306 week 9 pt 2

book7

The expected return of an asset is the sum of each return times the probability of that return occurring. So, the expected return of each stock asset is: E(RA) = .10(.04) + .60(.09) + .30(.17) E(RA) = .1090, or 10.90% E(RB) = .10(-.17) + .60(.12) + .30(.27) E(RB) = .1360, or 13.60% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, then add all of these up. The result is the variance. So, the variance and standard deviation of each stock are: sA 2 = .10(.04 - .1090) 2 + .60(.09 - .1090) 2 + .30(.17 - .1090) 2 sA 2 = .00181 sA = .001811/2 sA = .0425, or 4.25% sB 2 = .10(-.17 - .1360)2 + .60(.12 - .1360)2 + .30(.27 - .1360)2 sB 2 = .01490 sB = .014901/2 sB = .1221, or 12.21%

book6

The expected return of an asset is the sum of each return times the probability of that return occurring. So, the expected return of the asset is: E(R) = .10(-.15) + .60(.09) + .30(.23) E(R) = .1080, or 10.80%

book 5

The expected return of an asset is the sum of each return times the probability of that return occurring. So, the expected return of the asset is: E(R) = .20(-.08) + .80(.15) E(R) = .1040, or 10.40%

1. Determining Portfolio Weights [LO1] What are the portfolio weights for a portfolio that has 115 shares of Stock A that sell for $43 per share and 180 shares of Stock B that sell for $19 per share?

The portfolio weight of an asset is the total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total portfolio value = 115($43) + 180($19) Total portfolio value = $8,365 The portfolio weight for each stock is: WeightA = 115($43)/$8,365 = .5912 WeightB = 180($19)/$8,365 = .4088

2. Information and Market Returns [LO3] Suppose the government announces that, based on a just-completed survey, the growth rate in the economy is likely to be 2 percent in the coming year, as compared to 5 percent for the past year. Will security prices increase, decrease, or stay the same following this announcement? Does it make any difference whether the 2 percent figure was anticipated by the market? Explain.

. If the market expected the growth rate in the coming year to be 2 percent, then there would be no change in security prices if this expectation had been fully anticipated and priced. However, if the market had been expecting a growth rate other than 2 percent and the expectation was incorporated into security prices, then the government's announcement would most likely cause security prices in general to change; prices would drop if the anticipated growth rate had been more than 2 percent, and prices would rise if the anticipated growth rate had been less than 2 percent.

4. Systematic versus Unsystematic Risk [LO3] Indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp.'s stock to change price: a. The government announces that inflation unexpectedly jumped by 2 percent last month. b. Big Widget's quarterly earnings report, just issued, generally fell in line with analysts' expectations.c. The government reports that economic growth last year was at 3 percent, which generally agreed with most economists' forecasts. d. The directors of Big Widget die in a plane crash. e. Congress approves changes to the tax code that will increase the top marginal corporate tax rate. The legislation had been debated for the previous six months.

. a. a change in systematic risk has occurred; market prices in general will most likely decline. b. no change in unsystematic risk; company price will most likely stay constant. c. no change in systematic risk; market prices in general will most likely stay constant. d. a change in unsystematic risk has occurred; company price will most likely decline. e. no change in systematic risk; market prices in general will most likely stay constant assuming the market believed the legislation would be passed.

1. Diversifiable and Nondiversifiable Risks [LO3] In broad terms, why are some risks diversifiable? Why are some risks nondiversifiable? Does it follow that an investor can control the level of unsystematic risk in a portfolio, but not the level of systematic risk?

1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of assets, this unique portion of the total risk can be eliminated at little cost. On the other hand, there are some risks that affect all investments. This portion of the total risk of an asset cannot be costlessly eliminated. In other words, systematic risk can be controlled, but only by a costly reduction in expected returns.

4. Portfolio Expected Return [LO1] You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 12.1 percent and Stock Y with an expected return of 9.8 percent. If your goal is to create a portfolio with an expected return of 10.85 percent, how much money will you invest in Stock X? In Stock Y?

Here we are given the expected return of the portfolio and the expected return of each asset in the portfolio and are asked to find the weight of each asset. We can use the equation for the expected return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1 (100%), the weight of Stock Y must be one minus the weight of Stock X. Mathematically speaking, this means: E(RP) = .1085 = .121wX + .098(1 - wX) We can now solve this equation for the weight of Stock X as: .1085 = .121wX + .098 - .098wX .0105 = .023wX wX = .4565 So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = .4565($10,000) Investment in X = $4,565.22 And the dollar amount invested in Stock Y is: Investment in Y = (1 - .4565)($10,000) Investment in Y = $5,434.78

12. Calculating Portfolio Betas [LO4] You own a portfolio equally invested in a risk-free asset and two stocks. If one of the stocks has a beta of 1.17 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?

