fin 533 exam 2 review

ch.8

RA questions

ch.24

ew

In a recent closely contested lawsuit, Apex sued Bpex for patent infringement. The jury came back today with its decision. The rate of return on Apex was rA = 3.7%. The rate of return on Bpex was only rB = 3.1%. The market today responded to very encouraging news about the unemployment rate, and rM = 3.4%. The historical relationship between returns on these stocks and the market portfolio has been estimated from index model regressions as:Apex: rA = 0.4% + 1.4rMBpex: rB = −0.1% + 0.7rMa. What is the predicted returns for Apex & Bpex?

use the model and do the multiplication first

start

whoop

chapter 6

you manage a risky portfolio ratio & mgmt of portfolios

A 9-year bond has a yield of 9.5% and a duration of 8.836 years. If the market yield changes by 50 basis points, what is the percentage change in the bond's price?

-(8.836/(1+.095))*(50/100)=-4.03 for what ever reason the answer should be typed as a negative

You manage a risky portfolio with an expected rate of return of 19% and a standard deviation of 33%. The T-bill rate is 7%. Your client chooses to invest 80% of a portfolio in your fund and 20% in a T-bill money market fund. Suppose that your risky portfolio includes the following investments in the given proportions: stock A: 35% stock B: 32% stock C: 33% What are the investment proportions of your client's overall portfolio, including the position in T-bills?

20% in T-bills (given) 28% in stock A (.80*35%) 25.6% stock B (.80*30%) 26.4% stock C (.80*33%)

You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 38%. The T-bill rate is 6%. Your client's degree of risk aversion is A = 3.0, assuming a utility function U=E(r)−½Aσ². a. What proportion, y, of the total investment should be invested in your fund? b. What are the expected value and standard deviation of the rate of return on your client's optimized portfolio?

A.) y*= (E(rp)-rf)/(Aσ2P) (.17-.06)/(3.0×.38^2)=.2539 B.) E(rC)=0.06 + 0.11 × y* = 0.06 + (0.2539 × 0.11) = 0.0879 = 8.79% σC=0.2539 × 38% = 9.65%

The following are estimates for two stocks: stock A: E(r) 15% Beta .6 firm-specific σ 26% stock B: E(r) 23% Beta 1.15 firm-specific σ 38% The market index has a standard deviation of 21% and the risk-free rate is 9%. a. What are the standard deviations of stocks A and B? b. Suppose that we were to construct a portfolio with proportions: Stock A: .35 Stock B: .40 T-bills: .25 Compute the expected return, standard deviation, beta, and nonsystematic standard deviation of the portfolio.

A.) σ=(β^2×σof market^2+σfirm specific^2)^.5 perform this for both stocks. B.) E(rP)=wA×E(rA)+wB×E(rB)+wf ×rf =(0.35×15%)+(0.40×23%)+(0.25 ×9%)=16.70% for variance: σ2P=(0.67^2×0.212)+0.0314=0.0512 for Std. dev. square root of .0512 Beta of portfolio βp=(0.35×0.6)+(0.40×1.1)+(0.25 ×0.0)=0.67 The variance of this portfolio is: = (0.35^2×0.26^2)+(0.40^2×0.38^2)+(0.25^2×0)=0.0314 The residual standard deviation of the portfolio is thus: σ(eP) = (0.0314)^.5=17.72%

Consider the rate of return of stocks ABC and XYZ. year 1-5 rABC 24% 13% 14% 3% 3% rXYZ 36% 11% 19% 1% -10% a. Calculate the arithmetic average return on these stocks over the sample period. b. Which stock has greater dispersion around the mean return? c. Calculate the geometric average returns of each stock. What do you conclude? d. If you were equally likely to earn a return of 24%, 13%, 14%, 3%, or 3% in each year (these are the five annual returns for stock ABC), what would be your expected rate of return? e. What if the five possible outcomes were those of stock XYZ? f. Given your answers to parts (d) and (e), which measure of average return, arithmetic or geometric, appears more useful for predicting future performance?

