1 / 10

Portfolio Management

Portfolio Management. Grenoble Ecole de Management MSc Finance 2011 Exercises chapter 3. How to determine optimal weights.

mab
Télécharger la présentation

Portfolio Management

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Portfolio Management Grenoble Ecole de Management MSc Finance 2011 Exercises chapter 3

  2. How to determine optimal weights We are in a two-asset world: stock AA and stock BB. Stock AA has a mean return of 6% and a standard deviation of 18%. Stock BB has a mean return of 12% and a standard deviation of 27%. Correlation is 0.4. Graph the efficient frontier and point the Global Minimum Variance portfolio. Your customer, Miss Jones, would like a portfolio with a return of 9%. Which portfolio (weights) do you propose ? What do you say about risk to Miss Jones ? Mr Jones would like 11% of return but with risk below 20%. Which portfolio (weights) do you propose ? Global Minimum Variance Portfolio

  3. How to determine optimal weights We are in a two-asset world: stock AA and stock BB. Stock AA has a mean return of 6% and a standard deviation of 18%. Stock BB has a mean return of 12% and a standard deviation of 27%. Correlation is -0.3. Graph the efficient frontier and point the Global Minimum Variance portfolio. Your customer, Miss Jones, would like a portfolio with a return of 9%. Which portfolio (weights) do you propose ? What do you say about risk to Miss Jones ? Mr Jones would like 11% of return but with risk below 20%. Which portfolio (weights) do you propose ? Global Minimum Variance Portfolio

  4. Lending and Borrowing S has an expected return of 15% and a Sd-dev of 25%. T-bill offer a risk-free rate (rf) of 5%. If you invest half your money in T-bill and half in S. What is the expected return of your portfolio ? Its st-dev ? Then you borrow at rf an amount initial to your original wealth and you invest everything in portfolio S. What is the expected return of your portfolio ? Its st-dev ?

  5. CAL calculations The risk-free rate is 5%, the expected return to an investor’s tangency portfolio is 15% and the St-dev of the tangency portfolio is 25%. How much return does this investor demand in order to take on an extra unit of risk? The investors wants a portfolio sd-dev of 10%. Which are the weights of the risk-free rate and the tangency portfolio in his own portfolio ? The investor wants to put 40% of the portfolio in the risk free asset. What is the return and the sd-dev of this portfolio ? What return can expect the investor for a portfolio with sd-dev of 35% ? If the investor has EUR10 million to invest, how much she borrow at the risk-free rate to have a portfolio with an expected return of 19% ?

  6. CAL calculations 1) 2) 3)

  7. CAL calculations 4) 5) The investor must borrow EUR 4 million at the risk-free rate to increase the holdings of the tangency portfolio to EUR 14 million.

  8. CAPM calculations • the market has an expected return of 8% and a variance of returns of 18%. The risk-free rate stands at 3.0%. • there are 3 assets, AA with covariance with the market of 0.130; BB with covariance with the market of 0.230 ; CC with covariance with the market of 0.190. • what are the β of these assets ? βAA = 0.72; βBB = 1.27 ; βCC = 1.05 • what can you say in term of risk ? βAA < βCC < βBB • what are the expected returns ? RAA = 6.61%; RBB = 9.29 %; RCC = 8.28% • what is the β of a portfolio P mixing 50% of AA and 50% of BB ? Βp= 1 • what is the marginal risk to add CC to a portfolio that mimics the market ? 0.37%

  9. APT for a single factor representation We are in a 3-asset world: A, B, C with the following characteristics. β For λ = 0.66 the portfolio AC has a β of 1 and an expected return of 10.4%. With the same β, stock B has a return of 9%. Therefore one can take profit of this situation by selling EUR 100 of stock B and buying the equivalent of portfolio AC. This is an arbitrage because the operation is cost-free. The return is EUR 1.4 or 1.4%.

  10. APT calculations We are in a 3-asset world: A, B, C with the following characteristics. β For λ = 0.7 the portfolio AC has a β of 0,8 and an expected return of 10.0%. With the same β, stock B has a return of 15%. Therefore one can take profit of this situation by buying EUR 100 of stock B and selling the equivalent of portfolio AC. This is an arbitrage because the operation is cost-free. The return is EUR 5 or 5%.

More Related