Homework4 (1)

pdf

School

New York University *

*We aren’t endorsed by this school

Course

1014

Subject

Finance

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by DeaconPowerRhinoceros26

Foundations of Finance Homework 4 Prof. Simone Lenzu Due on October 31 st Portfolio Theory with 2 Risky Assets 1. The expected returns and standard deviation of returns for two securities are as follows: Security Z Security Y Expected Return 15% 35% Standard Deviation 20% 40% The correlation between the returns is + .25. (a) Calculate the expected return and standard deviation for the following portfolios: i. all in Z ii. .75 in Z and .25 in Y iii. .5 in Z and .5 in Y iv. .25 in Z and .75 in Y v. all in Y (b) Draw the mean-standard deviation frontier. (c) Which portfolios might be held by an investor who likes high mean and low standard deviation? Portfolio Theory with a Riskless Assets 2. Suppose that a fund that tracks the S&P has mean E ( R m ) = 16% and standard deviation σ M = 10%, and suppose that the T-bill rate R f = 8%. Answer the following questions about efficient portfolios: (a) What is the expected return and standard deviation of a portfolio that is totally invested in the risk-free asset? (b) What is the expected return and standard deviation of a portfolio that has 50% of its wealth in the risk-free asset and 50% in the S&P? 1

(c) What is the expected return and standard deviation of a portfolio that has 125% of its wealth in the S&P, financed by borrowing 25% of its wealth at the risk-free rate? (d) What are the weights for investing in the risk-free asset and the S&P that produce a standard deviation for the entire portfolio that is twice the standard deviation of the S&P? What is the expected return on that portfolio? 3. Consider the following data: Expected Return Standard Deviation Russell Fund 16% 12% Windsor Fund 14% 10% S&P Fund 12% 8% The correlation between the returns on the Russell Fund and the S&P Fund is .7. The rate on T-bills is 6%. Which of the following portfolios would you prefer to hold in combination with T-bills and why? (a) Russell Fund (b) Windsor Fund (c) S&P Fund (d) A portfolio of 60% Russell Fund and 40% S&P Fund. 4. Excel Question . Open the excel document “04 portfolio optimizer.xls” attached to the assignment on Brightspace . Play around with the optimizer to see what happens to the share of asset 3 in the optimal risky portfolio (MVE) in the following cases. Explain in words why you think this happens. 5. The expected return of asset 3 is increased. (a) The standard deviation of asset 3 is increased. (b) The standard deviation of asset 2 is increased. (c) The correlation between assets 2 and 5 is increased. 2

The Capital Asset Pricing Model 6. Understanding weights of different assets in the market portfolio. Suppose the market consists of only 2 stocks, asset A and asset B (of course, this is an oversimplification of our theory: we know that hundred of thousand of different tradable assets form the market portfolio). Suppose the assets trade at the following per unit prices : p A = $2 and p B = $5 . Also suppose that the outstanding amounts of each assets (e.g, the number of stocks that are traded) are n A = 25 and n B = 50. What is the weight of each asset in the market portfolio? 7. Assume the risk free rate equals R f = 4%, and the return on the market portfolio has expectation E [ R M ] = 12% and standard deviation σ M = 15%. (a) What is the equilibrium risk premium (that is, the excess return on the market portfolio)? (b) If a certain stock has a realized return of 14%, what can we say about the beta of this stock? (c) If a certain stock has an expected return of 14%, what can we say about the beta of this stock? 8. You are given the following two equations: E ( R i ) = R f + ( E ( R M ) - R f ) β i (1) E ( R p ) = R f + E ( R M ) - R f σ M σ p (2) You also have the following information: E ( R M ) = . 15, R f = . 06, σ M = . 15. Answer the following questions, assuming that the capital asset pricing model is correct: (a) Which equation would you use to determine the expected return on an individ- ual security with a standard deviation of returns =.5 and a β = 2? Given the parameters above, what is the expected return for that security? (b) Which equation would you use to determine the expected return on a portfolio knowing that it is an efficient portfolio (consisting of the market portfolio M combined with the risk-free rate)? If you were told that the standard deviation of returns on that portfolio is equal to σ M and you were given the above parameters, what is the expected return on that portfolio? (c) Can you determine the β of the portfolio in (b)? (d) Given your answers above, expand on what type of risky assets equation (1) can be used for, and what type of risky assets equation (2) can be used for. 9. Consider the Security Market Line (SML) under CAPM: 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

(a) Intuitively, what does it mean for a stock to have a β of zero? What does it imply for his expected return under CAPM? Under CAPIM, a stock with a zero β is a stock with no systematic risk. This implies that, under CAPM, the expected return of the stock must be equal to the risk free rate: E ( R i ) = R f . (b) Can a stock have a negative β a? If no, why? Can you think of some example of assets that tend to have a negative betas? Please provide a crisp but concise answer of roughly 3 sentences. 4