This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Σ is diagonal.
13.5 Log-optimal investment strategy. In this problem you will solve a speciﬁc instance of the log-optimal
investment problem described in exercise 4.60, with n = 5 assets and m = 10 possible outcomes in
each period. The problem data are deﬁned in log_opt_invest.m, with the rows of the matrix P
giving the asset return vectors pT . The outcomes are equiprobable, i.e., we have πj = 1/m. Each
column of the matrix P gives the return of the associated asset in the diﬀerent posible outcomes.
You can examine the columns to get an idea of the types of assets. For example, the last asset gives
a ﬁxed and certain return of 1%; the ﬁrst asset is a very risky one, with occasional large return,
and (more often) substantial loss.
Find the log-optimal investment strategy x⋆ , and its associated long term growth rate Rlt . Compare
this to the long term growth rate obtained with a uniform allocation strategy, i.e., x = (1/n)1, and
also with a pure investment in each asset. For the o...
View Full Document
- Fall '13
- The Aeneid