**Instructions:**

The assignment contains analytical questions which require the use of MS Excel.

Submit a separate file (.doc or .pdf) with your written answers and make clear which question you are answering. You should also submit the Excel file which includes your work. The assignment is due before the lecture. Late submission (after lecture) will have 10% deduction per day late.

Maximum number of students in submitted work is 2. You can submit it individually. Solution will be posted on Avenue along with the grades.

## The portion of the investment opportunity set that lies above the global minimum vari-ance portfolio

**Multiple Choice Questions **(20, 2 each)

- Other things equal, diversification is most effective when securities’ returns are…
- positively correlated.

- negatively correlated.

- uncorrelated.

- higher than the market average.

- higher than the market average and uncorrelated.

- The efficient frontier of the risky assets is
- the portion of the investment opportunity set that lies above the global minimum vari-ance portfolio.

- the portion of the investment opportunity set that represents the highest standard de-viations.

- the portion of the investment opportunity set which includes the portfolios with thelowest standard deviation.

- the set of portfolios that have zero standard deviation.

- the line that connects the risk-free asset with the optimal risky portfolio.

- Consider an investment opportunity set formed with 2 securities that are perfectly negativelycorrelated. The global minimum variance portfolio has a standard deviation that is always
- greater than zero.

- less than zero.

- equal to zero.

- equal to the sum of the securities’ standard deviations.

- equal to the lowest standard deviation of the 2 securities.

- Portfolio theory as described by Markowitz is most concerned with:
- the elimination of systematic risk.

- the effect of diversification on portfolio risk.

- the identification of unsystematic risk.

- active portfolio management to enhance portfolio returns.

- the determination of investors’ risk aversion.

- Which statement about portfolio diversification is correct?
- Typically, as more securities are added to a portfolio, total risk would be expected todecrease at a decreasing rate.

- The risk-reducing benefits of diversification do not occur meaningfully until at least50-60 individual securities have been purchased.

- Because diversification reduces a portfolio’s total risk, it necessarily reduces the portfo-lio’s expected return.

- Proper diversification can reduce or eliminate systematic risk.

- None of these statements are correct.

- According to the Capital Asset Pricing Model (CAPM), fairly priced securities have…
- positive betas.

- negative betas.

- zero alphas.

- positive alphas.

- none of these.

- Standard deviation and beta both measure risk, but they are different in that
- beta measures both systematic and unsystematic risk while standard deviation measuresonly systematic risk.

- beta measures only systematic risk while standard deviation is a measure of total risk.

- beta measures only unsystematic risk while standard deviation is a measure of total risk

- beta measures total risk while standard deviation measures only nonsystematic risk.

- There is no difference since both measure total risk.

- An underpriced security will be
- on the Security Market Line.

- below the Security Market Line.C. above the Security Market Line.

- either above or below the Security Market Line depending on its covariance with themarket.

- either above or below the Security Market Line depending on its standard deviation.

- As diversification increases, the total variance of a portfolio approaches…
- 0.B. 1.

- infinity.

- the variance of the global minimum variance portfolio.

- the variance of the market portfolio.

- Which of the following statements are
**true**regarding the APT?- The Security Market Line (SML) does not apply to APT.

- More than one risk factors can determine security returns.

- Almost all individual securities satisfy the APT relationship.

- It doesn’t rely on the market portfolio that contains all assets.

- I, II and III

- II, III and IV

- I and II

- II and IIIE. III and IV
**Analytical Questions**(80)

For the next questions use the posted file Assignment1.xlsx which contains daily returns of the following 8 stocks: Apple (AAPL), Bank of America (BAC), Facebook (FB), IBM, Intel (ITC), Coca Cola (KO), Microsoft (MSFT) and Pfizer (PFE) for the period 02/01/2018-31/12/2020 (756 daily observations) obtained from CRSP through WRDS. Also for the same period includes the 1month T-bill returns (*Rf*) the Market portfolio’s excess returns (*RM *−*Rf*) from Kenneth French’s website.

**Question 1 **(40)

- Report the mean values of the 8 stock returns. Use up to three decimal points. (5)
- Report the variance-covariance matrix of the 8 stock returns. Use up to three decimal points.

(5)

- Using Excel Solver, find and report the portfolio weights of the 8 stocks that form the globalminimum variance portfolio. How much is the lowest portfolio variance? What is the expected portfolio return? (15)
- Find and report the portfolio weights of the 8 stocks that form the portfolio with the maximum

Sharpe ratio. How much is the Sharpe ratio value? Use the average *Rf *for the Sharpe ratio. (15)

**Question 2 **(40)

Use the AAPL returns for the period 02/01/2018-30/12/2020 (755 observations – do not use the last one) to estimate the model:

AAPL* _{t }*−

*Rf*=

_{t }*c*+

*β*(

_{M}*RM*−

*Rf*)

*(1) a. Report the estimated coefficients, standard errors and p-values for the model parameters*

_{t }*c,β*. (10)

_{M}- How much of the variation of AAPL excess returns does the model in (1) explains? (10)
- What is the interpretation of
*β*coefficient? (10)_{M } - Denoting the values you get from (a.) as ˆ
*c*and*β*^{ˆ}, use them for the day of December 31st, 2020 to calculate the model based expected excess returns of AAPL for that day. Compared to the realized AAPL excess returns for that day, what is your conclusion? Is AAPL overvalued or undervalued in the market? (10)_{M}