A.) add them all up for each stock and divide by years B.) difference between highest and lowest number for each stock C.)do all numbers for each stock (1.24+1.13.......)^1/5 -1 D.)probability*rate of return=expected return E.)Even though the dispersion is greater, your expected rate of return would still be the arithmetic average, or 11.40% F.)In terms of "forward-looking" statistics, the arithmetic average is the better estimate of expected rate of return. Therefore, if the data reflect the probabilities of future returns, 11.40 percent is the expected rate of return for both stocks.

A manager buys three shares of stock today, and then sells one of those shares each year for the next 3 years. His actions and the price history of the stock are summarized below. The stock pays no dividends. time 0-3 price: 90, 110, 110, 110 action: buy 3, sell 1, sell 1, sell 1 a. Calculate the time-weighted geometric average return on this "portfolio." b. Calculate the time-weighted arithmetic average return on this portfolio. c. Calculate the dollar-weighted average return on this portfolio.

A.) same as the A in the flashcard above. then do the geometric mean to get the percentage. B.)Time-weighted arithmetic average rate of return = (22.22% + 0 + 0)/3 = 7.41%The arithmetic average is always greater than or equal to the geometric average; the greater the dispersion, the greater the difference. C.)Dollar-weighted average rate of return = IRR = 10.75%[Using a financial calculator, enter: n = 3, PV = -270, FV = 0, PMT = 110. Then compute the interest rate, or use the CF0 = -330, CF1 = 110, F1 = 3, then compute IRR]. The IRR exceeds the other averages because the investment fund was the largest when the highest return occurred.

You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 38%. The T-bill rate is 6%. Suppose that your client prefers to invest in your fund a proportion y that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio's standard deviation will not exceed 17% a. What is the investment proportion, y? b. What is the expected rate of return on the complete portfolio?

A.) σC = y × 38% If your client prefers a standard deviation of at most 17%, then: y=17/38=0.4474=44.74% invested in the risky portfolio. B.) E(rc)=(1 − y)×T-bill rate+(y)× Risky rate 10.92%=(1−0.4474)×0.06+0.4474 × 0.17

A stock recently has been estimated to have a beta of 1.34: a. What will a beta book compute as the "adjusted beta" of this stock? b. Suppose that you estimate the following regression describing the evolution of beta over time. βt = 0.8 + 0.2βt-1 What would be your predicted beta for next year?

A.)Beta books adjusts beta by taking the sample estimate of beta and averaging it with 1, using the weights of 2/3 and 1/3, as follows: Adjusted beta = [(2/3) × 1.34] + [(1/3) × 1] = 1.23 B.) If you use your current estimate of beta to be βt−1 = 1.34, thenβt = 0.8 + (0.2 × 1.34) = 1.068

Consider the two (excess return) index model regression results for A and B: RA = 0.7% + 1.1RM R-square = 0.584 Residual standard deviation = 10.6% RB = -1% + 1RM R-square = 0.444 Residual standard deviation = 8.9% a. Which stock has more firm-specific risk? b. Which stock has greater market risk? c. For which stock does market movement has a greater fraction of return variability? d. If rf were constant at 4.2% and the regression had been run using total rather than excess returns, what would have been the regression intercept for stock A?

A.)Firm-specific risk is same as the residual standard deviation B.)Market risk is measured by beta, the slope coefficient of the regression higher the beta higher the risk C.)R^2 measures the fraction of total variance of return explained by the market return. which ever one is higher D.)Rewriting the SCL equation in terms of total return (r) rather than excess return (R): 0.7% + 4.2%(1 - 1.1) = 0.7% - 0.42% = 0.28%

A portfolio management organization analyzes 64 stocks and constructs a mean-variance efficient portfolio using only these 64 securities. a. How many estimates of expected returns, variances, and covariances are needed to optimize this portfolio? b. If one could safely assume that stock market returns closely resemble a single-index structure, how many estimates would be needed?

A.)To optimize this portfolio one would need: n = 64 estimates of means n = 64 estimates of variances (n^2-n)/2=2016 estimates of covariances. in total: (n^2+3n)/2=2144 B.) n = 64 estimates of the mean E(ri) n = 64 estimates of the sensitivity coefficient βi n = 64 estimates of the firm-specific variance σ2(ei) 1 estimate of the market mean E(RM) 1 estimate of the market variance σ2MTherefore, in total, 194 estimates.

