Corporate Finance Chapter 7 Model Questions

QUESTION 1 Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively. ​ ​ Compute the standard deviation of the returns on the portfolio assuming that the two stocks' returns are uncorrelated. 17.4%. 27.4%. 7.4%. 11.4%. QUESTION 2 Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively. ​ ​  Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation ρ decreases. The standard deviation of the portfolio returns decreases as the coefficient of correlation decreases. The standard deviation of the portfolio returns increases as the coefficient…

Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively. ​ ​  Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation ρ decreases. The standard deviation of the portfolio returns decreases as the coefficient of correlation decreases. The standard deviation of the portfolio returns increases as the coefficient of correlation increases. The standard deviation of the portfolio returns decreases as the coefficient of correlation increases. The standard deviation of the portfolio returns increases as the coefficient of correlation decreases.

which one is correct? QUESTION 12 Exhibit 6B.1 USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)   The general equation for the weight of the first security to achieve the minimum variance (in a two-stock portfolio) is given by:   W1 = [E(σ1)2 − r1.2 E(σ1) E(σ2)] &χεδιλ; [E(σ1)2 + E(σ2)2 − 2 r1.2 E(σ1) E(σ2)]   Refer to Exhibit 6B.1. Show the minimum portfolio variance for a portfolio of two risky assets when r1.2 = − 1.   a. E(σ1) &χεδιλ; [E(σ1) − E(σ2)]   b. E(σ2) &χεδιλ; [E(σ1) − E(σ2)]   c. None of these are correct.   d. E(σ1) &χεδιλ; [E(σ1) + E(σ2)]   e. E(σ2) &χεδιλ; [E(σ1) + E(σ2)]

ANSWER PART 4 PLEASE Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = x^n/n . There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w−A is invested in the safe asset. What are risk preferences of this investor, are they risk-averse, risk- neutral or risk-loving? Find A as a function of w. Does the investor put more or less of his portfolio into the risky asset as his wealth increases? Now find the share of wealth, α, invested in the risky asset. How does α change with wealth?

QUESTION 2 Elizabeth has decided to form a portfolio by putting 30% of her money into stock 1 and 70% into stock 2. She assumes that the expected returns will be 10% and 18%, respectively, and that the standard deviations will be 15% and 24%, respectively. ​ ​  Describe what happens to the standard deviation of the portfolio returns when the coefficient of correlation ρ decreases. The standard deviation of the portfolio returns decreases as the coefficient of correlation decreases. The standard deviation of the portfolio returns increases as the coefficient of correlation increases. The standard deviation of the portfolio returns decreases as the coefficient of correlation increases. The standard deviation of the portfolio returns increases as the coefficient of correlation decreases.

Which statement about portfolio diversification is CORRECT? i) Typically, as more securities are added to a portfolio, total risk would be expected to decrease at an increasing rate.ii) Proper diversification can reduce or eliminate total risk.iii) The risk-reducing benefits of diversification do not occur meaningfully until at least 50-60 individual securities have been purchased.iv) Because diversification reduces a portfolio's total risk, it necessarily reduces the portfolio's expected return.

A moderately risk-averse investor has 50% of her portfolio invested in stocks and 50% in risk-free Treasury bills. Show how each of the following events will affect the investor’s budget line and proportion of stocks in her portfolio: A. The standard deviation of the return on the stock market increases, but the expected return on the stock market remains the same. B. The expected return on the stock market increases, but the standard deviation of the stock market remains the same. C. The return on risk-free Treasury bills increases.

Consider the expected return and standard deviation of the following two assets: Asset 1:               E[r1]=0.1             and                s1=0.2 Asset 2:               E[r2]=0.3            and                s2=0.4 (a) Draw (e.g. with Excel) the set of achievable portfolios in mean-standard deviation space for the cases: (i) r12=-1, (ii) r12=0. (b) Suppose r12=-1. Which portfolio has the minimal variance? What is the variance and expected return of that portfolio?   (c) Derive the formula for the variance of a portfolio with four assets.

If investors want portfolios with small risk, should they look for investments that have positive covariance, have negative covariance, or are uncorrelated? Does a portfolio formed from the mix of three investments have more risk than a portfolio formed from two?

From the following equation for expected returns, explain what may cause stock prices to decrease in economic recessions: E(r) – risk-free rate = A*Var(r) A is the risk aversion for the average investor, and Var(r) is the variance of the market portfolio. Assume that investor risk aversion is constant.

Suppose the expected return on the tangent portfolio is 12% and its volatility is 30%.The risk-free rate is 3%.(a) What is the equation of the Capital Market Line (CML)?(b) What is the standard deviation of an efficient portfolio whose expected return of16.5%? How would you allocate $3,000 to achieve this position

Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = X^n/n  . There is a safe asset (such as a US government bond) that has a net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w−A is invested in the safe asset.    Now find the share of wealth, α, invested in the risky asset. How does α change with wealth?