The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio is as risky as the market, it must have the same beta as the market. Since the beta of the market is one, we know the beta of our portfolio is one. We also need to remember that the beta of the risk-free asset is zero. It has to be zero since the asset has no risk. Setting up the equation for the beta of our portfolio, we get: bP = 1.0 = 1/3(0) + 1/3(1.17) + 1/3(bX) Solving for the beta of Stock X, we get: bX = 1.83

Calculating Portfolio Betas [LO4] You own a stock portfolio invested 20 percent in Stock Q, 30 percent in Stock R, 35 percent in Stock S, and 15 percent in Stock T. The betas for these four stocks are .79, 1.23, 1.13, and 1.36, respectively. What is the portfolio beta?

The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta of the portfolio is: bP = .20(.79) + .30(1.23) + .35(1.13) + .15(1.36) bP = 1.13

8. Calculating Expected Returns [LO1] A portfolio is invested 25 percent in Stock G, 55 percent in Stock J, and 20 percent in Stock K. The expected returns on these stocks are 11 percent, 9 percent, and 15 percent, respectively. What is the portfolio's expected return? How do you interpret your answer?

The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. So, the expected return of the portfolio is: E(RP) = .25(.11) + .55(.09) + .20(.15) E(RP) = .1070, or 10.70% If we own this portfolio, we would expect to get a return of 10.70 percent.

3. Portfolio Expected Return [LO1] You own a portfolio that is invested 35 percent in Stock X, 20 percent in Stock Y, and 45 percent in Stock Z. The expected returns on these three stocks are 9 percent, 15 percent, and 12 percent, respectively. What is the expected return on the portfolio?

The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. So, the expected return of the portfolio is: E(RP) = .35(.09) + .20(.15) + .45(.12) E(RP) = .1155, or 11.55%

2. Portfolio Expected Return [LO1] You own a portfolio that has $3,480 invested in Stock A and $7,430 invested in Stock B. If the expected returns on these stocks are 8 percent and 11 percent, respectively, what is the expected return on the portfolio?

The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total portfolio value = $3,480 + 7,430 Total portfolio value = $10,910 CHAPTER 13 - 3 So, the expected return of this portfolio is: E(RP) = ($3,480/$10,910)(.08) + ($7,430/$10,910)(.11) E(RP) = .1004, or 10.04%

book9

a. To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the expected return of an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets, so the return of the portfolio in each state of the economy is: Boom: RP = (.08 + .17 + .24)/3 = .1633, or 16.33% Bust: RP = (.11 - .05 -.08)/3 = -.0067, or -.67% To find the expected return of the portfolio, we multiply the return in each state of the economy by the probability of that state occurring, and then sum the products. Doing so, we find: E(RP) = .75(.1633) + .25(-.0067) E(RP) = .1208, or 12.08% CHAPTER 13 - 5 b. This portfolio does not have an equal weight in each asset. We still need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get: Boom: RP = .20(.08) +.20(.17) + .60(.24) = .1940, or 19.40% Bust: RP = .20(.11) +.20(-.05) + .60(-.08) = -.0360, or -3.60% And the expected return of the portfolio is: E(RP) = .75(.1940) + .25(-.0360) E(RP) = .1365, or 13.65% To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, than add all of these up. The result is the variance. So, the variance of the portfolio is: sp 2 = .75(.1940 - .1365) 2 + .25(-.0360 - .1365) 2 sp 2 = .009919

3. Systematic versus Unsystematic Risk [LO3] Classify the following events as mostly systematic or mostly unsystematic. Is the distinction clear in every case? a. Short-term interest rates increase unexpectedly. b. The interest rate a company pays on its short-term debt borrowing is increased by its bank. c. Oil prices unexpectedly decline. d. An oil tanker ruptures, creating a large oil spill. e. A manufacturer loses a multimillion-dollar product liability suit. f. A Supreme Court decision substantially broadens producer liability for injuries suffered by product users.

a. systematic b. unsystematic c. both; probably mostly systematic d. unsystematic e. unsystematic f. systematic