**Investimentos **

**Investimentos**

**Second Midterm**

投资考试代考 Rules:You cannot separate the exam sheets; Explicitly state any assumptions you take, either to numerically solve the problems or

**Rules:**

**You cannot separate the exam sheets;**- Explicitly state any assumptions you take, either to numerically solve the problems or in the essay questions

Good luck!

**Case 1 (3 points) **

**Case 1 (3 points)**

Answer (briefly and objectively) to ** only two **of the following questions:

1.[1,5p] Suppose that there is no risk free asset and that investor’s preferences can be adequately represented by the following utility function:

Show that the risk aversion parameter * A *has to be greater than zero for the optimal portfolio to be on the efficient frontier of the Markowitz model.

2.[1,5p] Suppose you want to build a ** frontier portfolio **with expected return of 16% using a combination of the three assets described below:

Write down the optimization problem that you would need to solve in order to identify the composition of this frontier portfolio. (Note: you don’t need to actually solve the problem, just write it down.)

3.[1,5p] Prove that, with constant * ROE *and payout ration

*, the growth rate of dividends*

*p**is a constant and equal to*

*g*

*ROE**(1*

*×*

*−**).*

*p*

**Case 2 (6 points) 投资考试代考**

**Case 2 (6 points) 投资考试代考**

For a settlement date of June 9th, 2015, we know the following annual effective Treasury rates (calendar 30/360):

The treasury bond X, with a 6% annual coupon rate (calendar 30/360), was issued in August 21st, 2011 with a 6 year maturity.

The Treasury Capitalization bond Y, was issued at par on June 9th, 2012, with a 4 year maturity and a 5% semi-annual coupon (calendar 30/360).

**1.[1,5p] **

Find the Bond X’s fair value, knowing that at the settlement date, it has 288 days of accrued interest.

**2.[1p] **

Find the Fisher-Weil Duration of Bond X.

**3.[1p] 投资考试代考**

Find the Fair Value of Bond Y.

**4.[1p] **

How much should you invest in Bonds X and Y given that you want to build a portfolio with a Fisher-Weil Duration of 1,6 years and invest a total of 5 million Euros? Assume that both Bonds currently trade at their fair value.

**5.[1,5p]**

Consider the following variable rate Bond, with a Euribor6M +2% semi-annual coupon, BBB rating, with maturity on March 4th, 2016. The issuer offers a 5% redemption premium.

You also know that the risk premium between BBB and Treasury is 5% and that the risk premium between Money Market and Treasury is 1%. The Treasury is less risky than the BBB rating and the Money Market. By March 4th 2015, Euribor6M was 2%. Find this Bond’s fair value, considering that there are 85 days between June 9th and September 4th, 2015 (according to 30/360 calendar).

** **

**Case 3 (8 points) 投资考试代考**

**Case 3 (8 points) 投资考试代考**

**1.[1,5p] **

Assuming that you ** cannot **use the risk free asset, check if portfolio A is efficient (this obviously means that portfolio is made up only risky assets).

**2.[1p] **

If you found ** A not to be efficient**, find the highest possible gain in expected return possible, using risky assets only, for the same risk level of portfolio A. If you found A to be efficient, find the lowest possible expected return, for the same risk level of portfolio A. (

**If you didn’t answer part 1, make an assumption over the efficiency of portfolio A).**

**Note:****3.[0,5p] **

Show whether it is possible that portfolio ** B **is made up

**of risky assets.**

**exclusively****4.[1p] 投资考试代考**

Find the expected return and standard deviation of the optimal portfolio, among those exclusively composed by risky assets, given Mr. AB’s preferences.

**5.[1p] **

Consider that you are ** now able to include **the risk free asset in your investment choices. Assuming the CAPM holds and that the market is in equilibrium, find the expected return, standard deviation and the

**of Mr. AB’s optimal portfolio**

**composition****6.[0,75p] **

Consider that, you are only able to take a long position in the risk free asset, i.e., you are ** allowed to lend but not borrow **at the risk free rate. In this situation, there is no longer A single market portfolio, that would correspond to the tangency portfolio, as the CAPM assumptions would not hold anymore. Let’s anyway consider that

**, as before. In light of this, determine the expected return and the standard deviation of the Mr. AB’s optimal portfolio.**

**the Market Portfolio will still be the tangency portfolio****7.[2,25p] **

Considering that the CAPM holds, that ** the market is in equilibrium **(i.e., all assets have a zero Jensen’s alpha), consider the following portfolios:

(a) [0,75p] Analyze the efficiency of each of these portfolio, according to the CAPM.

(b) [0,75p] Determine the Total, Systematic and Specific risk (expressed as standard deviations) of all three portfolios, and identify those that are completely diversified

(c) [0,75p] Determine the Sharpe and Treynor ratios for all three portfolios.

** **

**Case 4 (3 points) 投资考试代考**

**Case 4 (3 points) 投资考试代考**

We present below the data for Madeup Inc., (year 0 data corresponds to actual values, years 1, 2 and 3 correspond to projections):

The risk free rate is 3%, the market risk premium is 6% and the beta for the stock is 1,5.

From year 3 onwards, the firm will have a constant growth rate, a constant 80% payout ratio and constant 15% Return on Equity.

The stock currently trades at 13,95€/14,05€ (Bid/Ask).

**1.[1,5p] **

What is the stock’s fair value, immediately after the last dividend was paid (i.e., exactly one year from receiving year 1’s dividend)? What is your trading recommendation?

**2.[0,75p] 投资考试代考**

Consider now that from year 3 onwards there will be zero earnings and dividend growth. Determine the stock’s fair value and, consequently, what is the implied Present Value of Growth Opportunities implied in the ** mid **market price.

**3.[0,75p] **

Consider the following information on the average industry values for Madeup Inc’s industry:

How do you compare Madeup with the industry and, with that in mind, would you keep the trading decision formulated in part 1? Explain.

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