(b) Now build the covariance using just the same 8 8 matrix of yearly returns as you did for the mean
returns. Again remove the short sell constraint and plot the e cient frontier. [4]
(c) You should observe a strange behaviour in the second case. Can you comment on why this is the case?
[12]
4. Mean-absolute deviation model.
(a) Set up the model so that it minimizes MAD(x) subject to the average return being larger than a given
R. The average return should be measured by the geometric mean.
Details:
You should introduce variables rett;t = 1;:::;T in your model that measure the return of portfolio
x in year t only. You will also need a variable ret = 1T Ptrett that measures the average return of
the portfolio over all time periods. Note that ret is the arithmetic mean.
Mean-absolute deviation can be expressed as
MAD(x) = 1Tkret ret ek1
where ret2IRT and e2IRT is the vector of all ones.
cvx allows you to use the 1-norm (norm( , 1) in Matlab) directly in the objective function of a
model.
[5]
(b) Again produce a graph of the portfolio return Tx against its risk (now measured by MAD(x)) for
a sensible range of values of R (the E cient Frontier). Also plot how the optimal asset allocation x
changes with R (using Matlab’s area function). [10]
Notes
You should hand in (electronically on Learn)
A matlab le mvo.m that solves part 1: it should read in data from all.csv, solves model (EP2) for a range
of values of R and produces a plot of the e cient frontiers and a plot of the change of asset weights as R
changes.
A matlab le mvolam.m that solves part 2(a). The same as before but it now implements formulation (EP3).
A matlab le mvo2.m that solves part 3(b): No short sell constraint and covariance matrix build from yearly
returns.
A matlab le mad.m that solves part 4(a).
A document that includes
{ For Task 1, the plots (R( )) and asset weights x against R) for Task 1, and your answers to part 1(f).
{ The plots for Task 2(b) (again (R) and asset weights x against R) and your answer to 2(b).
{ Your answer to 3(c). If you refer to plots of the e cient frontiers from 3(a)/(b) those should be included.
{ The plots (E cient frontier and asset weights x against R) for part 4(b). No discussion/description is
needed for this part.