Risk and return

Suppose you forecast that the standard deviation of the market return will be 20% in the coming year. If the measure of risk aversion in A=E(rM)−rfσ2MA=ErM-rfσM2 is A = 4: Required: a. What would be a reasonable guess for the expected market risk premium? b. What value of A is consistent with a risk premium of 9%? c. What will happen to the risk premium if investors become more risk tolerant?

0Explanation A) Given that A = 4 and the projected standard deviation of the market return = 20%, we can use the below equation to solve for the expected market risk premium: A = 4 = (Average(rM) − rf)/(Sample σM2) = (Average(rM) − rf)/((20%)2)E(rM) − rf = AσM2 = 4 × (0.20)2 = 0.16 = 16% B) Solve E(rM) − rf = 0.09 = AσM2 = A × (0.20)2, we can get A = 0.09/(0.04) = 2.25 C) Decrease

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000. d. What are the expected value, variance, and standard deviation of your profit

EXPECTED RETURN: 20 Variance: 19,989,960 Standard Dev. 4,471

Here are rates of return for six months for Generic Risk, Incorporated. MonthMarket ReturnGeneric Return10%+2%2003−104−1−25+1+46+1+2 Required: Select the scatter diagram that shows Generic's beta.

A graph plots market return percent ranging from negative 1 to 1 with an increment of 0.5 unit on the horizontal axis and generic return percent ranging from negative 2 to 4 with an increment of 1 unit on the vertical axis. A line labeled y = 1.0 + 2.0 x starts at point (negative 1, negative 1) moves up to the right through points (negative 0.5, 0) and (0, 1) and ends at (1, 3). Explanation The slope of the regression line is 2.0 and intercept is 1.0.

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Stock fund (S)15% 32% Bond fund (B)9% 23% The correlation between the fund returns is 0.15. Suppose now that your portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL. a. What is the standard deviation of your portfolio? b-1. What is the proportion invested in the T-bill fund? b-2. What is the proportion invested in each of the two risky funds?

A) 20.56 B) 11.92 B2) Stocks 56.95 Bonds: 31.12

Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%.A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 20%. Required: a. What is the investment proportion, y? b. What is the expected rate of return on the overall portfolio?

A) 74.07 B) 14.41 Explanation a.Standard deviation of the complete portfolio = σC = y × 0.27 If the client wants the standard deviation to be equal or less than 20%, then: y = (0.20/0.27) = 0.7407 = 74.07% He should invest, at most, 74.07% in the risky fund. b. E(rC) = rf + y × [E(rP) − rf]= 0.07 + 0.7407 × 0.10 = 0.1441 or 14.41%

Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%.Your risky portfolio includes the following investments in the given proportions: Stock A27%Stock B33Stock C40 Your client decides to invest in your risky portfolio a proportion (y) of his total investment budget with the remainder in a T-bill money market fund so that his overall portfolio will have an expected rate of return of 15%. Required: a. What is the proportion y? b. What are your client's investment proportions in your three stocks and in T-bills? c. What is the standard deviation of the rate of return on your client's portfolio?

A) 80% B) T-bills 20% StockA 21.6% StockB 26.4% StockC 32% C) 21.6 Explanation a.E(rC) = y × E(rP) + (1 − y) × rf= y × 0.17 + (1 − y) × 0.07 = 0.15 or 15% per yearSolving for y, we get y = (0.15 − 0.07) / 0.10 = 0.8 or 80.0%Therefore, in order to achieve an expected rate of return of 15%, the client must invest 80% of total funds in the risky portfolio and 20% in T-bills. b.The investment proportions of the client's overall portfolio can be calculated by the proportion of risky asset in the whole portfolio times the proportion allocated in each stock. Security Investment ProportionsT-Bills 20.0%Stock A0.8 × 27% =21.6%Stock B0.8 × 33% =26.4%Stock C0.8 × 40% =32.0% c.The standard deviation of the complete portfolio is the standard deviation of the risky portfolio times the fraction of the portfolio invested in the risky asset:σC = y × σP = 0.8 × 0.27 = 0.216 or 21.6% per year

The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: DividendStock PriceBoom$ 2.00$ 50Normal economy1.0043Recession0.5034 a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%.

