[R-SIG-Finance] Portfolio Optimisation as a function of targeted Risk rather than return.

[Pierre Org]

Hi Ilya

 

Many thanks for pointing me toward the PARMA package. I have tried to use it but  I seem to fail, I am not sure I am doing things right. When I optimise  for a given level of risk  (7% annualised) and then check what the portfolio volatility with the  in-sample weights  the level  risk does not seem to equate to the intended target risk.

 

                   Gilts World Ex UK Stocks     UK Stocks

2014-02-28  1.548142e-03       0.0279529433  4.838851e-02

2014-03-31  7.806639e-05       0.0105305699 -2.702980e-02

2014-04-30  7.377730e-03      -0.0052597245  3.158530e-02

2014-05-31  9.628424e-03       0.0282594842  1.481751e-02

2014-06-30 -5.580206e-03       0.0001037494 -1.283548e-02

2014-07-31  1.057991e-02      -0.0034606566 -3.263463e-05

2014-08-31  3.487462e-02       0.0404001701  2.027569e-02

2014-09-30 -6.982201e-03      -0.0005089251 -2.937074e-02

2014-10-31  1.384694e-02       0.0226491298 -1.050032e-02

2014-11-30  3.209176e-02       0.0427556870  2.914371e-02

 

I use the above data as an input (m) to the optimiser then force my monthly standard deviation to 0.07/sqrt(12)

 

spec   <- parmaspec(S = cov(m) ,riskB= 0.07/sqrt(12) ,risk="EV",riskType="maxreward", LB = rep(0,3), UB = rep(1,3), budget=1, forecast=colMeans(m))

parmasolve(spec, solver="SOCP")}

 

The annualised standard deviation of my series are : 

 

> apply(m,2,sd)*sqrt(12)

 

        Gilts World Ex UK Stocks          UK Stocks 

        0.04938711         0.06359545         0.09144821 

 

so a 7% target risk portfolio that maximise return should exist as a solution. Anyhow the resulting weights from the above dataseries are calculated as:

 

>  spec   <- parmaspec(S = cov(m) ,riskB= 0.07/sqrt(12) ,risk="EV",riskType="maxreward", LB = rep(0,3), UB = rep(1,3), budget=1, forecast=colMeans(m))

>  parmasolve(spec, solver="SOCP")}

 

 

+---------------------------------+

|        PARMA Portfolio          |

+---------------------------------+ 

No.Assets                           : 3

Problem                              : SOCP

Risk Measure                     : EV

Objective                            : maxreward

Risk                                      : 0.0005859

Reward                               : 0.0110454

 

                   Optimal_Weights

World Ex UK Stocks          0.9581

Gilts                                      0.0419

 

 

 

Now when I use the solution weights I do not get the same monthly targeted risk. I realise that the risk 

 

 

> w <- parmasolve(spec, solver="SOCP")@solution$weights

> sd(rowSums(t(apply(m,1,function(x) x*t(w)))))*sqrt(12)

[1] 0.0624795

> 

 

 

My portfolio do not have a standard deviation of 0.7 as I was expecting……

 

 

It is probably obvious to many of the PARMA users…but I can t  understand where I get it wrong as the portfolio is obviously feasible. What I want is the portfolio  that maximise return amongst all the possible portfolios with a 7% annualised vol.

Any idea ? 

 

 

From: Ilya Kipnis [mailto:ilya.kipnis at gmail.com] 
Sent: 21 January 2015 15:50
To: Pierre Org
Cc: r-sig-finance at r-project.org
Subject: Re: [R-SIG-Finance] Portfolio Optimisation as a function of targeted Risk rather than return.

 

Check out the PortfolioAnalytics package.

 

On Wed, Jan 21, 2015 at 6:13 AM, Pierre Org <pierre at lequeux.org> wrote:

I am currently working on a portfolio optimisation strategy that would
involves optimising  a portfolio so that it maximises the returns for a user
defined level of risk.   E.g. keeping the volatility of the portfolio at 10%
annualised whilst maximising the return for this level. For that purpose I
was hoping to use the function maxreturnPortfolio  in fPortfolio that should
return the portfolio with the maximal return for a fixed target risk.
Clearly  though showing in this great package the function has been/is  in
development by the authors of the package and currently does not work as
intended. This is confirmed  by various posts and answer to those by the
authors.   I wonder if anyone knows of another more up to date  package or
way of doing this in R ?



Any help would be really appreciated.








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