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $55,000 or $300,000 with equal probabilities of 0.5. The alternative risk-free investment in T-bills pays 6% per year. a. If you require a risk premium of 5%, how much will you be willing to pay for the portfolio? b. Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? c. Now suppose that you require a risk premium of 10%. What price are you willing to pay?

A.)calculate expected cashflow from portfolio CFs1*p(s1)+CFs2*p(s2) (55k*.5)+(300k*.5)=177500 calculate required return (r)=rf+(rm-rf) 6%+5%=11% calculate amount investor would pay. 177,500/(1+.11)=159,909.909 B.)expected return on portfolio (177500-159909.90)/159909.90=11%

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 1.80% + 0.75RM + eA RB = -2.00% + 1.10RM + eB σM = 23%; R-squareA = 0.18; R-squareB = 0.10 Assume you create portfolio P with investment proportions of 0.60 in A and 0.40 in B. a. What is the standard deviation of the portfolio? b. What is the beta of your portfolio? c. What is the firm-specific variance of your portfolio? d. What is the covariance between the portfolio and the market index?

A.)first do what you did in previous questions then ((weightA)^2x(var.A)+(weightB)^2x(var.B)+2*(weightA)*(weightB)*covar.) B.) weightA*betaA+weightB*betaB C.) var.of portfolio-(beta of portfolio)^2 D.) just check chegg

You manage a risky portfolio with an expected rate of return of 21% and a standard deviation of 35%. The T-bill rate is 5%. Your risky portfolio includes the following investments in the given proportions: Stock A: 25% Stock B: 35% Stock C: 40% Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate of return of 17%. a. What is the proportion y? b. What are your client's investment proportions in your three stocks and the T-bill fund? c. What is the standard deviation of the rate of return on your client's portfolio?

A.)proportion y= (.17-.05)/(.21-.05)=75% B) 25% T-bills (1-.75) 18.75% stock A (25%*75%) 26.25%stock B (35%*75%) 30.0% stock c (40%*75%) C) σ=(35%*75%)=26.25%

XYZ's stock price and dividend history are as follows: years 2018-2021 Beg. price: 140, 168, 126, 140 dividend paid@year end =4 all years An investor buys three shares of XYZ at the beginning of 2018, buys another two shares at the beginning of 2019, sells one share at the beginning of 2020, and sells all four remaining shares at the beginning of 2021. a. What are the arithmetic and geometric average time-weighted rates of return for the investor? b. What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2018, to January 1, 2021

A.)time-weighted returns return=(capital gains+dividend)/price do this for each of the years 2018-2019 [(168-140)+4]/140=22.86% 2019-2020 2020-2021 arithmetic mean: add them all up and divide by 3 Geometric mean: performed same as previous flash card B.) you know how to do it just read the question carefully then use the cashflow keys. hint you get paid dividends on each share

A 30-year maturity bond making annual coupon payments with a coupon rate of 10.2% has duration of 11.03 years and convexity of 176.83. The bond currently sells at a yield to maturity of 9%. a. Find the price of the bond if its yield to maturity falls to 8%. b. What price would be predicted by the duration rule? c. What price would be predicted by the duration-with-convexity rule? d-1. What is the percent error for each rule? d-2. What do you conclude about the accuracy of the two rules? e-1. Find the price of the bond if its yield to maturity increases to 10%. e-2. What price would be predicted by the duration rule? e-3. What price would be predicted by the duration-with-convexity rule? e-4. What is the percent error for each rule?

Bond Maturity = 30 years, Coupon Rate = 10.2 % with annual payments and Yield to Maturity = 9 % Duration = 11.03 years and Convexity = 176.83 par vale=1000(assumed) present price=1123.28(calculated with TVM) a.) N=30 i/y=8% PV=CPT=1247.67 PMT=-102 (10.2%x1000) FV=-1000 B.) -duration*(change in yield/1+yield) -11.03*(-.01/1+.08)=.102129 present pricexincrease 1123.28+(1123.28x.102129)=1238 C.)

Baa-rated bonds currently yield 6%, while Aa-rated bonds yield 5%. Suppose that due to an increase in the expected inflation rate, the yields on both bonds increase by 1.3%.a. Calculate the new confidence index?

