Mean-Variance frontier and BlackLittermant

Please check "Input & Output.png" for quick reference of input and output.

0. Preset

1. This program needs "eigen" library to perform matrix operations.

2. "data.txt" as an example input:

   (a) This file contains daily closing prices for 7 random picked stocks during the past year.(20141120-20151121)

   (b) Data was extracted from "Google Finance".

1. Mean-variance frontier

1. Input:

   (a) The program will try to read a file name "data.txt" in default directory. "data.txt" is tab-delimited DOS text file.

   (b) If you have N assets and I observations, this file will have I+1 rows and N columns.

   (c) The first row contains the names(tickers) of the assets(stocks).

   (d) User needs to input the number of assets and number of observations according to the hints showed in the program.

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2. Codes for improving efficiency

   This program utilizes symmetry of covariance matrix, so it only needs to compute half of the covariance matrix.

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2. BlackLitterman

0. Please be aware that all of the input should be consistent. For example, the data in backtest "data.txt" is daily closing prices of a year. Therefore the risk-free rate and excess return should be expressed in terms of daily value.(which are very small).

1. Input:

   (a) The BlackLitterman process is based on same the data from Mean-variance problem.

   (b) User needs specify:

    (1)equilibrium return(here defined as risk-free return);
   
    (2)tau：level of accuracy of expected excess returns(between 0 and 1, close to zero by definition)；
   
    (3)risk aversion constant;
   
    (4)number of views;
   
    (5)view: a view consists of P, Q, OMEGA
   
    	Assume we have N assets, then a view would consist of (N + 2)parameters:
   
    		P: The first N parameters is coefficient correponding to each asset;
   
    		Q: The next ((N+1)th) parameter is relative difference of returns;
    		
    		OMEGA: The level of viewer's confidence about the view；
   
    	In a word, user needs to input (N+2) parameters for a view.