0.05 north air 2009 return = 147-153+2.94 /153 = -0.02 north air 2010 return = 157.29 - 147 + 2.94 / 147 = 0.09 Return = 1/6(.21)(.30)(.07)(-.05)(-.02)(.09)=.10 Var = 1/6-1(.21-.10)^2 + (.30-.10)^2 + (.07 -.10)^2 + (-.05-.10)^2 + (-.02-.10)^2 + (.09-.10)^2 = 0.018 square root = 0.13 or 13% West Air 2005 return = 54-50+.50/50 = .09 West Air 2006 return = 64-54+1.34/54 =.21 West Air 2007 return = 67-64+1.48/64 = 0.07 West Air 2008 return = 64-67+1.66/67 = -.02 West Air 2009 return = 59-64+1.80/64 = -.05 West Air 2010 return = 74.90-59+1.80/59 = .30 Return = .09+.21+.07-.02-.05.+.30 /6 = .10 Variance = 1/6-1 (.09-.10)^2 + (.21-.10)^2 + (.07-.10)^2 + (-.02-.10)^2 + (-.05-.10)^2 + (.30-.10)^2 = 0.018 square root = 13% Tex Oil 2005 return = 49 -50 + 0 /50 = -.02 Tex Oil 2006 return = 46-49+.55 / 49 = -.05 Tex Oil 2007 return = 49-46+1.14/46 = .09 Tex Oil 2008 return = 58-49+1.29/49 = .21 Tex Oil 2009 return = 74-58+1.40/58 = .30 Tex Oil 2010 return = 77.78-74+1.40 = 0.07 Return = -0.02+ -0.05 + .09 + .21 + .30 + 0.07 = 10% Var = 1/6-1 (-.02-.10)^2 + (-.05-.10)^2 + (.09-.10)^2 + (.21-.10)^2 + (.30-.10)^2 + (.07-.10)^2 = 0.018 square root = .13 or 13 % B. Expected Return = .33*.1+.14*.1+.53*.1 = 10 Standard Deviation = (0.33)^2 x (0.1341)^2+(.14)^2 x (0.1341)^2 + (.53)^2 x (.1341)^2+2(.33)(.14)(.62)(.1341)(.1341)+2(.33)(.53)(-.9233)(.1341)(.1341) + 2 (.14)(.53)(-.7133)(.1341)(.1341) = 0.0006809 square root = 2.61%

Ten annual returns are listed in the following table. 12345678910−19.9%16.7%17%−50%43.4%1.1%−16.6%−45.7%45.3%−4% (a) What is the average annual return over the ten-year period (as a percent)? % (b) What is the standard deviation of annual returns over the ten-year period (as a percent)? (Round your answer to two decimal places.) % (c) What is the 95% confidence interval on the return of this stock next year (as a percent) if the past average returns and volatility of returns are unbiased estimators of expected returns and future volatility. (Round your answers to two decimal places.) % to %

A. Return = 1/t (R1+R2+R3 + +) 1/10(-.199+.167+.17-.50+.434+.011-.166-.457+.453-.04) = -0.0127 = -1.27% B. Standard Deviation = 1/t-1 (R1 +R)^2 + (R2 + R)^2 + = 1/9 (-.199 +-.0.127)^2 + = 0.1092133 = square root = 33.05 % C R - 2 x SDEV (-.0127 - 2 x .3305) = -67.37% (-.0127 + 2 x .3305) = 64.83%

Suppose Johnson & Johnson and the Walgreen Company have the expected returns and volatilities shown below, with a correlation of 22%. E[R]SD[R]Johnson & Johnson7%18%Walgreen Company10%20% Consider a portfolio that is equally invested in Johnson & Johnson's and Walgreen's stock (a) Calculate the expected return as a percent. % (b) Calculate the volatility (standard deviation) of returns as a percent. (Round your answer to two decimal places.) %

A. Rp = 0.5 (0.07)+0.5(.10) =0.04 B. Var = 0.5^2(.18)^2 + 0.5^2(.20)^2 + 2(0.5)(0.5)(0.22)(.18)(.2) = square root = 14.85%

