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principles of finance

Questions and Answers of Principles Of Finance

How do we calculate the market value of a firm’s equity, E?
14. (Regression, Sharpe, Jensen’s alpha, Treynor for portfolio) Using the data for the S&P 500, FedEx, IBM, and 3M from exercises 10, 11, and 13 above, compute the portfolio alpha, αP, and the
c. Does 3M have excess performance?
b. Calculate the Sharpe ratio, Jensen’s alpha, and Treynor ratio for 3M.
a. Graph the excess returns of 3M against those of the S&P 500. Use Excel to compute the regression line and the R2.
e. Calculate the Sharpe ratio, Jensen’s alpha, and Treynor ratio for the portfolio.
d. Compute the portfolio R2, and compare it to the average R2 of IBM and FedEx. What can you conclude about the diversification advantages of the portfolio?
By taking the weighted average of the αs of the two portfolio components IBM and FedEx.
By using Excel’s Intercept function.
c. Compute the portfolio αP. Show two different ways to calculate the portfolio αP:
By averaging the βs of the two portfolio components IBM and FedEx.
By using the formula P = Cov(rP ,rM ) /Var (rM ).
By using Excel’s Slope function.
b. Compute the portfolio βP. Show three different ways to calculate the portfolio βP:
a. Compute the excess return of the portfolio.
12. (Regression, Sharpe, Jensen’s alpha, Treynor for portfolio) Using the data from exercises 10 and 11, assume you invested in a portfolio composed of 30% IBM stock and 70% FedEx stock.
e. Calculate the Sharpe ratio, Jensen’s alpha, and Treynor ratio for IBM.
d. Is IBM an aggressive or a defensive stock?
c. Does IBM have excess performance over the S&P 500?
b. Show by graph the excess return of IBM against those of the S&P 500. Use Excel to compute the regression line and the R2.
a. Compute the excess returns for the S&P 500 and for IBM.
d. Calculate the Sharpe ratio, Jensen’s alpha, and Treynor ratio for FedEx.
c. Is FedEx stock an aggressive or a defensive stock?
b. Graph the excess return of FedEx against those of the S&P 500. Use Excel to compute the regression line and the R2.
a. Compute the excess returns for the S&P 500 and for FedEx.
c. Calculate the Sharpe ratio, Jensen’s alpha, and Treynor ratio for the S&P 500 and Apple stock.
b. Calculate the average, standard deviation, alpha, and beta of the S&P 500 and Apple with respect to the S&P 500.
a. Calculate the annual return of the S&P 500 and of Apple, and the return over the risk- free rate of return.
b. Calculate the Treynor ratio for each stock and the market portfolio
7. (Treynor ratio) Apple stock has a beta of 1.27, the risk- free rate of return is 1.5%, and Apple’s mean return is 67.28%. What is the Treynor ratio of Apple?
c. Calculate Jensen’s alpha for each stock and the market portfolio.
b. Calculate the “Normative return” based on the SML for each stock and the market portfolio.
a. Calculate the beta of each stock and the market portfolio.
5. (Jensen’s alpha) Thomas manages an investment firm. His firm’s investments have beta of 0.7. The market risk premium is 6%, and the risk- free rate in the economy is 2%. Thomas presents you
4. (Jensen’s alpha) Apple stock has a beta of 1.27. During 2014, the market return was 11.29%, the risk- free rate of return was 0.1%, and Apple’s return was 67.28%. What was Jensen’s alpha for
3. (Sharpe ratio) Ms. Johns manages a mutual fund. Her fund has an annual standard deviation of 15%. Her competitor is running a mutual fund with an expected return of 8% and an annual standard
b. Assume that you would like to invest in a portfolio with standard deviation of 16% (the same risk as Genjamin Braham’s). Show how to construct this portfolio using the risk- free asset and
a. Use the Sharpe ratio to determine which fund manager is better.
b. The mean, standard deviation, and Sharpe ratio of the S&P 500.
a. The S&P 500 annual return and the annual return in excess of the risk- free rate.
1. (Descriptive statistics for S&P 500) The exercise file online contains longterm data on the S&P 500 index and on the annual risk- free rate of return.Use the data to calculate:
b. Calculate the systematic risk (beta) for each of the three stocks.
a. Calculate the covariance between each stock and the market portfolio.
29. (Covariance with the market portfolio, finding beta) Assume that there are only three stocks in the market and that the optimal investment proportions in each stock A, B, and C is 1/ 3. Also
b. Calculate the market portfolio M when the risk- free rate of return is 5%. (Recall that the M portfolio is the portfolio which maximizes the Sharpe ratio).
a. Show that a portfolio invested 80% in Company A and 20% in Company B is not optimal by showing a better portfolio.
a. What will be the expected return and the expected risk (standard deviation) for this more daring portfolio?b. In what proportion will you invest your $6,000 in each stock and the risk- free asset,
15. (CML with leverage) With reference to exercise 14 above, you are feeling lucky and decide to take on a riskier portfolio. In particular, in addition to your $5,000 gift, you are able to borrow
b. Suppose you decide to invest in the following proportions: 40%government bonds, 60% in the market portfolio M. Calculate the expected return and variance of returns for this portfolio
a. Graph the capital market line—that is, all the combinations of investment in the risk- free asset and the two companies. Provide results in table form as well. Start by finding the proportions
14. (CML) On the occasion of your birthday, your wealthy Aunt Hilda sends you a check for $5,000, under the express condition that you invest the money in either (or all) of the following: government
