# What are the differences between a well-diversified portfolio, an arbitrage portfolio and a factor portfolio?

Investments

Exam #3 – Take Home portion

Total Value: 50 points

April 11th, 2017

Name:_____________________________________________________________________________________

Part I: Short Answer Questions (20 points)

(3 points) Explain the differences between Capital Allocation Line, Capital Market Line, Security Characteristic Line and Security Market Line. Which of these lines can be used to determine whether an asset is over or undervalued according to the CAPM? Use graphs to illustrate your point as appropriate.

(2 points) What are the differences between a well-diversified portfolio, an arbitrage portfolio and a factor portfolio?

(5 points) Explain how you can use the single-index model to identify assets that have been over or undervalued by the market. You can use a graph of the characteristic line if that helps make your case.

(10 points) Read the following article on Dimensional Fund Advisors:

http://www.wsj.com/articles/making-billions-with-one-belief-the-markets-cant-be-beat-1476989975

Based on this article’s reading, answer the following questions:

(2.5 points) How can DFA be considered an active and passive investor at the same time?

(2.5 points) What is the guiding principle of DFA’s investment strategy?

(2.5 points) What is the most prevalent stock class in DFA’s portfolio? What market anomaly is the fund capitalizing on? When was this anomaly first discovered and by whom?

(2.5 points) Why are shares of this fund only available to large financial institutions and not to small retail investors like you and I?

Section II: Analytical problems (30 points)

Problem 1 (5 points): One of my retail clients just joined my investment securities firm and believes the only way to invest is to form a complete portfolio following Tobin’s separation theorem. My client believes the optimal portfolio to be the S&P500 index. After performing a risk aversion profile, I determine that my client can tolerate a maximum standard deviation of 22.70% in his portfolio. Given that the S&P500 index has an average return of 11% and standard deviation of 18.59%, and that the 30-day T-bills have an average return of 2.8%, determine

The weights (y) of the complete portfolio to satisfy my client’s needs

The client portfolio’s expected return

Problem 2 (5 points): The following tables show variance, covariance and correlations for Tesla, GM and the S&P500 index using monthly returns for the past five years:

Variance-covariance table

S&P500 TSLA GM

S&P500 0,0009

TSLA 0,0011 0,0278

GM 0,0013 0,0027 0,0055

Correlation coefficients

S&P500 TSLA GM

S&P500 1

TSLA 0,2316 1

GM 0,5751 0,218 1

(2 points) Calculate the CAPM betas of Tesla, GM and a risky portfolio with weights of 60% Tesla and 40% GM

(3 points) Build the SML for the market using the current average returns for 30 day T-bills (0.1% EAR) and the S&P 500 index (8.8% EAR). Identify the betas of Tesla, GM and the risky portfolio in the SML. Measure the CAPM alphas of each asset using the current average returns for Tesla (26.79% EAR), GM (-4.39%), and the risky portfolio (10.19%). Determine whether each asset is over or undervalued according to the CAPM.

Problem 3 (10 points): Use the regression output for Tesla’s market model equation according to the CAPM, FF3F and FF5F models in Excel Assignment #4:

(3 points) Write out the market model equations for each of the models and select one model as the best based on Goodness of Fit and Treynor ratios. Based on these measures, which model gives the most accurate representation of Tesla’s expected returns?

(3 ponts) Write out the FF3F model equation for Tesla. Using the following factor information make a forecast of Tesla’s next year’s returns: Market excess return (8.01% EAR), SMB (1.97% EAR), HML (9.93% EAR), Risk-free rate (0.2% EAR)

(4 points) Given the analysts’ projected return for Tesla for FY 2017 of -8.7% EAR, determine whether the stock is over or undervalued in comparison to the FF3F’s projection. The analysts’ current recommendation for Tesla is to “hold” the stock. Do you agree with this recommendation?

Problem 4 (5 points): Consider the following data for a one-factor economy (i.e. the CAPM). All portfolios are well diversified:

Portfolio E(r) Beta

A 10% 1

F 5% 0

Suppose another portfolio E is well diversified with a beta of 4/5 and expected return of 18%. Would an arbitrage opportunity exist? If so, what would the arbitrage strategy be?

Problem 5 (5 points) I am an investor with a risk-aversion coefficient (A) of 0.5, if the S&P500 index has an average return of 15% and standard deviation of 22%, the 30-day T-bills have average return of 4% and the investor’s portfolio has average return of 12%, what standard deviation is the investor willing to accept in its complete portfolio?