Portfolios A, B, and C all lie on the efficient frontier that allows for risk-free borrowing and lending. Portfolio A and B have the following expected returns and return variances: A: μ_A=0.0925 , σ_A^2=0.0225 ; B: μ_B=0.11 , σ_B^2=0.04. Portfolio C’s return has variance σ_C^2=0.1225. What is the expected return and Sharpe ratio of Portfolio C? What is the risk-free interest rate? Explain your calculations

Consider two investors A and B.If the Certainty-Equivalent end-of-period wealth of A is less than the Certainty-Equivalent end-of-period wealth of B for the same portfolio choice,then A. Risk aversion of A > Risk aversion of B B. Risk aversion of A = Risk aversion of B C. Risk aversion of A< Risk aversion of B D. Not enough Information Justify your choice in a sentence or two：

Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = x^n/n . There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A is invested in the safe asset. 1. What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving? 2. Find A as a function of w. 3. Does the investor put more or less of his portfolio into the risky asset as his wealth increases? 4. Now find the share of wealth, α, invested in the risky asset. How does α change with wealth? 5. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?

Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = (x^n)/n . There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 − q and R0 with probability q. We assume R1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w−A is invested in the safe asset. What are risk preferences of this investor, are they risk-averse, risk- neutral or risk-loving? Find A as a function of w. Does the investor put more or less of his portfolio into the risky asset as his wealth increases?.

There are two risky assets, namely Asset 1 and Asset 2, in the economy and only two investors, namely Alice and Bob, who can borrow or lend at the risk-free rate of 2%. The risk-free asset, though, is in a net supply of zero. Alice's initial wealth is $70,000, and Bob's initial wealth is $50,000. Alice has invested $80,000 in Asset 1 and $20,000 in Asset 2. Assume that both Alice and Bob are mean-variance efficient investors, which of the following statements is wrong? Bob has invested $16,000 in Asset 2 The market capitalization of Asset 2 is $24,000 Bob has lent Alice $30,000 The market capitalization of Asset 1 is $80,000

Which of the following statements is most correct? If you add enough randomly selected stocks to a portfolio, you can completely eliminate all of the market risk from the portfolio. If you form a large portfolio of stocks each with a beta greater than 1.0, this portfolio will have more market risk than a single stock with a beta = 0.8. Company-specific risk can be reduced by forming a large portfolio, but normally even highly diversified portfolios are subject to market risk. Answers a, b, and c are correct. Answers b and c are correct.

Using the Utility Function in Portfolio Management, where the utility function is the constant relative risk aversion utility of wealth function U(W) = W^(gamma)/gamma, set gamma to 0.5 and consider a 50-50 bet on winning 50,000 or getting nothing. What is the certainty equivalent wealth for this bet under these assumptions? Group of answer choices 30,000   10,000   25,000   12,500

The value of a portfolio to investors equals its expected return minus 35 times its variance. There is one stock in the economy. Rational investors believe that its expected return is 1. Irrational investors believe that its expected return is 1.8. All agree that the variance of the stock is 0.02. Graph on one graph the price of the stock as the number of shares go from 20 to 60 in three different circumstances: A: There are 260 investors, and all are rational. B: There are 260 investors. 200 are rational and 60 are irrational. Shorting is allowed. C: There are 260 investors. 200 are rational and 60 are irrational. Shorting is not allowed.

Explain why the variance of an investment is a useful measure of the risk associated with it

You are a risk-averse investor with a CRRA utility function. You are faced with the decision to invest your total wealth W of £1,000,000 into a riskless asset which generates a return of 5% or into a risky asset which either generates a return of 20% or a loss of −4% with equal probability. Find the optimal investment allocation with a coefficient of relative risk aversion η=2, and comment on your results.

The value of Jon’s stock portfolio is given by the function v(t) = 50 + 77t + 3t2,  where v is the value of the portfolio in hundreds of dollars and t is the time in months.  How much money did Jon start with? (y-intercept) What is the minimum value of Jon’s portfolio? (vertex)

Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 30% standard deviation of expected returns. Stock Y has a 12.0% expected return, a beta coefficient of 1.1, and a 30.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. Calculate the required return of a portfolio that has $7,500 invested in Stock X and $5,500 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places. rp = %

Explain how a given investor chooses an optimal portfolio. Will this choice always be a diversified portfolio, or could it be a single asset? Explain your answer based on the utility curves and the efficient frontier.

You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The following table represents the annual return (per $1,000) of each of these investments under various economic conditions and the probability that each of those economic conditions will occur. Compute the expected return for the corporate bond and for the common stock fund. Show your calculations on excel for expected returns.  Compute the standard deviation for the corporate bond fund and for the common stock fund.  Would you invest in the corporate bond fund or the common stock fund? Explain.  If  choose to invest in the common stock fund and in (c), what do you think about the possibility of losing $999 of every $1,000 invested if there is depression. Explain.

Studies have concluded that a college degree is a very good investment. Suppose that a college graduate earns about 75% more money per hour than a high-school graduate. If the lifetime earnings of a high-school graduate average $1,200,000, what is the expected value of earning a college degree?

Sarah has a coefficient of risk aversion of 2. Sheng has a coefficient of risk aversion of 4. Given their risk preferences, we do not expect that... Select one: a. The indifference curves of Sheng are steeper than those of Sarah. b. Sheng holds a higher weight of the risky assets than Sarah does. c. None of the options provided. d. Sarah and Sheng hold the same risky assets in their portfolios.