Confidence Index = high graded bond yield / lower grade bond yield Confidence index = 5/6 initially = 6.3/7.3=.863 after inflation as confidence index increases, the tech. analyst interprets it as *Bullish*

Calculate cumulative breadth.

Cumulative breadth on any day = Sum total of all the daily breadth till that day. negative total =bearish

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 2.4% + 0.85RM + eA RB = -2.4% + 1.30RM + eB σM = 25%; R-squareA = 0.17; R-squareB = 0.11 Break down the variance of each stock to the systematic and firm-specific components.

Risk for A: first find σ^2A (.85^2×.25^2)/.17=.2656 systematic= 0.85^2×0.25^2=0.0452 Firm specific= 0.2656 − 0.0452 = 0.2205 Risk for B: first find σ^2B (1.30^2×.25^2)/.11=.9602 systematic= 1.30^2 × 0.25^2 = 0.1056 Firm specific= 0.9602 − 0.1056 = 0.8546

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 3.6% + 1.20RM + eA RB = -1.6% + 1.5RM + eB σM = 16%; R-squareA = 0.25; R-squareB = 0.15 What is the standard deviation of each stock?

Stock A: (1.20^2×.16^2)/.25=.1475 then square root .1475 Stock B: (1.5^2×.16^2)/.15=.3840 then square root .3840

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 4.5% + 1.4RM + eA RB = -2.2% + 1.7RM + eB σM = 24%; R-squareA = 0.30; R-squareB = 0.20 What is the covariance between each stock and the market index?

Stock A: (1.40^2×.24^2)/.30=.3763 then square root .3763 and get .6134 then to get the covariance 0.30^.5 × 0.6134 × 0.24 = 0.081 Stock B: (1.7^2×.24^2)/.20=.8323 then square root .8323 and get .9123 then to get the covariance 0.20^.5×0.9123 × 0.24 = 0.098

An index model regression applied to past monthly returns in Ford's stock price produces the following estimates, which are believed to be stable over time :rF = 0.1% + 1.1rM If the market index subsequently rises by 10.3% and Ford's stock price rises by 9%, what is the abnormal change in Ford's stock price?

The return on the market is 10.3%. Therefore, the forecast monthly return for Ford is: 0.1% + (1.1 × 10.3%) = 11.43%. Ford's actual return was 9%, so the abnormal return was =9%-11.43%=-2.43%

Consider a portfolio that offers an expected rate of return of 12% and a standard deviation of 23%. T-bills offer a risk-free 4% rate of return. What is the maximum level of risk aversion for which the risky portfolio is still preferred to T-bills?

When we specify utility by U = E(r) − 0.5Aσ2, the utility level for T-bills is: 0.04 U=.12-.5*A*(.23)^2 .12-.0265*A In order for the risky portfolio to be preferred to bills, the following must hold: 0.12 − 0.0265A > 0.04 A < 0.08/0.0265 = 3.02

You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 38%. The T-bill rate is 6%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund. What is the reward-to-volatility (Sharpe) ratio (S) of your risky portfolio? Your client's?

Your reward-to-volatility ratio: (.17-.06)/.38=.2895 Client's expected return = (0.85 × 17%) + (0.15 × 6%) = 15.35% Client's standard deviation = 0.85 × 38% = 32.30% Client's reward-to-volatility ratio: (.1535-.06)/.323=.2895

You are managing a portfolio of $1 million. Your target duration is 10 years, and you can invest in two bonds, a zero-coupon bond with maturity of five years and a perpetuity, each currently yielding 7.8%. a. What weight of each bond will you hold to immunize your portfolio? b. How will these weights change next year if target duration is now nine years?

a) Duration of Perpetuity = (1+.078)/.078 = 13.8205 years 10 = 5X + (1-X)*13.8205 10 = 5X + 13.8205-13.8205X X (Weight of Zero-Coupon Bond)= (13.8205-10)/(8.8205) = .43313 or 43.313% Weight of Perpetuity=1-.43313 = .56686or 56.686% b.) same thing as above but 10 is replaced with 9 and 5 is replaced with 4

Calculate breadth for the NASDAQ using the data in Figure 12.5.

