This project is worth 10% and is due on Thursday 30th October @ 5PM
This is mostly a computational project so you must submit all computer programs
with your project formulations, descriptions and outputs. Assessment will be based
on: accuracy, programming and presentation. Normal level students do Qs 1 to 4
only; advanced level students do all the Questions.
The Scenario: Euclid Smith has just inherited $100,000 and wishes to invest this
sum in the five funds listed below.
Fund Name Code Return Risk
P1 Bottom Harbour Pensions (BHP) .065 .020
P2 New Aussie Battlers (NAB) .080 .015
P3 Christmas Stocking Revenues (CSR) .100 .025
P4 Antarctic Gilded Lily (AGL) .115 .040
P5 Nature Call Productions (NCP) .120 .050
Funds P1, P3 have a negative correlation coefficient −0.2 and funds P2, P5 a positive
correlation coefficient +0.5. All other pairs of funds are uncorrelated. There are no
restrictions on short selling and Euclid has a risk aversion parameter measured to
be t = 0.005 units.
1. Determine which investors short sell in this market and which funds they short
sell. Are there any funds which no-one will short sell?2. Euclids Optimal Portfolio: Carry out the following computational tasks for
Euclids optimal portfolio P∗.
(a) Obtain the dollar investment in each of the five funds and obtain the
corresponding expected return and risk of P∗.
(b) Obtain the µσ-plane graphical representation and include (all on the same
(i) The five investment funds.
(ii) The minimum variance and efficient frontiers. Use a t-range |t| ≤
0.06 for your display.
(iii) A plot of 1000 random feasible portfolios satisfying |xi| ≤ 2 (for
each of the 5 funds) and σi ≤ 0.1 for i = 1,..., 1000.
(iv) Euclids indifference curve and optimal portfolio P∗.
3. Adding a Riskless Cash Fund: Suppose now that a riskless cash fund P0
is also available to invest in. The risk free rate is 0.05 for both lending and
borrowing. Obtain Euclids new allocation of his inheritance to the (now) six
funds. State clearly Euclids investment in the riskless cash fund and describe
in detail the tangency portfolio.
4. The Capital Market Line: Make a new µσ-plane graph showing the riskless
cash fund, tangency portfolio, Euclids new optimal portfolio and the Capital
Market Line relative to the risky efficient frontier. If the five original funds
have a net worth of $100 million, estimate (to the nearest $0.1 million) the
total value of each fund.
5A The Security Mar