Financial Toolbox- frontcon and portalloc - risk aversion and risk free asset bounds

Hi, I was wondering if it was possible to set a minimum bound for the (1-riskyfraction) (the amount allocated to risk free asset) while respecting minimum asset bounds set in frontcon.

That's to say I hope that the entire allocation will add to one while respecting minimum allocation restrictions for each asset type.

Also can someone provide some kind of relevant reading about the riskaversion coefficient in portalloc?

I am estimating a portfolio with highly correlated assets with low volatility (I'm talking a covariance matrix with tiny values (i.e. e-03)) and seem to have a difficult time getting the tangent point without blindly setting the risk aversion level to insanely high numbers.

Thanks!

Answer 1

[Oleg Komarov]

EDITED

In general, you build the frontier with frontcon/portopt and with portalloc you simply use the two separation fund theorem to move along the Capital Market Line.

Increasing (decreasing) the risk aversion you move closer to the risk free rate by lending (further away by borrowing).

% Expected returns and covariance
Eret = [0.1 0.2 0.15]; 
Ecov = [0.005   -0.010    0.004 
       -0.010    0.040   -0.002 
        0.004   -0.002    0.023];
% Build 100 ptfs for the frontier (I dind't include constraints)
[Prisk, Pret, Pwts] = portopt(Eret,Ecov,100);
% Risk free rate
Rf = 0.08;

EDIT

Note: frontcon is a wrapper for portopt, for this problem you can use them interchangeably.

EDIT #2

• Without specifying the borrowing rate, portopt doesn't constrain the optimization to the tangency portfolio and varies the risky portoflio along the frontier according to the risk aversion.To visualize the effect:

portalloc(Prisk,Pret,Pwts,Rf,NaN,3);
portalloc(Prisk,Pret,Pwts,Rf,NaN,28);

• With the borrowing rate (lets keep it equal to Rf) you form the Capital Market Line and move on it according the risk aversion. To visualize it:

portalloc(Prisk,Pret,Pwts,Rf,Rf,3);
portalloc(Prisk,Pret,Pwts,Rf,Rf,28);

[Ben]

I think my intuition about the two functions is wrong. So you're saying that I should provide a covariance matrix that includes the risk free asset and then provide its rate of return for portalloc?

Thanks again

[Oleg Komarov]

No, the covariance matrix contains only risky assets.

Once you formed your market portfolio you will have with portopt/frontcon use portalloc to mix it with the rf. The risk aversion of the agent determines how much rf is used.