By careful reflection and analysis, Mr Fabian Factoriensis has developed the following two-factor model:

R_i = a + b_i,1F₁ + b_i,2F₂ + _i,

where R_i is the return of a company b_i,j is the factor loading of company i against factor j, F_j is the factor j, and _i is a mean zero idiosyncratic error term.

Compute the value of the constant a in the two-factor model.

Instructions:

• The answer is given using two decimal places.

• Should

  there be intermediate steps in your calculations, please remember to

  keep a large number of decimal places in all intermediate calculations,

  as the final answer needs to be exact.

Mr Swimmer, Mrs Runner, and Mrs Skier are friends and co-investors. Their risk aversion coefficients are 2, 3, and 5, respectively. After careful analysis, they have figured out that the expected stock market return is 7.9 per cent, while the expected return on gold is -2.5 per cent. The volatilities are 18.4 per cent, and 7.6 per cent, respectively. Further, the correlation between stocks and gold is 0.59. No risk-free security is available.

Which

of the following statements is most accurate in this case? A correct answer yields

100% of the points for this question, a wrong answer -50% (minus fifty

per cent), and no answer zero points.

Suppose that an investor uses the following mean-variance utility function:

Dr Activitus Riskusson with a risk aversion coefficient of 9 currently owns a portfolio with an expected return of 4.8 per cent, and a volatility of 40.7 per cent. Suddenly, the volatility changes to 57.5 per cent. What is the lowest possible new expected return such that Dr Riskusson's utility remains at least on the previous level?

Instructions:

• The answer is given in per cent using one decimal place. This means that a return of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign.

• Should

  there be intermediate steps in your calculations, please remember to

  keep a large number of decimal places in all intermediate calculations,

  as the final answer needs to be exact.

• Although the final answer is given in per cent, in this question all intermediate calculations should be done in decimal format in order to get it right.

Mr Runar Rikeman invests in US stocks. His home currency is the euro. In the beginning of a 12-year investment period, the direct foreign exchange quote against the US dollar was 0.91. The holding period return on the shares that were bought was -58 per cent in local US terms. In the end, the FX quote was 0.99. Compute the annualised rate of return in per cent from a euro point of view.

• The answer is given in per cent using one decimal place. This means that a return of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign.

• Should there be intermediate steps in your calculations, please remember to keep a large number of decimal places in all intermediate calculations, as the final answer needs to be exact.

Abraham, Bernie, and Cecilia are Sharpe ratio maximisers. Having analysed all the companies on the stock market, they have uniform expectations on the future returns of all stocks, their volatilities, and the correlations between all the stocks. Based on this information, they have estimated that the expected return on the portfolio that maximises the Sharpe ratio is 3.9 per cent with a volatility of 11.3 per cent. The risk-free rate of return is 5.6 per cent. However, the persons are not uniform in their personal risk preferences. The risk aversion coefficients are the following:

• Abraham's risk aversion coefficient is 5. Let us call Abraham Person 1.
• Bernie's risk aversion coefficient is 6. Let us call Bernie Person 2.
• Cecilia's risk aversion coefficient is 2.5. Let us call Cecilia Person 3.

What is the Sharpe ratio of Person 2's portfolio?

Instructions:

• The answer is given using two decimal places.

• Should

  there be intermediate steps in your calculations, please remember to

  keep a large number of decimal places in all intermediate calculations,

  as the final answer needs to be exact.

A very large number of factor models has been suggested in the literature. Based on the information below for a company, and given that the risk-free rate of return is 3.2 per cent, compute the return in per cent suggested by the Fama-French three-factor model (FF3, 1993).

Instructions:

• The answer is given in per cent using one decimal place. This means that a return of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign.

• Should

  there be intermediate steps in your calculations, please remember to

  keep a large number of decimal places in all intermediate calculations,

  as the final answer needs to be exact.

• Note that you cannot move backwards to an earlier question once you have clicked Next page.

The expected return on the stock of BungaBonga Industries, Inc (BBI) is 9.3 per cent, volatility 39 per cent, CAPM beta 0.9, and tracking error 22.7 per cent. The expected market risk premium is 2.7 per cent, and the risk-free rate is 2 per cent.

Which of the following statements is most accurate? A correct answer

yields 100% of the points for this question, a wrong answer -50% (minus

fifty per cent), and no answer zero points.

Once upon a time, three investors, Mr Folio Hatt (Person 1), Mrs Ulburling von Knottenfeld (Person 2), and Mrs Cinnamon Bulldeg (Person 3) were keen on investing exactly according to their risk preferences. They combined the stock market benchmark portfolio and the risk-free asset. The expected return of the benchmark was 6.8 per cent with a volatility of 21 per cent. Further, the risk-free rate was 2.2 per cent. The risk aversion coefficients of the three persons are 1.6, 5, and 9.8, listed in the same order as the names above. Compute the weight in per cent of the benchmark portfolio in Person 2's overall portfolio.

Instructions:

• The answer is given in per cent using one decimal place. This means that a weight of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign.

• Should

  there be intermediate steps in your calculations, please remember to

  keep a large number of decimal places in all intermediate calculations,

  as the final answer needs to be exact.

Mrs Lily Flower is investing both in domestic stocks denominated in euro (EUR) and the stocks of the Switzerreich stock market, denominated in Switzerreich Urban Rupel (SUR). Compute the volatility in per cent for Mrs Flower's portfolio, given that she invests 16.9 per cent of her wealth in domestic stocks, having a volatility of 24.2 per cent, and the rest in the Switzerreich stock market, having a volatility of 15.6 per cent. The volatility of the FX rate is 8.9 per cent. Finally, it has been estimated that the correlation between the stock markets is 0.17, between domestic stocks and FX -0.1, and between the foreign stocks and FX 0.19.

Instructions:

• The answer is given in per cent using one decimal place. This means that a volatility of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign.

• Should

  there be intermediate steps in your calculations, please remember to

  keep a large number of decimal places in all intermediate calculations,

  as the final answer needs to be exact.

Suppose that an investor uses the following mean-variance utility function:

Dr Activitus Riskusson with a risk aversion coefficient of 9 currently owns a portfolio with an expected return of 4,8 per cent, and a volatility of 40,7 per cent. Suddenly, the volatility changes to 57,5 per cent. What is the lowest possible new expected return such that Dr Riskusson's utility remains at least on the previous level?

Instructions:

• The answer is given in per cent using one decimal place. This means that a return of, say, 10.1 per cent, is expressed as 10.1. Do not add anything else, not even the "%" sign.

• Should

  there be intermediate steps in your calculations, please remember to

  keep a large number of decimal places in all intermediate calculations,

  as the final answer needs to be exact.

• Although the final answer is given in per cent, in this question all intermediate calculations should be done in decimal format in order to get it right.