The realized returns for stock A and stock B from 2004-2009 are provided in the table below Year200420052006200720082009Stock A−8%22%7%−3%4%11%Stock B23%9%32%−1%−6%27% (a) Calculate the expected returns (as percents) over the next year for the stocks assuming the average annual realized returns and past volatility from 2004-2009 are unbiased estimators of expected returns and future volatility. stock A % stock B % Calculate the volatilities (as percents) for returns over the next year for the stocks. (Round your answers to two decimal places.) stock A % stock B % (b) Calculate the expected return and volatility (as percents) of an equally-weighted portfolio. The correlation between the returns of the two stocks is 6.27%. (Round your answer for volatility to two decimal places.) expected return %volatility % (c) Explain why the portfolio has a lower volatility than the average volatility of the two stocks. The correlation of 6.27% is low, so most of factors that affect the returns of one stock have ---Select--- no impact a large impact on the returns of the other asset. Consequently, the risk is ---Select--- lower higher when they are combined in a portfolio.

A. Stock A Return = -8+22+7+-3+4+11/6 = 5.5% Stock B Return = 23+9+32+-1+-6+27/6=14% Variance equation = 1/t-1(R1-R)^2+(R2-R)^2 + + +) Variance for stock a = 10.60% 1/5(-.08-.055)^2+(.22-.055)^2+(.07-.055)^2+(-.03+-.055)^2+(.04-.055)^2+(.11-.055)^2 = square root Variance for stock b = 1/5(.23-.14)^2+(.09-.14)^2+(.32-.14)^2+(-.01-.14)^2+(-.06-.14)^2+(.27-.14)^2 = square root = 15.65% B. Rp = 0.5(0.055)+0.5(.14) =9.75% C. Var P 0.5^2(.1060)^2+0.5^2(.1565)^2 + 2(0.5)(0.5)(0.0627)(0.1060)(0.1565) = square root 0.00945212 = 9.72 %

A portfolio of stocks can achieve diversification benefits if the stocks that comprise the portfolio are perfectly correlated. not perfectly correlated. susceptible to market-wide risks only. both B and C

B

We can reduce volatility by investing in less than perfectly correlated assets through diversification because the expected return of a portfolio is the weighted average of the expected returns of its stocks, but the volatility of returns of a portfolio is less than the weighted average volatility of the assets in the portfolio. is independent of weights of the assets in the portfolio. is higher than the weighted average volatility of the assets in the portfolio. depends on the expected return of the assets in the portfolio.

B

The volatility of Home Depot and General Motors stock returns are identical; volatility of returns for each stock is 30%. When I hold both stocks in my portfolio with an equal amount in each, and the stocks returns have a correlation of less than 1, the overall volatility of returns of the portfolio is less than 30%. cannot say for sure. unchanged at 30%. more than 30%.

C

The volatility of Home Depot stock returns is 30% and that of General Motors stock is 30%. When I hold both stocks in my portfolio and the stocks returns have zero correlation, the overall volatility of returns of the portfolio is unchanged at 30%. more than 30%. less than 30%. cannot say for sure.

C

Which of the following statements is FALSE? A. The expected return of a portfolio is simply the weighted average of the expected returns of the investments within the portfolio. B. Portfolio weights add up to 1 so that they represent the way we have divided our money between the different individual investments in the portfolio. C. Without trading, the portfolio weights will decrease for the stocks in the portfolio whose returns are above the overall portfolio return. D. A portfolio weight is the fraction of the total investment in the portfolio held in an individual investment in the portfolio.

C

Stocks tend to move together if they are affected by common economic events. idiosyncratic shocks. company specific events .unrelated to the economy.

Common economic events

Stocks A, B, and C all have an expected return of 10% and a standard deviation of 25%. Stocks A and B have returns that are independent of one another, i.e., their correlation coefficient equals zero. Stocks A and C have returns that are negatively correlated with one another, i.e., it is less than 0. Portfolio AB is a portfolio with half of its money invested in Stock A and half in Stock B. Portfolio AC is a portfolio with half of its money invested in Stock A and half invested in Stock C. Which of the following statements is CORRECT? Portfolio AB has a standard deviation that is equal to 25% .Portfolio AC has an expected return that is less than 10%. Portfolio AC has an expected return that is greater than 10%. Portfolio AC has a standard deviation that is less than 25%. Portfolio AB has a standard deviation that is greater than 25%.