breadth= advancing-declining issues

An insurance company must make payments to a customer of $7 million in one year and $3 million in three years. The yield curve is flat at 8%. a. If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero-coupon bond, what maturity bond must it purchase? b. what must be the face value and market value of that zero-coupon bond? (Do not round intermediate calculations. Enter your answers in millions rounded to 2 decimal places.)

check notebook

Find the duration of a 5.0% coupon bond making semiannually coupon payments if it has three years until maturity and has a yield to maturity of 6.0%. What is the duration if the yield to maturity is 8.0%? Note: The face value of the bond is $100. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

check notebook

Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $2.8 million per year to beneficiaries. The yield to maturity on all bonds is 13.5%. If the duration of 5-year maturity bonds with coupon rates of 13.2% (paid annually) is four years and the duration of 20-year maturity bonds with coupon rates of 6% (paid annually) is 11 years, how much of each of these coupon bonds (in market value) will you want to hold to both fully fund and immunize your obligation? b. What will be the par value of your holdings in the 20-year coupon bond?

check notebook

You will be paying $10,800 a year in tuition expenses at the end of the next two years. Bonds currently yield 8%. a. What is the present value and duration of your obligation? b. What maturity zero-coupon bond would immunize your obligation? c. Suppose you buy a zero-coupon bond with value and duration equal to your obligation. Now suppose that rates immediately increase to 10%. What happens to your net position, that is, to the difference between the value of the bond and that of your tuition obligation?d. What if rates fall immediately to 6%?

check notebook

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 3.5% + 0.65RM + eA RB = -1.6% + 0.80RM + eB σM = 21%; R-squareA = 0.22; R-squareB = 0.14 What are the covariance and correlation coefficient between the two stocks?

for stock A: σ^2A= (.65^2×.21^2)/.22=.0847 For stock B: σ^2B= (.80^2×.21^2)/.14=.2016 The covariance between the returns of A and B is (since the residuals are assumed to be uncorrelated): to find covariance 0.65 × 0.80 × 0.0441=0.0229 The correlation coefficient between the returns of A and B is: .0229/(.2910×.4490)=.1755

MF Corp. has an ROE of 14% and a plowback ratio of 75%. The market capitalization rate is 13%. a. If the coming year's earnings are expected to be $2.30 per share, at what price will the stock sell? b. What price do you expect MF shares to sell for in three years?

growth rate=ROE*retention ratio =(0.14*0.75)=10.5% Hence price of stock=(dividend next period/(required rate-growth rate)) =2.3(1-0.75)/(0.13-0.105)=$23. Hence price after 3 years=23(1.105)^3 =$31.03(approx).

The market consensus is that Analog Electronic Corporation has an ROE = 12%, a beta of 1.55, and plans to maintain indefinitely its traditional plowback ratio of 2/5. This year's earnings were $2.40 per share. The annual dividend was just paid. The consensus estimate of the coming year's market return is 16%, and T-bills currently offer a 6% return. a. Find the price at which Analog stock should sell. b. Calculate the P/E ratio. c. Calculate the present value of growth opportunities. d. Suppose your research convinces you Analog will announce momentarily that it will immediately reduce its plowback ratio to 3/5. Find the intrinsic value of the stock.

notebook

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky funds are as follows Stock fund (S): expected return 23% standard dev. 29% Bond fund (B): expected return 14% standard dev. 17% The correlation between the fund returns is 0.12 a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds? a-2. What are the expected value and standard deviation of the minimum-variance portfolio rate of return?

parameters set E(rS) = 23%, E(rB) = 14%, σS = 29%, σB = 17%, ρ = 0.12 A-1) Cov(rS, rB) = ρ × σS × σB]

Table 12A presents price data for Computers, Inc., and a computer industry index. Does Computers, Inc., show relative strength over this period?

take price/industry index. if it continues to rise or even surpass the industry index it is an indicator of out performance over the rest of the industry.

Use the data from The Wall Street Journal in Figure 12.5 to calculate the trin ratio for the NASDAQ. Is the trin ratio bullish or bearish?

trin=(volume declining/number decling)/(volume advancing/number advancing) if trin is over 1 than it would be bearish, if it is lower than 1 it is bullish.