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estimateAssetMoments

Estimate mean and covariance of asset returns from data

Use the estimateAssetMoments function with a Portfolio object to estimate mean and covariance of asset returns from data.

For details on the workflow, see Portfolio Object Workflow.

Syntax

obj = estimateAssetMoments(obj,AssetReturns)
obj] = estimateAssetMoments(obj,AssetReturns,Name,Value)

Description

example

obj = estimateAssetMoments(obj,AssetReturns) estimates mean and covariance of asset returns from data for a Portfolio object.

example

obj] = estimateAssetMoments(obj,AssetReturns,Name,Value) estimates mean and covariance of asset returns from data for a Portfolio object with additional options for one or more Name,Value pair arguments.

Examples

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To illustrate using the estimateAssetMoments function, generate random samples of 120 observations of asset returns for four assets from the mean and covariance of asset returns in the variables m and C with the portsim function. The default behavior portsim creates simulated data with estimated mean and covariance identical to the input moments m and C. In addition to a return series created by the portsim function in the variable X, a price series is created in the variable Y:

m = [ 0.05; 0.1; 0.12; 0.18 ];
C = [ 0.0064 0.00408 0.00192 0; 
      0.00408 0.0289 0.0204 0.0119;
      0.00192 0.0204 0.0576 0.0336;
      0 0.0119 0.0336 0.1225 ];
m = m/12;
C = C/12;
X = portsim(m', C, 120);
Y = ret2tick(X);

Given asset returns and prices in the variables X and Y from above, the following examples demonstrate equivalent ways to estimate asset moments for the Portfolio object. A Portfolio object is created in p with the moments of asset returns set directly in the Portfolio function and a second Portfolio object is created in q to obtain the mean and covariance of asset returns from asset return data in X using the estimateAssetMoments function.

m = [ 0.05; 0.1; 0.12; 0.18 ];
C = [ 0.0064 0.00408 0.00192 0; 
      0.00408 0.0289 0.0204 0.0119;
      0.00192 0.0204 0.0576 0.0336;
      0 0.0119 0.0336 0.1225 ];
m = m/12;
C = C/12;
 
X = portsim(m', C, 120);
p = Portfolio('mean',m,'covar',C);
q = Portfolio;
q = estimateAssetMoments(q, X);
 
[passetmean, passetcovar] = getAssetMoments(p)
passetmean = 

    0.0042
    0.0083
    0.0100
    0.0150

passetcovar = 

    0.0005    0.0003    0.0002         0
    0.0003    0.0024    0.0017    0.0010
    0.0002    0.0017    0.0048    0.0028
         0    0.0010    0.0028    0.0102

[qassetmean, qassetcovar] = getAssetMoments(q)
qassetmean = 

    0.0042
    0.0083
    0.0100
    0.0150

qassetcovar = 

    0.0005    0.0003    0.0002    0.0000
    0.0003    0.0024    0.0017    0.0010
    0.0002    0.0017    0.0048    0.0028
    0.0000    0.0010    0.0028    0.0102

Notice how either approach yields the same moments. The default behavior of the estimateAssetMoments function is to work with asset returns. If, instead, you have asset prices, such as in the variable Y, the estimateAssetMoments function accepts a parameter name 'DataFormat' with a corresponding value set to 'prices' to indicate that the input to the method is in the form of asset prices and not returns (the default parameter value for 'DataFormat' is 'returns'). The following example compares direct assignment of moments in the Portfolio object p with estimated moments from asset price data in Y in the Portfolio object q:

m = [ 0.05; 0.1; 0.12; 0.18 ];
C = [ 0.0064 0.00408 0.00192 0; 
      0.00408 0.0289 0.0204 0.0119;
      0.00192 0.0204 0.0576 0.0336;
      0 0.0119 0.0336 0.1225 ];
m = m/12;
C = C/12;
 
X = portsim(m', C, 120);
Y = ret2tick(X);

p = Portfolio('mean',m,'covar',C);
        
q = Portfolio;
q = estimateAssetMoments(q, Y, 'dataformat', 'prices');
 
[passetmean, passetcovar] = getAssetMoments(p)
passetmean = 

    0.0042
    0.0083
    0.0100
    0.0150

passetcovar = 

    0.0005    0.0003    0.0002         0
    0.0003    0.0024    0.0017    0.0010
    0.0002    0.0017    0.0048    0.0028
         0    0.0010    0.0028    0.0102

[qassetmean, qassetcovar] = getAssetMoments(q)
qassetmean = 

    0.0042
    0.0083
    0.0100
    0.0150

qassetcovar = 

    0.0005    0.0003    0.0002    0.0000
    0.0003    0.0024    0.0017    0.0010
    0.0002    0.0017    0.0048    0.0028
    0.0000    0.0010    0.0028    0.0102

Input Arguments

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Object for portfolio, specified using a Portfolio object. For more information on creating a portfolio object, see

Matrix or fints object that contains asset price data that can be converted to asset returns, specified by a fints object or NumSamples-by-NumAssets matrix for asset returns. Use the optional 'DataFormat' argument to convert AssetReturns input data that is asset prices into asset returns. Be careful when using asset price data because portfolio optimization usually requires total returns and not simply price returns.

Data Types: double

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: p= estimateAssetMoments(p, Y, 'dataformat', 'prices')

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Flag to convert input data as prices into returns, specified using a character vector with the values:

  • 'Returns' — Data in AssetReturns contains asset total returns.

  • 'Prices' — Data in AssetReturns contains asset total return prices.

Data Types: char

Flag indicating whether to use ECM algorithm or excludes samples with NaN values, specified as a logical with a value of true or false.

To handle time series with missing data (indicated with NaN values), the MissingData flag either uses the ECM algorithm to obtain maximum likelihood estimates in the presences of NaN values or excludes samples with NaN values. Since the default is false, it is necessary to specify MissingData as true to use the ECM algorithm.

Acceptable values for MissingData are:

  • false — Do not use ECM algorithm to handle NaN values (exclude NaN values).

  • true — Use ECM algorithm to handle NaN values.

For more information on the ECM algorithm, see ecmnmle and Multivariate Normal Regression.

Data Types: logical

Flag indicating which asset names to use for the asset list, specified as a logical with a value of true or false. Acceptable values for GetAssetList are:

  • false — Do not extract or create asset names.

  • true — Extract or create asset names from fints object.

If a fints object is passed into this function and the GetAssetList flag is true, the series names from the fints object are used as asset names in obj.AssetList.

If a matrix is passed and the GetAssetList flag is true, default asset names are created based on the AbstractPortfolio property defaultforAssetList, which is 'Asset'.

If the GetAssetList flag is false, no action occurs, which is the default behavior.

Data Types: logical

Output Arguments

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Updated portfolio object, returned as a Portfolio object. For more information on creating a portfolio object, see

Tips

You can also use dot notation to estimate the mean and covariance of asset returns from data.

obj = obj.estimateAssetMoments(AssetReturns);

Introduced in R2011a

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