To lay the theoretical foundations of PSP portfolio management, this article constructs a portfolio balancing strategy that maximizes the expected value of CRRA (constant relative risk aversion) utility function in discrete time where assets consist of one

risk-free asset and one risky asset and proportional and fixed costs are paid for risky asset trades.

There are J kinds of risk assets (stocks) and a

risk-free asset, risk-free rate of return is determined, and the total rate of return of each asset risk is random.

The missing bits of sovereignty include a fiscal transfer system to respond to asymmetric shocks; a

risk-free asset (eurobonds) in which to park redundant money; a single system for supervising banks and capital markets; a central bank able to act as lender of last resort; and the ability to organize an EU-wide stabilisation/recovery programme.

When the investor both has access to the

risk-free asset, and the weight in the

risk-free asset is [w.

Hence, their work illustrates that, under a representative agent economy, the welfare cost of business cycles can be approximated by the risk premium between an aggregate stochastic consumption claim and a

risk-free asset, regardless of the assumptions about utility function.

The risk-free rate of return on the

risk-free asset is r, an n x 1 vector of the expected excess rates of return is R - r, and the n x n non-singular covariance matrix of risky assets' rates of return is [OMEGA].

We also show that, when target returns are close to the risk-free, portfolios weights are heavily dependent on the

risk-free asset.

The

risk-free asset (denoted by i = f) is exactly what the name implies: an asset that pays the same dividend in all states of nature.

I undertook a benchmark investigation where the performance of the optimal portfolio is compared to a naive strategy (equal weights on all assets), holding a market index strategy (investing in an index) and finally frill investment in a

risk-free asset.

In other words, the portfolios are always long in the 30% of stocks, which yields the highest risk-adjusted returns, short in the 30% of stocks which yields the lowest risk-adjusted returns, and 100% long in a

risk-free asset.

According to the CAPM, the expected return of an asset is a linear function of a

risk-free asset, the systematic risk (or market or non-diversifiable risk) of the asset or portfolio of interest, represented by beta, and a risk premium in relation to the

risk-free asset, as shown in Equation 1.

The natural starting point in their strategic asset allocation is the government bond market which tends to be a

risk-free asset for any specific market.