c. Which portfolio is better, yours or your sister’s?
b. Your sister also has $1,000 to invest, but she wants to borrow another$1,000 in order to make an investment of $2,000 in the market portfolio M. What will be the mean and standard deviation of her
a. What is the mean and standard deviation of your investment if you invest $500 in the risk- free asset and $500 in the market portfolio?
13. (CML with leverage) You have $1,000 to invest. The risk- free rate is rf = 6%.The market portfolio has expected return E(rM) = 15% and σM = 20%.
b. Find the difference in standard deviation between a portfolio on the CML and a portfolio on the efficient frontier, both with average return of 19%. What will be the weight of the risk- free asset
a. Calculate the capital market line (CML) using this data.
c. Answer this question again assuming the risk- free return is 0%.
b. Will the market portfolio change if the risk- free return changes to 3%? If yes, explain why and calculate the new market portfolio.
a. The market portfolio is composed of 37.5% stock A and 62.5%stock Z. Find the equation of the capital market line (CML).
vi. A portfolio with standard deviation of 5%.
v. A portfolio with standard deviation of 35%.
iv. A portfolio that yields a return of 23%.
iii. A portfolio that yields a return of 15%.
ii. A portfolio composed of 120% of the market portfolio.
i. A portfolio composed of 35% risk- free asset and 65% market portfolio.
b. Compute the following CML portfolios:
a. What is the equation of the Tierra del Fuego CML?
10. (CML) The market portfolio of the Tierra del Fuego stock market has an expected return E rM ( )= 22% and a standard deviation of returns σM = 19%.The risk- free rate is rf = 7%.
e. Suppose an investor wants the same return as the above portfolio(partd) but invests only in the risk- free asset and a portfolio composed of equal weights of Xirkind and Yirkind stocks. What will
d. What is the expected return and standard deviation of a portfolio composed of 30% of the risk- free asset and 70% of the market portfolio?
c. What does the CML mean, and why are we interested in it?
b. What is the equation of the capital market line (CML) in Golkoland?
a. What is the market portfolio M in Golkoland?
d. Is your answer to part c the minimum variance portfolio? If not, calculate the Sharpe ratio of the minimum variance portfolio as well.
c. Find the market portfolio using the Sharpe ratio, assuming the riskfree asset return is 4%.
b. Calculate the returns and standard deviations for portfolios composed of these two stocks.
a. For the years 2003– 2014, calculate the following statistics for the two shares: average annual return, variance and standard deviation of returns, covariance of returns, and correlation
6. (Sharpe ratio) What is the Sharpe ratio of the minimum variance portfolio of exercise 5? Show another portfolio composed of stocks X and Y that has a better Sharpe ratio.
d. Kaid Benfield wants a portfolio composed of the risk- free asset and the minimum variance portfolio. Find a portfolio for Kaid that has a standard deviation of returns of 5%.
c. Mary Jones asks you to create a portfolio composed of the risk- free asset and the minimum variance portfolio. Mary wants an expected return of 9%. What will the percentage of the portfolio
b. What is the return and standard deviation of a portfolio composed of 30% of the minimum variance portfolio and 70% of the risk- free asset? Repeat this question with weights of 50% for the risk-
a. What is the return and standard deviation of the minimum variance portfolio of stocks X and Y?
4. (Portfolio of a risk- free asset and a risky stock) You are considering investing in a combination of a stock and a risk- free asset. The stock has an expected return of 7% and standard deviation
3. (Portfolio of a risk- free asset and a risky stock) Consider a stock with an expected return of 6% and standard deviation of return of 15%. Suppose that the risk- free asset has a return of 1%.
e. What does this question has to do with investing in stocks?
d. Which game would you prefer to play? Why?
c. Which game is riskier: Mary’s die throw or John’s coin toss (previous exercise)?
b. What is the standard deviation of the returns?
a. What are the expected returns from playing this game?
2. (Risk diversification on gambles) Still in Spartanburg, you encounter a second street hustler named Mary. Her game is more complicated: After you pay Mary $0.80, she throws a die. If the die comes
b. What is the standard deviation of your return from playing this game?
a. What is your expected return from this game?
1. (Risk diversification on gambles) Walking down the street of Spartanburg (your hometown), you encounter John, a street hustler. John, is running a coin- toss game, which works like this: You pay
The security market line (SML) describes the relation between the expected returns of any stock and its beta.Because the material in this chapter is not easy, we start the chapter with a summary of
The beta of a stock (denoted by the Greek letter β) is a measure of the stock’s market risk.
The capital market line (CML) is the set of all optimal investment portfolios for an investor. The CML contains an important piece of investment advice: It tells us that every investor’s optimal
The market portfolio (denoted by the letter M) is the best portfolio of risky assets available to all investors.
c. Find the portfolio having maximum return given that the portfolio standard deviation is 30%.
b. Find the minimum variance portfolio and its statistics.

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