A) expected return: 8.75 Standard Dev: 17.88 B)expected return: 6.38 Standard Dev: 8.94

ScenarioProbabilityStock FundRate of ReturnBond FundRate of ReturnSevere recession0.05−40%−9%Mild recession0.25−14%15%Normal growth0.4017%8%Boom0.3033%−5% Required: a. Calculate the values of mean return and variance for the stock fund. b. Calculate the value of the covariance between the stock and bond funds.

A) mean: 11.2 var: 445.86 B) cov: (85.60)

Consider a risky portfolio. The end-of-year cash flow derived from the portfolio will be either $50,000 or $150,000, with equal probabilities of 0.5. The alternative riskless investment in T-bills pays 5%. a. If you require a risk premium of 10%, how much will you be willing to pay for the portfolio? (Round your answer to the nearest dollar amount.) b. Suppose the portfolio can be purchased for the amount you found in (a). What will the expected rate of return on the portfolio be? c. Now suppose you require a risk premium of 15%. What is the price you will be willing to pay now?

A)$86,957 B) 15% C)$83,333 Explanation: A)The expected cash flow is: (0.5 × $50,000) + (0.5 × $150,000) = $100,000With a risk premium of 10%, the required rate of return is 15%. Therefore, if the value of the portfolio is X, then, in order to earn a 15% expected return:Solving X × (1 + 0.15) = $100,000, we get X = $86,957 B)If the portfolio is purchased at $86,957, and the expected payoff is $100,000, then the expected rate of return, E(r), is:($100,000 − $86,957 / $86,957) = 0.15 = 15%The portfolio price is set to equate the expected return with the required rate of return. C)If the risk premium over T-bills is now 15%, then the required return is:5% + 15% = 20%The value of the portfolio (X) must satisfy:X × (1 + 0.20) = $100, 000 ⇒⇒ X = $83,333

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000. Required: a. Make a table of the two possible payouts on each policy with the probability of each.

A: no Fire = $110 B: Fire! (99,890)

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000. b. Suppose you own the entire firm, and the company issues only one policy. What are the expected value, variance, and standard deviation of your profit?

Expected return: $10 Variance: 9,990,000 Standard Deviation: 3,161

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000. g. What are the expected value and variance of your profit?

Expected: 10 Variance: 4,997,490 Standard dev: 2,236

Investors expect the market rate of return this year to be 10%. The expected rate of return on a stock with a beta of 1.2 is currently 12%. If the market return this year turns out to be 8%, how would you revise your expectation of the rate of return on the stock?

Explanation The expected rate of return on the stock will change by beta times the unanticipated change in the market return: 1.2 × (0.08 − 0.10) = −2.4%Therefore, the expected rate of return on the stock should be revised to: 0.120 − 0.024 = 0.096 = 9.6%

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000. e. Compare your answers to (b) and (d). Did risk pooling increase or decrease the variance of your profit?

Increase

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000. f. Continue to assume the company has issued two policies, but now assume you take on a partner, so that you each own one-half of the firm. Make a table of your share of the possible payouts the company may have to make on the two policies, along with their associated probabilities.

outcome No fire: Payout: 110 Probability: 99.8000 OUTCOME: ONE FIRE Payout:(49,890) Probability:0.1999 OUTCOME TWO FIRES: Payout: (99,890) Probability: 0.0001

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $110, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $100,000. c. Now suppose your company issues two policies. The risk of fire is independent across the two policies. Make a table of the three possible payouts along with their associated probabilities

outcome No fire: Payout: 220 Probability:99.8000 OUTCOME: ON FIRE Payout:(99,780) Probability:0.1999 OUTCOME TWO FIRES: Payout: (199,780) Probability: 0.0001