D

The amount of a stock's risk that is diversified away depends on the other stocks in the portfolio but not how much is invested in the stocks. depends on market risk premium. is independent of the portfolio that you add it to. depends on the portfolio that you add it to. depends on risk-free rate of interest.

D

Which of the following statements is FALSE? To find the risk of a portfolio, we need to know more than the risk and return of the component stocks; we need to know the degree to which the stocks' returns move together. Independent risks are uncorrelated. Because the prices of the stocks do not move identically, some of the risk is averaged out in a portfolio. The variance of a portfolio depends only on the variance of the individual stocks.

D

Over the past 75 years, we have observed that investments with the highest average annual returns also tend to have the highest standard deviations of annual returns. This observation supports the notion that there is a positive correlation between risk and return. Which of the following answers correctly ranks investments from highest to lowest risk (and return), where the security with the highest risk is shown first, the one with the lowest risk last?

Small-company stocks, large-company stocks, long-term corporate bonds, long-term government bonds, U.S. Treasury bills.

You have a portfolio with a standard deviation of 35% and an expected return of 16%. You are considering adding one of the two stocks in the table below. After adding the stock you will have 20% of your money in the new stock and 80% in your existing portfolio. Expected returnStandard DeviationCorrelation withyour portfolio's returnsStock A13%25%0.2 Stock B13%20%0.6 Calculate the expected return and volatility (as percents) if you choose stock A. (Round your answer for volatility to two decimal places.) expected return % volatility % Calculate the expected return and volatility (as percents) if you choose stock B. (Round your answer for volatility to two decimal places.) expected return % volatility % Which one should you add? stock A stock B

Stock A = E(Rp) = w1(R1)+w2(R2) = .80(.16)+.20(.13) = 0.154 or 15.4 % Variance = .80^2x.35^2+.2^2x.25^^2 + 2(.8)(.2)(.2)(.35).25) = 0.0865 square root = 29.41 Stock B = E(Rp) = w1(R1)+w2(R2) =.80(.16)+ .20(.13) =0.154 or 15.4% variance = .80^2x.35^2+.20^2x.20^2+2(.8)(.20)(.6)(.35)(.20)= 0.09344 square root = 30.57

A portfolio comprises two stocks, A and B, with equal amounts of money invested in each. If stock A's stock price increases and that of stock B decreases, the weight of stock A in the portfolio will increase. FALSE TRUE

True

Even if the correlation between the returns on two securities is +1.0, if the securities are combined in the correct proportions with positive weights, the resulting 2-asset portfolio can have less risk than either security held alone. FALSE TRUE

True

Portfolio A has but one security, while Portfolio B has 100 securities. Because of diversification effects, we would expect Portfolio B to have the lower risk. However, it is possible for Portfolio A to be less risky. TRUE FALSE

True

The correlation of the returns of the two assets does not play any role in computation of the expected return of the two asset portfolio. FALSE TRUE

True

When adding a new stock to an existing portfolio, the higher (or more positive) the degree of correlation between the new stock and those already in the portfolio, the less the additional stock will reduce the portfolio's risk. FALSE TRUE

True

When we combine stocks in a portfolio, the amount of risk that is eliminated depends on the degree to which the stocks face common risks and move together. TRUE FALSE

True

The realized returns for stock A and stock B from 2004-2009 are provided in the table below Year200420052006200720082009Stock A−8%22%7%−3%4%11%Stock B20%6%29%−4%−9%24% Suppose you create a portfolio that is 80% invested in stock A and 20% invested in stock B. The correlation between the returns of the two stocks is 6.27%. (a) Calculate the expected return and volatility (as percents) of this portfolio. (Round your answer for volatility to two decimal places.) expected return %volatility % (b) Calculate the relevant risk (as a percent) of each asset in this portfolio (the risk the investor cares about). The correlation between the returns of this portfolio and stock A, Corr(RA, RP), is 94.09%. The correlation between the returns of this portfolio and stock B, Corr(RB, RP), is 39.71%. (Round your answers to two decimal places.) stock A %stock B %

Varp = 0.8^2 (.1060)^2 + .2^2(.1565)^2+2(.80)(.2)(.0627)(.1060)(.1565) = square root = 9.22 B. Relevant Risk stock A = SDA*Cor(RaRp) = 0.1060(.9409) = .10% Stock B = .1565(.3971) = 0.06 = 6%

Stocks A and B have the following historical returns: YearStock A's returnsStock B's returns2003−19.00%(−15.50%200434.00%21.80%200514.00%31.50%2006−0.50%−8.60%200726.00%25.30% (a) Calculate the average rate of return and standard deviation of returns (as percents) for each stock during the 5-year period. (Round your standard deviations to two decimal places.) stock Aaverage rate of return %standard deviation % stock Baverage rate of return %standard deviation % (b) Assume that someone held a portfolio consisting of 50% of stock A and 50% of stock B and that the average annual realized returns and past volatility of each stock are unbiased estimators of their expected returns and future volatility. What is the portfolio's expected return and the volatility of next year's returns (as percents)? The correlation between the returns of the two stock is 85.28%. (Round your answers to two decimal places.) expected return %volatility %

a Return A = 1/t (R1+R2+R3+R4+R5) = (-.19)+(.34)+(.14)+(-.50)+(.26)/5 = .01 or 1% Variance = 1/t-1 [(r1-R)^2 +(r2-R)^2 + + + ] square root 1/4[(-.19-.01)^2+(.34-.01)^2 + (.14-.01)^2 + (-.50-.01)^2 + (.26-.01)^2 = 0.0911101 square root = 30.18 Return B = (-.1550)+(.2180)+(.3150)+(-.0860)+(.2530)/5 = 0.109 or 10.9% variance = 1/4 [(-.1550-.109)^2 + (.2180-.109)^2 + (.3150-.109)^2 + (-.0860-.109)^2 + (.2530-.109)^2 = 0.0456935 square root = 21.38 B. Expected Return E(Rp) =w1(R1)+w2(R2) = .50 (.01) + .50 (.109) = 0.0595 or 5.95% Volatility= Wa^2[SD(ra)]^2 + Wb^2 [SD(rb)]^2+2WaWbCorr (Ra1)(Rb)SD(Ra)SD(rb) = (.50)^2 [.3018]^2 + (.50)^2[.2138]^2 + 2(.50)(.50)(.8528)(.3018)(.8528)(.2138) = 5.77

Your client has $100,000 invested in stock A. She would like to build a two-stock portfolio by investing another $100,000 in either stock B or C. Expected returnStandard DeviationCorrelation with AStock A13%60% Stock B11%30%0.4 Stock C11%30%0.3 Which stock do you advise her to choose? stock B stock C What will be the expected return and standard deviation (as percents) of the portfolio she chooses? (Round your answer for standard deviation to two decimal places.) expected return % standard deviation %

choose stock B lowest correlation to stock A Expected Return E(Rp) = w1(R1) + w2(R2) =.50 (.13) + .50 (.11) = 0.12 or 12% Variance = .50^2(.60)^2+.50^2(.30)^2+2(.50)(.50)(.04)(.60)(.30) = 34.07

A portfolio's risk is measured by the weighted average of the standard deviations of the securities in the portfolio. It is this aspect of portfolios that allows investors to combine stocks and actually reduce the riskiness of a portfolio. FALSE TRUE

false

On average, stocks with high returns are expected to have

high variability.

Which of the following investments offered the highest overall return over the past eighty years?

small stocks

Investors demand a higher return for investments that have larger fluctuations in values because

they do not like risk

You observe a portfolio for five years and determine that its average annual return is 15% and the standard deviation of its returns is 21%. Can you be 95% confident that this portfolio will not lose more than 30% of its value next year? Yes No

yes